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Materials Science
Medicine

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Effect of water-DNA interactions on elastic properties of DNA self-assembled monolayers

DNA-water interactions have revealed as very important actor in DNA mechanics, from the molecular to the macroscopic scale. Given the particularly useful properties of DNA molecules to engineer novel materials through self-assembly and by bridging organic and inorganic materials, the interest in understanding DNA elasticity has crossed the boundaries of life science to reach also materials science and engineering. Here we show that thin films of DNA constructed through the self-assembly of sulfur tethered ssDNA strands demonstrate a Young’s modulus tuning range of about 10 GPa by simply varying the environment relative humidity from 0% up to 70%. We observe that the highest tuning range occurs for ssDNA grafting densities of about 3.5 × 1013 molecules/cm 2, where the distance between the molecules maximizes the water mediated interactions between the strands. Upon hybridization with the complementary strand, the DNA self-assembled monolayers significantly soften by one order of magnitude and their Young’s modulus dependency on the hydration state drastically decreases. The experimental observations are in agreement with molecular dynamics simulations.

S2. Experimental setup
In the optical beam deflection method, a laser is focused onto the free end of a cantilever beam and its reflection is collected by a quadrant photodetector or by a position sensitive detector (PSD). However, it is known that the response of a PSD is not uniform along its whole surface; therefore, a static cantilever bending, which moves the laser spot at the surface of the detector, will induce a non-real shift in the measured resonance frequency. In order to prevent this undesirable measurement artifact, we have introduced two mirrors in the optical path actuated by an automatized motor in a feedback closed loop configuration: the output of the PSD is converted into a voltage input signal to the motors controlling the mirror angles in such a way that the change of the angle maintains the laser spot at the central point of the detector surface all the time, Fig. S2. Therefore, the input signal of the mirror angle is translated into the static deflection of the cantilever, whereas the resonance frequency obtained by the Fast Fourier Transform (FFT) of the signal coming from the spot at the center of the PSD is free from undesirable artifacts. The output signal of the photodetector is split up into two different signals, one is injected into the feedback loop controlling the mirrors and the other one is analyzed by a locking amplifier with a phase locked loop (PLL). In order to demonstrate the low noise level, and reproducibility of the dynamic characterization, the upper chart in Fig. S3 shows a sample of the frequency measurement obtained by the PLL, with a frequency noise of barely 50 mHz. By using the locking amplifier, the signal-to-noise ratio of the resonance peak is enhanced reaching a value of 6 at resonance frequency of 5.1 kHz with a mechanical quality factor of about 20, shown in the lower chart of Fig. S3. S4. X-ray photoelectron spectra (XPS) measurements X-ray photoelectron spectra (XPS) were recorded using a Escalab 200R (VG, UK) electron spectrometer equipped with a hemispherical analyzer, operating in the constant pass energy mode, and a MgKa (hn = 1253.6 eV, 1 eV = 1.603×10 '() ) X-ray source operated at 10 mA and 12 kV. The detection angle of photoelectrons was 60º to the surface of the specimen. The spectrometer was calibrated against Au4f7/2 line at 84.0 eV using a gold sheet and Cu2p3/2 at 932.5 eV from a copper sheet. Charge effects on the samples were removed by taking the C1s line from adventitious carbon at 284.8 eV. In order to estimate the photoelectron peak intensities, the background was subtracted from the measured spectra according to the Shirley method and using a combination of Gaussian and Lorentzian lines (90G-10L). The relative surface atomic ratios were determined from the corresponding peak intensities, corrected with tabulated atomic sensitivity factors. The reproducibility of the results was confirmed several times under the same conditions.

S3. Dynamic Characterization
In order to determine the number of molecules at the cantilever surface we have performed a quantitative characterization of the DNA film by X-ray photoelectron spectroscopy (XPS). The presence of nitrogen atoms is typically used as the experimental indicator of adsorbed DNA; however, since the used buffers in the immobilization and subsequent cleaning process are unspecific sources of nitrogen we have chosen the phosphorous as signature indicator. The signal coming from the gold 4f peak is attenuated as the immobilization time for the ssDNA is increased. From this attenuation, it is possible to calculate the actual thickness of the DNA layer by using the clean Au4f spectrum as reference. Then, the calculated thicknesses are used to correct the measured XPS peak ratios of the N and P atoms for attenuation. In order to do this, we have to calculate the practical effective attenuation length (PEAL, LAu) for electrons in the film using a reference film, whose thickness we have measured by atomic force microscopy.
The relationship between the intensity of the XPS peak, -. , and the thickness, , is given by -. = -. 1 − -. . Table S1 shows the results obtained for the surface coverage by looking at the P 2p peak intensity relative to the Au 4f peak. Although the presence of nitrogen atoms is typically used as the experimental indicator of adsorbed DNA, since the used buffers in the immobilization and subsequent cleaning process are unspecific sources of nitrogen we have used the phosphorous as signature indicator.
Table S1 | Molecular surface density determination. By using the number of P atoms per Au atoms N 8 N 9: and the relative coverage Note the saturation at 6.5x10 13 molecules/cm 2 . Fig. S6 shows the thickness of DNA layers calculated from XPS measurements as blue and red circles for ssDNA and dsDNA, respectively.
As it was previously explained, thickness was obtained by means of the Au 4f peak attenuation (the gold signal exponentially depends on the inverse of the thickness). The larger the immobilization time, the thicker the ssDNA layer. This is due to the molecular interactions between the strands that arise when the molecular surface density grows 1    In order to account for the hydration dynamics, the hydration/dehydration cycles were simulated by linearly sweeping the number of water molecules from zero to the maximum number per molecule described above. The water uptake by DNA as a function of the relative humidity has extensively been studied in samples consisting of DNA fibers obtained by standard desiccation methods 5 . In these studies, firstly established by Falk and collaborators the water adsorption isotherms closely follow the Brunauer-Emmett-Teller (BET) equation 6 ; however, it has been demonstrated that a linear dependency is a good approximation 5 . Since the calculation of the mass density takes into account the number of water molecules, it was also correspondingly changed.
S6. Molecular Dynamics Simulations. DNA layer thickness  On the other hand, as the surface density increases, the thickness also increases due to the intermolecular forces between the DNA strands.  In order to study the dynamics of the SAM formation, we simulate the thickness of the layer as a function of the immobilization time for both the ssDNA and dsDNA at fully hydrated state and at high vacuum, Fig. S10. As it was described above, the thickness of the dsDNA is larger than the ssDNA. From these simulations, it is also possible to see how the dsDNA reaches a saturation value of the thickness in barely two hours, which is indicative of the shielding effect of the double helix. Note also that the thickness of the hydrated layer is larger. This is because of the extra rigidity provided by the water molecules placed around the DNA strands.

Simulated bending experiments
Until now we have shown how increasing packing density of DNA molecules has important effects in the layer thickness. As the distance between the strands decreases, there is an increasing attractive collective force due to hydrogen bonding between bases, base-phosphorous interactions, and base stacking. Thus, we expect that the collective elastic properties present a similar dependency. In order to study the elasticity of the DNA layer, we have simulated bending experiments by using a potential mean force using WHAM method 7 . Fig.   S12 shows the simulated bending experiments for ssDNA (blue circles series ranging from dark to light blue for increasing molecular surface density) and dsDNA (red circles series ranging from dark to light red). The energy cost increases accordingly with the increasing molecular density packing of the ssDNA, being the corresponding layer of 3.86x10 13 molecules/cm 2 six times stiffer than the 3.1x10 12 molecules/cm 2 one; indicating a stiffening effect given by the intermolecular forces. Note that the stiffening of the dsDNA is virtually negligible when compared with the ssDNA.

S11. Thickness Uncertainty
Attending the simulations (commercially available software Schrödinger), the length of a 20-base long ssDNA is 6.4nm, far away from the measured value of 1.2nm, but the measured thickness is still in reasonable agreement with the MD simulations, as can be seen from the following images. The first one corresponds to the length calculation in Schrödinger, and the second one is the fig. S8  At this point, we should take into account the way this thickness was calculated. The final point of the thickness growing curve was measured by AFM at the maximum molecular surface density. We set a DNA step by simply shadowing a gold area and measure the thickness variation.
Please, take a look at one of the performed measurements for the grafting density of 6x10 13 molecules/cm 2 .
Although all the trends are correct, we attribute the difference among measurements and the MD simulations to the attractive force in between the gold and the bases composing the ssDNA layer, note that the simulations are done on an inert surface (graphene). Nevertheless, it seems that is too much material to pack into such a small thickness. We really think that the MD simulations could provide a better estimation for the thickness tan the experimental XPS and AFM measurements presented. Note that the AFM measurements averages the thickness measurement in an area equivalent to the tip surface area, and, as it was observed in previous studies, the DNA forms growing coalescent islands.
Thus, the AFM averages with the bare surface.
We must take into account the error in the thickness estimation by using AFM. As it was explained above, this error comes from the calibration method employed. The calibration of AFM was made by using a calibration sample trenches of height -21 ± 1 nm. The maximum tolerance after AFM calibration is of 1%. Therefore, the average of our DNA thickness measurements retains and propagates that error, giving as a result 1.2 ± 1.1 nm. This uncertainty propagates to the Young's modulus determination to reach an error of 33% in the value determination.

S12. Error Propagation Calculation
The calibration of AFM was made by using a calibration sample made of trenches of height -21 ± 1 nm. The maximum tolerance after AFM calibration is of 1%. Therefore, the average of our DNA thickness measurements retains and propagates that error, giving as a result 1.2 ± 1 nm.
We can neglect the cantilever's thickness error (


Factors controlling the reactivity of divalent metal ions towards pheophytin a

In this study, we evaluate the factors which determine the reactivity of divalent metal ions in the spontaneous formation of metallochlorophylls, using experimental and computational approaches. Kinetic studies were carried out using pheophytin a in reactions with various divalent metal ions combined with non- or weakly-coordinative counter ions in a series of organic solvents. To obtain detailed insights into the solvent effect, the metalations with the whole set of cations were investigated in three solvents and with Zn2+ in seven solvents. The reactions were monitored using electronic absorption spectroscopy and the stopped-flow technique. DFT calculations were employed to shed light on the role of solvent in activating the metal ions towards porphyrinoids. This experimental and computational analysis gives detailed information regarding how the solvent and the counter ion assist/hinder the metalation reaction as activators/inhibitors. The metalation course is dictated to a large extent by the reaction medium, via either the activation or deactivation of the incoming metal ion. The solvent may affect the metalation in several ways, mainly via H-bonding with pyrrolenine nitrogens and the activation/deactivation of the incoming cation. It also seems to affect the activation enthalpy by causing slight conformational changes in the macrocyclic ligand. These new mechanistic insights contribute to a better understanding of the “metal–counterion–solvent” interplay in the metalation of porphyrinoids. In addition, they are highly relevant to the mechanisms of metalation reactions catalyzed by chelatases and explain the differences between the insertion of Mg2+ and other divalent cations.

Introduction
Metalloporphyrinoids play key roles as photocatalytic and catalytic centers, and as carriers of electrons and small molecules in biological systems. Many such metallocomplexes, especially those with transition metal ions, are important catalysts in industry and the laboratory [1], and can be used as photosensitizers in various kinds of phototherapy and diagnostics. Often their functioning relies on those photophysical and photochemical features which result from the interactions of the π-electron system with the central metal ion [2][3][4][5][6][7][8]. In addition, the formation of metallosubstituted chlorophylls (Chls) and bacteriochlorophylls (BChls) is relevant from the biological point of view [9] and such modified pigments are useful as model compounds [6,8,10]. The chemistry of metalloporphyrins has been extensively explored for over a century and the literature on synthetic approaches to their preparation is indeed vast [11][12][13].
The impact of metal ion reactivity on metalation of porphyrins has frequently been discussed. Most of these studies, carried out in aqueous solutions, showed analogies between the rates of metalation and water exchange both in simple aquacomplexes [14,15] and in organic media [16][17][18], thus pointing to the solvent release step as an important factor in the kinetics of metalloporphyrin formation. Thus, the reaction medium needs to be taken into account, even if it does not explicitly appear in the general reaction equation: where M 2+ is the incoming metal ion, H 2 P is the free base porphyrinoid and M-P is the metalated product. Obviously, the ligands to M 2+ , including solvent molecules, may either increase or lower its activity. For instance, acetate ions act on both partners of the metalation reaction, which underlies the mechanism of the well-known general "acetate method" of porphyrinoid metalation [30].
The synthesis of metalloporphyrinoids in vivo is catalyzed by chelatases, which act to overcome the activation barrier for the insertion of metal ions into free bases [19][20][21][22]. The mechanisms of reactions catalyzed by chelatases, i.e. cation recognition, binding and its activation, are not completely understood. In most cases, their catalytic action relies on the activation of the macrocyclic substrate via its deformation in the transition state and clearly, the interior of the enzyme provides a highly controlled reaction medium. Such a deformation seems to occur during metalation in vitro as the activation barrier for metal ion insertion into the free base is correlated with the rigidity of the macrocycle [23]. The reports show opposite trends related to the effect of the size of metal ions on the kinetic and thermodynamic parameters for complex formation [24][25][26] and two types of macrocycle bending are considered [27,28]. First, there is the saddle type, in which a bulky metal ion and tetrapyrrolic ligand form the out-of-plane tetradentate complex. Second, the ruffle type is considered, with a "sitting-atop" metal ion coordinated by two core N atoms, while the free electron pairs from the other two are exposed on the opposite side of the macrocycle. The formation of complexes with a bulky metal ion can be expected to facilitate the binding of smaller metal ions [26]. Such a model of "assisted" metal ion insertion shows the essence of the metalation of rigid macrocyclic ligands, such as hemes, Chls and BChls. Recently, we have shown that the reactivity of porphyrinoids in metalation reactions is determined by both the extended aromatic π-electronic system and the peripheral groups, whose interplay creates the energetic barrier to be overcome [29]. Moreover, the type of bonding between the central metal ion and porphyrinoids depends on the structural details of the chelating molecules [6,8]. Therefore, the effects observed for simple unsubstituted porphyrins cannot be generalized and directly applied to Chls.
In the quest for new metallocomplexes, especially of chemically labile macrocycles and π-electron systems, such as Chls and BChls, and those with less common or inert transition metal ions that would introduce novel and interesting properties, the narrow choice of synthetic methods available becomes limiting. Many reports on the formation of metallo-Chls and metallo-BChls have been published [3,[30][31][32][33][34][35][36][37][38][39][40], but only a few of them provide kinetic and mechanistic details. Often it becomes problematic to compare these results because various approaches and methods that employ different tetrapyrrolic chelators had been used. The knowledge of these aspects is more complete in the case of the metalation of simpler porphyrins, but it is based mostly on reactions carried out in aqueous solutions [23]. As this reaction medium is very different from that offered by the protein interior, they appear only partly related to reactions catalyzed by chelatases in vivo and in vitro and may not apply to water-insoluble porphyrinoids. Therefore, we set out to assess, in a systematic manner, the roles of the solvent and M 2+ , their mutual interactions and macrocycle solvation in controlling the metalation of pheophytin a (Pheoa). Our approach was to carry out a comprehensive analysis of Pheoa metalation using the highest number of M 2+ -solvent combinations possible. Thus, the interactions between Pheoa and nine divalent metal ions (Cd 2+ , Co 2+ , Cu 2+ , Hg 2+ , Mn 2+ , Ni 2+ , Pb 2+ , Sn 2+ and Zn 2+ ) in the form of chlorides, acetates and salts with non-coordinating counterions were investigated in several organic solvents. To reveal the environmental effects on the kinetic parameters of metalation, a detailed study on the formation of the Zn-Pheoa complex in a series of seven organic solvents was carried out.
The interactions of various divalent metal ions with Chls have recently been investigated computationally but mainly in the context of the transmetalation of the complex [41]. In the present study, because the solvent exchange rate constants relevant to our model system are not available, DFT-based computations were carried out to examine the interactions of the Pheo macrocycle and M 2+ and estimate the role of solvent in their activation. The present analysis enables us to outline a hierarchy of factors which determine the kinetics of metalation and to identify the mechanisms by which the components of the reaction are activated.

Pigment preparation
Pheoa was prepared from stereochemically pure chlorophyll a (Chla), extracted from the cyanobacterium Arthrospira maxima and purified following the methods described earlier [29]. Chla was demetalated by a short treatment with glacial acetic acid, which was then evaporated under a stream of N 2 . Pheoa was further purified on a short silica gel column using chloroform as the eluent and then stored at −30 °C under argon. All experiments involving pigments were carried out in dim light with freshly prepared solutions.

General metalation procedure
The pigment solution (2.5 µM) was mixed in a tandem cuvette with a solution of at least 200-fold excess of metal salt. The reactions were monitored spectrophotometrically until significant changes ceased. In the case of slower reactions, the kinetic traces were derived from the absorption spectra recorded. To minimize the effects of pigment degradation, the time limit for reaction monitoring was set at 24 h. When the progress of metal insertion was negligibly slow compared to that of bleaching, the reaction was deemed not to be occurring. The experiments were carried out at 298 K.

Kinetic and spectroscopic measurements
The reactions with metal salts were monitored using Lambda 35 and Lambda 950 spectrophotometers (Perkin Elmer, USA), both equipped with PTP-6 Peltier modules to control the sample temperature. The rapid reactions were monitored on an SX-20 stopped flow system (Applied Photophysics, UK) combined with an LTD6G thermostat (Grant, UK). The electronic absorption spectra were recorded between 350 and 1100 nm.

DFT calculations
The density functional theory (DFT) calculations were carried out using the program Turbomole v. 6.3. [42]. The non-local Becke-Perdew functional [43][44][45][46] was used to estimate the desolvation energy of Zn 2+ , and a dispersion-corrected B97-D functional [47] to account for the solvation of Pheoa. The computations involved geometry optimization of the structures, further confirmed via vibrational analysis. The electronic energies were corrected for zero-point vibrational energy. The Resolution-of-identity (RI) algorithm was used to accelerate computations [48,49]. All-electron Gaussian type orbitals of def2-TZVP quality were used to define the atomic orbitals [50]. The electronic structures were additionally studied using Lowdin population analysis [51], as in our previous study [29]. The standard convergence criteria for geometry optimization were applied, i.e. 10 −6 a.u. for the energy, 10 −3 for the gradient, and 10 −6 for the root mean square of the density matrix. The computations were carried out at the Academic Computer Centre Cyfronet AGH using PLGrid+ infrastructure.

Results
The reactions of Pheoa with the salts of divalent metal ions were carried out under ambient conditions in MeOH, ACN, MeNO 2 , acetone, EtAcO, DMF and DMSO. This choice of solvents was dictated by both the solubility of the salts and occurrence of the insertion at ambient conditions. The following metal ions, Cd 2+ , Co 2+ , Cu 2+ , Hg 2+ , Mn 2+ , Ni 2+ , Pb 2+ , Sn 2+ and Zn 2+ , were used in the form of chlorides and acetates, and salts with trifluoromethanesulfonate (triflate, Tf − ), ClO 4 − or NO 3 − , i.e. counterions commonly regarded as non-coordinating. Assuming that in the latter case the solvatocomplexes of M 2+ are predominant in the reaction medium, the effect of M 2+ can be separated from the ligand effect. To account for the effect of residual water in the reaction medium, the kinetics of Zn 2+ insertion was determined in hydrated MeOH containing between 0 and 10% (v/v) water. Apparently, the addition of water to an organic solvent slows down the metalation [ The reactions were carried out under pseudo-first order conditions secured by the use of a considerable excess of M 2+ . To ensure reasonable reaction rates and enable direct comparison with the results obtained previously [29,36], the concentration of Pheoa was kept constant at 2.5 μM and M 2+ concentrations ranged between 0.5 and 5.0 mM. The progress of the reactions was followed by monitoring the changes in the Q Y spectral region, as exemplified in Fig. 1. The position of the Q Y maximum is the most indicative as it reflects the occurrence of interactions between the M 2+ valence electrons and the π-electron system. In most cases, in the course of metalation the Q Y band of Pheoa undergoes a hypsochromic shift. In addition, due to the replacement of two core protons in Pheoa with M 2+ , the low intensity bands located around 500-550 nm disappear.
Almost all the kinetic traces were satisfactorily fitted with the mono-exponential functions, while in a few cases a double-exponential decay was observed, which assembles the values of k obs in the form: Such kinetic traces are typical of reactions with redoxactive cations, e.g. Cu 2+ , which allow us to associate the slower component with the pigment degradation. The plots of k obs and k ′ obs against [M 2+ ] are linear (see Fig. 1b and Fig. S2 in ESM), and thus a simple rate law: can be applied.

Solvent effect
In a more detailed study, the reactions of Pheoa with Zn 2+ , as a representative M 2+ , were analyzed in seven organic solvents, viz. MeOH, ACN, MeNO 2 , acetone, EtAcO, DMF and DMSO. In all cases, ZnTf 2 was used as the source of Zn 2+ . In MeNO 2 , ACN and acetone the Zn 2+ insertion runs to completion within minutes and with the second-order rate constants greater than 1 M −1 s −1 ( Table 1). In the other solvents, metalation is markedly slower. The slowest reaction, in DMSO, shows only slight progress after 24 h. Thus, in terms of metalation rates, the following relationships between reaction media were found: MeNO 2 > ACN > acetone > AcOEt >> MeOH>DMF >> DMSO.

Cation and counterion effects
To reveal how the metalation rates depend on the M 2+ type, reactions of the divalent ions of Co, Cd, Cu, Hg, Mn, Ni, Pb, Sn, and Zn with Pheoa were carried out in MeOH, ACN and DMF. To assess the counterion effect, the reactivities of their chlorides, acetates and salts with non-coordinating counterions (each of a similar degree of constitutive hydration) were individually compared. Because Pheoa degradation may also affect the kinetics, only the results obtained for reactions completed within 72 h were considered most reliable. In slower reactions, wherever possible, the kinetic parameters were estimated by fitting the tails of the kinetic traces with linear function, and then deducing it from a combined exponentiallylinear function used to model the entire trace. The kinetic parameters of the reactions of Pheoa with the Cd, Co, Cu, Ni, Pb and Zn salts with non-coordinative counter ions are compared in Fig. 2 and listed in Table S1 (in ESM).
In MeOH, practically all cations undergo insertion and, except Ni 2+ , the k 1 values of their reactions range between 8.8 × 10 −3 M −1 s −1 (Zn 2+ ) and 6.6 × 10 −1 M −1 s −1 (Cu 2+ ). The formation of Cd-Pheoa and Cu-Pheoa is slightly faster than that of Pb-Pheoa, and considerably faster than that of Ni-Pheoa, which requires more than 150 h to run to completion. The metalations in DMF are generally slower (k 1 values between 1.3 × 10 −6 and 1.4 × 10 −2 M −1 s −1 ) and Co 2+ and Ni 2+ show no sign of insertion after 24 h. Pb 2+ turns out to insert slightly faster than most of the other M 2+ . The insertion of Cu 2+ (triflate) is the fastest in the whole series but an excess of it leads to Pheoa degradation, due to the high oxidation potential of this cation [52]. The broadest range of metalation rates was observed in ACN, in which hardly any reaction can be observed with Cd 2+ , the formation of Co-Pheoa is slower than in MeOH (k 1 = 3.9 × 10 −4 vs. 7.2 × 10 −2 s −1 M −1 ) and the insertion of Zn 2+ occurs particularly fast (k 1 = 2.6 × 10 0 s −1 M −1 ).
The interactions of Pheoa with the chlorides of Co 2+ , Cu 2+ , Mn 2+ , Sn 2+ , Hg 2+ and Zn 2+ were investigated in MeOH, ACN and DMF. In MeOH, Mn 2+ and Co 2+ do not react with Pheoa at all, while the other cations react quickly, within minutes, with the lifetime of the reaction not exceeding 42 min ( Fig. 2 and Table S2 in ESM). In ACN, τ of Co-Pheoa formation is 1.8 h, while the reaction with Sn 2+ is exceptionally fast and occurs within seconds (τ ~ 1 s). In the latter case, the reaction could be followed only using the stopped-flow technique (Fig. 3). The significant contribution of the intercept in the observed rate constants (inset in Fig. 3) indicates a competition between two species in reaction with Pheoa, probably due to the presence of Sn in two oxidized forms, Sn(II) and Sn(IV) [53]. The insertion of Sn 2+ is slower in DMF (τ = 8.8 min, k 1 = 2.6 × 10 −1 s −1 M −1 ), but still it is faster than that of other cations by at least one order of magnitude.
Due to the poor solubility of the acetates in ACN these salts are not very useful for the synthesis of metallosubstituted Chls in this medium. In MeOH the reactions with acetates are significantly faster and their k 1 values range between 10 −1 and 10 −2 s −1 M −1 (Fig. 2 and Table S3 in ESM). In DMF, compared to MeOH, the insertion rates are much slower and the k 1 values drop by two orders of magnitude, with the remarkable exception of Pb 2+ , whose insertion is the fastest of all cations tested. Cd 2+ in these two solvents inserts as fast as smaller cations. The selection of solvents considered in the computations reflects both the varying rates of metalation (Table 1) as well as differences in their character (protic MeOH, aprotic ACN). As the Lowdin population analysis shows, the net charge on Zn 2+ in Zn(solvent) 4 2+ decreases substantially when changing the ligating/solvating species from ACN to MeOH and then to DMF and acetone, in both the tetra-(ACN 0.44, MeOH 0.31, DMF 0.29 and acetone 0.26) and tri-coordinate (ACN 0.65, MeOH 0.53, DMF 0.48 and acetone 0.46) complexes (Table S5 in ESM). The results of the computations (DFT accuracy ± 2.5 kcal mol −1 [54,55], Next, the solvation of the Pheoa system was considered. In the calculations, the number of solvent molecules was increased gradually from two to twelve, but qualitatively the results did not change above two molecules. Additional solvent molecules were either placed further from the center of the macrocycle or formed a second solvation sphere. Therefore, for simplicity, only the systems containing Pheoa and two solvent molecules (ACN or DMF) and four (for MeOH, due to the strong H-bonding interactions between solvent molecules) are presented. Their geometries were optimized with the use of the DFT method applying a dispersion-corrected B97-D functional to account for the weak solutesolvent interactions. The resulting structures are shown in Fig. 4. The solvent-induced changes in the angles between the "meso" carbon atoms are rather minor (2.1° in ACN, 2.0° in MeOH, and 1.8° in DMF), while larger differences are observed in the torsion angles between the N-H bonds and the macrocycle plane. The largest deformation (13.3°) is found in MeOH, which is the strongest H-bond donor. The effects of other solvents are weaker, amounting to 4.5° in ACN and 3.0° in DMF. The DFT calculations also predict that MeOH molecules do form H-bonds with the pyrrolenine Ns and may block the central cavity (see Fig. 4), which concurs with experimental observations [56].

Experimental model system
Addressing the question of how the M 2+ properties determine metalation rates requires a comparison of kinetic data from a series of reactions in which M 2+ is the only variable. This, in practical terms, is quite limiting, because the M 2+ oxidation state, the solvent and the counter ion need to be invariant or at least very similar along the series. Most of these requirements are met in the present model system comprising the metalation of Pheoa in organic solvents, which facilitates the comparative kinetic analysis of a large set of reactions.
The metalation rate constants were determined under pseudo-first order conditions as they provide a direct comparison of the effects of M 2+ . At large excess of M 2+ , the kinetics of Pheoa metalation in all systems tested can be satisfactorily described by a simple Eq. 3. In the most complex case, i.e. Cu 2+ , it has a double set of parameters (Eq. 2), which indicates the contribution of at least two processes to the overall kinetics. The minor one is either a slow macrocycle degradation [52] or it is a parallel formation of Cu 2+ -Pheoa, e.g. by some less-populated metal species present in a particular solvent [36,52]. The slower components, contributing to k ′′ obs , may be disregarded in the subsequent discussion, because k ′ obs ≫ k ′′ obs . All the other systems can be satisfactorily approximated to the simple rate law (Eq. 3), in which the k 2 term can be assigned to a parallel rather than a reverse reaction due to the following: (1) the kinetics profiles are independent of [M 2+ ], (2) M 2+ -Pheoa complexes in non-acidic solutions are stable [29,36,57,58], and (3) the metal ions used have complex speciation in organic solvents [36,52]. The [M 2+ ]-independent reaction most Fig. 4 The DFT optimized geometry of pheophytin a in acetonitrile (a), methanol (b), and dimethylformamide (c). Note the network of hydrogen bonds formed by methanol around the central cavity and the interaction with the dimethylformamide molecule (see the text for details) likely relates to metalation involving minor coordinative forms of M 2+ .

Solvent effect
The kinetics of Zn-Pheoa formation in a series of solvents shows that the more innocent the medium (i.e. less coordinative), the faster M 2+ incorporation, which seems roughly to correlate with both the increasing solvent nucleophilicity and a reverse proportionality of the logs of k obs to Gutmann's donor numbers (Fig. 5). This indicates that the activation energy of the rate-limiting step, i.e. the formation of the first M 2+ -N bond, can be widely modulated by solvation. In terms of thermodynamics, the solvent affects ΔG ≠ of metalation in two ways: (1) solvation of the reactants contributes to ΔS ≠ and (2) solvent-macrocycle interactions facilitate conformational changes which affect ΔH ≠ . A strong metal ligation, i.e. an increase in the coordination number in the activated complex, lowers ΔS ≠ . A similar but weaker effect on the entropic component is expected to come from strong interactions in the solvation spheres of the reactants. At the same time, depending on whether they block the central pocket or expose the donor atoms of the macrocycle, specific solvent-macrocycle interactions will either lower or increase ΔH ≠ . The second-order rate constant (k 1 ) for Zn 2+ insertion in DMF is 3 and 6 orders of magnitude lower than in MeOH and ACN, respectively. An even greater difference can be seen in the rate constants for metalation with other M 2+ (Tables S1-S3 in ESM). Indeed, the electrostatic interactions are weaker in DMF (ε ~ 37; Table S5 in ESM) than in MeOH and ACN (ε ~ 33), which should lower the driving force for metalation. The low reactivity of Zn 2+ , at least in DMF, can be rationalized by the DFT-based predictions, as DMF molecules are the most difficult to dissociate from Zn 2+ . In general, the desolvation energies correlate to the kinetic parameters of the reactions with Zn 2+ in the solvents studied, in a similar way to that reported previously [59,60]. However, the theoretical predictions do not entirely agree with the experimental observations, which suggests that in addition to solvation of M 2+ there are some other factors at play, such as the formation of an electrostatically stabilized complex between the solvated metal ion and the tetrapyrrolic macrocycle, known as the sittingatop complex (SAT) [30,59,61]. The Lowdin population analysis shows ( Table S5 in ESM) that the experimental trend in ZnTf 2 reactivity (ACN > MeOH > DMF) reflects the modulation of the positive charge on Zn 2+ by its solvation sphere, which corresponds to a reciprocal relationship between solvent donor number and M 2+ reactivity (Fig. 5).
The solvent acceptor number seems to play a minor role. These results are in line with previous studies which showed that the solvent is a key factor controlling the rates of metal exchange in porphyrinoids, mostly via the solvation of metal ions [30,36,61]. Yet, specific solvent-macrocyclic ligand interactions also play a role [29], and because the degree of macrocycle distortion is directly related to the value of ΔH ≠ of metalation [18,29,62], one should consider the geometrical factor in solvent-porphyrinoid systems. Such effects are seen in the acetate-assisted transmetalation of Chla [30] and have been indicated in computational studies on Chla ligation [63], ascribed to solvents that can stabilize the pentadentate structure of Chla. Also H-bonding to the core Ns may result in a slight distortion of the macrocycle or, at least, out-of-plane deviation of the electron pairs on the core Ns, which is expected to increase the M 2+ -tetrapyrrole interface [36]. On the other hand, because the incorporation of metal ion into free base porphyrin involves a rate-determining solvent exchange with the core Ns, followed by faster proton substitution [17,36,61], those protic solvents which are likely to interact with the core Ns will be stronger inhibitors of metalation than the H-bond acceptors. Thus, the low values of the rate constants of the reaction in MeOH can in part be attributed to this type of solvent-induced deactivation of the macrocycle. The present computational analysis shows the formation of H-bonds between MeOH and the chelator (Fig. 4), and predicts that solvent-induced ring deformation will correlate with the strength of H-bonds. The largest deformation occurs in MeOH, which was also noted experimentally [56]. Similarly, H-bonding to pyrrolenine Ns and hindrance of the central cavity due to DMF molecules leads to lower reaction rates in this solvent as compared to ACN. The interactions between the macrocycle and DMF, obviously a bulkier and electron-rich molecule, are expected to be strong, while ACN, not able to H-bond, leaves the core Ns prone to the attack of incoming metal ion. H-bonding may be another reason for the significant difference in the k 1 values for Zn 2+ insertions in MeOH and ACN (Table 1). Yet, the kinetics of metalation in MeOH is not entirely consistent with the one determined in ACN (Tables S1-S3 in ESM), which, together with considerable differences between metal ions in the reaction rate constants, point to the dominant role of M 2+ -solvent over M 2+ -macrocycle interactions. The effect of H-bonding is less straightforward when one considers the reactions with other cations. In these cases, some other factors seem to be critical, e.g. the valence configuration of the ion, its ionic radii, charge density or the coordination strength of the counterions (see below). Further complications occur in solvents that favor complex speciation of M 2+ .

Incoming metal ion
The use of salts with non-coordinating counterions provides direct information about the impact of M 2+ properties on metalation rates (Tables S1-S3), which kinetically order the cations as follows: Cu 2+ ~ Zn 2+ > Cd 2+ > Ni 2+ > Pb 2+ ~ Mn 2+ , and allow them to be classified into several groups (Fig. 2). Both Cu 2+ and Zn 2+ insert exceptionally rapidly, regardless of solvent and salt type. Their very high reactivity may be related in part to their ionic radii, 0.65 Å for Cu 2+ and 0.68 Å for Zn 2+ [64], matching that of the inner cavity. However, the insertion of the latter is somewhat slower and slows down in the presence of weakly coordinative counterions. This shows that the dependence of the reaction rate on M 2+ may be underestimated for chlorides and in particular for acetates (see below), in line with predictions based on the Irving-Williams series [15,16,65]. The second class, including Ni 2+ , Co 2+ and Mn 2+ , shows moderate rates of insertion and, typically, the second-order rate constants in this group vary between 10 −4 and 10 −7 M −1 s −1 . This makes kinetic analysis difficult as metalation may compete with chelator degradation. The differences in the metalation rates between Zn 2+ and Ni 2+ /Co 2+ /Mn 2+ could be due in part to the fact that the latter cations form a mixed, i.e. coordinative-covalent type of bonds with the core Ns in Pheoa, in contrast to Zn 2+ , bound via purely coordinative bonds [6]. The insertion of these cations requires their valence configuration to be rebuilt along the reaction pathway, which may elevate the energetic barrier for this reaction.
The ions of heavy metals-Hg 2+ , Pb 2+ and to a lesser extent Cd 2+ -belong to another, more specific group. They do bind to Pheoa with second-order rate constants of either near 10 −1 M −1 s −1 or well below 10 −7 M −1 s −1 .
Because of their large ionic radii, 0.96, 0.98 and 0.78 Å, respectively [64], they hardly form "in plane" complexes, such that their binding is usually accompanied by a considerable macrocycle distortion. The rates of M 2+ -Pheoa formation with these cations were found to be considerably higher than those of smaller ionic radii (Tables S1-S3 in ESM), which again indicates the key role of macrocycle distortion in metalation [17,25,26,66]. Also the lower metalation rates seen for Pheoa, as compared to porphyrins, may reflect an increased rigidity of its macrocycle. A separate issue is the unusually fast rate of the reaction between Pheoa and SnCl 2 in ACN. The large ionic radius of Sn 2+ (0.93 Å in the 6-coordinate form [67]) favors the formation of non-planar complexes with tetrapyrroles, especially taking into account the ability of Sn 2+ to form tetrahedral and pyramidal complexes. Furthermore, SnCl 2 is one of the most potent Lewis acids [64,68].

The counterion
One of the major concerns when choosing a counterion suitable for the synthesis of metallosubstituted (B)Chls is its capacity to lower the oxidation potential of M 2+ . A comparison of reactions with three types of counterion, non-coordinating (perchlorate, triflate and nitrate), coordinating monodentate (Cl − ) and chelating (AcO − ) reveals drastic differences. For instance, Ni 2+ with noncoordinative counterion in DMF shows no reaction at all while NiCl 2 reacts very fast. In other cases, the reaction rates differ by several orders of magnitude, depending on the counterion (Fig. 2 and compare data in Tables S1, S2 and S4 in the ESM). Interestingly, the solvatocomplexes of Zn 2+ , Cu 2+ and Co 2+ react with Pheoa in MeOH considerably more slowly than their chlorides and acetates, both prone to form less reactive complexes with M 2+ due to their charge. Acetate, even if it accelerates transmetalation [30], in solution forms inert binuclear (or polymeric) complexes that lower the effective concentration of reactive M 2+ , but importantly, it prevents macrocycle oxidation. This makes the acetate/MeOH system an efficient and versatile medium for the preparation of metallochlorophylls [30,36].
The explanation of the counterion effect is not straightforward for the following reasons: (1) the ligand exchange rates are faster than the formation of the first M 2+ -Pheoa bond, (2) a relatively low population of inert [M 2 (AcO) n ] 4−n complexes, (3) the presence of some vacant coordination sites on mononuclear Cl − /AcO − complexes, and (4) the solvation of counterions. The latter effect could contribute to the higher rates of the reactions with Cu(AcO) 2 and Zn(AcO) 2 in MeOH than in ACN.
The fate of counterion in reaction medium may also be of some importance when a large excess of salt is applied. Chloride and triflate in polar solvents are likely to remain in the ionic form, whereas AcO − , a strong nucleophile, will tend to capture protons from the environment. In aprotic solvents, the free base Pheoa may be the source of protons, which will promote the progress of the reaction by affecting the equilibrium described in Eq. 1. For the same reason, i.e. due to its high basicity [69], MeOH can be considered the most favorable of the solvents used.
The comparison of the kinetics of Zn-Pheoa formation using three salts of Zn 2+ , triflate, chloride and acetate, in MeOH, ACN and DMF, as presented in Fig. 6, provides additional information. Clearly, the reactivity of Zn 2+ is a product of many factors and the effects of counterions seem to depend on solvent properties. In MeOH, which is both a relatively good ligand as well as H bond donor, the reactivity of Zn salts increases in the following way: Tf − < Cl − < AcO − . This can be explained by the destabilization of the Zn-AcO mononuclear and inert polymeric complexes due to solvation. A reverse trend is observed in ACN, a poorly coordinating and solvating medium, in which the metalation rate is inversely proportional to the coordinative properties of the counterion. Such dependencies are less obvious in DMF, but the exceptionally low rate constant of Zn-Pheoa formation with ZnCl 2 may be associated with complicated speciation, which, by analogy to CuCl 2 [65], significantly reduces the concentration of Zn 2+ reactive species.

Mg 2+ insertion in biological systems
Any direct comparison between the insertion of Mg 2+ and the metal ions discussed above is not really feasible due to the fact that the former does not spontaneously insert into Pheo. Indeed, the insertion of Mg 2+ into protoporphyrin IX requires extraordinary components and high amounts of energy [70,71]. This energy is used to transfer Mg 2+ from its output complexes, most likely aquacomplexes, to the enzyme's binding site, presumably formed by two serines, aspartic acid and threonine [72]. Such conditions cannot be achieved in a simple in vitro system easily. The high energy demand of this process seems to be related to the fact that Mg 2+ is bound in the central cavity of porphyrinoids not by coordinative bonds but by much weaker electrostatic forces [6]. As a consequence, in the course of Mg 2+ insertion a significant change in its coordination state must take place, from a (most likely) hexacoordinated species to a singly or doubly axially coordinated ion electrostatically bound in the central cavity. Large amounts of energy in the form of ATP would be required first to activate the Mg 2+ ion by stripping off its coordination sphere and then to protect this reactive species during its attack on the enzymebound protoporphyrin IX.

Conclusions
By applying the same approach across many solvents and ions in the model system for pheophytin a metalation, we were able to reveal and compare the key factors that influence the kinetics of this reaction. Both the solvent, as the reaction medium, and the counterion to the incoming metal cation, have to be regarded as decisive participants in the reaction, able either to inhibit or greatly facilitate the metalation of porphyrinoids. Hence, the overall reaction is certainly an interplay of various factors, with the energetic, steric and electrostatic effects coming from all participants in the process. The M 2+ size brings about the clearest effect on the metalation rate, which may dominate over other factors. In this respect, the series of metal ions investigated can be divided into three classes: (1) smallsized cations which incorporate rapidly (Zn 2+ and Cu 2+ ), (2) medium-sized cations which incorporate rather slowly (Ni 2+ , Co 2+ and Mn 2+ ), and (3) bulky metal ions which insert rapidly; these latter form non-planar complexes (Cd 2+ , Hg 2+ and Pb 2+ ).
On the solvent side, several factors have to be considered. Metalation is retarded by any strong interaction of incoming M 2+ with solvent molecules as well as solvent H-bonding to pyrrolenine nitrogens that increase the steric hindrance for an incoming M 2+ and contribute to higher activation energies of Pheoa metalation. On the other hand, the increased exposure of pyrrolenine nitrogens, due to the interactions with solvent molecules, may render Pheoa prone to M 2+ attack. In addition, the rate of formation of the first M 2+ -N bond is controlled by solvation.
The comparison of the metalation rates shown in Fig. 2 leads to other general conclusions. The effects of counterion and solvent seem to be diminished with bulky metal ions. Apparently, the large ionic size favors the associative mechanism of ligand substitution and reduces the importance of the leaving group. Moreover, large M 2+ in the out-of-plane position may retain some of their original ligands, in contrast to relatively small ions that do not exceed the size of Mg 2+ . The differences in solvent donor properties, reflected in both the coordination and solvation, must play a more significant role, at least because of the need to release specific binding sites for pyrrolenine nitrogens.
The present results have relevance to the synthetic applications. First, the ligands in the coordination sphere of the incoming metal ions determine the kinetics of the reaction with Pheoa because they limit the concentration of the reactive species. Second, the ligands may also determine the direction of the reaction by tuning the redox potential of the cations. Therefore, with some metal ions, when redox reactions may be involved, it is not always of benefit to use their unprotected forms in metalation reactions. The best example is acetate, which on the one hand limits the concentration of reactive M 2+ species but on the other lowers the M 2+ oxidative potential. An analogous principle applies to solvents. Thus, in spite of the exceptionally high rate of metalations in MeNO 2 , the synthetic application of this solvent is limited because it does not provide adequate protection against redox-active metal ions and the solubility of many inorganic salts in it is poor.