On the dynamic nature of the transition state for protein-protein association as determined by double-mutant cycle analysis and simulation

The process of protein-protein association starts with their random collision, which may develop into an encounter complex followed by a transition state and final complex formation. Here we aim to experimentally characterize the nature of the transition state of protein-protein association for three different protein-protein interactions; Barnase-Barstar, TEM1-BLIP and IFNalpha2-IFNAR2, and use the data to model the transition state structures. To model the transition state, we determined inter-protein distance-constraints of the activated complex by using double mutant cycles (DMC) assuming that interacting residues are spatially close. Significant DeltaDeltaG(double dagger)(int) values were obtained only between residues on Barnase and Barstar. However, introducing specific mutations that optimize the charge complementarity between BLIP and TEM1 resulted in the introduction of significant DeltaDeltaG(double dagger)(int) values also between residues of these two proteins. While electrostatic interactions make major contributions towards stabilizing the transition state, we show two examples where steric hindrance exerts an effect on the transition state as well. To model the transition-state structures from the experimental DeltaDeltaG(double dagger)(int) values, we introduced a method for structure perturbation, searching for those inter-protein orientations that best support the experimental DeltaDeltaG(double dagger)(int) values. Two types of transition states were found, specific as observed for Barnase-Barstar and the electrostatically optimized TEM1-BLIP mutants, and diffusive as shown for wild-type TEM1-BLIP and IFNalpha2-IFNAR2. The specific transition states are characterized by defined inter-protein orientations, which cannot be modeled for the diffusive transition states. Mutations introduced through rational design can change the transition state from diffusive to specific. Together, these data provide a structural view of the mechanism allowing rates of association to differ by five orders of magnitude between different protein complexes.     

Electrostatic rate enhancement and transient complex of protein-protein association

The association of two proteins is bounded by the rate at which they, via diffusion, find each other while in appropriate relative orientations. Orientational constraints restrict this rate to approximately 10(5)-10(6) M(-1) s(-1). Proteins with higher association rates generally have complementary electrostatic surfaces; proteins with lower association rates generally are slowed down by conformational changes upon complex formation. Previous studies (Zhou, Biophys J 1997;73:2441-2445) have shown that electrostatic enhancement of the diffusion-limited association rate can be accurately modeled by $k_{\bf D}$ = $k_{D}0\ {exp} ( - \langle U_{el} \rangle;{\star}/k_{B} T),$ where k(D) and k(D0) are the rates in the presence and absence of electrostatic interactions, respectively, U(el) is the average electrostatic interaction energy in a "transient-complex" ensemble, and k(B)T is the thermal energy. The transient-complex ensemble separates the bound state from the unbound state. Predictions of the transient-complex theory on four protein complexes were found to agree well with the experiment when the electrostatic interaction energy was calculated with the linearized Poisson-Boltzmann (PB) equation (Alsallaq and Zhou, Structure 2007;15:215-224). Here we show that the agreement is further improved when the nonlinear PB equation is used. These predictions are obtained with the dielectric boundary defined as the protein van der Waals surface. When the dielectric boundary is instead specified as the molecular surface, electrostatic interactions in the transient complex become repulsive and are thus predicted to retard association. Together these results demonstrate that the transient-complex theory is predictive of electrostatic rate enhancement and can help parameterize PB calculations.     

Energy landscape and transition state of protein-protein association

Formation of a stereospecific protein complex is favored by specific interactions between two proteins but disfavored by the loss of translational and rotational freedom. Echoing the protein folding process, we have previously proposed a transition state for protein-protein association. Here we clarify the specification of the transition state by working with two types of toy models for protein association. A “hemisphere” model consists of two matching hemispheres as associating proteins, and a “crater” model consists of a spherical protein with a crater to which another spherical protein fits snugly. Short-range pairwise interactions between sites across the interface hold together the bound complex. Small relative translation and rotation between the subunits quickly destroy the interactions, leading to a sharp transition between the bound state with numerous short-range interactions but restricted translation and rotational freedom and the unbound state with, at most, a small number of interactions but expanded configurational freedom. This transition sets the outer boundary of the bound state as well as the transition state for association. The energy landscape is funnel-like, with the deep well of the bound state surrounded by a broad shallow basin. Calculations with the toy models suggest that mutational change in the interaction energy in the x-ray structure of a protein-protein complex, commonly used to approximate the effect on the association constant, overestimates the effect of mutation by 10–20%. With an eye toward specifying the transition states of actual protein complexes, we find that the total number of contacts between the subunits serves as a good surrogate of the interaction energy. This formalism of protein-protein association is applied to the barnase-barstar complex, reproducing the experimental results for the association rate over a wide range of ionic strength.     

An early transition state for folding of the P4-P6 RNA domain

Tertiary folding of the 160-nt P4-P6 domain of the Tetrahymena group I intron RNA involves burying of substantial surface area, providing a model for the folding of other large RNA domains involved in catalysis. Stopped-flow fluorescence was used to monitor the Mg2+-induced tertiary folding of pyrene-labeled P4-P6. At 35 degrees C with [Mg2+] approximately 10 mM, P4-P6 folds on the tens of milliseconds timescale with k(obs) = 15-31 s(-1). From these values, an activation free energy deltaG(double dagger) of approximately 8-16 kcal/mol is calculated, where the large range for deltaG(double dagger) arises from uncertainty in the pre-exponential factor relating k(obs) and delta G(double dagger). The folding rates of six mutant P4-P6 RNAs were measured and found to be similar to that of the wild-type RNA, in spite of significant thermodynamic destabilization or stabilization. The ratios of the kinetic and thermodynamic free energy changes phi = delta deltaG(double dagger)/delta deltaG(o') are approximately 0, implying a folding transition state in which most of the native-state tertiary contacts are not yet formed (an early folding transition state). The k(obs) depends on the Mg2+ concentration, and the initial slope of k(obs) versus [Mg2+] suggests that only approximately 1 Mg2+ ion is bound in the rate-limiting folding step. This is consistent with an early folding transition state, because folded P4-P6 binds many Mg2+ ions. The observation of a substantial deltaG(double dagger) despite an early folding transition state suggests that a simple two-state folding diagram for Mg2+-induced P4-P6 folding is incomplete. Our kinetic data are some of the first to provide quantitative values for an activation barrier and location of a transition state for tertiary folding of an RNA domain.     

Transition state characterization of the low- to physiological-temperature nondenaturational conformational change in bovine adenosine deaminase by slow scan rate differential scanning calorimetry

Bovine adenosine deaminase undergoes a nondenaturational conformational change at 29 degrees C upon heating which is characterized by a large increase in heat capacity. We have determined the transition state thermodynamics of the conformational change using a novel application of differential scanning calorimetry (DSC) which employs very slow scan rates. DSC scans at the conventional, and arbitrary, scan rate of 1 degree C/min show no evidence of the transition. Scan rates from 0.030 to 0.20 degrees C/min reveal the transition indicating it is under kinetic control. The transition temperature T(t) and the transition temperature interval deltaT increase with scan rate. A first order rate constant k1 is calculated at each T(t) from k1 = r(scan)/deltaT, where r(scan) is the scan rate, and an Arrhenius plot is constructed. Standard transition state analysis reveals an activation free energy deltaG(double dagger) of 88.1 kJ/mole and suggests that the conformational change has an unfolding quality that appears to be on the direct path to the physiological-temperature conformer.     

Dynamic mechanism for the serpin loop insertion as revealed by quantitative kinetics

The serpin conformational change by insertion of the reactive center loop into beta-sheet A plays a central role in multiple physiological consequences such as serine proteinase inhibition, latency and serpinopathic polymerization. To study the dynamic mechanism for the loop insertion, a novel kinetic method was established utilizing the ovalbumin mutant R339T/A352R; the loop insertion progressed after the cleavage of P1-P1' (Arg352-Ser353) by trypsin was quenched at pH 8 and 0.5 degrees C, and different conformers were quantified by separation using ion-exchange HPLC. The apparent first-order rate constant k(app) determined for various R339T/A352R derivatives differing in conformational stability was greatly increased by lowering the pH. The pH-dependence of k(app) indicated that the protonation of side-chain(s) with a pK(a) value of around 4.6 is a pre-requisite for the loop insertion. The theoretical rate constant k for the protonated form calculated from k(app) was highly variable, depending on the ovalbumin derivative; structural modifications that give increased mobility to helix F and the sheet-A half (s3A/s2A/s1A) resulted in a striking increase in the loop insertion rate constant k. The k values were determined at different temperatures for all the ovalbumin derivatives, and DeltaH(double dagger) and DeltaS(double dagger) values for the loop insertion reaction were determined according to the transition theory. The formation of the transition state was highly endothermic with minor entropy gain, requiring a DeltaG(double dagger) larger than 18 kcal/mol, which can offset the hydrogen-bond cleavages between s3A and s5A. These results are consistent with the transition state with an opened sheet A and altered orientation of helix F.     

Predicting the rate enhancement of protein complex formation from the electrostatic energy of interaction

The rate of association of proteins is dictated by diffusion, but can be enhanced by favorable electrostatic forces. Here the relationship between the electrostatic energy of interaction, and the kinetics of protein-complex formation was analyzed for the protein pairs of: hirudin-thrombin, acetylcholinesterase-fasciculin and barnase-barstar, and for a panel of point mutants of these proteins. Electrostatic energies of interaction were calculated as the difference between the electrostatic energy of the complex and the sum of the energies of the two individual proteins, using the computer simulation package DelPhi. Calculated electrostatic energies of interaction were compared to experimentally determined rates of association. One kcal/mol of Coulombic interaction energy increased the rate of association by a factor of 2.8, independent of the protein-complex or mutant analyzed. Electrostatic energies of interaction were also determined from the salt dependence of the association rate constant, using the same basic equation as for the theoretical calculation. A Br?nsted analysis of the electrostatic energies of interactions plotted versus experimentally determined ln(rate)s of association shows a linear relation between the two, with a beta value close to 1. This is interpreted as the energy of the transition state varies according to the electrostatic interaction energy, fitting a two state model for the association reaction. Calculating electrostatic rate enhancement from the electrostatic interaction energy can be used as a powerful tool to design protein complexes with altered rates of association and affinities.     

Continuum electrostatic model for the binding of cytochrome c2 to the photosynthetic reaction center from Rhodobacter sphaeroides

Electrostatic interactions are important for protein-protein association. In this study, we examined the electrostatic interactions between two proteins, cytochrome c(2) (cyt c(2)) and the reaction center (RC) from the photosynthetic bacterium Rhodobacter sphaeroides, that function in intermolecular electron transfer in photosynthesis. Electrostatic contributions to the binding energy for the cyt c(2)-RC complex were calculated using continuum electrostatic methods based on the recent cocrystal structure [Axelrod, H. L., et al. (2002) J. Mol. Biol. 319, 501-515]. Calculated changes in binding energy due to mutations of charged interface residues agreed with experimental results for a protein dielectric constant epsilon(in) of 10. However, the electrostatic contribution to the binding energy for the complex was close to zero due to unfavorable desolvation energies that compensate for the favorable Coulomb attraction. The electrostatic energy calculated as a function of displacement of the cyt c(2) from the bound position showed a shallow minimum at a position near but displaced from the cocrystal configuration. These results show that although electrostatic steering is present, other short-range interactions must be present to contribute to the binding energy and to determine the structure of the complex. Calculations made to model the experimental data on association rates indicate a solvent-separated transition state for binding in which the cyt c(2) is displaced approximately 8 A above its position in the bound complex. These results are consistent with a two-step model for protein association: electrostatic docking of the cyt c(2) followed by desolvation to form short-range van der Waals contacts for rapid electron transfer.     

Free Energy Diagram for the Heterogeneous Enzymatic Hydrolysis of Glycosidic Bonds in Cellulose

Kinetic and thermodynamic data have been analyzed according to transition state theory and a simplified reaction scheme for the enzymatic hydrolysis of insoluble cellulose. For the cellobiohydrolase Cel7A from Hypocrea jecorina (Trichoderma reesei), we were able to measure or collect relevant values for all stable and activated complexes defined by the reaction scheme and hence propose a free energy diagram for the full heterogeneous process. For other Cel7A enzymes, including variants with and without carbohydrate binding module (CBM), we obtained activation parameters for the association and dissociation of the enzyme-substrate complex. The results showed that the kinetics of enzyme-substrate association (i.e. formation of the Michaelis complex) was almost entirely entropy-controlled and that the activation entropy corresponded approximately to the loss of translational and rotational degrees of freedom of the dissolved enzyme. This implied that the transition state occurred early in the path where the enzyme has lost these degrees of freedom but not yet established extensive contact interactions in the binding tunnel. For dissociation, a similar analysis suggested that the transition state was late in the path where most enzyme-substrate contacts were broken. Activation enthalpies revealed that the rate of dissociation was far more temperature-sensitive than the rates of both association and the inner catalytic cycle. Comparisons of one- and two-domain variants showed that the CBM had no influence on the transition state for association but increased the free energy barrier for dissociation. Hence, the CBM appeared to promote the stability of the complex by delaying dissociation rather than accelerating association.     

The DMPC lipid phase transition influences differently the first and the second electron transfer reactions in bacterial reaction centers

Photosynthetic reaction centers (RCs) from Rhodobacter sphaeroides were incorporated in dimyristoylphosphatidylcholine (DMPC) liposomes. The first and second electron transfer rates (k(AB)(1) and k(AB)(2), respectively) between the first and the second quinone electron acceptors have been measured as a function of temperature, across the phase transition of DMPC (23 degrees C). The Eyring plots of k(AB)(1) display straight lines. In contrast, the Eyring plots for k(AB)(2) in proteoliposomes show a break at about 23.5 degrees C. This physical discrimination between the two electron transfer reactions demonstrates that the stiffness of the lipid environment of the RCs and/or the protein-protein interactions influence the parameters governing k(AB)(2), but not the gating process limiting k(AB)(1).     

Electrostatic interactions during electron transfer reactions between c-type cytochromes and flavodoxin

The interaction of three different c-type cytochromes with flavodoxin has been studied by computer graphics modelling and computational methods. Flavodoxin and each cytochrome can make similar hypothetical electron transfer complexes that are characterized by nearly coplanar arrangement of the prosthetic groups, close intermolecular contacts at the protein-protein interface, and complementary intermolecular salt linkages. Computation of the electrostatic free energy of each complex showed that all were electrostatically stable. However, both the magnitude and behavior of the electrostatic stabilization as a function of solution ionic strength differed for the three cytochrome c-flavodoxin complexes. Variation in the computed electrostatic stabilization appears to reflect differences in the surface distribution of all charged groups in the complex, rather than differences localized at the site of intermolecular contact. The computed electrostatic association constants for the complexes and the measured kinetic rates of electron transfer in solution show a remarkable similarity in their ionic strength dependence. This correlation suggests electrostatic interactions influence electron transfer rates between protein molecules at the intermolecular association step. Comparative calculations for the three cytochrome c-flavodoxin complexes show that these ionic strength effects also involve all charged groups in both redox partners.     

Exploring the charge space of protein-protein association: a proteomic study

The rate of association of a protein complex is a function of an intrinsic basal rate and of the magnitude of electrostatic steering. In the present study we analyze the contribution of electrostatics towards the association rate of proteins in a database of 68 transient hetero-protein-protein complexes. Our calculations are based on an upgraded version of the computer algorithm PARE, which was shown to successfully predict the impact of mutations on k(on) by calculating the difference in Columbic energy of interaction of a pair of proteins. HyPare (http://bip.weizmann.ac.il/HyPare), automatically calculates the impact of mutations on a per-residue basis for all residues of a protein-protein interaction, achieving a precision similar to that of PARE. Our calculations show that electrostatics play a marginal role (<10 fold) in determining the rate of association for about half of the complexes in the database. Strong electrostatic steering, which results in an increase of over 100-fold in k(on), was calculated for about 25% of the complexes. Applying HyPare to all 68 complexes in the database shows that a small number of residues are hotspots for association. About 40% of the hotspots are calculated to increase the rate of association upon mutation, and thus increase binding affinity. This is a much higher ratio than found for hotspots for dissociation, where the large majority cause weaker binding. About 40% of the hotspots are located outside the physical boundary of the binding site, making them ideal candidates for protein engineering. Our data shows that a majority of protein-protein complexes are not optimized for fast association. Hotspots are not evenly distributed between all types of amino acids. About 75% of all hotspots are of charged residues. This is understandable, as a charge-reverse mutant changes the total charge by 2. The small number of hydrophobic residues that are hotspots upon mutation probably relates to their location and surrounding. For 18 out of the 68 complexes in the database, experimental values of k(on) are available. For these, a basal rate of association was calculated to be in the range of 10(4)M(-1)s(-1) to 10(7)M(-1)s(-1). Some of these rates were verified independently from experimental mutant data. The basal rates were correlated with the size of the proteins and the shape of the interface.     

Evaluation of direct and cooperative contributions towards the strength of buried hydrogen bonds and salt bridges

An experimental approach to evaluate the net binding free energy of buried hydrogen bonds and salt bridges is presented. The approach, which involves a modified multiple-mutant cycle protocol, was applied to selected interactions between TEM-1-beta-lactamase and its protein inhibitor, BLIP. The selected interactions (two salt bridges and two hydrogen bonds) all involving BLIP-D49, define a distinct binding unit. The penta mutant, where all side-chains constructing the binding unit were mutated to Ala, was used as a reference state to which combinations of side-chains were introduced. At first, pairs of interacting residues were added allowing the determination of interaction energies in the absence of neighbors, using double mutant cycles. Addition of neighboring residues allowed the evaluation of their cooperative effects on the interaction. The two isolated salt bridges were either neutral or repulsive whereas the two hydrogen bonds contribute 0.3 kcal mol(-1 )each. Conversely, a double mutant cycle analysis of these interactions in their native environment showed that they all stabilize the complex by 1-1.5 kcal mol(-1). Examination of the effects of neighboring residues on each of the interactions revealed that the formation of a salt bridge triad, which involves two connected salt bridges, had a strong cooperative effect on stabilizing the complex independent of the presence or absence of additional neighbors. These results demonstrate the importance of forming net-works of buried salt bridges. We present theoretical electrostatic calculations which predict the observed mode of cooperativity, and suggest that the cooperative networking effect results from the favorable contribution of the protein to the interaction. Furthermore, a good correlation between calculated and experimentally determined interaction energies for the two salt bridges, and to a lesser extent for the two hydrogen bonds, is shown. The data analysis was performed on values of DeltaDeltaG(double dagger)K(d) which reflect the strength of short range interactions, while DeltaDeltaG(o)K(D) values which include the effects of long range electrostatic forces that alter specifically DeltaDeltaG(double dagger)k(a) were treated separately.     

Thermodynamic analysis of catalysis by the dihydroorotases from hamster and Bacillus caldolyticus, as compared with the uncatalyzed reaction

Dihydroorotase (DHOase, EC 3.5.2.3) from the extreme thermophile Bacillus caldolyticus has been subcloned, sequenced, expressed, and purified as a monomer. The catalytic properties of this thermophilic DHOase have been compared with another type I enzyme, the DHOase domain from hamster, to investigate how the thermophilic enzyme is adapted to higher temperatures. B. caldolyticus DHOase has higher Vmax and Ks values than hamster DHOase at the same temperature. The thermodynamic parameters for the binding of L-dihydroorotate were determined at 25 degrees C for hamster DHOase (deltaG = -6.9 kcal/mol, deltaH = -11.5 kcal/mol, TdeltaS = -4.6 kcal/mol) and B. caldolyticus DHOase (deltaG = -5.6 kcal/mol, deltaH = -4.2 kcal/mol, TdeltaS = +1.4 kcal/mol). The smaller enthalpy release and positive entropy for thermophilic DHOase are indicative of a weakly interacting Michaelis complex. Hamster DHOase has an enthalpy of activation of 12.3 kcal/mol, similar to the release of enthalpy upon substrate binding, rendering the kcat/Ks value almost temperature independent. B. caldolyticus DHOase shows a decrease in the enthalpy of activation from 12.2 kcal/mol at temperatures from 30 to 50 degrees C to 5.3 kcal/mol for temperatures of 50-70 degrees C. Vibrational energy at higher temperatures may facilitate the transition ES --> ES(double dagger), making kcat/Ks almost temperature independent. The pseudo-first-order rate constant for water attack on L-dihydroorotate, based on experiments at elevated temperature, is 3.2 x 10(-11) s(-1) at 25 degrees C, with deltaH(double dagger) = 24.7 kcal/mol and TdeltaS(double dagger) = -6.9 kcal/mol. Thus, hamster DHOase enhances the rate of substrate hydrolysis by a factor of 1.6 x 10(14), achieving this rate enhancement almost entirely by lowering the enthalpy of activation (delta deltaH(double dagger) = -19.5 kcal/mol). Both the rate enhancement and transition state affinity of hamster DHOase increase steeply with decreasing temperature, consistent with the development of H-bonds and electrostatic interactions in the transition state that were not present in the enzyme-substrate complex in the ground state.     

New insights into the mechanism of protein-protein association

Association of a protein complex follows a two-step mechanism, with the first step being the formation of an encounter complex that evolves into the final complex. Here, we analyze recent experimental data of the association of TEM1-beta-lactamase with BLIP using theoretical calculations and simulation. We show that the calculated Debye-Hückel energy of interaction for a pair of proteins during association resembles an energy funnel, with the final complex at the minima. All attraction is lost at inter-protein distances of 20 A, or rotation angles of >60 degrees from the orientation of the final complex. For faster-associating protein complexes, the energy funnel deepens and its volume increases. Mutations with the largest impact on association (hotspots for association) have the largest effect on the size and depth of the energy funnel. Analyzing existing evidence, we suggest that the transition state along the association pathway is the formation of the final complex from the encounter complex. Consequently, pairs of proteins forming an encounter complex will tend to dissociate more readily than to evolve into the final complex. Increasing directional diffusion by increasing favorable electrostatic attraction results in a faster forming and slower dissociating encounter complex. The possible applicability of electrostatic calculations for protein-protein docking is discussed.     

Protein docking using continuum electrostatics and geometric fit

The computer program DOT quickly finds low-energy docked structures for two proteins by performing a systematic search over six degrees of freedom. A novel feature of DOT is its energy function, which is the sum of both a Poisson-Boltzmann electrostatic energy and a van der Waals energy, each represented as a grid-based correlation function. DOT evaluates the energy of interaction for many orientations of the moving molecule and maintains separate lists scored by either the electrostatic energy, the van der Waals energy or the composite sum of both. The free energy is obtained by summing the Boltzmann factor over all rotations at each grid point. Three important findings are presented. First, for a wide variety of protein-protein interactions, the composite-energy function is shown to produce larger clusters of correct answers than found by scoring with either van der Waals energy (geometric fit) or electrostatic energy alone. Second, free-energy clusters are demonstrated to be indicators of binding sites. Third, the contributions of electrostatic and attractive van der Waals energies to the total energy term appropriately reflect the nature of the various types of protein-protein interactions studied.     

Partial phase diagram of aqueous bovine carbonic anhydrase: analyses of the pressure-dependent temperatures of the low- to physiological-temperature nondenaturational conformational change and of unfolding to the molten globule state

At 1.0 atm pressure and in 150 mM sodium phosphate (pH = 7.0), bovine carbonic anhydrase undergoes a nondenaturational conformational change at 30.3 degrees C and an unfolding transition from the physiological conformer to the molten globule state at 67.4 degrees C. The pressure dependences of the temperatures of these transitions have been studied under reversible conditions for the purpose of understanding DeltaH degrees , DeltaS degrees , and DeltaV for each conformational change. Temperatures for the low-temperature to physiological-temperature conformational change T(L-->P) are obtained from physiologically relevant conditions using slow-scan-rate differential scanning calorimetry. Temperatures for the physiological-temperature conformation to molten globule state conversion T(P-->MG) are obtained from differential scanning calorimetry measurements of the apparent transition temperature in the presence of guanidine hydrochloride extrapolated to zero molar denaturant. The use of slow-scan-rate differential scanning calorimetry permits the calculation of the activation volume for the conversion of the low-temperature conformer to the physiological-temperature conformer DeltaV(double dagger)(L-->P). At 1.0 atm pressure, the transition from the low-temperature conformer to the physiological-temperature conformer involves a volume change DeltaV(L-->P) = 15 +/- 2 L/mole, which contrasts with the partial unfolding of the physiological-temperature conformer to the molten globule state (DeltaV(P-->MG) = 26 +/- 9 L/mole). The activation volume for this process DeltaV(double dagger)(L-->P) = 51 +/- 9 L/mole and is consistent with a prior thermodynamic analysis that suggests the conformational transition from the low-temperature conformation to the physiological-temperature conformation possesses a substantial unfolding quality. These results provide further evidence the structure of the enzyme obtained from crystals grown below 30 degrees C should not be regarded as the physiological structure (the normal bovine body temperature is 38.3 degrees C). These results should therefore have implications in any area that seeks to correlate the crystal structure of bovine carbonic anhydrase to physiological function.     

Metal-ligand bonding in metallocenes: Differentiation between spin state, electrostatic and covalent bonding

We have analyzed metal-ligand bonding in metallocenes using density functional theory (DFT) at the OPBE/TZP level. This level of theory was recently shown to be the only DFT method able to correctly predict the spin ground state of iron complexes, and similar accuracy for spin ground states is found here. We considered metallocenes along the first-row transition metals (Sc-Zn) extended with alkaline-earth metals (Mg, Ca) and several second-row transition metals (Ru, Pd, Ag, Cd). Using an energy decomposition analysis, we have studied trends in metal-ligand bonding in these complexes. The OPBE/TZP enthalpy of heterolytic association for ferrocene (−658 kcal/mol) as obtained from the decomposition analysis is in excellent agreement with benchmark CCSD(T) and CASPT2 results. Covalent bonding is shown to vary largely for the different metallocenes and is found in the range from −155 to −635 kcal/mol. Much smaller variation is observed for Pauli repulsion (55-345 kcal/mol) or electrostatic interactions, which are however strong (−480 to −620 kcal/mol). The covalent bonding, and thus the metal-ligand bonding, is larger for low spin states than for higher spin states, due to better suitability of acceptor d-orbitals of the metal in the low spin state. Therefore, spin ground states of transition metal complexes can be seen as the result of a delicate interplay between metal-ligand bonding and Hund’s rule of maximum multiplicity.     

Optimization of electrostatic interactions in protein-protein complexes

In this article, we present a statistical analysis of the electrostatic properties of 298 protein-protein complexes and 356 domain-domain structures extracted from the previously developed database of protein complexes (ProtCom, http://www.ces.clemson.edu/compbio/protcom). For each structure in the dataset we calculated the total electrostatic energy of the binding and its two components, Coulombic and reaction field energy. It was found that in a vast majority of the cases (>90%), the total electrostatic component of the binding energy was unfavorable. At the same time, the Coulombic component of the binding energy was found to favor the complex formation while the reaction field component of the binding energy opposed the binding. It was also demonstrated that the components in a wild-type (WT) structure are optimized/anti-optimized with respect to the corresponding distributions, arising from random shuffling of the charged side chains. The degree of this optimization was assessed through the Z-score of WT energy in respect to the random distribution. It was found that the Z-scores of Coulombic interactions peak at a considerably negative value for all 654 cases considered while the Z-score of the reaction field energy varied among different types of complexes. All these findings indicate that the Coulombic interactions within WT protein-protein complexes are optimized to favor the complex formation while the total electrostatic energy predominantly opposes the binding. This observation was used to discriminate WT structures among sets of structural decoys and showed that the electrostatic component of the binding energy is not a good discriminator of the WT; while, Coulombic or reaction field energies perform better depending upon the decoy set used.