Who is going to talk about understanding exponential trajectory, balance growth, and cell size? Is it audible in the back? Audible? Thanks very much to the organizers for inviting me to this stimulating meeting and giving me this opportunity to present some work. I'll be talking about some work that has been done in Delhi with PhD students, Parth Pratim Pandey, Pooja Sharma, Harshad Singh, and Nagpal Sethi, Shagun, who is in the meeting, who has a poster up. I'd like to talk about some theoretical questions related to bacterial physiology and cells in general. So first is the origin of exponential growth and how come a non-linear system exhibits something which is characteristic of a linear system, exponential growth. How do cells, as they grow, all the diverse chemicals which are all whose dynamics is decentralized, how do they all manage to double together? How do they all manage to grow, exhibit what's called balanced growth? And so this would be some general sort of, I'll talk about some structural properties of models which have these features and how these properties might arise. And then I will briefly turn to some specific things, a class of models that I'll be describing. I'll show how bacterial growth laws arise from an optimization principle. And if time permits, I will say something about stochastic dynamics, about a timekeeper molecule, the stochasticity of a timekeeper molecule whose threshold commits the cell to division, the adder property, and intracellular molecular fluctuation patterns, and so on. So this is the early result that suggests that single cells grow exponentially from birth to division in exponential cultures. So the length of the cell on a logarithmic scale is plotted on the y-axis versus time from division on the x-axis. And these straight lines means that cells are growing exponentially at a certain rate. These things have been measured in more precision in recent times. Of course, since the time that the cell takes to divide only allows it a two-fold growth, there could be other fits. Nevertheless, an exponential fit seems to be quite good. And at least it's a working hypothesis that certain cells, certain bacterial cells, grow exponentially in time from birth to division. Now, so what kind of a description of cellular dynamics can address questions like this? So a cell consists of lots of molecules of various types, metabolites, amino acids, nucleotides, messenger RNA molecules, proteins, ribosomes, of various kinds. And one description of the state of the cell at time t is just the set of populations of all the molecular species. So there are, let's say, capital N distinct molecular species of various kinds inside the cell. And we specify the number, how many molecules of each type. And again, this is a crude description of what's going on inside the cell, but it's a description, which is very useful. And of course, these variables xi of t, they are integers. They are populations. So they are non-negative integers. And they change stochastically. But it is often convenient to write down deterministic dynamics for the change of their populations. In the form dxi by dt, that is xi dot, is some function of the populations, of the populations at that time. And these functions fi contain all the complexity of the cell, all the reactions and interactions and processes that are going on inside the cell. And these are coming from reaction kinetics. They are highly non-linear functions of the variables in question. So exponential growth is a characteristic of linear systems. And here is the simplest possible system that one can talk about. A one-dimensional variable, a single variable system x, dx by dt is r, a positive constant, times x to the alpha. Where if alpha is one, so that's a linear system, x dot is equal to r of x, that's the central picture. And x grows exponentially, r is positive. And that's a hallmark of a linear system. But if you depart from linearity, let's say alpha becomes less than 1, then the growth pattern, let's say alpha is half, then the growth pattern is not exponential. It at large times is given by a power of time. And if alpha is greater than 1, then it grows faster than exponential. And there is a finite time singularity that you can have in such things. So departure from linearity means also departure from exponential trajectories. That's a standard understanding. And what we are trying to understand is why do cells grow exponentially, assuming that they do, assuming that that approximation is correct, why do they grow exponentially if they're described by nonlinear systems? So here is a higher-dimensional linear system. And again, because of linearity, you see exponential growth. So here, you have n variables, but the functions fi are linear functions, aij xj. So a is a matrix of real numbers, let's say. And that describes the dynamics. And now, in this case, so one can represent it x as a column vector and write down the dynamics in terms of a column vector and matrix. And the eigenvectors and eigenvalues of a play an important role in this dynamics. And in particular, asymptotically, as time becomes large, the dynamics x of t, the vector x of t, is attracted to the eigenvector of a corresponding to its largest eigenvalue. So x lambda are the eigenvectors of a. Lambda are the corresponding eigenvalues. And the largest of these, assuming it's real, is the one that determines the asymptotic behavior of the trajectories. And in that asymptotic regime, you get exponential behavior again. Transients are mixtures of exponentials of different kinds. But once the system has, once the transients are over, then there is exponential growth again. So in that sense, you see exponential growth in this linear system. And this is also an example of balanced growth because the largest eigenvector, it has some components which are fixed because a is a fixed matrix. So x is a fixed vector. x lambda 1 is a fixed vector. And therefore, it's a fixed vector up to normalization. And therefore, the ratios of its components are constant. And so once you have gotten onto this attractor, once you've gotten to this eigenvector, all the populations, all the variables x are increasing with the same rate. They are increasing in proportion to each other. They're all growing exponentially with the same rate. It's an example of balanced growth. So for a cell, just to take a nonlinear example, just to consider a concrete nonlinear example, we'll consider a particular coarse-grained model of a cell described by three variables. So x is a triple. And the populations are p of t, denoted p of t, capital T of t, and capital R of t. So p is supposed to be the pool of precursors of macromolecules, that is amino acids. Let's take p to be just the amino acid pool. T of t is the pool of all transporter and other metabolic enzymes, which bring in the food and convert it to amino acids. That's what t does. And R is the pool of ribosomes, it's the number of ribosomes, which catalyze the production of t as well as themselves from p, from the amino acids. So that's a coarse-grained version of the model of the set of variables. And here is a possible set of equations that one might use to describe certain aspects of the cell. So the box brackets, of course, denote concentrations of these pools. And without box brackets, it's populations. And I will sometimes use box brackets for concentrations and sometimes use lower case letters for concentrations and capital letters for populations. So the amino acids are produced by the transporter and metabolic enzymes. And Kp is a proportionality constant that represents many things. It represents the efficiencies of these enzymes, of this enzyme pool. It represents the nature of the medium, et cetera. So Kp is doing many duties there. That's the production term for amino acids. And amino acids are used up to make proteins and ribosomes. So in proportion to their concentrations, p-concentration and r-concentration with some rate constant K. And that results, of course, in the production of T and r. And the positive terms are, of course, of the same type, proportional to the r and p-concentration. And the rate constants are proportional, in some sense, fractions of. So Ft and Fr are the fraction of ribosomes that are making, respectively, the transporter and enzymes. That's Ft. And the ribosomes, that's Fr. These are, at the moment, parameters of the model. And mt and mr are the number of amino acids used up in each transporter molecule or enzyme molecule that's mt. And mr is the number of amino acids used up to make a ribosome. So that explains those kinds of equations. I just want to put this up here in part because I wanted to just say that this is a nonlinear model because the right-hand side has quadratic terms. And it's more complicated than linear. And in models of this kind, which are nonlinear, you do not expect. I mean, even for a single variable, you don't expect exponential growth. Models of this kind, which have many variables that are nonlinear, you don't expect exponential growth. Now, we are in an expanding cell. So therefore, we must add the dilution terms to all these three equations. And these dilution terms are minus v dot by v into the respective concentration. So those are the equations on the right-hand side. And that's typically the kind of starting point that we have in this core-screen modeling of cells. Now, it's important to note that this dynamic, supposing I know all the constants, kp, kft, mt, fr, et cetera, everything, supposing I know those, and I start with some initial concentration, this dynamics does not tell me how to do it because it's not completed yet because v dot by v has not been specified. So v dot by v is appearing in this dynamics, but we don't know what it is. And v dot by v is the growth rate, which I will be denoting by mu of the cell. And if the cell is expanding, then mu is a function of time. And unless one specifies that as a function of time, we have not specified the dynamics and we can't really integrate it and can't really find out the trajectories of things. So we need to specify this. But we don't want to do it exogenously by just assuming that v dot by v is some constant mu or lambda, or that will be then determined later. We want the dynamics to tell us what the growth rate will be of the cell. And therefore, this v dot by v has to be determined in some endogenous way. And what I will do in the next slide, where the model will be completely described, is that this v dot by v, this mu, it will turn out to be in the model a function of the concentrations themselves. So all these p, t, and r with box brackets, mu will turn out to be a function. And that function has to be substituted here. And then that specifies the dynamics completely. That function will be explicitly specified. And that then specifies the dynamics, which you can then use to integrate these equations. The system will be completely defined. So in order to do that, I first want to think in terms of populations instead of concentrations. So the populations xi are just the concentrations times the volume. And therefore, the d by dt of xi has two terms in which you differentiate the concentration and one in which you differentiate the volume with respect to time. And for the first term, you can use the equations that we had on the previous slide. And so when you do that, you find that the v dot term, so there is a v dot term which existed in that equation on the previous slide. That was the v dot by v terms. These v dot by v terms cancel the new v dot term that is there on the right-hand side of this equation. And you get even simpler looking equations for the populations. So those are the equations that you get for all the populations. But notice that even this is not well defined because it contains v. And we've not specified what v is. So that's something that we would like to do. And this is where I will make a key assumption that we will take v to be, in this case, a linear function of the populations themselves. So v is an extensive variable. And it can be expressed in terms of populations but not in terms of concentrations directly. So that's why we have gone to the population level. We express v in terms of the populations as a linear function. In general, I will be considering v to be a homogeneous degree one function of the populations. And this is going to be an ingredient of the model. And these constants vp, vt, vr are therefore also parameters of the model. The model is not specified without that. So and these constants, it will turn out, affect everything that the cell does. So let's take a particular case in which all the v's, little v's are equal.  And now you can see that with this choice, both the models, both the versions of the model, the population as well as the concentration is completely defined, are completely defined. Because if you were to now calculate, so the population version is clearly defined because you've specified v. But as far as the concentration version is concerned, note that v dot by v, since capital V is little v into p plus t plus r, so you have v dot, capital V dot by v, is given by that expression, little v by capital V, into p dot plus t dot plus r dot. And we know what p dot, t dot, and r dot are from those equations, from those equations. So you can substitute that. And so the p dot term, there is a kp t term. And when divided by the v, which is sitting in this expression, it will become kp into box t. And then there are the quadratic terms, pr by v terms in each of those p dot, t dot, and r dot. And they will all combine. And notice that there was a volume factor that was sitting there before. That volume factor will be augmented by another volume factor that is coming in the definition of mu in the denominator. And so you will get concentration of p, concentration of r, multiplied by the constants. So you have expressed the growth rate in terms of concentrations. This particular choice, this linear, this choice of v being linear in the populations, is crucial to be able to express mu as a function of the concentrations. So if it was not, then it would involve populations themselves and not just concentrations. So now, once we have this mu, you can substitute this back in this equation, in these three equations. And now the concentration dynamics is defined and self-contained. So you have dynamics which has been defined at both levels, at the level of the populations, and at the level of the concentrations. And they are both consistent with each other. So that's what we've done. And now you can, of course, start this dynamics off with any concentration, initial concentration, of the three chemicals. And you can ask what the concentrations will do. So notice, I mean, so this is a cell that is growing, maybe whose volume is changing. But the concentrations themselves have a dynamics of their own, given by this. But notice that the dynamics has been crucially modified by what we've done on the next slide. It's not as straightforward as it appears here. These v dot by v terms are themselves concentration dependent. And in that particular case, v dot by v had a linear term and a quadratic term, which makes this dynamics even more nonlinear. So that's the structure that we have of this dynamics. Now, imagine that you have some concentration dynamics, some nonlinear concentration dynamics, and we can analyze it by the usual tools of dynamical systems. And we will be looking for fixed points, we'll be looking for stable fixed points, we might be looking for unstable fixed points, we might be looking for limit cycles, various kinds of attractors of this concentration dynamics. And let us say that you have, you found some fixed point of this dynamics, which is a stable fixed point. Let's call that stable fixed point p star, t star, r star. That's our stable fixed point of this dynamics. The moment you have a stable fixed point of this dynamics, you have the following situation. So what would happen to the system after it has reached that fixed point? So once the system has reached that fixed point, p star, r star, p star, t star, r star, then after that, of course, being a fixed point, being a stable fixed point, these would not change with time. And therefore, mu has become a constant in time. So once the system reaches that fixed point, mu becomes independent of time, which means that v dot by v, which is mu is independent of time, and therefore, v increases exponentially with time. So v will have the behavior, something like v naught e to the mu star. So mu star is the value of mu at the fixed point. So we will have some kind of a behavior like that, where the zero of time, let's say, is the time where once it has reached the fixed point. So that's from there you start, and we will then, from there on, increase exponentially. And it is clear that all the other variables must also increase exponentially. They must increase exponentially, because v is, after all, a linear function of p, t, and r. And if v is increasing exponentially, and p by v, t by v, r by v, they are all constants, then it must be that p, t, and r are also increasing exponentially at the same rate. So we have found a situation using this approach, where the very existence of a stable fixed point of the concentration dynamics that we have constructed means that we have constructed an exponentially growing trajectory of the cell in time. And although we have a nonlinear system here, we have been able to construct exponentially growing trajectories. And the crucial ingredient here, of course, was this key assumption here. It is with that that we are able to have nonlinear dynamical systems, which still obey exponential trajectories. And these trajectories, if the fixed point is an attractive fixed point, then these trajectories would be attractive trajectories for the population dynamics as well. So one can actually do this for this PTR model, and if you just simulate it at some choice of parameters with different initial conditions. So the top two plots are different, starting p, t, and r with different initial conditions. There is some transient, and then you can see that on a semi log plot, they are growing linearly with the same slope. So they're all growing exponentially at the same rate, yes. Yes, so I'll show you a simulation later in which you can choose the volume to be, let's say, two thirds the power of the surface area of the cell. And you can say that the surface area is proportional to let's say t, okay? And you can say, let's say, supposing you were to say that v being instead, yeah, maybe I should, yeah, I'll show you those similarly. And if you do that, if you depart from linearity or in general, homogeneous degree one character of the function v, then you find that you don't have you know, things reaching constant ratios asymptotically. They don't get attracted to being constant ratios. You can see in the lower two curves here, the ratios t by r and p by r doesn't matter what initial condition you start from. This is a model in which the concentration dynamics has one stable fixed point. This is a simple example in which it has one stable fixed point and which is a global attractor of the entire phase space. And so doesn't matter what initial condition you start with. Once the parameters are fixed, you tend to that those particular ratios, the concentrations are fixed, okay? So that's what you end up with, which you do not if the volume does not satisfy this property. I'd like to demystify this as to why we are getting exponential trajectories in a non-linear system, okay? And the reason is that this particular choice of v has rendered our dynamics closely related to linear systems. So these are non-linear, but homogeneous degree one function. So our dynamics, let's write down our population dynamics, which are the ones which are growing exponentially. Of course, concentrations are going to a fixed point. So it's the populations that are growing exponentially. So let's write down xi dot in terms of these functions fi, okay? And look at these functions f one, f two, f three for p dot, t dot, r dot respectively that we have, okay? These functions have the following property that if you scale all the variables, all the three variables by the same parameter beta, okay? Then these functions also scale by the same single power of beta, okay? That's the feature that they have. So that's why they're referring to them as homogeneous degree one functions.  Is that the same as saying that reaction rates actually depend on concentrations? Is that the same statement? It is. It is the same statement. I will just elaborate on that, yes, indeed. That's what it is. Cool. Okay. So, okay, so this is what we have this character. And whenever you have this character of a set of nonlinear differential equations, which is defined by homogeneous degree one functions, then you always have, you can always find exponentially growing solutions. You can substitute the non-zarts. Xi of t is equal to Xi of zero e to the mu t, where mu is the same for all the i's, okay? Same mu for all the i's, all growing exponentially at the same rate. And you can take this anzarts and plug it into that equation, the differential equation. The left-hand side is mu times Xi of zero e to the mu t, trivially by differentiating this anzarts. And the right-hand side, you have to substitute the anzarts. And when you substitute the anzarts, it has n arguments, but each one of them has this factor e to the mu t. And this e to the mu t, is like our beta, right? So, since it is multiplying all the arguments, and since our function has this homogeneous degree one property, we can use it to scale it out of the function. That's the last step of the second-last line, okay? So it scales out. And therefore, you can see that e to the mu t cancels out from both left and right-hand sides. And you are left with a condition on the assumed mu in the anzarts, on the growth rate, and the initial conditions from which you've started. So, this means that if you start with certain initial conditions, okay? There is a set of initial conditions which you can discover by solving these equations. These will typically be algebraic equations. The last equation, mu Xi of zero, is equal to fi x1 of zero, x2 of zero, xn of zero. It will be typically for mass action, kinetics, and so on. A set of algebraic equations, no time. And you can, you know... So, how many unknowns are there? There are actually... It might seem that there are n plus one unknowns, mu and x1 to xn. But actually, there are only n unknowns here that you can determine from these because you can only determine the ratios, x1 of zero to all the others because of this property of f. So, I'm calling this the generalized eigenvalue equation because for the special case where these functions are linear, okay? So, let's say fi was what we had earlier. Fi of x is aij xj. Then what does that equation look like? That equation looks like mu Xi of zero is equal to aij xj zero, summed over j. That's what that equation is because I simply have to substitute it in the function. The last equation on the left-hand side is mu Xi of zero, and the right-hand side is fi at the initial point, okay? So if we do that, that equation is nothing but the eigenvalue equation of the A matrix, okay? And for a linear system, that naturally comes out, of course, and we know that every eigenvector of A, assuming it's a real eigenvector, defines a direction, and if you start from that direction, then you will keep going exponentially at a rate lambda i in that direction for a linear system. We know that, okay? So something like that is what is happening for this nonlinear system. This equation, the right-hand side is nonlinear. It's not linear in the x's, in the variables x1, 0, x2, 0, xn, 0. It's not linear. So it's some kind of a nonlinear generalization of the eigenvalue equation of a matrix, and I don't know whether such structures, I would be curious to know in case someone knows whether such structures have been studied by mathematicians in some context, or somebody else in some context. But they seem to very naturally arise in the context of bacterial physiology in this way of thinking, okay? So anyway, right. So here I'm just pointing out that if you define the ratios of the xi's, psi i is given by xi by xn. You've divided everything by the last xn, okay? Then that same equation is, you know, you can write it down in terms of... So now there are explicitly n-1 ratios and 1 mu, and you can see that you have n equations for these n variables. And generically, you could find a solution. Of course, you have to find a feasible solution in which these x's are non-negative, if they're populations.  But in general, you have n equations and n unknowns, and there would be generically solutions for that. And those solutions are exactly, it turns out, the fixed points of the ratios, I mean, as far as the ratios are concerned, at those solutions, you can find out xi by v, and that's the concentration. So those are precisely the fixed point, the concentration. So this set of x's which solves this equation, it defines a line which passes through the origin of this n-dimensional space. So we have this phase space which is n-dimensional, and you have a solution of this that defines a line, and what this means is that if your initial conditions lie on that line, you will have exponential trajectories, all the x's will grow exponentially with the same growth rate mu. So it's a very special curve in your n-dimensional space, which is this line of balanced growth, if you like. But the point is that is an attractor of the dynamics. So you can start from anywhere, if your fixed point is a stable fixed point, and that is an attractor of the dynamics, and you can start from anywhere and you will converge to this line. That's what's happening. So here I will address precisely the point as to how this class one property is arising. And what I want to say is that it is simply a consequence of two things, that the rate of change of concentration is a function of concentrations, point number one that you mentioned, and the second point is that v is a homogeneous degree one function of the x's. So we started with some particular functions g1, g2, g3 in the PTR model, but now let's be general, some nonlinear function of the concentrations. So little xi denote concentrations now, and capital xi will denote the populations. So little xi dot, this is mass action kinetics, you can include Michaelis-Menten, whatever one is interested in, as long as it's a function of the concentration. In an expanding volume, you will add the minus v dot by v xi term, which we did, and then in the capital, in the population language, when you write down the equations, the equations will, the v dot by v term will cancel out, and you will have equations xi dot is equal to v times g i of little x. Capital xi is given by that. And now, let's assume that the volume v is some function of the populations. So then, we can write down capital xi as a function of capital xi dot, as a function of the capital x's, just to complete that dynamical system. We can do that by plugging in v as a function of x into the above equation, and that's what I'm calling this function capital, little fi of x. That's the other ones that we wrote down earlier for the PTR model. So these are the functions fi, and we need to ask whether these functions have this homogeneous degree one property or not. And the claim is that they will always, doesn't matter what the form of g is, it's not that we've taken some very special dynamics and we're getting this homogeneous degree one property, it's generically going to arise always. It will, provided v itself is a homogeneous degree one function of its arguments. So that's the last line of the proof. So basically, this property is, you can see where this property is coming from and it's very generic. So the key assumption here again, I want to emphasize is this linearity or homogeneous degree one character of v, which is giving us exponential trajectories which is giving us this character. So just to note a couple of points that the solution to that generalized Eigenvalue equation, any feasible solution of that one gives us a quote unquote line of balanced truth, already mentioned. A special set of initial conditions. And I've already mentioned that to every stable point, there corresponds a line of balanced truth to which the population are attracted. And notice here that we've not assumed any regulatory mechanism. So things are growing, they're growing in a coordinated way, they're all growing with the same ratios. It is being assumed here that all the components of this vector, x10, x20, x30, they're all non-zero so that all the populations are growing and that actually requires a further assumption of a kind of a auto-catalytic nature of the whole system such that every chemical species is being created somewhere in that system. Then you will have all the components non-zero and all of them will then be growing exponentially at that same rate. And so one point is that no regulatory mechanism is needed, so it's a very generic mechanism. And there's no fine tuning involved here. It's as long as v has this property, it'll work. And notice that the constants in v, they do affect things. So just to remind you that in this equation for mu, we had this little v sitting out here. But if we had vp, vt and vr, those constants would also have been sitting here and they would have affected the growth rate, they would have affected the eigenvector components and so on. They are observables in that sense, they are affecting our observables. So that's an important thing. This bringing in this linear answers for v is not harmless in that sense, it is actually introducing some new parameters that matter to the dynamics. So you can write down a much more complicated model. We wrote down one which had about 30 odd cellular variables with sort of 40 odd interactions and so on. And we wrote down a set of equations and just put it on the computer. And because it was class 1, because it was homogenous degree 1, we found that, again, for this complicated model, it's a very generic thing that's going to happen. That you had these exponential trajectories and balanced growth. On the other hand, in this example, this is the one that I mentioned that you change the homogenous degree 1 character of v. v is now t to the 2 thirds instead of a linear function. And what you find is that there is no, it's not going to do any constant ratios asymptotically. So this is the generalities about these homogenous degree 1 systems and how they might help us to understand the phenomenon of balanced growth and exponential trajectories in a generic fashion. I will now briefly, since time is short, I will mention that this PTR model that I introduced in this talk as an illustration of this homogenous degree 1 is actually a model that can teach us a few things. I mean, teach us in the sense that at least it allows us a very explicit working out of things. So it's an exactly solvable model. You can actually work out explicit analytical expressions for the growth rate and all the ratios. So in spite of the non-linearity, you can just work those out. And because you can work out the ratios, you can also talk about the ribosomal fraction, which is phi r is m r r by m t t plus m r r. And if you fix all the parameters of the model, which include the ones that were listed earlier, including the fr and the ft, which add up to 1, and the v's and all that stuff, if you do that, then you don't see any growth loss.  So you, for example, get phi r is equal to fr plus some other terms that depend upon. So in these formulae, I've introduced death rates of the t and the r species, d t and d r. So one can solve it analytically with those. And you get something, which if you keep all the other parameters fixed, I mean, you can keep changing the other parameters, like, for example, k or k p. k p was the medium, the medium and the efficiency of the enzymes. So you can change them, but nothing happens to, in this case, where d t and d r is 0, phi r is just fixed. So there's no growth loss seen. And you see growth loss, however. Here, if you employ an optimization principle, if you say that given that this parameter f, fr, ft plus fr is 1, but if this parameter fr is the one that the cell is actually regulating in some fashion or the other, and you say that you assume that the cell is always tuning this parameter in such a way that when all the other parameters are fixed, this parameter is chosen so that you get the maximal growth rate. If you make that assumption, then you find that you can analytically derive the growth rate. So you can get these kinds of things from this. I just wanted to mention this. And of course, you can make the model more complicated by adding the q-sector. That's not much of a complication. You can do various other things with it. And okay, so that's some of those things Shagun has on her poster that she is trying to get around. And yeah, notice that this model, you know, if you look at the model originally, yeah, so here the equations are the same as the PTR model, although this is, the volume is defined differently in this case, but just to have the equation on the board, the the peptide elongation rate is actually not K, but it's K times P by V. So it's also a dynamical variable in the model. It's not a fixed constant in the model. And one of the results that Shagun has observed is that as you increase the growth rate, this has qualitatively an increase in saturating character. But the amount of increase is not by a factor of 2. It's much less. So anyway, this is a very simple model and so it's not expected to reproduce all the nice, all the features that we would like. So at any rate, I will then briefly mention some other things that we've done in terms of extending the model that we added a timekeeper molecule which we called Z. So there is this X sector which is the PTR sector and it can contain other things, whatever. Which is homogeneous Degree 1. But then there is this other molecule which is a molecule whose I'll wrap up in two or three minutes. Yeah, so this timekeeper molecule is yeah, so anyway, so there are these, so it has you know, it's also produced, some protein let's say, and it is produced you know, in the same way as let's say T is same kind of dynamics. Homogen is Degree 1 and this molecule however has the role in the cell that when it reaches a critical value Zc the cell divides or commits itself to division. And when it divides then all the XIs are halved and Z might also be halved but it might also be reset to some other value which we are calling Zb. So you can do this, this is motivated by DNAA type dynamics. And anyway, so you can again analytically solve this with the PTR model when the X sector is the PTR model and and now of course, we are talking of stochastic dynamics because Z the dynamics of Z, we are interested in cell-to-cell variability here and so you can do stochastic dynamics and Z in order to reach its threshold will take a variable amount of time and so you will have an inter-division time variability and birth volume and division volume variability. So you can work out those things and we compared this with the data of I have not mentioned that Tahiri Aragi et al Sakchun June's group and what we found was that it matches the data best when this value Zc is between is of the order of 20 to 60 that's the range in which it matches the data best. It reproduces, I mean it matches to a fair extent the other distributions but it doesn't reproduce the growth rate distribution very well. So there's something else happening in the growth rate distribution which it reproduces the adder property and also this mechanism you can use to address this question which was raised by the work of Tahiri et al where they measured protein number fluctuations and they found this crossover from intrinsic noise to something that they called extrinsic noise. And this behaviour is actually reproduced by this model putting another protein in the dynamics and study its number fluctuations and of course at small numbers it has the universal fluctuations but it also has this crossover because at some point its variability is set by this timekeeper Z molecule so that is what determines its what is considered extrinsic noise is actually something which is part of the cell itself which is this generated noise generated by the cell. So I will conclude by summarizing that this mechanism for exponential trajectories and balanced growth is probably also relevant for proto-cells because proto-cells also near the origin of life needed to have identity and so they needed to have maintain their composition across generations so because it is very generic this kind of dynamics maybe it was used by proto-cells okay and I would like to emphasise that it is perhaps relevant to work out empirical consequences of the new parameters, the VIs that have been introduced and simple models of this type are possibly useful for bacterial physiology and they are at least very explicit and clean at least in the sense that the assumptions are all on the table and they are explicit okay thank you very much


is up a welcome back to technical difficulty Tuesday we are live but I can't find us I can't see your comments I can't find the video so yeah oh wait I clicked on the Facebook thing to get there all right I see you guys all right I see Tyra and Rebecca and the Biebs Helen Nancy Dawn Tom Nicole Genby Christian oh it's posted as unlisted so what's that mean did you fix it I just hit copy from last time well I don't I don't know if I should start or not start I don't know if you could see it in the thumbnail because I can't see it in the thumbnail but this is what we're doing we took our owls and we made them bees thanks to Kim Lance this was her idea she said I totally could see it as a welcome to her hive so I did this a couple weeks ago Garrett just had to turn it into a cut file today don't worry I have a bunch of new ones still in the hopper I already did another ladybug one and working on that five o'clock somewhere I haven't quite figured out how I wear I want to take that one so Scott if you're watching that one's coming and as I look at this does this seem giant size this fits on the 16 inch right are you guys still there I made some changes let's see hey worked all right so now it popped up all right all right all right we're still there let's see I'll give people a minute give people a minute to join I'll bust out my so if it was unlisted does that mean only the people going in through maybe discord or something yeah they have a link but I updated it what time is it it's only 408 look your teacher doesn't show up for eight minutes you can go but too bad we're here six so now you got to stay I still see it here but I guess I will yeah hit refresh now go to our channel not just the lives I think those were just there it is there we go and I see comments all right back in business there should be a quick one so but there's a bunch of people here so you got but I recognize everyone's name so I think you guys are all patrons right they all had the back door came in the back door all right so here's what we're doing today if you weren't able to see the thumbnail because it was unlisted return the owls and bees little magic little magic wand poof owls or bees but isn't it cute I think that's a great newbie hanger yeah I think that's better than our old be hanger I don't know it's just different and I like them both the cricket and stuff and I actually have made this one into a vertical leaner too Garrett just hasn't made the cut file for that I guess I got to start making these cut files myself right it's time he's getting annoyed and having to stay in his chair just to make cut files because I've been so in designs like over the wall of them have so much to do so much to do so all right well let's see let's get on it what's happening here let me see what's happening in the chat yeah I'm on it because I'm running late everybody says hello hello hello hello hangers not sure if they know what's happening it was we were sitting here standing here trying to refresh our screen getting to show up Tom said I thought it wasn't showing up on the page as an upcoming event yeah that's because you had an unlisted some had to be in the know yeah all he did is copy them from last week Harold Bieber said technical difficulties yeah had that one pig pegged it's Tuesday it happens up Alan said this live appeared as unlisted yeah you guys are on it you guys are on it before I read I should have read the comments yeah we're sitting here for like five minutes trying to figure out why we couldn't see ourselves you guys are on it you fixed it I saw it pop up Garrett fixed it yep all right all right all right that work are we got some updates oh yeah I got a couple of reminders hold on let me read my hand but why why do you need so much like I know you got this figured out right now because this is how much you need to cover a backer in one coat we don't cover in one way I am gonna take it because then you're gonna make it look all fine it's good it's gonna look like it's got swim leans in it just let me fix it oh let me spread it out and then you can grab the excess yes Christian I hear you in my head just it's not too much paint if you keep it right that's what I'm doing I keep it moving it's good to go look at that look really can't really even doubt whatever you guys do don't do not like this video yet oh no I got a good reason why you guys need to like this video there you go look at that it's fine it's good hold on let me do this well if I just give it one good way I got it right here whoa no why are you doing that that was too far now you're gonna just have sorry guys but you could not see it's gone all right that's a little better a little bit now well that's what happens with the first coat that's what we call first kill you doing I'm just getting off that Jason's back so watch yourself go get all right you guys see my hand Kim did not see that he poured half the bag of paint on this he's distracted yes lottery and laser everything yeah two announcements one go play a lottery it's like a billion dollars who couldn't use a billion dollars and then two we're on a podcast tonight laser everything at nine o'clock now does it go live tonight I mean is that a lot yeah we're on live oh wow just double live in it today okay so we do yeah come back and see us at 9 p.m. Eastern well not here just over on their channel laser everything yeah it's a like yellow me yeah follow us and see what see where things go I don't know how well they know Garrett you guys can come on and tell them a little bit about I mean I saw the thumbnail feel like they might know who I am and why me what about you why did I just get singled out I'm the straight man in this are you now yeah yeah there you go all right wait oh what no that's that's old okay so you don't actually this test cut was done around one so I did get to see it and the first cut file if you downloaded it early over there on the patreon this was all cut up it was like a million pieces I just made it two pieces now these are all the pieces of the beehive nobody wants to paint that why is here right nobody's gonna and I had to use the tape because I was in a rush I didn't put any tabs on this thing just out there in the raw all raw dog laser do you need a I'm using my nails I've been growing them out for this reason just for this reason see them I just nibble on them now and then all right and we decided we're doing a brown a brown color tree this time we did gray last time and then just in contrast against the white and we have since done the owls with a brown tree well these don't like birds trees yeah they don't hang out in birds do they is this brown Jennifer said thought it was eight did you mean the laser everything thing cuz it is nine I'm gonna confirm yes those are the same brown I don't know why we have two of them it's nine Eastern standard time I just posted the way so it's fresh in my head is that whack-back wood yes it is is that this good job yes it is they're all over it 9 p.m. Eastern yes okay just wanted to confirm oh Erica says she just got an F1 congratulations I see Scott Hamlin just ordered himself an F1 this weekend to me and I wish I had more time to mess with my F1 you could you could spend days messing with the F1 you could put it on like I really want to go put it on things I want to engrave one of my helmets I have things that I need to get done with that thing oh guess who else is here oh peg egg is doing this she's excited about a B theme and it looks like a lot of our friends might join us tonight Helen said will they have a chat and resin dragon studio says yes resin dragon studios are you familiar with their podcast setup yes she said the laser everything dudes are cool can't wait yeah they're cool I was listening to their podcast and watching their videos but then busy season hit and all my podcasting had stopped well that in last year I was production so I was in the back a lot so I got to wear my headphones all the time and I can listen to my podcast and just do my thing back there because Taylor was supposed to be doing all the marketing and video editing but we switch back this year now I get a lot less podcasting happening I was gonna say something else but how Helen said where she said so they made the cartoon B file even harder why just why do you hate me so much actually I'm thinking it's not harder that's right it's not harder this one's gonna be easier you keep keep it dropping those comments Helen and then I'll make all of this font print so you'll have to place each letter Mandy's excited she loves the bees her her niece who's two years younger than her loves bees everybody says they love bees but why are they going extinct then Jennifer asked with the X-toe P2 do you have to puzzle the 16 inch inch backer piece yes it's still a desktop well it not if you get the automatic pass through yeah I was gonna say well yes I guess there's two answers to that you can either use the automatic pass through which would mean needing a room plenty of room in the front and the back to run the backers through I'll show you or you can use it as is and you'll need the riser base like ours is set up behind us and over here can you see that it's on its little riser base and there's still and that's so that we can run the rails the pass through rails on it and we have to pull the table out and make sure there's room in the front and the back for the rails and then or you can puzzle piece the backer you can do it either way that was a long-winded answer to your question which is typically how I answer questions and I keep here in the term have do I have to puzzle piece the backer puzzle piece in is easy like watch the video it's really not that hard super easy you could probably do it in like two minutes tops something once you learn to do it you got it it's not hard after that and not everything can be puzzle piece like this one maybe in the tree yeah do we have a measure you can puzzle piece it right there oh yeah puzzle piece it right there I think I actually did with the somebody asked you for it didn't they yeah somebody asked me for it with the owls I think the owl one is puzzle piece let's see here JJ saw there I am here the softball every Tuesday y'all are what keeps me awake laughing and enjoying the time it usually takes me an hour and a half to get wherever I'm going oh well I hope hopefully we're entertaining yeah well that's a long trip for some baseball softball softball same how's the softball coach for so many years Sean tall is here Alan says come on Gary you have time to play with your F1 after all who needs sleep we do need some time to play with the F1 there's more you guys see my goals this week I have no time for F1 in this week and he didn't have them all I actually saw I read it over his shoulders and I was laughing because I was like that's I hope that you don't think that's everything you have to do that's not everything that's on my list there is so much more like for example at home oh yeah at home at home goals this week too yeah we didn't put those I don't actually live here he's his side of the sink we have like double sinks in the tiniest bathroom ever actually it's not too bad it's a tiny shower ever it's like showering in a linen closet for sure yeah it's like showering in the every time I try to wash my feet I hit my head well that the his sink is dripping and it's constant dripping and it's been dripping for like two three weeks yeah at least a couple of weeks and he was supposed to fix it last night he went up there to fix it and came back down maybe five minutes and I was like I replaced the shower head anyway yeah oh yeah that's a whole other story so he goes up with a new shower head for our master shower yeah he goes up with a new shower head and a new what do you call that sink fixture faucet faucet yes thank you thank you a new faucet for his side of the sink and it comes back down five minutes later and he's like well I can't fix that I said yeah I said he didn't say anything he was just moseying on through I said is that thing it was that thing the original is that the original faucet up there and I said yeah it's not that old and it ain't happening today walk down through to my office yep walk down through the kitchen I'm over there making dinner like a regular old housewife I hardly ever do but anyway so today this is why my hair looks like it does today because I went in there to take a shower this morning oh you're being ridiculous about it there no I know I'm not so I go in there to take the shower I turn the shower on and let's just start already that the faucet or the spout that comes out of the wall for the shower head is way up high I mean it's way up there so I don't know why it's mounted that little pipe coming out of the wall is so far up but it is and when we use like your little shower caddy and you hang one of those on there the first shelf of the shower caddy is actually taller than the shower because the pipe coming out is so tall well Garrett insists we need a new one with a little spray handle you know the detachable spray handle I gotta wash my feet and my lower half because it's so high up and I can't bend over to like wash my feet and stuff you gotta try to wash your feet like this no any washes feet I'm not kidding it is the smallest shower so anyway he gets it installed and that thing now sits up even higher so the shower the water stream is now shooting to the back of the shower whoa and it's up high it's actually probably face level to me so it hits the wall at my face so I can't stand in front of the shower because it's now spring directly in my face and I said I can't use that shower you still in bed this morning when I get back in there I was like I can't use that because I saw it when I installed it he said turn it sideways not turning it sideways to take it off and use it like it's intended and I was like how am I gonna do that how am I supposed to juggle that which by the way I have to get on my tippy toes to reach it and get it off of its little cradle and I was like and use my little loofa sponge and shave my legs and hold this wand I was like that is not happening look all I'm saying is if something ever goes down how are you gonna clean yourself I mean if we find a waterfall same type of I still have both hands free and I can stand in or out of the water you're gonna have to hold your bottle of shampoo otherwise it's gonna float away anyway he comes in after I'm done after I decide I'm not to actually get in there and I'm standing literally in the underneath of it there's so much it's so high up I'm standing under it and I'm not even getting wet my hair never gets wet and I was like I'm not doing this I'm not even sure how I'm gonna do this so I step back out and turn it off and I was like it's not happening and what are you doing you only got your shoulders wet he goes in there he is like here's what you do and he turns it sideways so now the shower head is now spraying to the other wall but it's now going horizontal I'm not gonna get your pits clean right I guess I could have gotten up in there like that anyway we are still this is an ongoing saga that was not resolved this morning and I still didn't get a full shower and look how much paint is on that you didn't even have to put it in the back overhead I'm sorry our drama yeah so on Garrett's list of things to do is still to fix the faucet and now I guess it's still to fix the shower I don't know what we're gonna do about that in the backyard well that's another story it's another story and I'm not even I'm not even ready to acknowledge that Mandy says my faucet my bathroom faucet is dripping too I'm just waiting for my dad to come over lol yeah Garrett's I said what do you need it's like some pipe and I was like looked at my watch he's like seven o'clock on a Sunday I was like I have files to work on I don't have time for home projects what is this a home project what is this a home project let's see oh catching some people up on what's happening tonight who made that shower design at Christian Lapis I'll tell you who made that shower design it was a giant I'm not kidding jelly green because it's even tall for me like my arms were falling asleep because it was so high up just changing the changing the shower head when you go to reach it isn't tall to reach the thing because I have to stand on my tiptoes probably slip hazard going on imagine wet bare feet slip in that shower right so you slip and what you fall up against the wedge yourself in between two walls you're not going anywhere in that shower you're not gonna fall down you can't fall down you might get clumped up towards the bottom you're just stuck like you're stuck in a tube but no one's getting but you're not getting flat on the floor you're fine oh my gosh Lois says they have an attachment that sticks on the wall that you can put the shower head on at an easier height and it makes the shower head adjustable there you go oh like mouth that little head lower oh that was the other thing yeah my idea is I'm just gonna take the handle to the wall oh gosh I'm not doing that but he did come in come in with his sassy attitude takes it off of the little mount and tries to jam it in like the shower caddy he's trying to wedge it in the shower caddy somewhere and it just kept falling everywhere I was like no no that's not happening you're the last person I'm taking with me on the zombie apocalypse Kim Christian said he'd love it being six four yeah right the step still for sure well I knew you think so until you go to wash your legs and feet and you hit your head you know how many times I've hit my head in that shower on what just the wall yeah but because I don't shower had being that tall it's great oh yeah that's great yeah but I got hotels cuz hotels I don't have to duck in the shower I'm not even as tall as Christian I couldn't imagine oh we've got some buffering going on let's see I'm watching you doesn't look like it's slow I was just moving too fast I do that yep other people a lot of people are saying you can get a little holder to suction cup it to the wall gotta do some parkour and scale those shower walls yeah you don't even do do parrot parkour I can just lean up against the back and walk up the wall well that's the whole reason why you know I mentioned this before that we had a whole week going on from that shower yeah I still have to replace the ceiling in the living room yeah the ceiling in the living room has not been repaired yet because I said no I'm not doing that until we replace we do that whole bathroom I want to take out the jet of tub and make where the jet of tub is an actual super wide shower and then where the shower is can become an actual linen closet fine by me I don't know what that space is gonna be I don't know it's it might be a tight linen closet we're gonna fit like three hand towels full Gemino the fourth one in there well that's the reason why so yeah so there's like I refuse and the floor is still half the floor hasn't been repaired we've got subfloor showing I feel like we're squatting yeah yeah we're squatting in a home that was under construction this yeah I don't know what we only moved from our other house which was nice because you know what sometimes you get knocked down but you gotta get back up again never gonna keep me down go ahead you drink a whiskey drink a vodka drink a cider drink this is what happens when you're a squatter so fun fact Chumbo Wombo were squatters when they wrote this song is that something you just made up now look it up for you interesting that's why I came to my head Lois is I if you have two bathrooms his and hers I know Lois I was thinking you know what I might have to start using the kid shower which is disgusting but now that there's only one kid and that's the neat kid it's not as bad I hope all the other kids are watching they are not watching they're not they do not watch the parents YouTube channel except maybe Tanner Tanner will watch on occasion that's only during lives cuz we make them everybody just notice the time up 433 oh Christine just got here she just noticed the time thanks Christine and Scott I guess Scott's there too so Scott so Christine oh what's up everybody ask Godhandle just got here I'm just putting the base coat away on things I'm gonna tell him that now I will not be able to get that song out of my head right right song bomb and just know that nobody's ever gonna get you Christian said Friday video laser cut shower slash tanning booth spray tanning booth we did spray tan in there once yeah it was like the perfect size but then the fumes got everywhere in the bathroom and everything was everything in the bathroom got a little bit of tan be learned that lesson yeah I'll do that one it more I was like woo sink you're looking tropical other letters black are these all gonna be black yes yeah if you guys just joined us this is what we're doing welcome to our hive we turn the owls into a hive and these are all gonna be green I see you left a couple of them pink and blue for fun oh no yeah that was I was trying to get that so I changed them in the design make it easy see how easy this is going to be Helen I actually made less layers to the bees see it just made this piece that's it they don't have a bottom pieces right there's no bottom piece oh and eyes but I just thought that would be easier to put together all right well the wings are gonna stay white so they should go somewhere else maybe I'll I'll make your little leaves do these come out oh no no you just this time yeah this time he just scored them trying to make this thing easy I know sometimes that we hear you guys like I can hear Helen Helen yelling at me for making it difficult I hear whoa well get it that's too many too many pieces is that what she says whoa why do you hate me why do you make me hate the difficult ones cuz they look what is what I told Kim it is what he just said to me the other day this is what our signature is it's our signature style and that's what people are like whoa that looks cool cuz it was hard what like hard I love paint black it's my favorite color to paint it's the easiest one all right I think these are gonna have to well yeah I think I was just gonna remove the things that are gonna stay white did you put two coats on like the eyes and stuff yes man take it it's our business line it's probably just going to say your stuff is great Ed calling back to tell me have you are you gonna do my design for me I'm working on it Ed I'm working on it it's actually up right after my submarine sign yeah and actually before in my military sign no not before that that got that guy has been waiting two weeks and Jenny's got to have her so she can get to making it yes I know I'm on it trying to keep the eyes and pieces I was gonna paint the nose is pink okay so you put those back but there's somewhere else there we go heading into April anybody have any good April fools jokes the one key we got left at home is the ungettable grace Garrett always tries to get her somehow she foils his plans every time every time and that's what he calls her the ungettable grace you can use that yellow yeah that's it that's not apples no that you want this gypsy go gypsy gold yes look you guys are always asking about not always but I've been seeing people asking about the paint and the fact that you've got to shake them yes because they do separate because they have all those well I mean just like any outdoor paint like when you get it in the court you got to shake it as far as you can actually see this the stuff now we know why there's actual additives in ours we I guess as to why they always do gallons of paint and non see-through containers I think you know that right I don't want to go see through I enjoy the non see-through I enjoy the transparency well I was gonna say if you hold them by the sides this is a good way to shake them in my opinion I showed you guys how to shake them what when you shook that one upside down no you got to juggle step one learn to juggle that's right that's what you're doing I forgot you did that pretty easy how many people saw that I missed one of those green leaves and we're thinking of themselves oh that's not getting painted that's not getting painted alright go back overhead I see we're not overhead that's not getting that's not getting in and I'm out of here yeah Lois suggested that we could do that roller thing that makes us look like wood and we could Lois but ain't nobody got time for that if you are making this as a one-off go for it but if you're making it for a craft show well I think for a craft show if you wind them all up you can go through the ding-dong-bang-bang swipe swipe swipe a bunch of them in the swipe clang clang clang goes the trolley what is happening let's see what did I miss about the squirrels oh Tyra says you I love these you could do so many options like squirrels let's say welcome to our nut house man we've been working on a squirrel one two years at least welcome to the nut house we've been trying to do when we started one it never looked right but I think this is a great idea totally gonna become squirrel one too totally doing that write that down right now because I love it good one for the fall yes oh you can make one that with the squirrels and say I'm nuts like acorns takes it too far that's what he does you guys he always takes it too far Tyra Christian said yes some crazed looking squirrels like from ice age oh yeah that's a good one somebody caught my legally blonde reference nice job I do that one all the time I did not think anyone was gonna catch it what's the way we bought what I say what it what is it I do it all the time what what like it's hard nice job I'm so dressed Veronica says I got married on April Fool's Day hey that's a good one that's a easy one to get out of then like you even need a divorce at just some point you just scream April Fool's and walk out right let's see Amy says I like the paint in the clear packages you can see when it's all mixed up and you don't have to guess true right Christine is on it there are 112 of us watching and only 35 likes what hey go ahead and hit that like button because tonight is the drawing for $1.1 billion and everybody that hits that like button will get a prize if I win cash prize cash prize cash money we got you on film saying that now that's right I'll do it I'll do it I'll do it I'll do it depends if we get over you want us to win the lottery get that like I said of the other day if I hit the lottery I'm going dark that's it you won't see me anymore but before I go somebody's gonna get my business in like 250,000 bucks like here go do something Alan said we're approaching the Garrett after dark portion of the show so here's what happened I didn't want to be a bummer like last week so I drank an energy drink yeah remember last week a lot of load I was gonna say something low tea not low tea maybe it was a little low tea I don't know you took it to afternoon all right go overhead we don't even know what's happening you want to go overhead because you're already yes because I'm embarrassed all right there's so many of the squirrel things Tyra said my husband just said acorns and squirrels that look like Ed from the Lion King well no he got it there aren't acorns and squirrels in the Lion King and I don't know which one was it oops there you go spit that right out here you have a twisted sense of humor I love it maybe the April oh for grace here's one for grace Mandy's got a suggestion for you no no okay let me hear the suggestion and I will tell you all the things that I've tried she said that there is no joke prank like drop hints all week that you're planning the ultimate prank and just watch everyone squirm all day waiting for it that was last year she came at me and she's like what what you gave up you just that side of prank you gave up I've tried the old bucket on the water bucket on the on the door frame you did I put a bucket of water balanced on the door right about just balanced like a one gallon bucket of water on the door and I left it cracked and she swung the door open and it didn't fall and I came in and I was like you didn't even get and then the bucket fell on me I tried to give her begging strips for breakfast she didn't care didn't care asked for another yeah it's like give me another she's dead serious she's like salt and the sugar didn't notice so anything I put fake toilet paper on the roll like wouldn't it wouldn't rip so she just used it and left it there she was young but she just there was no getting her the prank was on me I had to clean it up I put I put the cellophane over the toilet again didn't even notice I had to clean it up so I was really just pranking myself this is how click yeah it's not that she's un-gettable because she's so good yeah she's so clueless yeah so clueless that pranks don't work so that's we still call her the un-gettable grace yep she doesn't really get why though she still does she's still clueless and doesn't why she's so funny and for for the tricks that I play it on the older kids those are gonna have to be saved for the cruise they might have crossed in the cruel cruel pranks so all right you have a second code on your backer because you wouldn't have yes you would have done by now all right you probably can just go with the roller that you have before you go and add and if you guys are watching you can see that it is not dry and he still has plenty on his plate right get you by oh he was the funny-looking hyena oh yeah I remember hyenas I thought they were hilarious and go give me a cub sandwich but the only one that remember that it was the funniest thing for me forever I thought it was hilarious I don't know what year did that come out well grace well I mean Courtney was little so Tanner would have been little I would have said she was probably three so maybe 96 95 96 early no I didn't start watching cartoons again until about 98 and there was a lot of Thomas tank engine in my at that time yeah not a lot of Thomas the tank a lot of Pokemon brownies get sprinkled with baking soda instead of powdered sugar I don't know maybe said lol grace has been getting you this whole time yeah she's been getting me I stopped torturing myself and gave up but now that she's older I think it's time I think it's time for the torture I mean time for the tricks to begin again and one says he's got one how about a dollop of whipped sour cream on a bowl of Jell-O or pudding I've been on the receiving end of that one I don't know I thought I went deep with the swap in the sugar and salt and give her big and strips Don says Lion King was released in 1994 make sense I think I think Courtney was maybe three because I remember that because I bought her a Hawaiian King toy when I was trying to convince her to get her ears well what they did is they pierced one ear and then the kid refused to get the second one your ear pierced you know they do both now well back then they hadn't figured that out yet and they did one year and then was trying to go in for the second year and she was not having it and she was only like three and I had to promise her toy from the Disney Store wait that was for April Fool's that's messed up that was that was Lion King I was back to the Lion King and when the Lion King came out nothing to do with April's well April Fool's get her ears pierced I thought we were getting ice cream nope yeah poor kid but that's okay she got her Lion King toy and she got her second ear pierced that's okay I put another hole in her body oh my gosh oh my gosh that was look and you wonder what happened there you go but it was like maybe if you know Courtney now Courtney's got like 27 piercings now yeah that's all she needed was like a half hour in between so that this one stopped hurting and then she was willing to do the other one just a little bit of time to forget yeah like just it wasn't you know it's just like a only painful for a moment hmm yeah this one yeah were you trying to figure out which wing I thought that's what yeah me too look how easy this is so easy so easy it should be illegal look it's only 452 that's how quickly we're getting through this and we're eight minutes late right technical difficulties this line isn't so bad I'm not really helping sure Helen says I love how we're talking to April Fool's but not Easter Easter came too fast yeah it's way too early she told me yesterday when Easter was and I was like wait what yeah that was funny because he said something about his the marketing calendar so if you're now part of the master of tier you will see that you've got an April marketing calendar and he had a bunch of Easter stuff in there and he goes oh I gotta go back and adjust my calendar there's a lot of Easter stuff in that one and I was like yeah no it's over yeah we kind of missed it this year we didn't do and I know that I go like I have like three more weeks yeah it's usually in April I have to talk to the pope my sister told me she's gonna be she always hosts Easter and we do a whole egg hunt and the whole thing she was like oh by the way I've got and I've got invited to something she's going some bed and breakfast or something and she's like I'm not gonna be around for Easter you guys are gonna have to handle it yourselves any egg hunters anymore my nephews well no they're all great grand kids for her now yeah yeah no everybody's too old on tags anymore Grace will still go hunt eggs whoo that's how we get her when is it the 31st yes we we don't hide any eggs and we let her look for them for 24 hours or grace or grace for me she's doing she was calling the ultimate I'm rubber your glue wait a minute I think this goes up there this goes in man I think you're gonna have time for a little shading or something on this tree yeah oh that's the second person somebody else earlier and I forgot to come back and acknowledge you joined us on high from Italy like they were sound like she was on vacation in it from Italy in Italy but join us anyway but I don't even know how to say this Massa Miliano that's pretty good Dave Bernardo says hello from Italy well hello in Italy that's super cool what time is it there is it early in the morning this is like the wee hours in the morning so cast wants to know when did we announce the master it here we haven't fully announced it yet Garrett a little bit jumped the gun but it's out there on Patreon so some of the patrons that have seen it have joined it this is how I operate I jump first and then I assume that somebody's gonna help me yeah I heard your thing where did you say that I jump first and then figure out how to open the parachute yeah on the way down that's pretty much how I operate yeah I jump first and ask questions next on the way okay you got it like if Kimmerley you come into the room and yell oh my god quick we have to jump out of whatever that hold her hand and we jump let's see it but if I ran in the room and I'd be like oh my god quick we got a jump can I be like why how far how much what did you do there'd be a lot of questions by the way it is 10 p.m. in Italy who does it sound bad yeah that's not bad let's put us on like a little podcast go to sleep too let's see are you still overhead you sure look at how cute this little guy is goes together like breeze look I saw you kept the bees right where I put them good job babe I move this guy a little bit only so you would touch both hold him on a little bit yeah otherwise Kim is becoming quite the designer I'm just relegated to cut file guy not loving it Martin asks are you using superglue to glue those items together and how does it hold up outside in the sun in the rain start about big you can get this in our store you can get this kid in our store I guess I should plug us a little bit right yeah we're using our foxy hues paints so if you haven't heard about them they are outdoor paints most you guys have joined us before know about all about them but those are the paints we're doing we're using those are now back in stock then you know what you know did you see Mandy's uh yeah you guys actually saw that Mandy posted she did her whole bathroom cabinet in the foxy hues paints Garrett was saying the same thing he's like we should paint a piece of furniture and then Mandy shows up with bathroom cabinet a piece of furniture painted and then we were talking about needing the hummingbird and then Mandy created a hummingbird round and he's on point yeah she's all over it she's been oh I know Mandy's tapped your phone I think and your and the phone in your basement she tapped your cell and your phone in the basement now what do you think about that yellow should I have used a yes less fluorescent yellow should we have used Apple stars no you hate the pop it's bright yeah it is like a bee is yep cat says the tree definitely needs some bark or some shading well we got time what time is it it's only 459 you have one minute get some shading in there one minute to show you yeah I could see it on the on the screen over here he's cute well you're not gonna use that black are you I see you pulled this black plate you're thinking like dark brown right where are you going you want some antiquing wax would that not be right maybe paint wax would only be if it were chalk me I don't know Kyle says this whole time I've been five minutes behind the live I'm a goof but experienced time travel when I well Mandy says I took Garrett's advice and bought an older phone on eBay instead of a new camera to make video slash take pictures there you go yeah that's what we did well it says should you make the tree look like a birch tree well wait why black comes look watch yeah I hate that about brown you're just wetting it he he's trying to thin it out but why why not why not dark brown cuz I was just trying something new I did dark blue and blue last week blue long gray yeah blue and gray so this week I was trying a little water down we're experimenting this is a test paint Tuesday Kim test paint Tuesday we're the dragon studio says LOL no I hate that that's how she does design work to Scott says the F1 will be here on Friday let the madness begin we were talking about that before you got here Scott somebody else got a new F1 and I was like oh yeah Scott got himself an F1 I can't wait to see what you guys do with it I know you'll be using it at the craft shows still hate that still Mandy says I say we need a shading techniques masterclass Christian says black edge and some woodgrain tool with dark brown on top right you guys got all day all day to paint signs the sign is eighty five dollars I was gonna say 120 122 whatever it takes 120 121 can you guys see it I guess you can see it some you don't like that black washed out it's fine I think it's something new a little different different kind of Jewish so the shading is supposed to make it look round right yeah that rounded edge look why did you hold it up if you need to hold it up and hold it flat for a second in your little you held it sideways or something you can really see it I was I didn't know where the camera was I was just guessing right that's enough I've got plenty of time Kim no you but you're it's too much shading it'll dry later yeah do you want to be an artist or do you want to make some money Amy said shaking like to come back in with the little mark and hit those score mark for a quick yeah they need to be maybe engraved I mean here's a sharpie but don't mess it up every time half the time he makes a sign on the live we can't sell it what you could totally sell it you just don't want to you want to keep it hoard it all for yourself give it to the public Kim I don't think I love this what this marker why not look let it sink in first there you go I mean it looks good on the video from a distance but I can see it real-time you guys wow yeah Mandy says it looks great on camera the M and welcome looks odd I get it designer does look a little weird maybe you could stretch it yes all right you're getting they think Kim is fiery today yeah I also had the other half of that energy drink we were making sure we were in it oh you're going wait okay I'll see what you're doing there oh how well you can see the camera we're gonna use some real white paint do you want a dab and do you need the micro q-tips these guys oh sure says gotta say thank you for your videos I've been learning a lot from them and I've also been learning more about Adobe illustrator so thanks for that from Galliano Island British Columbia oh cool you are welcome everybody to do their thing where's the clay round to we thing oh yeah that might work to you you know your little ball thing these micro ones work well well wait till you see this up close you're not gonna love those get them what they keep it going keep well I just think maybe the brown maybe brown paint with the micro tips I'll just go back over yeah with some brown paint the micro tip yeah now you got it yeah I understand now the extra details and dimension add so much value to differ differentiate it just need to find the right balance of time and investment per sign who does that sound like Christian on things where I have tiny things like this I'll make a spray paint template so I can lay it down and spray it lay it down and spray well a batch amount like the jolly is bunch of the a-holes the car I do six cars at a time and I lay down a template where I spray paint I spray the whole car I lay it down where I spray the green I lay it down where I spray the lights and offenders and then I come back in and just do the woodgrain look real quick yeah but that's like a whole spray-paid thing but you only do that for a few of them right just for you yeah the car what else oh the trees in the pine trees so it was like a Christmas winter yeah see what you can do to break that I reinforce this guy right here nobody else saw the eye roll I think it's great I love it be the best be the best all right you want to wrap it up all right I gotta wrap it up I got things to do I gotta go get some enchiladas and don't forget your lottery tickets you go get your lottery tickets I will meet you there and I will see you tonight at 9 over there on laser everything go hang with the boys see if you can keep up


I realize this is a record rainfall year, but are there years in the past that you've been in operation that have had similar challenges? Oh, definitely. And that's kind of why we have switched over to raising more cover crops was because we usually follow winter wheat with corn, and in the spring, that's the toughest part to get corn planted is in the wheat stubble.  So that's why we started cover crops was to basically get corn on the ground, I don't know, till acres. And further west in Aurora County, we have poorer draining soils, which is a big challenge. A lot of potholes, and so we definitely need to use our moisture up more. So we've had issues every year, but just not quite as bad as this year. Do you have a favorite cover crop blend you like to go with, or you're always changing the species that you plant? For years, we did the, my brother likes to go as cheap as possible. And we are very conservative. And so we do a cover crop blend mainly brassicas for a number of years. And then we found out that we need some micro-risal friendly blends in there. So we've been adding flax and some other crops or covers to get that. But yeah, we try to keep the price low use small seeded covers. And it's worked out well.  But the last, I'd say four or five years, it's been a lot better. We've had really good growth and good activity in our carvers. Have you guys looked at changing cover crop species? You talked about the wetness in June and needing to utilize some moisture. I know you raise winter wheat, so rye might be a bad word. But have you used, look at it, use winter wheat as a cover crop to utilize some of that excess spring moisture or cereal rye or anything like that?  In fact, I think it was a year ago, I think it was middle of December. We had a few nice days. They got above 50 and so I went out there and killed some volunteer wheat out because I hadn't done so prior this year. However, it's a different story when we have stripper headers on our on our combines and there is more loss. I don't like that fact. But one thing I do like about it is it's a uniform cover crop that you're receiving. So we basically do a burn down before the cover crops, plant the cover crops. And then in the past, I had actually terminated winter wheat. But the last several years I've let it grow. The cover crops are pretty aggressive. The brassicas can't compete very well with the winter wheat. And so especially this year, I'd seen a lot of farmers out there spraying their winter wheat down this fall and I'm thinking, boy, why not have something growing there? I know it's typically not good to have wheat growing in the spring. But in this situation, I think I'd rather have that than a lot of residue on the surface and not being able to dry anything out underneath.


The floor may not be in the robot. To be more specific, I'm talking about the kid's apps. There are so many kid's apps on the Google Store, and at first that does not seem to be a big issue, right? Well in early 2018, that wasn't the case. An app was uploaded to the Google Play Store called, called Blaze and the Monster Machines 2018, and at first considering that it's based of the show with the same name on the Junior, you'd think it will be innocent. Well, not really. I'll give you a description on the app, and I will explain how this not only caused controversy, but also got the attention of Google. At first it will seem like a shitty and poorly designed app, with a screenshot of the app icon on the top, and a copy-pasting phone options like you would see on a regular phone, but the text was in a different language on the bottom. Here is where things take a turn for the worst. After a couple of ads, you will be taken to the other menu as described, and you will hear a voice of someone with an Irish accent, and the voice has been slowed down to give a demonic feel to the voice, or a voice that sounds similar to Jack Nicholson's Joker voice. The man will say the following. A mother who discovered the app, posted a video to YouTube, discussing how Google should be more careful when it comes to letting apps onto the Google Play Store. Google has since deleted the app, however you can still download the APK file, and transfer it onto your Android device.


The paper that we wish to address with this video is identifying analytics for high-throughput bioprocessor development studies. The impetus for the paper really comes from the industrial need to be able to move quickly in a high-throughput mode through bioprocessor development studies and to avoid the analytical methods they deploy from becoming a bottleneck to those high-throughput applications. We then set out to understand what it is about particular analytical methods that makes them appropriate or not appropriate for deployment in a high-throughput mode. I'm now going to hand over to the first of the course of Simi Kong and Spiritus Consonides to talk about the way in which we've addressed this problem. Our investigation starts by looking into features of analytical methods that can affect the high-throughput nature. In our paper we have defined the high-throughput nature as a function of time and simple amount of requirements. For this purpose, we have defined features relating to these two types of requirements as seen on the figure. After defining these features, we have tabulated and discussed them in the paper for a selection of 70 analytical methods from the perspective of a map purification process. These methods are divided into six categories such as spectroscopic, PCR, immuno-assays, electrophoretic, chromatographic, and their tests for analyte such as endotoxins, lipids, total proteins, nucleic acids, maps and the variants, HCPs and Leach Protein A. All this information is available digitally in the company and supporting information. The link is shown here. Having defined and tabulated features of analytical methods, we then focus on how to employ these in order to judge the suitability of analytics to high-throughput applications. This made apparent that the time-related features of analytics are best considered collectively instead of on a standalone basis. This is because the total time requirements posed by an analytical method as a function of the number of samples it analyzes may not follow a single linear trend, as opposed to the total sample amount of requirements. This revealed to us an additional factor affecting the high-throughput nature of analytical methods, and this is the InVision Experimental Study itself. We therefore proposed that the assessment of the high-throughput nature of analytics should consider all features of analytics in a collective fashion, and at the same time issued also taking into account the general characteristics of planned experimental work. This would give valuable insights on the criticality of the contribution of the different features of analytical methods towards the high-throughput nature. Carrying out this assessment in parallel to the planning of experimental work, we therefore allowed to identify analytics that provide the best fit to purpose and hence, should facilitate the completion of the study. So in conclusion, SIME has taken us through how the nature of the analytical methods can be defined in terms of their capacity to be used in a high-throughput mode of operation. We then demonstrated how those features have been tabulated in an easily accessible format, and that is to enable readers and people accessing this article to be able to apply the same methodology to other analytical techniques. And then SPIROS has identified how we can use those parameters and metrics to identify those particular analytical methods that can be operated in a high-throughput mode, taking into account the particular features that make them suitable for that mode of operation. The work reported in this paper has been carried out by SPIROS Consonides as an engineering doctorate, sponsored by GE Healthcare and by SIME.com, a post-doctoral researcher in the EPSLC Centre for Innovative Manufacturing of Immersion to Macromolecular Therapies.


Post-traumatic stress disorder is an anxiety disorder that is triggered as a result of some serious trauma. The Diagnostic Statistic Manual version 5 states that post-traumatic stress disorder is characterized by the re-experiencing of an extremely traumatic event accompanied by symptoms of increased arousal and by avoidance of stimuli associated with the trauma. In layman's terms, this means that some people tend to re-experience the feelings of distress and horror from after having gone through some extreme negative event. This can be very disruptive to the person's life and cause a high level of dysfunction. In the most extreme cases, people have resorted to suicide in a desperate attempt to obtain relief. The classic example of PTSD is that of the returned war veteran has experienced severe trauma in the battlefield and keeps having flashbacks to being back in the battlefield. This is a serious trauma. If you suspect you or a loved one may be suffering from post-traumatic stress disorder, I suggest you to talk to us or to another fully qualified mental health professional fast. In the meantime, make sure you provide appropriate first aid. On the positive side, note that while it is normal for people to have a reaction to a traumatic event, most people recover naturally with time, never get to experience PTSD and go on to lead trouble-free lives. Yet, in some individuals, these experiences do turn into trauma and could be diagnosed as having PTSD. There are good and valid reasons as to why this happens and the good news is that there are effective treatments that can help you recover. Please, if you suspect you or a loved one may be suffering from post-traumatic stress disorder, I suggest you get help fast. If you would like to further your training, you might want to consider running the mental health essentials course in your workplace where we deal with disorders in greater detail and we show you how to apply a first aid response to mental health emergencies at work. This video is being released each week so when you subscribe, you'll get a notification letting you know when a new one has just been published. So make sure to hit that subscribe button and don't miss out on this vital information for yourself, your colleagues and your loved ones.


So you should all be reading Opa. So let me first say before we, I want to talk more about the spiritual value of productiveness. But you know, one of the things that I've mentioned many times on the show, and I actually get a lot of flack from some objectivists for this, is how much I admire Silicon Valley and how much I admire the people who work in Silicon Valley and the entrepreneurs and the creation.  What I admire about these people is their sense of purpose. They have a vision. They have an idea and they dedicate it to that idea. And they work hard and they change the world by focusing, using their mind to achieve that vision that they have, to achieve that purpose that they've set for themselves. And they don't settle. So you don't find, I don't know, Apple saying, okay, we did the personal computer. That's fine. We're done. Right? Steve Jobs had to do an iPhone and then iPad. And then I watch, and even though otherwise he came out after him, and he was trying to solve the problem of television, he would say. And you know, he was always, always trying to solve problems, applying his mind. Constantly, constantly throughout his adulthood to problems that existed in the world. And drove himself, drove himself, worked incredibly hard, put the team together that he drove to work very, very hard in order to solve. So, I mean, the amount of respect I have for people like that is unbelievable.  And using objectivism as an excuse for their own failure in life and in their careers. And then blaming the people in Silicon Valley who actually have a life, have a career, have a purpose, have embraced Iron Rans, core moral virtues implicitly.   But first I say, wow. First I say, thank you. And first I say, they are unbelievable moral people. Here's what Dr. Pieckhoff writes in Opal about this, right? Iron Rand is the first thinker to reject the mind-body dichotomy methodologically by reference to a theory of reality and of concepts. We'll get to that at some point, not today. That is why she's also the first fully to practice the virtue of justice in the present context. She is the first to identify in terms of philosophical system, the source of wealth and therefore the proper estimate of those who created. Next paragraph. A productive man is a moral man, period. Let me repeat that. A productive man is a moral man. In a more intellectually demanding and innovating fields, he is the epitome of morality. He deserves to be admired accordingly. I love that paragraph. Let me repeat it, because this so applies to Silicon Valley. A productive man is a moral man. In the more intellectually demanding and innovative fields, he is the epitome of morality. He deserves to be admired accordingly. Wow. And this relates to the idea of love of ability, which I in Rand had, think about all the heroes in her books and think about all the talks to businessmen, the love of ability. And I love the people in Silicon Valley because of the amazing things that they create and they produce. Now, it's not limited to Silicon Valley. I love businessmen all over this country. But what does it say here? Oops, where did I go? The more intellectually demanding and innovative fields, the valley and everything represents is demanding, intellectually demanding. It's taking, cutting its science and turning it into products that make my life and your life and everybody's life better. It doesn't get any better than that. It doesn't get any more admirable than that. Now, yeah, when they do something politically horrible, you have to attack them. You have to condemn them. But within the context of how admirable they are as producers. And if you take that approach, if you take the approach of admiring productive ability, admiring and loving productive ability, loving, admiring, production and people are production and viewing production as moral, productiveness as this key virtue.  Yeah, some of them are bums. Some of them come here to leech off the system. Condemn them. But respect the ones who don't. Respect the one who wanna make and create and build and produce, don't start slashing back on immigration when people wanna come to this country because it's still free enough for them to be able to be productive. Right? Now somebody's asking about Elon Musk. Look, Elon Musk, to be a crony, to be in a sense, to base all your production on government favors, that's not productiveness.  That's, and a crook is not productive, right? Now, Elon Musk is this real mixed case and I have a huge love-hate relationship with him. On the one hand, he made his money at PayPal which was real innovation, real production. And he has a vision to going to Mars in 30 years which I think is just astounding for an entrepreneur to have a 30-year vision and to put in place a program to actually achieve that vision, talk about goal-directed action, talk about having a purpose in life. I mean, that's amazing, right? And I don't resent the fact that he gets his money in the space program from government because that's really right now the way the economy structured, the only way to get it. But I resent his solar energy plans. I resent his Tesla plans. It's not just that he take government loan. He gets subsidized heavily, heavily, heavily by all these people, right? So Elon Musk is a very mixed case. He's very difficult to have the right attitude towards and I have a very mixed view of Elon Musk as a consequence.  In some mixed cases, I admire and hate Elon Musk, right? Now, we're gonna get to a question Ethan asked in a few minutes. But so let me deal, let's say so, I just wanna make the case that being productive is at the core of what it means to be a model and being successful at production requires that one be successful at least in the realm of production, in the other virtues of objectivism. You're not gonna be successful in your career, in production, if you're not honest, if you don't have integrity, if you don't have a sense of justice in the way you treat your employees, if you don't have pride, think of Steve Jobs, right? And of course, if you're not rational, forget it, right?  I mean, that's just, so to me, again, the people in Silicon Valley are incredible productive and they're being egoistic about it.  Think of Michael Dell, who's, I don't know, with $20 billion, just risked a huge amount of his wealth and taking his company, Dell, private, and then merging it with EMC, I think it's EMC, with the largest takeover in technology history, right? And trying to create something even bigger than Dell ever was. And maybe in the process of becoming the richest man in the world. But I can tell you, Michael Dell doesn't know what to do with the money he already has. There's no way he can spend it. But why is money important in that place? Because it's a way to measure how successful you are. It's a way to measure how productive you've been. I mean, think of the virtue that that takes, think of the rationality that takes, the drive, the purposefulness that that takes, and the self-esteem. I've made $20 billion, I'm gonna make another. I mean, wow. So I love these guys. I love these people and their politics, you know? If that were the only problem in the world, we could solve it. Everybody was as productive and creative and innovative and purposefulness and rational as people in Silicon Valley. Then we could deal. We could deal with their politics. I'm convinced we can convince them that their politics is wrong. But try to convince people who don't wanna work. Try to convince people who don't use their minds. Try to convince people who drift through life, who don't engage with reality to be moral. That's much harder. That is so much more hard.