extfieldsofstudy: Physics Biology Chemistry

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Designability, thermodynamic stability, and dynamics in protein folding: a lattice model study

In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against mutating the amino-acid sequence, and must be fast folders. We find two criteria which, together, guarantee that a sequence will be ``protein like'': i) the ground state is a highly designable stucture, i. e. the native structure is the ground state of a large number of sequences, and ii) the sequence has a large $\Delta/\Gamma$ ratio, $\Delta$ being the average energy separation between the ground state and the excited compact conformations, and $\Gamma$ the dispersion in energy of excited compact conformations. These two criteria are not incompatible since, on average, sequences whose ground states are highly designable structures have large $\Delta/\Gamma$ values. These two criteria require knowledge only of the compact-state spectrum. These claims are substantiated by the study of 45 sequences, with various values of $\Delta/\Gamma$ and various degrees of designability, by means of a Borst-Kalos-Lebowitz algorithm, and the Ferrenberg-Swendsen histogram optimization method. Finally, we report on the reasons for slow folding. A comparison between a very slow folding sequence, an average folding one and a fast folding one suggests that slow folding originates from a proliferation of nearly compact low-energy conformations, not present for fast folders.

Introduction
Among the set of all possible linear amino-acid heteropolymers, only very few are "protein like". For a heteropolymer to be "protein like", three requirements must be met: (i) The heteropolymer must be thermodynamically stable: at thermal equilibrium, it must spend a large fraction of its time in the ground state. (Anfissen [1] has shown the ground state of a protein to be the biologically active configuration.) (ii) The heteropolymer must have a fast folding time: the native state should be kinetically accessible, typically within milliseconds to seconds for real proteins. (iii) The "proteinlike" heteropolymer must be stable against mutations: if an amino acid is mutated into another one, the native structure should typically be preserved.
Why are some sequences of amino acids "protein like" while others are not? Since theoretical methods cannot yet reliably find the ground state of real amino-acid chains, we address this question within a simple lattice model. Lattice models have been widely used in the study of protein folding dynamics [2,3,4,5,6,7,8]. The main ingredients of these lattice models are (i) the protein is viewed as a heteropolymer on a cubic lattice, and (ii) non-covalently-bonded nearest neighbor monomers experience an interaction that depends on monomer type. In one class of lattice models, the interactions between adjacent monomers are chosen as random variables from a continuous probability distribution (see for instance [3,4,6]). We adopt another approach, namely a so-called H-P model, where the monomers come in only two types, H(ydrophobic) or P(olar) [2,7]. The main physical motivation for studying H-P models is that the specific ground-state configuration of real proteins appears to be largely determined by optimal burial of hydrophobic amino acids away from water [9]. It was also shown [10], from an analysis of the Miyazawa and Jernigan matrix [11], that the uncharged amino acids fall into two sets: hydrophobic and polar, according to their affinity for water. Moreover, there is experimental evidence that the native structures of certain proteins are stable when hydrophobic amino acids are substituted within the hydrophobic class and polar amino acids are substituted within the polar class [12]. The small number of possible interactions in an H-P model (H-H, H-P, and P-P) and the finite number of possible sequences of a given length provide realistic constraints on the design of particular structures. Li et al. [13] took advantage of these constraints to study some design properties of an H-P model in the complete space of possible sequences. In particular these authors introduced the concept of designability. In the terminology of Li et al., the designability of a given compact structure is defined as the number N S of sequences that have this structure as their nondegenerate compact ground state; a highly designable structure is the nondegenerate ground state of an atypically large number of sequences. These authors reached the conclusion that (i) highly designable structures are likely to be thermodynamically stable since they have a large gap in their compact state spectrum, (ii) highly designable structures are likely to be stable against point mutations, and (iii) highly designable structures have protein-like motifs. These observations suggest that Nature's selection of protein structures is not accidental but a consequence of thermodynamic stability and stability against mutations.
The aim of the present article is to push further the analysis of Li et al.. In particular, the study in [13] is limited to the compact-state spectra of H-P heteropolymers of 27 monomers length (the compact states of which fill a 3×3×3 cube), and the dynamical aspects are not discussed. Here we address thermodynamic and dynamic properties including all states, not only the compact ones. Of course, our present study is therefore limited to a small number of sequences (45), in contrast to the complete enumeration in [13]. More precisely, we address the following questions: • (i) In the compact-state-spectrum studies, thermodynamic stability is measured by the gap in the compact-state spectrum. By gap, we mean the energy difference between the first excited compact state(s) and the ground compact state. How does the compact-state-spectrum gap correlate with the "true" thermodynamic stability where all the possible conformations (including the open and partially open ones) are taken into account? Also, how does the "true" thermodynamic stability correlate with the degree of designability?
• (ii) How does the folding time correlate with the compact-state spectrum? An answer to this question was postulated in [4]: a small gap in the compact-state spectrum leads to low foldability and a large gap in the compact-state spectrum leads to fast folders. It was shown in [6] that this postulate is wrong in the framework of a random interaction model: even though sequences with a large compact state gap are fast folders, sequences with a small compact state gap can fold either slow or fast. Is the postulate right or wrong for H-P heteropolymers?
• (iii) Are highly designable structures also fast folders ? Sequences that have highly designable ground states and thus are stable against mutations are also typically thermodynamically stable according to the analysis of the compact-state spectrum carried out in Ref. [13]. Moreover, Vendruscolo et al. [14] showed, in different lattice models, that both types of stability are equivalent. One would like to know whether the requirement of fast folding dynamics introduces new constraints on the set of "protein-like" sequences. Finally, one can ask why are some sequences fast folders while others are slow?
This article is organized as follows: section 2 is devoted to the details of the model and the technical aspects of the simulations. We implement several techniques that were developed in the context of statistical mechanics of spin models. These techniques are next used in sections 3 and 4 to analyze the thermodynamics and dynamics of a set of sequences. Section 5 summarizes our answers to the questions presented above.

Model and simulation techniques
The aim of this section is to briefly recall the definition of the heteropolymer H-P model, and to describe the simulation techniques.

The model
In the model analyzed in [13], a protein is a self-avoiding walk of monomers on a cubic lattice. A sequence is defined by the set {σ i } of amino acids along the chain, where σ i ∈ {H(ydrophobic), P (olar)}, and i runs over the monomers along the chain (i = 1, ..., 27 for a chain which folds into a compact 3×3×3 cube). The different structures are defined by assigning a position r i to the i-th monomer on the cubic lattice, such that the distance between two consecutive monomers is equal to unity and two monomers cannot lie at the same site (self-avoidance condition). Given a sequence σ, the Hamiltonian is where E H,H , E H,P , and E P,P are the energies of H-H, H-P, and P-P contacts, respectively, and ∆(r i , r j ) = 1 if r i and r j are nearest-neighboring sites with i and j not adjacent along the chain, and zero otherwise. For instance, in the case of the two dimensional conformation of Fig. 1 These dimensionless coefficients define the energy scale in which the temperature will be measured. very few sequences have a non-compact ground state. However, E C should not be too large since, as was shown in [7], as E C increases above a certain threshold, the folded phase gives way to a collapsed glassy phase. In practice, after preliminary simulations, we have chosen E C = 1.5.

Dynamics
The most commonly used algorithm in three-dimensional lattice-heteropolymer folding dynamics is the Monte-Carlo algorithm with two one-monomer moves (end moves, corner moves) and one twomonomer move (crankshaft move) [see [7] for a pedagogical description of this algorithm]. However, for the model we simulated, this algorithm spends most of the time refusing moves, leading to large computation times. Hence, we chose to implement a Bortz-Kalos-Lebowitz (BKL) type algorithm [15], an algorithm especially efficient in the presence of slow relaxation. In contrast to the standard Monte-Carlo algorithm, this algorithm never rejects moves. In practice, one keeps track of all the possible states α that can be reached after the three types of moves listed above, starting from a state α 0 . Once the list of all possible moves is established, together with the Monte-Carlo transition probabilities, one move is picked according to its relative transition probability and that move is then performed.
The time spent in the state α 0 is randomly chosen from the exponential distribution One need not recalculate this list of possible final states at each step, but instead one updates this list by canceling moves that are no longer possible and adding new moves that become possible.
The energy costs ∆E α 0 →α of all these moves are also updated. This algorithm is especially efficient for slow and average folders, but still does not allow systematic studies at low temperatures. One unit time of this BKL algorithm (noted BKL unit in the following) corresponds to 27 Monte-Carlo- Steps (MCSs) of the usual Monte-Carlo algorithm (in lattice heteropolymer folding and for the usual Monte-Carlo algorithm, one MCS usually corresponds to attempting to move one monomer).

Thermodynamics
One possibility to compute thermodynamic quantities is to carry out an exhaustive enumeration of all the possible conformations, including the noncompact ones. Such an exact method was used for instance in [6] in the case of a 15-mer in three dimensions, and in [14] for a 16-mer in two dimensions.
Since, in practice, we could not apply this exact method to 27-mers in three dimensions, we have should remain close to T 0 since the simulation at temperature T 0 is carried out over a finite time and the phase space is thus only partially sampled. We did not in fact use this "naive" histogram technique but rather made use of the powerful method invented by Ferrenberg and Swendsen [16,17].
This method consists in optimizing several histograms calculated at different temperatures to obtain the temperature dependence of various thermodynamic quantities. Moreover, the accuracy of the optimized thermodynamic quantities can be evaluated, and additional simulations can be carried out when necessary. Following [16], we briefly summarize this technique by focusing on the case of the single energy histogram, the generalization to joint histograms of various quantities being straightforward. We consider R energy histograms labeled by n = 1, ..R, carried out over t n time units at the temperatures T 1 , ..., T n , ..., T R , with the normalization where N n (E) is the number of times a state (or states) with energy E is sampled in the n-th histogram.
The partition function Z(T ) is expanded over the density of states W (E) as Each of the R histogram simulations carried out at a temperature T n leads to a "naive" estimate of the density of states with F n the free energy at temperature T n . The Ferrenberg and Swendsen method [16] consists in expanding the density of states W (E) as a combination of the "naive" densities of states (4) the coefficients of this expansion (as well as the free energies F n in (4)) being determined by minimizing the error in this estimation of W (E). The result is a closed set of multiple-histogram equations for the F n [16] P Once (5) and (6) have been solved by successive iterations, the average of an energy-dependent operator is calculated as

Thermodynamics
The compact state spectrum was previously determined by means of exact enumerations [13]. Thanks to this work, we know for each sequence the lowest energy compact state. However, it is possible that the true ground state is not compact. We therefore checked during the histogram calculations that no open state has a lower energy than the compact ground state. We eliminated a few sequences with noncompact ground states. Since we were not able to perform an exact enumeration of the noncompact states, we cannot exclude the possibility of a noncompact ground state that was not found during the simulations. However, we believe that this possibility is rather unlikely. We will comment later on the characteristics of those few sequences with a noncompact ground state.

Qualitative study of a thermodynamically stable and unstable sequence
We first begin with a qualitative analysis of a "protein-like" and a "non-protein-like" sequence, from the point of view of thermodynamics. As stated in the introduction, one necessary condition for a sequence to be "protein-like" is that it be thermodynamically stable. Hence, we have to find a quantitative way to measure thermal stability. It has been proposed [18] that real proteins undergo a folding transition at some temperature T f larger than the glass transition T g , below which the dynamics dramatically freezes. For "protein-like" sequences, folding should be a first-order-like transition, with T f much larger than T g , thus allowing the possibility of a temperature regime in which the ground state is thermodynamically favored and kinetically accessible. By "first-order-like", we mean that as a function of temperature the native state occupancy has a narrow transition from a low value in the unfolded phase to a high value in the folded phase. We will use the width of this transition as a measure of thermodynamic stablility, the thermodynamically stable sequences having a narrow transition. The first-order-like behavior of the folding transition was put on a quantitative basis for a lattice H-P model by Socci and Onuchic [7]. These authors studied the shape of the energy histogram and observed a transition from a unimodal shape to a bimodal shape as the temperature was lowered below T f , suggesting the occurrence of a first-order-like transition.
On the other hand, in the case of a thermodynamically unstable sequence (and thus one that is not "protein-like"), there are low-lying states competing with the ground state, and the transition to the folded ground state as the temperature is decreased is thus broad. In order to compare different sequences, we measure thermodynamic stability in terms of the width in temperature of the transition to the native state compared to the transition temperature. In biological situations, the temperature is usually fixed and the notion of thermal stability is then not only sequence-dependent but also temperature-dependent. For instance, some sequences could have a narrow transition to the folded state but with too low a T f , so that in practice, the protein is unfolded at the temperature of interest. Our definition of thermodynamic stability is thus, in the context of real proteins, only a necessary condition.
Following Socci and Onuchic [7], we employ the optimized histogram method described in section 2.2.2, and determine the probability P 25 (T ) that the sequence is in any conformation having more than 25 correct ground-state contacts, or "native" contacts, out of 28 possible contacts for the fully folded structure. Throughout this paper, this set of conformations will be referred to as "native states". We will consider a heteropolymer as correctly folded if the number of native contacts is larger than or equal to 25. This assumption speeds up computations and is sensible from the point of view of real proteins since structure fluctuations around the folded conformation are expected, and do not prevent the protein from being functional (see for instance [19]). The variation of P 25 (T ) as a function of temperature T are shown on Fig. 2 for the thermodynamically stable sequence A and the thermodynamically unstable sequence C. [These two sequences will be studied in detail in the present article]. The larger width of the transition to the folded conformation in the case of sequence C is due to the existence of low-lying semi compact conformations, not present for thermodynamically stable sequences. The consequences of these low-lying states for the folding dynamics will be investigated in what follows.

Thermodynamic stability: compact state spectrum versus transition width
In order to answer the first question in item (i) in the introductory section, we want to compare the compact-state-spectrum estimation of the thermodynamic stability, in terms of the folding temperature T f and the glass-transition temperature T g [18,20], to the thermodynamic stability estimated with the method of section 3.1.

Compact-state-spectrum results
We first review the results of Goldstein et al. [18], and Bryngelson et al. [20], who estimated the folding temperature T f and the glass temperature T g in terms of simple spectral quantities. These authors derived their criteria from the complete energy spectrum, dividing phase space into two components: on the one hand, the native state with a nearly zero entropy and, on the other hand, uncorrelated "liquid-like" states at higher energy with a large entropy. If ∆ denotes the average energy difference between the native and the liquid-like states, and Γ is the width in energy of the liquid-like states, it is shown in [18,20] that the ratio T f /T g is maximal if ∆/Γ is maximal. In other words, the ratio ∆/Γ should measure how "protein-like" a sequence is. We take here as a working hypothesis the application of the results in [18,20] to our lattice model including the compact states only. In order to test the hypothesis, we calculate ∆ and Γ from the compact-state spectra, the compact states being conformations exactly filling the 3×3×3 cube, and the compact-state spectrum of a given sequence being the set of energies of all compact conformations. More precisely, where the E α (α > 0) denote the energies of the excited compact conformations, E 0 is the lowest compact state energy, and N C is the number of excited compact conformations.
where T (x) is the temperature for which the probability is x to find the heteropolymer in a state with 25 or more native contacts. [This is the inverse function of P 25 (T ) as plotted on Fig. 2]. We have plotted in Fig. 3 the width δ of the transition as a function of ∆/Γ defined by (7) and (8). We have separated the sequences into a set "L(arge)"of sequences with large values of ∆/Γ and a set "S(mall)" with small values of this ratio. (For further consideration, we have extracted from the "L" set two subsets "LA" and "LB" with a fixed ∆/Γ ratio, of order 4.5 and 4.7 respectively. Also, the set "SA" has been extracted from the "S" set, with a ∆/Γ ratio of order 3.7.) It is clear in Fig. 3 that in spite of some scatter, the "L", "LA" and "LB" sets, with a high ∆/Γ ratio (larger that 4.3) correspond to thermodynamically stable sequences, with a narrow transition to the native structure (i.e., a small δ value), whereas the transition to the native structure for the sequences belonging to the "S" and "SA" sets (∆/Γ < 4.3) is rather broad. This shows that "protein-like" sequences (at least as far as thermodynamics is concerned) correspond to sequences with a large ∆/Γ ratio, i.
e. sequences with a low-energy native state compared to the energy width of the distribution of compact states.
One can also ask how the transition width δ correlates with ∆ alone, independent of Γ. It turns out that ∆/Γ is almost a monotonically increasing function of ∆, as shown in Fig. 4, Γ being nearly constant at Γ ≃ 2, and therefore ∆ alone is also a good predictor of thermodynamic stability.

Thermodynamic stability versus designability
The designability of a given structure is measured in terms of the number N S of sequences that have this structure as their nondegenerate ground state, and, as proposed in [13], the sequences corresponding to highly designable structures should be "protein-like". Interestingly, the highly designable structures show regular helix-like and β-sheet-like patterns [13], quite reminiscent of the regular patterns in real proteins. Moreover, since these highly designable structures have on average a large gap to their first compact excited state [13], they are likely to be thermodynamically stable.
More specifically, the average gap in the compact state spectrum suddenly jumps from a low value to a high value as N S increases above N S ∼ 1400. It is thus of interest to relate the thermodynamic stability of sequences, measured in terms of δ in equation (9), to the degree of designability of their native state structure measured by N S . We will reach the conclusion that ∆/Γ is a better predictor of thermodynamic stability than designability. Qualitatively, this could be anticipated since high designability of a structure still allows for very different behaviors of the sequences which design that structure.
The correlation between the transition width δ of the various sequences analyzed here, and the number N S of sequences that design their native structures is plotted in Fig. 5. Clearly, the sequences whose ground states are highly designable structures are likely to be thermodynamically stable. However, we observe that several sequences belonging to the sets "S" and "SA" of thermody- Crosses denote sequences with a small ∆/Γ ratio and squares, diamonds and triangles sequences with a large ∆/Γ. Some sequences in the SA sub-set with ∆/Γ ≃ 3.7 can have a large designability in spite of being thermodynamically unstable.
namically unstable sequences have a relatively high designability N s . These sequences, despite high designability, have a small value of ∆/Γ. Such sequences are expected to emerge due to the fact that, even for a structure with large N S , the ratio ∆/Γ is not necessarily large for all sequences having that structure as a ground state [21]. In other words, it is possible to find atypical sequences with a low value of ∆/Γ even for structures with a large N S . For instance, using the compact-state spectra, we have plotted in Fig. 6 the distribution of ∆/Γ for the top structure (this is the structure with the maximal N S = 3794) and a structure with N S = 300. On average the sequences corresponding to the structure with N S = 3794 have larger ∆/Γ than the sequences corresponding to the structure with N S = 300. However, the tail of the distribution for the N S = 3794 structure still extends to very small ∆/Γ. In summary, large ∆/Γ ratio is a good predictor that a sequence will be thermodynamically stable. A high designability N S for a structure is consistent with, but does not guarantee, large ∆/Γ and hence thermodynamic stability of its associated sequences. However, they showed that the thermodynamic stability is flat as a function of N S , in contradiction with our present results, and also in contradiction with unpublished data [22] where the gap in the compact state spectrum in two dimensions was shown to increase as a function of N S . In our opinion, this discrepancy is due to the fact that in [14] the overall compactness energy E C in the inter-residue interactions was set to zero, thereby weighting open state configurations too strongly with respect to compact states. We expect that a larger E C would have led to an N S -dependence of the thermodynamic stability in Ref. [14].

Conclusions on the thermodynamics
This section was devoted to the analysis of the thermodynamics of several sequences, selected from highly and poorly designable sequences, and with large and small values of ∆/Γ. The known compact state spectra allow for the calculation of the ratio ∆/Γ, which is thought to be proportional to the ratio of the folding temperature to the glass temperature [18,20], and thus predicts to what extent a given sequence is thermodynamically "protein-like". The Monte-Carlo data calculated with open and partially open states also allowed us to characterize the thermodynamic stability of a given sequence, in terms of the width δ of its folding transition. We have shown that these two quantities, δ and ∆/Γ, are well correlated, signaling the validity of the compact-state-spectrum analysis. We have also shown that stability with respect to mutations (measured in terms of designability) is not directly equivalent to thermal stability.
Finally, it is worth noting that we eliminated three sequences with partially open ground states.
These sequences had a very low ∆/Γ ratio (2.17, 2.18, 2.52) [this ratio has been calculated with the ground state energy E 0 being the lowest compact state energy]. By contrast, none of the simulated sequences with a high or moderate ∆/Γ ratio were found to have a partially open ground state. This suggests that the ground state conformation of some of the remaining sequences with a small ∆/Γ ratio may not be compact. However, since these sequences are among the most unstable ones, our calculation of the transition widths as far as "protein-like" sequences are concerned is unaffected.

Folding simulations
Besides thermodynamic stability and stability with respect to mutations of the amino-acid code, the native state of a "protein-like" sequence should be dynamically accessible. Clearly, the dynamics of all the sequences, including the thermodynamically stable ones, becomes glassy at low temperatures in our model since all the inter-residue interactions are attractive. As the temperature is lowered, the average folding time (the average time required to first reach the native states, starting from a stretched conformation) will first decrease and then, below a certain temperature, will start to increase drastically, presumably scaling like ln ( τ f ) ∼ 1/T . Conversely, as we have already seen, the native state occupancy increases as the temperature is decreased. Since we want to investigate the balance between thermodynamic stability and dynamical accessibility of the native state, we chose to examine the dynamics at the temperature T f such that the native state occupancy is fixed at some predetermined P f . The question is then: do the sequences with a large ∆/Γ ratio, thermodymic stability, and mutational stability also fold fast at T f ?
In order to examine this question, we measured the average folding time, namely the average time τ f necessary for the heteropolymer to first reach any of the native states (with 25 ground state contacts, out of 28), starting from a stretched conformation. Because in our model all interaction energies are attractive, and individual non-native contacts may be as strong as native contacts, the folding dynamics is very slow compared to other models. For this reason, we simulated folding of the heteropolymers at the temperature T f such that the average occupancy of the native states is only P f = 10%. Compared to other works where models with a faster folding time were investigated, this occupancy of the native states is quite small. For instance, Abkevich et al. [23] could fold a few sequences at a temperature for which the average similarity with ground state was up to 95%. Their slowest average folding time was then of the order of 2 × 10 8 MCS, which is one order of magnitude smaller than the fastest folding time in our simulations (given that 1 BKL unit = 27 MCS). However, models with faster folding times generally require unrealistic assumptions such as artificially lower energy for individual native contacts compared to the non-native ones. Even though we could not go systematically to lower temperatures, the effect of lowering the temperature was examined for a few sequences.

Average folding times
One folding simulation consists in starting from a stretched heteropolymer, and running the dynamics until one of the native states is first reached. The time required is the folding time, which should then be averaged over several folding simulations. In practice, we have averaged the folding time over 20 folding simulations. For each sequence, the temperature is fixed at T f (at this temperature, the native-states occupancy is P f = 10%). The average folding times are plotted in Fig. 7  We observe in Fig. 7 that sequences with a large ∆/Γ ratio fold fast. We thus conclude, in response to question (iii) in the introductory section, that folding dynamics does not add any constraint in the selection of "protein-like" sequences: once a structure is stable against mutations and thermodynamically stable (namely, a sequence with a large ∆/Γ ratio and a large N S ), it will be a fast folder.
A quite striking result visible in Fig. 7, is that sequences with a low ∆/Γ ratio (belonging to the "S" and "SA" sets of thermodynamically unstable sequences), may also fold fast, at least as fast as some of the sequences belonging to the "L", "LA" or "LB" sets. However, at lower temperatures and hence larger native-states occupancy, we find a stronger correlation between low ∆/Γ ratio and slow folding.
In order to go to lower temperatures, we selected four sequences (denoted by A, B, C, and D; A and C being the same sequences as in Fig. 2), with the same fast folding time, 0.14 × 10 9 MCS, at T f , i.e. with a 10% occupancy of conformations with 25 or more native contacts. We folded these sequences again at temperatures corresponding to larger native-states occupancy. The sequences A and B belong to the set "L" of thermodynamically stable sequences, and the sequences C and D belong to the set "S" of thermodynamically unstable sequences. As the native-states occupancy is increased, we observe in Fig. 8 that the folding times of the two thermodynamically unstable sequences, C and D, clearly become much larger than the folding times of the two thermodynamically stable sequences, A and B. Regarding the results of our study at a fixed native-states occupancy of 10% (see Fig. 7), this suggests that, as the native-states occupancy increases, the average folding times of the sequences with small ∆/Γ ratio will increase much more rapidly than the folding time of the sequences with large ∆/Γ ratio.
The conclusion regarding the variations of the average folding times as a function of the nativestates occupancy is similar to the one reached by Abkevich et al. [23], who proposed that the gap ∆ in the compact-state spectrum correlates with the average folding time calculated for large native-states occupancy.

Slow versus fast folding
Despite the complexity of protein energy landscapes, several authors have proposed simple effective descriptions of these landscapes. For instance, the role of traps (or folding intermediates) in the folding process was underlined by several authors, for instance by Bryngelson and Wolynes [24] and by Klimov and Thirumalai [6]. A scenario was proposed by Bryngelson et al. [25] in which there exists a "folding pathway" to the native state: in a first step, the protein collapses via many possible paths in phase space, and, in a second step, folds to the native structure via a small number of possible paths. Abkevich et al. found evidence for a nucleation process in a lattice model study [26].
The aim of the present section is to see if there exists any simple scenario in our H-P model.
Among all the sequences analyzed here at a P f = 10% occupancy of native states, one sequence has an anomalously long folding time, approximatively 4 × 10 9 MCS. This sequence belongs to the set of thermodynamically unstable sequences (∆/Γ = 2.7 and δ = 0.77). Since this sequence has the longest folding time among our sequence selection, we will denote this sequence by "W(orst)". We will compare this very slow folding sequence to a fast folding "protein-like" sequence (sequence A in Fig. 8), and also to a sequence which is thermodynamically unstable but folds fast at a native-states occupancy of P f = 10% (sequence C in Fig. 8).

Number of low-energy conformations
In order to obtain more information on low-energy traps, we carry out the following simulation. We start from a stretched conformation and let the dynamics evolve until a conformation is first reached whose energy above the ground state ∆E = E − E 0 is smaller than a given ∆E hit . We refer to the result of a single such simulation as a "hit". The contact matrix of this conformation is then We analyzed three sequences: sequence A (a "protein-like" sequence), sequence C (fast folding at P f = 10% occupation of native states, but thermodynamically unstable), and the very slow folding sequence W. We first study the number of different structures for the sequences A, C, and W. It turns out that the "protein-like" sequence A, no states other than the ground state were found with an energy ∆E < ∆E hit = 0.5. As far as the two other sequences C and W are concerned, we found 12 different structures for sequence C and 125 for sequence W. The list of these structures obtained is shown in Table 1 for sequence C and Table 2 for sequence W. The Hamming distance to the ground state in the second column of these tables is with C the contact matrix of a given hit and C (GS) the contact matrix of the ground state structure.
The contact matrices being symmetric, the summation in (10) is restricted to the matrix elements i ≤ j. The matrix elements j = i + 1 have been discarded since they correspond to covalent bonds; the matrix elements j = i + 2 have also been discarded since no contact can be made between these monomers.
We conclude that, going from the "protein-like" sequence A to sequence C and to the very slow folder W, one has a spectacular proliferation of different low-energy conformations that can be hit starting from a stretched conformation. It is also worth remarking that the ground state structure is not the most likely to be hit for either sequence C or W.
In order to determine if any structures with energy ∆E < ∆E hit = 0.5 have been missed, we first notice that for sequence C, the most unlikely hit has been reached 18 times out of N = 1500 simulations (the density of hits for this structure is 1.2%, as shown in Table 1). This number is much larger than unity, indicating that all structures of comparable or greater probability have been found.
For sequence W, the most unlikely hits have been reached only once out of the N = 1500 simulations, strongly suggesting that some of the low-energy structures have not been found. In order to estimate Density  We have also compared the states hit in the folding simulation to the complete set of compact low-energy states with an energy ∆E < ∆E hit = 0.5 (known from the compact-state enumeration [13]). In the case of sequence C, we found that all 12 low-energy states in Table 1 are indeed compact, and correspond exactly to all the compact states with an energy ∆E < ∆E hit = 0.5. For sequence W, we found 85 compact structures with an energy ∆E < ∆E hit = 0.5, a number considerably smaller than the 125 structures in Table 2, which include partially open structures as well. Moreover, five of the 85 compact-state structures were not hit in our simulations. It is very plausible that these five low-energy compact structures were missed because of poor statistics for the most unlikely hits; this is consistent with the earlier statistical estimate of a total of 10 missed structures.
The comparison between the low-energy compact structures and the hit simulations shows that, for the average folding sequence C, the full low-energy phase space is dynamically accessible, though some of these low-energy conformations are more likely to be hit (see Table 2). The proliferation of different low-energy conformations in the case of the slow folding sequence W closely matches the large number of low-energy compact conformations. This is natural because the low energy cut-off ∆E hit = 0.5 restricts "hits" to compact or very-close-to compact states. Sequence C Sequence W Figure 10: Evolution of the similarity S(t 0 , τ ) between the conformation at times t 0 and t 0 + τ .

"Trapping" time in the low energy conformations
We now turn to the question of how long the protein remains in the first states reached with an energy ∆E < ∆E hit . In particular, we would like to compare the magnitudes of the "trapping times" in these low-energy states. To do so, we start from a stretched conformation and let the dynamics evolve until a state with energy ∆E < ∆E hit is first met at time t 0 . We then calculate the similarity S(t 0 , τ ) between the conformation at time t 0 and at a later time t 0 +τ . This quantity is then averaged over N = 1500 complete simulations. The results are plotted in Fig. 10 for the sequences C and W, for ∆E hit = 0.5. As is visible in this figure, the typical "trapping time" in a conformation with an energy ∆E < ∆E hit differs by only a factor of 2 or 3 between the sequences C and W, compared to a factor of 30 difference in folding times. This observation further confirms that the slow folding of sequence W does not originate from the trapping in a few "valleys" in phase space with a very long trapping time. On the contrary, the trapping time of the average folder C and the very slow folder W is of the same order of magnitude and slow folding seems to originate primarily from the profusion of low-energy conformations for sequence W.

Conclusion
Let us now summarize our answers to the three questions presented in the introduction.
• (i) We have investigated the relation between compact-state-spectrum predictions, namely the ∆/Γ criterion, Eqs. (7) and (8), and thermodynamic stability, determined from Monte-Carlo simulations where all the states (not only the compact ones) are taken into account. We find that for high ∆/Γ the predictions of the compact-state-spectrum analysis are in good agreement with the Monte-Carlo simulations. Namely, sequences that have a high ∆/Γ ratio also have a sharp transition to the native state conformations ("thermodynamically stable"). For sequences with low and intermediate ∆/Γ ratio, the transition widths vary considerably and are generally broader. This suggests that low energy open configurations can be important in determining δ in this case. We find that designability (defined as the number of sequences that have a given structure as their nondegenerate ground state) is not in one-to-one correspondence with thermodynamic stability. Some sequences with highly designable ground states are thermodynamically unstable. However, we did find that sequences with highly designable ground states have on average a large ∆/Γ ratio, and that sequences with poorly designable ground states have on average a small ∆/Γ ratio.
• (ii) The folding simulations have shown that sequences with a large ∆/Γ ratio fold fast. Sequences with a low ∆/Γ ratio, and therefore sequences which are thermodynamically unstable, may fold slow or fast at the relatively high temperatures that we investigated. At these temperatures the protein spends only 10% of the time near its ground-state configuration. We have argued, with several examples, that at lower temperatures the thermodynamically unstable sequences are likely to become slow folders whereas the stable ones are likely to continue to fold fast.
• (iii) To be "protein-like" a sequence must first be thermodynamically stable, which follows if it has a large ∆/Γ ratio. Second, the sequence must be mutationally stable, which follows if it has a highly designable ground state. We find that the third requirement to be "protein-like", namely fast folding, does not introduce additional constraints on sequence selection. Once a sequence has been designed to be thermodynamically stable (large ∆/Γ) and stable against mutations (large N S ) its folding dynamics is fast.
We have also explored the reason for the slow folding of a sequence with an anomalously large average folding time. We found that the "traping time" in a given low energy state is of the same order of magnitude for both fast and slow sequences, and cannot explain the large differences in the average folding times. Instead, we have shown that the slow folder visits a large number of different low-energy states, whereas only a few low-energy states are visited by the fast folder. This suggests that slow folding dynamics originates from a large number of low energy conformations.
Finally, we make a few remarks to illustrate the magnitude of structure and sequence selection.
We started from a set of 2 27 sequences, only 4.75% (approximately 6, 000, 000) of these having a nondegenerate compact ground-state [13] structure. The total number of possible compact structures is 51, 704 [13]. Among all these structures, only 60 are highly designable (estimated from the jump of


extfieldsofstudy: Biology Medicine

text:
Unc-45 mutations in Caenorhabditis elegans implicate a CRO1/She4p-like domain in myosin assembly.

The Caenorhabditis elegans unc-45 locus has been proposed to encode a protein machine for myosin assembly. The UNC-45 protein is predicted to contain an NH2-terminal domain with three tetratricopeptide repeat motifs, a unique central region, and a COOH-terminal domain homologous to CRO1 and She4p. CRO1 and She4p are fungal proteins required for the segregation of other molecules in budding, endocytosis, and septation. Three mutations that lead to temperature-sensitive (ts) alleles have been localized to conserved residues within the CRO1/She4p-like domain, and two lethal alleles were found to result from stop codon mutations in the central region that would prevent translation of the COOH-terminal domain. Electron microscopy shows that thick filament accumulation in vivo is decreased by ∼50% in the CB286 ts mutant grown at the restrictive temperature. The thick filaments that assemble have abnormal structure. Immunofluorescence and immunoelectron microscopy show that myosins A and B are scrambled, in contrast to their assembly into distinct regions at the permissive temperature and in wild type. This abnormal structure correlates with the high degree of instability of the filaments in vitro as reflected by their extremely low yields and shortened lengths upon isolation. These results implicate the UNC-45 CRO1/She4p-like region in the assembly of myosin isoforms in C. elegans and suggest a possible common mechanism for the function of this UCS (UNC-45/CRO1/She4p) protein family.

T he localization of molecules to distinct regions within cells is a critical process in the establishment of cell polarity and cellular differentiation. Although the mechanisms and molecules responsible for these processes are incompletely known, considerable evidence points towards the cytoskeleton and its associated motor proteins as key players in the generation of cellular diversity. Studies seeking to understand the mechanisms underlying the differential segregation of determinants between mother and daughter cells in Saccharomyces cerevisiae discovered the protein She4p (Swi5p-dependent HO expression; Jansen et al., 1996). She4p and other SHE proteins, including the unconventional (class V) myosin Myo4p (She1p), are specifically required for the expression of the HO endonuclease in mother, but not daughter, cells. It has been hypothesized that these proteins are involved in the transport of the repressor Ash1p from mother cells to their buds, and thus help to establish a cellular difference in cells that are exposed to identical envi-ronmental conditions. She4p was independently found in a genetic screen seeking mutants with defects in endocytosis (Wendland et al., 1996). Beside their defect in the internalization of both bulk lipid and ␣ -factor, she4-⌬ cells displayed a loss of polarity of actin localization. CRO1, a protein homologous to She4p was found to be involved in the transition between the syncytial and cellular states of the filamentous fungus Podospora anserina (Berteaux-Lecellier et al., 1998).
We report here that mutations in a domain homologous to CRO1/She4p in the Caenorhabditis elegans protein UNC-45 disrupt myosin assembly in the thick filaments of body wall muscle cells. The structure of C . elegans thick filaments is known in considerable detail through the combination of genetic, biochemical and ultrastructural approaches. The thick filaments are bipolar tubular assemblies. They contain an inner core composed of paramyosin and the recently identified filagenins (Epstein et al., 1995;Liu et al., 1998). The outer layer contains two myosin isoforms, A and B, which are differentially localized along the length of the filament (Miller et al., 1983). Myosin A is restricted to a central 1.8-m-long region, whereas myosin B is present at the 4.4-m polar regions, but excluded from the central region. Two 0.45-m zones contain both isoforms at either side of the central region.
The unc-45 gene has been proposed to encode an activity necessary for the assembly of myosin into thick filaments (Epstein and Thomson, 1974). Three kinds of alleles have been described, based on their phenotypes: temperature sensitive ( ts ) 1 , constitutive lethal ( let ), and maternally rescuable lethal ( mr ; Epstein and Thomson, 1974;Venolia and Waterston, 1990). Strains carrying ts alleles display an Unc (uncoordinated or paralyzed) phenotype when grown at the restrictive temperature (25 Њ C), with marked myofibrillar disorganization and diminished accumulation of thick filaments. This temperature-dependent phenotype is reversible, but only during the developmental stages of the organism. Larvae that hatch at the permissive temperature (15 Њ C) have a wild-type phenotype, but develop into Unc adults if switched to 25 Њ C. The converse is also true. However, once the worms have reached adulthood, switching temperature has no effect on the phenotype. Heterozygous strains carrying lethal alleles lead to F 1 arrest at the twofold stage of embryonic development, a stage at which loss-of-function mutants in other essential genes that affect myofibril development also cause arrest (Barstead and Waterston, 1991;Williams and Waterston, 1994), including the mhc A gene myo-3 (Waterston, 1989). Heterozygous strains carrying the mr allele lead to viable, but Unc, F 1 progeny. These worms, in turn, produce F 2 eggs that arrest at the twofold stage. Functional interactions of unc-45 with myosins A and B have been described, based on the suppression or enhancement of the different unc-45 phenotypes in strains carrying mutations in the genes of these body wall mhc isoforms (Waterston, 1988;Venolia and Waterston, 1990).
Our analysis of the predicted unc-45 sequence and the characterization of its genetic alterations demonstrate that the CRO1/She4p-like domain of UNC-45 is the primary target of the different types of mutations studied. Our studies on the in vivo accumulation of thick filaments and body wall mhc isoform content demonstrate that the number of thick filaments and myosin heavy chain (mhc) B content in strain CB286 grown at 25 Њ C is decreased with respect to its 15 Њ C counterpart. We have investigated the nature of the molecular alterations in filaments isolated from the 25 Њ C strain and show that these consist of myosin isoform scrambling. Here we report that these mutant filaments are highly unstable in vitro, as evidenced by their significant decrease in length and number after isolation. These results are consistent with UNC-45 playing a role as a myosin assemblase (Liu et al., 1997) in the construction of body wall thick filaments.

Nematode Growth
Nematode strains to be used for obtaining genomic DNA to serve as template for PCR were grown on nematode growth medium plates with Escherichia coli OP50 (Brenner, 1974) at 15 Њ C ( unc-45 ts alleles e286 , r450 , su2002 , b131 , and m94 ), 20 Њ C (wild-type strain N2), or 25 Њ C ( unc-45 lethal alleles st601 and st603 ). For analysis of muscle structure, SDS-PAGE and isolation of thick filaments, CB286 nematodes were synchronized by seeding eggs obtained by standard methods (Lewis and Fleming, 1995) on peptone enriched plates with Escherichia coli NA22  and grown at 15 Њ C (permissive temperature) or 25 Њ C (restrictive temperature). The nematodes were harvested after 72 h of growth at 15 Њ C or 48 h of growth at 25 Њ C, times that corresponded to similar stages of development (young adult).

Sequence Analysis
The predicted unc-45 sequence was obtained from the C . elegans Genome Sequencing Project (The Sanger Centre, Hinxton Hall, Cambridge, UK, and the Washington University School of Medicine, St. Louis, MO). The similarity searches and multiple sequence alignments were performed over the World Wide Web with the Baylor College of Medicine Search Launcher (Smith et al., 1996). The predicted UNC-45 tetratricopeptide repeat (TPR) sequence was modeled to the three-dimensional structure of the human protein phosphatase 5 TPR domain (Das et al., 1998) using the SWISS-MODEL program (Guex and Peitsch, 1997).

cDNA Sequencing
A partial cDNA clone, yk44f2, starting from nucleotide number 820 and ending at the polyadenylation site, was obtained from Dr. Yuji Kohara (Gene Network Laboratory, National Institute of Genetics, Mishima, Japan). The 5 Ј end of the unc-45 gene was obtained by screening a stagespecific phage lambda library of embryonic cDNAs obtained from Dr. Peter Okkema (University of Illinois, Chicago, IL). Two primers were constructed: ( a ) Upstream primer Unc45GstUp 5 Ј GAA GAT CTC CCA TGG TTG CTC GAG TAC AGA CTG CGG AGG3 Ј and ( b ) downstream primer Unc45-2Ddn 5 Ј CCG TCC TCG AAG ATC TTC GTA CTC AGC3 Ј . Primer Unc45GstUp contained the C . elegans Genome Sequencing Project predicted unc-45 start codon and a unique BglII restriction endonuclease recognition site. Primer Unc45-2Ddn was designed to hybridize within the sequence covered by clone yk44f2. A unique ClaI site was present in the overlapping sequences. Long range PCR, using Taq Extender PCR Additive (Stratagene, La Jolla, CA) and Taq DNA Polymerase (Promega Corp., Madison, WI), was performed with an aliquot of the Okemma library as template. The expected 1.8-kbp product was obtained and digested with BglII and ClaI. Clone yk44f2 was digested with ClaI and a full-length unc-45 cDNA was obtained by joining these two fragments at the ClaI site. Exo 3 DNA exonuclease progressive deletion clones were obtained, following the Erase-a-Base protocol (Promega Corp.), and sequenced by the Molecular Genetics Core Facility of the University of Texas Houston Health Sciences Center (Houston, TX). Further PCR experiments searching for translation start sites upstream of the predicted start site, using primers ( a ) Unc45Exup 5 Ј TGC CCC ATG GAG ATC TAT GAA ACG GCG ACT CGG CAA C3 Ј and ( b ) Unc45Exdn 5 Ј CCC TCG TCG CGG ATC TCC TCC GC3 Ј did not yield any PCR products.

Electron Microscopy of Nematode Cross Sections
CB286 nematodes grown at 15 or 25ЊC were washed off the plates with 3% glutaraldehyde in 0.1 M sodium phosphate (pH 7.4) and fixed for 3-4 h at 0ЊC. The rest of the procedure was carried as described (Mackenzie, et al., 1978).

Immunoblots
Equivalent amounts of similarly staged CB286 worms grown at 15 or 25ЊC were placed in SDS-␤-mercaptoethanol buffer , heated at 95ЊC for 5 min and vortexed. The samples were then centrifuged at 16,000 g for 5 min and the supernatants collected and kept at 0ЊC. The supernatants were run on 4.5% SDS-PAGE (Mini-Protean II system; Bio-Rad Laboratories, Hercules, CA; 100 V for 100 min) and transferred (Mini Trans-Blot system; Bio-Rad, Laboratories; 100 V for 120 min) to an Immobilon-NC membrane (Millipore Corporation, Bedford, MA). The membrane was blocked with 3% BSA in Tris-buffered saline ϩ Tween 20 buffer (TBST: 50 mM Tris-HCl, 150 mM NaCl, 0.05% Tween 20, pH 7.6) for 1 h at room temperature and reacted simultaneously with isoform specific mAbs 5-23 (Epstein et al., 1985; anti-paramyosin, at 5 g/ml in 3% BSA-TBST) and 28.2 (anti-mhc B, at 5 g/ml in 3% BSA-TBST) for 1 h at room temperature. The reactions were detected using the ECL Western blotting analysis system (Amersham, Little Chalfont, Buckinghamshire, UK), using a 1:10,000 dilution of the provided peroxidase-labeled antimouse antibody, according to the manufacturer's instructions. The membrane was exposed for 30 s. The bands were quantitated using a Bio-Rad model 620 videodensitometer (Bio-Rad Laboratories). A second SDS-PAGE was performed, loading corrected volumes of supernatants in order to obtain equivalent optical densities for the bands corresponding to the anti-paramyosin reaction. The above procedure was followed for the preparation of the second membrane, with the addition of an antibody stripping step (1 h at 70ЊC in 100 mM ␤-mercaptoethanol, 2% SDS, 62.5 mM Tris-HCl, pH 6.7) followed by simultaneous reaction with monoclonal antibodies 5-23 (at 5 g/ml in 3% BSA-TBST) and 5-6 (anti-mhc A at 2 g/ml in 3% BSA-TBST; Miller et al., 1983), followed by detection and quantitation using the above procedure.
For analysis of protein from nematodes homogenized with Triton X-100, samples from the first tritonized fraction of the thick filament isolation procedure were used (Deitiker and Epstein, 1993). For analysis of soluble myosin heavy chain or paramyosin, samples were taken from the supernatants after centrifugation of the first tritonized fraction. Equal amounts of total protein, measured by the Bradford method (Bradford, 1976; Bio-Rad Laboratories), were separated on a 4.5% SDS-PAGE and the above procedure followed for detection of mhc A, mhc B, and paramyosin.

Thick Filament Isolation
The thick filament isolation procedure was carried out as described previously (Deitiker and Epstein, 1993). Two volumes of O.C.T. (Miles, Ekhart, IN) were added to each volume of nematodes and mixed. The samples were then stored in liquid nitrogen. 3-ml equivalent aliquots from the CB286 strain grown at 15 or 25ЊC were processed in parallel, using the same freshly prepared solutions and incubation times. Storage conditions of isolated filaments before immunofluorescence or immunoelectron microscopy were identical: 0ЊC for a maximum of 24 h.

Immunofluorescence Microscopy of Isolated Filaments
Thick filament enriched fractions in isolation buffer (IB: 80 mM KCl, 10 mM MgCl 2 , 1.0 mM EDTA, 5.2 mM K 2 HPO 4 , 1.5 mM KH 2 PO 4 , 5 mM ATP, 0.5 M sucrose, and 1 g/ml of the following protease inhibitors: chymostatin, pepstatin, leupeptin, trypsin inhibitor, N-benzoyl-L-arginine ethyl ester and p-toluidinyl sulfonyl-L-arginine methyl ester, pH 6.33-6.42) from the CB286 strain grown at 15 or 25ЊC were processed simultaneously. They were placed on precleaned (0.5 M KOH, 50% ethanol) microscope slides and incubated at room temperature for 5 min, washed once with IB and then blocked by incubation with 50% goat serum (GS) in IB for 1 h at room temperature in a humidification chamber. They were washed once with IB (10 min). For analysis of myosin isoform distribution, they were double-labeled with rhodamine-conjugated mAb 5-6 (specific for mhc A) and fluorescein-conjugated mAb 5-8 (specific for mhc B; Miller et al., 1983) at 2 and 5 g/ml, respectively, in 10% GS-IB for 2 h at 37ЊC in a humidification chamber. For analysis of paramyosin distribution, they were labeled with rhodamine-conjugated mAb 5-23 (specific for paramyosin) in 10% GS-IB for 2 h at 37ЊC in a humidification chamber. They were then washed three times with IB (10 min each), mounted in p-phenylenediamine solution (1 mg/ml in 90% glycerol/PBS [0.01 M PO 4 , pH 7.4 in 0.15 M NaCl], pH adjusted to 8.0 with 0.5 M carbonate-bicarbonate buffer, pH 9.0), and sealed with nail polish. Immunofluorescence microscopy was carried out on a Zeiss Photomicroscope III (Carl Zeiss, Thornwood, NY). Fluorochrome emission was visualized individually, and in combination through a 61002 DAPI/FITC/Texas red filter set (Carl Zeiss) and captured on Fujifilm Provia 1600 ASA film (color micrographs) or Kodak TMAX p3200 film (black and white micrographs).

Immunoelectron Microscopy of Isolated Filaments
Filament enriched fractions from CB286 strains grown at 15 or 25ЊC were processed simultaneously. They were placed on glow-discharged FORM-VAR carbon-coated copper grids (Ted Pella Inc., Redding, CA), incubated for 2 min at room temperature and washed with IB. They were then reacted with the primary mAb 5-6 (specific for mhc A, at 2 g/ml in IB) or 28.2 (specific for mhc B, at 10 g/ml in IB) and incubated for 10 min at room temperature in a humidification chamber. They were then washed with IB once and the secondary antibody (goat anti-mouse IgG at 20 g/ml in IB) was applied and incubated for 10 min at room temperature in a humidification chamber. They were then washed with 0.1 M ammonium acetate, negatively stained by incubation with 2% uranyl acetate (in water) for 15 s and blotted to dryness. Electron microscopy was carried out on a JEOL JEM 100CX microscope (JEOL; Tokyo, Japan) at 20,000 magnification.

The UNC-45 Protein Is Predicted to Contain Three Distinct Regions
The unc-45 gene was identified by phenotypic rescue experiments (ACeDB, The Genome Informatics Group, Accession: clone W10B10, D. Pilgrim, University of Alberta, Edmonton, Alberta, Canada) and is predicted to contain 11 exons (C. elegans Genome Sequencing Project, The Sanger Centre, Hinxton Hall, Cambridge, UK and the Washington University School of Medicine, St. Louis, MO; data available from GenBank/EMBL/DDBJ under accession number U29096). The predicted exon structure of the gene was verified by sequencing two partial cDNAs: clone yk44f2, which spans from part of exon 6 (starting at nucleotide 812) to the polyadenylation site, and a PCR product of exons 1 to 6. The full-length cDNA encodes a 961-amino acid residue protein. We searched the Gen-Bank Database (National Center for Biotechnology Information) using the basic local alignment search tool  with the predicted protein sequence as query to identify proteins with regions of similarity that might offer clues about the potential structure and mechanism of action of UNC-45.
The NH 2 -terminal region contains three TPR motifs (Hirano et al., 1990;Sikorski et al., 1990;Goebl and Yanagida, 1991; Fig. 1). These motifs are present in a wide variety of proteins in tandem arrays, their number ranging from 3 to 16. Each motif is composed of two antiparallel ␣-helices (Fig. 1, A and B, boxes), and adjacent motifs pack in an antiparallel fashion with respect to each other, so that they form a continuous ␣-helical array that serves as a protein-protein interaction module (Das et al., 1998). They are characterized by a canonical sequence pattern of small and large hydrophobic residues, which allows the ␣-helices to pack tightly to form the array, and share rather loose primary sequence similarity. Fig. 1 shows a multiple sequence alignment of UNC-45 with four other sequences from proteins that contain TPR domains composed of three motifs. The consensus pattern of small and large hydrophobic amino acids is indicated: arrows point to positions 8, 20, and 27 of each motif, occupied by small hydrophobic amino acids and asterisks point to positions 1, 4, 11, 12, 17, 21 24, 28, and 30, which typically contain large hydrophobic residues. As can be observed, each TPR motif of UNC-45 fits this consensus pattern, except for positions 21 of motif No. 1; 1, 10, and 21 of motif No. 2; and 10 and 11 of motif No. 3. (which account for only 16% of the positions in the consensus, in a pattern similar to the protein hTOM). The UNC-45 TPR domain is as similar (47%) to the TPR domain of hPP5 as human protein TPR domains are among themselves (e.g., TPR domains of hPP5 and hTOM are 43% similar). A five-amino acid residue insertion (DKALR) between TPR motifs 1 and 2 of UNC-45 is predicted to form a loop between the two adjoining ␣-helices (SwissModel program; Guex and Peitsch, 1997) and may provide specificity for interaction with partner proteins.
The COOH-terminal half of the molecule (amino acid residues 524 to 927, CRO1/She4p-like domain, Fig. 2) shows similarity to a region that spans roughly the COOHterminal three-fifths of the fungal proteins CRO1 and She4p, which function in the differential segregation of molecules in distinct cellular processes. Our analysis of previously published pairwise alignments of these two proteins (Berteaux-Lecellier et al., 1998) showed that the region that is similar to UNC-45 (amino acid residues 270-678 of CRO1 and 336-773 of She4p, region 2) actually displays a better alignment than their NH 2 -terminal two fifths (region 1). The identity for both regions is the same (20%), but region 2 has fewer gaps (8 vs. 12 in region 1), and these are much shorter (24 spaces present in gaps in region 2 vs. 121 in region 1), in spite of the fact that region 2 is considerably longer (three-fifths of the molecule). Our analysis of these sequences (Fig. 2) showed that region 2 of CRO1 is more similar to the CRO1/She4p-like domain of UNC-45 than to region 2 of She4p (25 vs. 20% identical; 36.2 vs. 31.5% similar). Region 2 of She4p is 18% identical and 28% similar to the UNC-45 CRO1/She4p-like domain. Several observations make our multiple sequence analysis result robust, even though the identity and similarity values of the pairwise comparisons by themselves may not appear highly significant. First, the presence of only 84 gap spaces within a total of 1,249 amino acid residue positions in the entire alignment is very low. The recurrence of regions of similarity in the three proteins suggests that this event is not due to chance (Altschul and Figure 1. Multiple sequence alignments on which the UNC-45 TPR domain designation is based. The UNC-45 NH 2 -terminal sequence is aligned with four other TPR-containing sequences. Identical residues have a black background; residues closely similar in charge or polarity, a gray one. Boxes A and B represent the anti-parallel ␣-helices of each motif. Consensus positions are indicated by arrows (small hydrophobic amino acid residues) and asterisks (large hydrophobic amino acid residues). Proteins listed are hPP5, human protein phosphatase 5 (U25174); hTOM, human putative outer mitochondrial membrane 34-kD translocase (U58970); mPPP, Mus musculus phosphoprotein phosphatase (U12204); ySTI1, Saccharomyces cerevisiae heat shock protein 1 (M28486).  . Also, as shown below, this alignment is most consistent with our mutational analysis. The above observations allow us to propose that in these three proteins, the sequences shown in Fig. 2 form a domain that is separate from the rest of the molecule.
A region of 409 amino acid residues located between the TPR and CRO1/She4p-like domains of UNC-45 displays no significant similarity to any known protein. We have termed this region the central region of UNC-45.
The results of our sequence analysis suggest that the UNC-45 protein may contain three structurally different and possibly functionally distinct regions: TPR, central, and CRO1/She4p-like.

Different Phenotypic Classes of unc-45 Alleles Result from Mutations Localized to Distinct Predicted Regions
We decided to characterize the mutations responsible for the different types of unc-45 alleles in order to identify regions of the molecule that might be critical for its wildtype function. The CCM method was chosen to locate these mutations because it provided an effective alternative to direct sequencing of each allele, considering the size of the unc-45 gene (11 kbp without the promoter region). CCM allows efficient screening of multiple alleles simultaneously, in a stepwise manner (Cotton et al., 1988). Once a mutation was located in a particular allele, the segment where the mutation resided was sequenced.
After screening all exons for every allele, the following segments showed chemical cleavage: (a) following hydroxylamine treatment: exon 6 (alleles st603 and st601), exon 7 (allele b131), exon 9 (alleles m94 and r450), and exon 10 (allele e286); (b) following osmium tetroxide treatment: exon 8 (allele su2002). The procedure was repeated, to discard random mutations introduced by PCR, and these products were then sequenced. A single nucleotide substitution was found in each case (see Table I). All mutations were in agreement with (a) their predicted location in the PCR product according to the observed size of the cleavage product and (b) the type of substitution detected by each reaction: G/C to N for hydroxylamine and A/T to N for osmium tetroxide. Alleles m94 and r450 were found to contain identical nucleotide substitutions, which abolished an EcoRI recognition site. The identity of this mutation was further confirmed by the inability of this enzyme to digest exon 9 PCR products amplified from genomic DNA of both strains newly ordered from the Caenorhabditis Genetics Center (University of Minnesota, St. Paul, MN), and its ability to digest exon 9 PCR products amplified from N2 and e286 genomic DNA.
Analysis of the location of these mutations with respect to the predicted structure of the molecule (Figs. 2 and 8; Table I) showed that distinct types of alleles are located in particular regions of the molecule. Three of the four ts mutations (su2002, m94 ϭ r450, and e286) were located in the CRO1/She4p-like domain. They were caused by missense substitutions in codons that encode residues conserved in the three proteins. A fourth ts allele (b131) was found in the central region, 97 codons upstream of the CRO1/ She4p-like domain. The mutations responsible for the let alleles were substitutions that produced stop codons and thereby led to premature chain termination. In these cases, the CRO1/She4p-like domain could not be expressed. The results of our mutation analysis provide further evidence of the genomic sequence as that of the unc-45 locus and confirm the validity of the predicted reading frame.

Accumulation of Thick Filaments and mhc B, but Not mhc A, Is Decreased in the CB286 Strain Grown at 25ЊC
Previous work shows myofibrillar disorganization in the ts strain CB286 grown at the restrictive temperature (Epstein and Thomson, 1974). This sarcomeric defect is similar to the one observed in the mhc B null strain  and is consistent with impaired assembly of thick filaments. To quantify the accumulation of thick filaments in this strain at either the permissive or the restrictive temperature, we compared equivalent anatomical zones (region II, which lies immediately posterior to the pharynx; Mackenzie et al., 1978). We counted the number of structures with diameters compatible with thick filaments in electron micrographs of transverse sections through the body wall muscles (Fig. 3). As can be observed, the strain grown at 15ЊC contained sarcomeres indistinguishable from wild-type (Fig. 3 a). However, the strain grown at 25ЊC produced disorganized myofibrillar structures such that individual sarcomeres could not be clearly delineated (Fig. 3 b). Therefore, the counts were performed on areas of equivalent dimensions, which cor-  1220 responded to that occupied by a wild-type sarcomere. The 15ЊC sections had an average count of 359 filaments (values ranging from 331 to 395) and the 25ЊC had an average count of 197 filaments (values ranging from 117 to 270). Although the decrease in filament number in the strain grown at the restrictive temperature is clear (average of 45%), there is a greater variability from section to section. Several factors may contribute to this finding. The filaments may not all be aligned in the same orientation, or there may be populations of significantly shorter filaments. Both situations would lead to some micrographs showing considerably low filament counts, even though their actual number in the nematode may not be so decreased.
Since the phenotype described above is similar to the mhc B null, we decided to analyze the total accumulation of body wall mhc isoforms by immunoblotting. Total protein homogenates from populations of CB286 nematodes grown at the restrictive or permissive temperatures similarly staged (young adult) were transferred to a nitrocellulose membrane and probed with mhc isoform-specific mAbs (Fig. 4). First, the membrane was reacted with a mixture of mAbs 28.2 (anti-mhc B) and 5-23 (anti-paramyosin), and the reactions detected via chemiluminescence (Fig. 4 b). Then, the same membrane was stripped and reacted with mAbs 5-6 (anti-mhc A) and 5-23 (anti-paramyosin) and the reactions again detected by chemiluminescence (Fig. 4 a). The optical density of the reactions corresponding to paramyosin is very similar for both lanes in both experiments (Fig. 4 a: CB286 at 15ЊC ϭ 0.164, CB286 at 25ЊC ϭ 0.188; Fig. 4 b: CB286 at 15ЊC ϭ 0.125, CB286 at 25ЊC ϭ 0.141). These values confirm equal protein loading in both lanes and serve as an internal control for the comparisons of the accumulation of the mhc isoforms. The optical density of the reactions corresponding to mhc A was similar in both lanes (Fig. 4 a: CB286 at 15ЊC ϭ 0.571, CB286 at 25ЊC ϭ 0.633). However, the optical density of the reaction corresponding to mhc B in the 25ЊC CB286 sample was reduced by %05ف when compared with the sample from the 15ЊC strain: CB286 at 15ЊC ϭ 0.609; CB286 at 25ЊC ϭ 0.305 (Fig. 4 b). An independent experiment using samples of nematodes homogenized with the detergent Triton X-100 was in agreement with these results. It also showed us that none of the mhc isoforms or paramyosin were present as soluble material in samples from CB286 nematodes grown at either temperature.

Myosin Heavy Chain Isoforms Become Scrambled in Strain CB286 at the Restrictive Temperature
Our next set of experiments was designed to examine the structural characteristics of filaments isolated from CB286 worms grown at 15 or 25ЊC. For this purpose, thick filament enriched fractions were examined by immunofluorescence microscopy. Samples were reacted simultaneously with specific anti-isoform mAbs directly conjugated with either rhodamine (anti-mhc A antibody) or fluorescein (anti-mhc B antibody; Fig. 5). Thick filaments isolated from the 15ЊC strain revealed a myosin isoform distribution indistinguishable from that of wild-type. When analyzing rhodamine emission by itself (Fig. 5 a), a zone of 4/1ف to 1/5 the total length of the filament was observed, which corresponds to the central myosin A region. The fluorescein emission (Fig. 5 b) was excluded from this central region, but present in the rest of the filament, creating a central gap characteristic of myosin B localization. Simultaneous observation of both emissions (Fig. 5 c) revealed two yellow points at either side of the central region, which correspond to zones of overlap of both myosin isoforms, since co-localization of both fluorochromes is observed as a gold-colored emission. In contrast to these findings, the filaments isolated from the 25ЊC CB286 strain displayed a markedly abnormal distribution of myosin isoforms. The rhodamine emission (Fig. 5 d) revealed a myosin A distribution encompassing the entire observable length of most filaments. The fluorescein emission (Fig. 5  e) was also continuous throughout the filament, with no apparent gap in the center, indicating that myosin B was now also present in the central region of the filament. Simultaneous observation of both fluorochromes (Fig. 5 f) showed filaments that were entirely yellow, confirming the myosin isoform overlap throughout the filament. Similar analyses with mAb 5-23, specific for paramyosin, showed  that filaments from CB286 grown at either temperature contain paramyosin throughout their lengths (data not shown). These results indicate that the differential localization of the myosin isoforms has been lost in filaments isolated from the CB286 strain grown at the restrictive temperature.
Because the result of immunofluorescence microscopy did not allow us to be certain that the structures being analyzed corresponded to single filaments, nor provided ultrastructural details, we examined individual filaments complexed with isoform-specific mAbs by electron microscopy. Isolated filaments were reacted independently with mAbs 5-6 and 28.2 and then an anti-mouse secondary antibody before being negatively stained (Fig. 6). Antibody reaction in electron micrographs of isolated filaments can be visualized as a continuous layer of additional protein complexes surrounding the filaments. It is especially evident when compared with unlabeled filaments (Fig. 6, a and aЈ). In filaments that contained zones of presence and absence of antibodies, a gradient of decreased labeling was observed as the reactions approached the regions devoid of antibodies. Boundaries between labeled and nonlabeled regions were clearly observed as transitions in the content of antibody complexes when observed at higher magnification (Fig. 6, bЈ, dЈ, and eЈ).
Thick filaments from the 15ЊC CB286 strain reacted with the mAbs in a pattern indistinguishable from that of wild-type, whereas their 25ЊC counterparts reacted in the abnormal manner consistent with the immunofluorescence microscopy experiments. Fig. 6, a-c show micrographs of lower magnification that allow comparison of the extent of the anti-mhc A reaction at either tempera-ture. In the 15ЊC filaments, anti-mhc A reaction was observed only in the central 2-m-long region of the filament (Fig. 6 b, inside the arrowheads), while the 25ЊC filaments reacted throughout their length (Fig. 6 c). Higher magnification showed the labeling transition in the 15ЊC filament (Fig. 6 bЈ) from the polar region devoid of anti-mhc A reaction to the central region recognized by this antibody; whereas it demonstrates the continuity of the reaction in the case of the 25ЊC filament (compare Fig. 6, aЈ-cЈ). Fig. 6, a, d, and e demonstrate the extent of the anti-mhc B reactions at lower magnification. Filaments isolated from the strain grown at 15ЊC displayed the wild-type distribution of anti-mhc B labeling: reaction present in the polar regions but excluded from a 0.7-m-long gap at the center (Fig. 6 d, outside the arrowheads). In contrast to this distribution, the anti-mhc B reaction entered the central region of the 25ЊC filaments: the anti-mhc B reaction occurred throughout most of the length of the filament (Fig. 6 e, outside the arrowheads), so that the gap was drastically shortened to as small as 0.3 m. Higher magnification allowed visualization of the transitions in the reaction from the polar regions into the central region devoid of antibody (compare Fig. 6, aЈ, dЈ, and eЈ). The extent of the anti-mhc B reaction in the 25ЊC filaments indicates the rods of myosin B, in addition to those of myosin A, must be contributing to the anti-parallel interactions of the central bare zone. This situation is similar to that observed in filaments isolated from paramyosin loss-of-function worms, where myosin isoforms A and B scramble in the central region of the filament (Epstein et al., 1986).
During our electron microscopy analysis, we also noticed that Ͼ50% of the filaments had areas devoid of myosin at their ends, where core structures could be observed. This is in agreement with our immunofluorescence microscopy observation that filaments from the 25ЊC CB286 strain contain paramyosin.
Taking into account the lower resolution of immunofluorescence microscopy, which was unable to detect the short area devoid of anti-mhc B reaction, the immunoelectron microscopy results confirmed the optical microscopy observations. They demonstrated that scrambling of the myosin isoforms occurred in filaments isolated from the CB286 strain grown at 25ЊC, and that these filaments contain paramyosin core structures.

Thick Filaments Assembled In Vivo in Strain CB286 at the Restrictive Temperature Are Unstable In Vitro
Apart from the myosin localization defect discussed above, thick filaments isolated from the CB286 strain grown at the restrictive temperature also displayed abnormally low yields after the isolation procedure, as well as reduced length.
Thick filaments were isolated simultaneously from equivalent amounts of similarly staged populations of CB286 worms grown at 15 or 25ЊC. However, as evidenced by immunofluorescence microscopy, the yield of thick filaments from the mutant strain grown at 25ЊC (Fig. 7 b) was drastically lower than its 15ЊC counterpart, (Fig. 7 a). To obtain fields with similar filament densities, the fractions of filaments from the 15ЊC specimens needed to be diluted 1:250 to 1:500. This decrease in yield was confirmed during the Figure 6. Immunoelectron microscopy of myosin isoform distribution in strain CB286. (a) Negatively stained 15ЊC filament; (b) mAb 5-6 (mhc A specific) labeling of 15ЊC filament, reaction can be seen inside arrowheads; (c) mAb 5-6 labeling of 25ЊC filament, reaction can be seen throughout its length; (d) mAb 28.2 (mhc B specific) labeling of 15ЊC filament, reaction can be seen outside arrowheads; (e) mAb 28.2 labeling of 25ЊC filament, reaction can be seen outside arrowheads. Zones of interest in a through e can be observed at higher magnification in aЈ through eЈ, respectively, and show the presence (bЈ, dЈ, and eЈ) or absence (aЈ and cЈ) of labeling transitions due to reacting and nonreacting regions along individual filaments. aЈ is unreacted and cЈ is labeled homogeneously by anti-mhc A antibody. Bars: (a-e and aЈ-eЈ) 0.2 m. electron microscopy analysis. This marked reduction of isolated filament number contrasts with only a 30-70% reduction observed in vivo. An explanation for this difference may be decreased stability of the filaments in the strain grown at 25ЊC.
Individual lengths of negatively stained isolated filaments from 15 or 25ЊC CB286 worms were measured. The average 15ЊC filament length was 5.87 m (n ϭ 90; s ϭ 4.41), while the average 25ЊC filament length was 3.47 m (n ϭ 90; s ϭ 2.25). This difference was found to be statistically significant, as judged by the t test: t(178) ϭ 9.79, P Ͻ 0.0001.
The marked reduction of filament length and number upon isolation beyond what was observed in the corresponding electron microscopy cross-sections from 25ЊC CB286 nematodes was most likely the result of filament disassembly during the isolation procedure. If the filaments were only being mechanically sheared because of increased fragility, the number of structures observed would be substantially increased. Each filament that breaks would produce at least two shorter fragments. This was not the case, and therefore we propose that thick filaments isolated from CB286 nematodes grown at the restrictive temperature underwent enhanced in vitro depolymerization.

Discussion
The predicted UNC-45 sequence contains three distinct regions: an NH 2 -terminal TPR domain, a central region with no significant similarity to any known protein, and a COOH-terminal CRO1/She4p-like domain. This last region is the target of three of the four ts mutations analyzed, which are caused by base substitutions leading to missense mutations in codons for conserved residues (Fig.  8). The two lethal alleles studied are the result of base substitutions in the central region, which lead to premature chain termination, so that the CRO1/She4p-like domain cannot be expressed.
This work has also provided discrete evidence of abnormal structure in unc-45 mutant thick filaments. Comparison of thick filaments from the CB286 strain grown at the restrictive versus the permissive temperature has demonstrated that this ts mutation, located within the CRO1/ She4p-like domain, affects the accumulation of assembled thick filaments, as well as their myosin isoform distribution and in vitro stability.
The results presented here suggest that UNC-45 functions as a thick filament assemblase through its CRO1/ She4p-like domain. Assemblase activity may be defined as a catalyst or chaperone that mediates the incorporation of myosin and related proteins into thick filaments (Liu et al., 1997). Several mechanisms may be involved, including catalysis of myosin folding at the ribosome, intracellular myosin transport, posttranslational modification of myosin and associated proteins, catalysis of myosin polymerization, sorting of myosin isoforms, and scaffolding of myosin, paramyosin and the filagenins during the actual formation of the filament. An assemblase molecule may participate in one or more of these processes as a catalyst and may be subject to regulation by the interaction of additional proteins.
The scrambling of myosins A and B in the central region of 25ЊC CB286 filaments indicates that both isoforms contribute to the anti-parallel interactions of the central region of the filament, as has been demonstrated to be the case in filaments isolated from paramyosin loss-of-function mutant nematodes (Epstein et al., 1986). Therefore, additional factors are necessary to recognize these isoforms and place them differentially along the length of the filament. One probable function of UNC-45 may be to sort each myosin isoform during the assembly process. This model of directed assembly of muscle thick filaments proposes that additional processes and specific proteins are required to explain the behavior of myosin besides its simple self-assembly as discussed by McLachlan and Karn (1982) and Hoppe and Waterston (1996).
Several independent lines of evidence support the requirement for additional functions during the construction of thick filaments. In Drosophila melanogaster, a single mhc gene is alternatively spliced to produce different iso- Figure 7. Immunofluorescence microscopy of thick filament isolation in strain CB286. Undiluted samples of 6.2 K supernatant thick filament enriched fractions (Deitiker and Epstein, 1993) from equivalent amounts of starting materials from nematodes grown at 15 or 25ЊC were reacted simultaneously with rhodamine-conjugated mAb 5-6 (specific for mhc A) and fluoresceinconjugated mAb 5-8 (specific for mhc B).  forms that assemble into thick filaments of different characteristics, depending on the tissue and developmental stage of the organism (Bernstein et al., 1983). Transgenic flies that express only a single mhc isoform, however, are still able to assemble different types of thick filaments with characteristics appropriate to the tissue and developmental stage (Wells et al., 1996). Additional factors must then enable this single myosin species to assemble into distinct structures. In C. elegans body wall muscle cells, thick filament length varies according to the developmental stage of the organism. Embryonic filaments cannot be longer than the greatest dimension of the embryonic muscle cell (Ͻ5 m; Epstein et al., 1993), whereas adult thick filaments are 9.7 m long (Mackenzie and Epstein, 1980). There must be factors that regulate filament elongation according to the developmental stage of the muscle cell other than myosins A and B and paramyosin, which are present continously. Moreover, myosins from different species that assemble in vivo into filaments of different characteristics (Epstein, 1989) form very similar filamentous structures under the same conditions in vitro (Harris and Epstein, 1977). Also, mutant CB675 myosin, which disrupts thick filament assembly in vivo, forms indistinguishable filamentous structures from those formed by wild-type molecules under the same conditions in vitro (Harris and Epstein, 1977). This indicates that myosin molecules must be interacting with additional factors in vivo that regulate their proper assembly into thick filaments. Three-dimensional structural work on nematode thick filament cores has shown that these consist of paramyosin subfilaments held together in a tubular arrangement by additional protein structures (Epstein et al., 1995). Several of these proteins have now been identified, including ␤-filagenin (Liu et al., 1998), and their role as cross-linking proteins demonstrates the presence of additional proteins involved in the assembly of myosin filaments.
One possible role for the TPR domain of UNC-45 may be to bring interacting proteins to the site of thick filament assembly. These may be proteins that are additional components of the proposed assemblase, which contribute their particular functions during the assembly process, including protein chaperones, prolyl isomerases, and phosphoprotein phosphatases. Other partner proteins brought to the site of filament assembly through TPR binding may provide regulatory properties on the assemblase, appropriate to tissue and developmental stage of thick filament construction. We currently have no information as to the functional role the central region. It may be involved in an assemblase activity because one of the ts mutations is localized within its boundaries. The multi-domain nature of UNC-45 (Fig. 8) suggests that each region may specifically interact with different kinds of protein molecules and perhaps act at distinct steps during thick filament assembly.
Several observations suggest that the actual process of thick filament assembly rather than the stability of the UNC-45 protein or the filaments themselves may be sensitive to elevated temperature in the unc-45 ts alleles. A significant loss of UNC-45 function leads to lethality (Venolia and Waterston, 1990). Therefore, the ts mutations cannot cause complete misfolding of UNC-45 at the restrictive temperature; a partial function (or set of func-tions) must be present to allow survival of the organism. Also, our finding that three ts alleles are caused by mutations in residues conserved in UNC-45, CRO1, and She4p suggests that these residues may represent key interactions in the UNC-45 active site and that their substitution causes specific defects rather than destabilization of the protein. Furthermore, there is genetic evidence that the protein product of the ts alleles is not wild-type at the permissive temperature (Venolia and Waterston, 1990); the mr/mr progeny of a mr/ts hermaphrodite are F 1 lethals at either 15 or 25ЊC, whereas the mr/mr progeny of a mr/ϩ hermaphrodite are viable and produce mostly F 2 lethals. A plausible interpretation of these interallelic interactions is that the UNC-45 protein may work as an oligomer, and the presence of a ts protein, even at 15ЊC, hinders UNC-45 activity. It is unlikely that the thick filaments are sensitive to the elevated temperature because adult nematodes from any of the ts strains grown at the permissive temperature do not show phenotypic reversal when switched to 25ЊC. This indicates that the myofibrils in these worms are stable structures not susceptible to depolymerization due to increased temperature.
Our results on the accumulation of mhc isoforms in the CB286 strain grown at 15 versus 25ЊC suggest that this mutation, localized within the CRO1/She4p-like domain, may affect the dynamics of myosin B polymerization. Work by others (Bejsovec and Anderson, 1990) has demonstrated that dominant lethal mutations in the myosin B head lead to impaired filament assembly and decreased accumulation of myosin B. A plausible interpretation of these results is that the mutations cause misfolding of the myosin molecule, which in turn hinders the thick filament assembly process. The presumably misfolded myosin B is then degraded. A similar situation may be occurring in CB286 nematodes at 25ЊC. A defect of UNC-45 function may lead to an abnormal myosin B, which then causes an impairment of filament assembly reflected by reduced numbers of filaments assembled in vivo, scrambling of myosin isoforms, and in vitro filament depolymerization. The decreased accumulation of myosin B may be explained by increased degradation of unincorporated molecules. Alternatively, the CB286 defect may cause a reduced number of functional myosin B molecules to be available for assembly. This could explain the similarity with the mhc B null phenotype observed in cross-sections by electron microscopy, and the decreased accumulation of mhc B. The yeast protein She4p may play a similar role to UNC-45 during the assembly of Myo4p (She1p) into structures capable of transporting the repressor Ahs1p. A common substrate of both molecules may be the myosin head, since this domain is conserved in both unconventional and sarcomeric myosins (Cheney and Mooseker, 1992).
An alternative, but unlikely, explanation for the observed myosin isoform scrambling in the 25ЊC CB286 strain could be myosin repolymerization in vitro. Our data indicated that there was substantial filament depolymerization during the isolation procedure. Some of the myosin molecules could have dissociated from the filament and reassembled in a disorganized fashion in vitro to produce the abnormal structures observed by immunofluorescence and immunoelectron microscopy. If these structures originally had a myosin isoform distribution similar to wild-type in vivo, they would contain a central myosin A region. It has been shown that this myosin isoform remains tightly associated with the filament until the paramyosin core itself depolymerizes (Deitiker and Epstein, 1993). Because the 25ЊC filaments contained paramyosin cores, which always retain myosin A in vitro, it appears unlikely that myosin A could have dissociated and then repolymerized with myosin B along nearly the entire length of the thick filament, including the central zone.
Biochemical investigation of the potential physical interactions between UNC-45 and the myosin isoforms is required in order to understand the mechanisms involved in its wild-type function(s). UNC-45 may associate with thick filament components in a stable fashion. In this case, it may act as part of a protein scaffold in the positioning of specific myosin isoforms and related proteins along the filament. As a scaffolding protein, UNC-45 may have additional nonstructural activities, in a manner analogous to twitchin, which is both a structural component of the sarcomere and a myosin light chain kinase (Hu et al., 1994;Lei et al., 1994) or the sarcomeric myosin itself, which is an ATPase, a protein motor and a structural protein (Harris and Epstein, 1977;Warrick and Spudich, 1987). In this case, the UNC-45 protein may be a structural component of the filament. On the other hand, involvement of UNC-45 in any of the other possible roles of a thick filament assemblase would require only transient association with filament components and not stable association with a particular sarcomeric structure.
The information related to myosin assembly presented here for UNC-45 suggests that UCS proteins (UNC-45/ CRO1/She4p) may serve as components of protein machines that recognize specific myosin isoforms and localize them to subcellular sites, where they can be assembled into structures appropriate for their particular cellular function.