8 Using pseudorotation as a reaction coordinate in free energy simulations of nucleic acids

Backbone sugar groups are central components of nucleic acids. The conformations of the ribose/deoxyribose can be elegantly described using the concept of pseudorotation (Altona and Sundaralingam, 1972), and are dominated by the C2′- and C3′-endo conformers. The free energy barrier of the transition between these two major puckering modes can be probed by NMR relaxation experiments (Johnson and Hoogstraten, 2008), but an atomic picture of the transition path per se is only available for several truncated nucleoside analogues (Brameld & Goddard III, 1999). Here, we implemented a new free energy simulation method for Molecular Dynamics simulations using pseudorotation as the reaction coordinate (Cremer and Pople, 1975). This allowed us to compute the free energy landscape of a complete pseudorotation cycle. The free energy landscape revealed not only the relative stability of C2′- and C3′-endo conformers, but also the main transition path and its free energy barrier. As a validation of our new approach, we calculated free energy surface of the pseudorotation of guanosine monophosphate. The free energy surface revealed that the C2′-endo conformation is ?1?kcal/mol that is more stable and the free energy barrier for the transition is 4.5–5?kcal/mol. These are in excellent agreement with previous NMR measurements (Zhang et al., 2012; Röder et al., 1975). We have further applied this method to other systems that are important in pre-biotic chemistry, including an RNA duplex with unique 2′, 5′-phosphodiester linkages.     

Proteome Folding Kinetics Is Limited by Protein Halflife

How heterogeneous are proteome folding timescales and what physical principles, if any, dictate its limits? We answer this by predicting copy number weighted folding speed distribution – using the native topology – for E.coli and Yeast proteome. E.coli and Yeast proteomes yield very similar distributions with average folding times of 100 milliseconds and 170 milliseconds, respectively. The topology-based folding time distribution is well described by a diffusion-drift mutation model on a flat-fitness landscape in free energy barrier between two boundaries: i) the lowest barrier height determined by the upper limit of folding speed and ii) the highest barrier height governed by the lower speed limit of folding. While the fastest time scale of the distribution is near the experimentally measured speed limit of 1 microsecond (typical of barrier-less folders), we find the slowest folding time to be around seconds (8 seconds for Yeast distribution), approximately an order of magnitude less than the fastest halflife (approximately 2 minutes) in the Yeast proteome. This separation of timescale implies even the fastest degrading protein will have moderately high (96%) probability of folding before degradation. The overall agreement with the flat-fitness landscape model further hints that proteome folding times did not undergo additional major selection pressures – to make proteins fold faster – other than the primary requirement to “sufficiently beat the clock” against its lifetime. Direct comparison between the predicted folding time and experimentally measured halflife further shows 99% of the proteome have a folding time less than their corresponding lifetime. These two findings together suggest that proteome folding kinetics may be bounded by protein halflife.     

An efficient conformational sampling method for homology modeling

The structural refinement of protein models is a challenging problem in protein structure prediction (Moult et al., Proteins 2003;53(Suppl 6):334-339). Most attempts to refine comparative models lead to degradation rather than improvement in model quality, so most current comparative modeling procedures omit the refinement step. However, it has been shown that even in the absence of alignment errors and using optimal templates, methods based on a single template have intrinsic limitations, and that refinement is needed to improve model accuracy. It is thought that failure of current methods originates on one hand from the inaccuracy of the effective free energy functions adopted, which do not represent properly the energetic balance in the native state, and on the other hand from the difficulty to sample the high dimensional and rugged free energy landscape of protein folding, in the search for the global minimum. Here, we address this second issue. We define the evolutionary and vibrational armonics subspace (EVA), a reduced sampling subspace that consists of a combination of evolutionarily favored directions, defined by the principal components of the structural variation within a homologous family, plus topologically favored directions, derived from the low frequency normal modes of the vibrational dynamics, up to 50 dimensions. This subspace is accurate enough so that the cores of most proteins can be represented within 1 A accuracy, and reduced enough so that Replica Exchange Monte Carlo (Hukushima and Nemoto, J Phys Soc Jpn 1996;65:1604-1608; Hukushima et al., Int J Mod Phys C: Phys Comput 1996;7:337-344; Mitsutake et al., J Chem Phys 2003;118:6664-6675; Mitsutake et al., J Chem Phys 2003;118:6676-6688) (REMC) can be applied. REMC is one of the best sampling methods currently available, but its applicability is restricted to spaces of small dimensionality. We show that the combination of the EVA subspace and REMC can essentially solve the optimization problem for backbone atoms in the reduced sampling subspace, even for rather rugged free energy landscapes. Applications and limitations of this methodology are finally discussed.     

Free energy landscape of a biomolecule in dihedral principal component space: sampling convergence and correspondence between structures and minima

Dihedral principal component analysis (dPCA) has recently been developed and shown to display complex features of the free energy landscape of a biomolecule that may be absent in the free energy landscape plotted in principal component space due to mixing of internal and overall rotational motion that can occur in principal component analysis (PCA) [Mu et al., Proteins: Struct Funct Bioinfo 2005;58:45-52]. Another difficulty in the implementation of PCA is sampling convergence, which we address here for both dPCA and PCA using a tetrapeptide as an example. We find that for both methods the sampling convergence can be reached over a similar time. Minima in the free energy landscape in the space of the two largest dihedral principal components often correspond to unique structures, though we also find some distinct minima to correspond to the same structure.     

Thermodynamic and kinetic characterization of a beta-hairpin peptide in solution: an extended phase space sampling by molecular dynamics simulations in explicit water

The folding of the amyloidogenic H1 peptide MKHMAGAAAAGAVV taken from the syrian hamster prion protein is explored in explicit aqueous solution at 300 K using long time scale all-atom molecular dynamics simulations for a total simulation time of 1.1 mus. The system, initially modeled as an alpha-helix, preferentially adopts a beta-hairpin structure and several unfolding/refolding events are observed, yielding a very short average beta-hairpin folding time of approximately 200 ns. The long time scale accessed by our simulations and the reversibility of the folding allow to properly explore the configurational space of the peptide in solution. The free energy profile, as a function of the principal components (essential eigenvectors) of motion, describing the main conformational transitions, shows the characteristic features of a funneled landscape, with a downhill surface toward the beta-hairpin folded basin. However, the analysis of the peptide thermodynamic stability, reveals that the beta-hairpin in solution is rather unstable. These results are in good agreement with several experimental evidences, according to which the isolated H1 peptide adopts very rapidly in water beta-sheet structure, leading to amyloid fibril precipitates [Nguyen et al., Biochemistry 1995;34:4186-4192; Inouye et al., J Struct Biol 1998;122:247-255]. Moreover, in this article we also characterize the diffusion behavior in conformational space, investigating its relations with folding/unfolding conditions.     

An efficient algorithm to compute the landscape of locally optimal RNA secondary structures with respect to the Nussinov-Jacobson energy model.

We make a novel contribution to the theory of biopolymer folding, by developing an efficient algorithm to compute the number of locally optimal secondary structures of an RNA molecule, with respect to the Nussinov-Jacobson energy model. Additionally, we apply our algorithm to analyze the folding landscape of selenocysteine insertion sequence (SECIS) elements from A. Bock (personal communication), hammerhead ribozymes from Rfam (Griffiths-Jones et al., 2003), and tRNAs from Sprinzl's database (Sprinzl et al., 1998). It had previously been reported that tRNA has lower minimum free energy than random RNA of the same compositional frequency (Clote et al., 2003; Rivas and Eddy, 2000), although the situation is less clear for mRNA (Seffens and Digby, 1999; Workman and Krogh, 1999; Cohen and Skienna, 2002),(1) which plays no structural role. Applications of our algorithm extend knowledge of the energy landscape differences between naturally occurring and random RNA. Given an RNA molecule a(1), ... , a(n) and an integer k > or = 0, a k-locally optimal secondary structure S is a secondary structure on a(1), ... , a(n) which has k fewer base pairs than the maximum possible number, yet for which no basepairs can be added without violation of the definition of secondary structure (e.g., introducing a pseudoknot). Despite the fact that the number numStr(k) of k-locally optimal structures for a given RNA molecule in general is exponential in n, we present an algorithm running in time O(n (4)) and space O(n (3)), which computes numStr(k) for each k. Structurally important RNA, such as SECIS elements, hammerhead ribozymes, and tRNA, all have a markedly smaller number of k-locally optimal structures than that of random RNA of the same dinucleotide frequency, for small and moderate values of k. This suggests a potential future role of our algorithm as a tool to detect noncoding RNA genes.     

The effects of nonnative interactions on protein folding rates: theory and simulation

Proteins are minimally frustrated polymers. However, for realistic protein models, nonnative interactions must be taken into account. In this paper, we analyze the effect of nonnative interactions on the folding rate and on the folding free energy barrier. We present an analytic theory to account for the modification on the free energy landscape upon introduction of nonnative contacts, added as a perturbation to the strong native interactions driving folding. Our theory predicts a rate-enhancement regime at fixed temperature, under the introduction of weak, nonnative interactions. We have thoroughly tested this theoretical prediction with simulations of a coarse-grained protein model, by using an off-lattice C(alpha)model of the src-SH3 domain. The strong agreement between results from simulations and theory confirm the nontrivial result that a relatively small amount of nonnative interaction energy can actually assist the folding to the native structure.     

Comparing the folding and misfolding energy landscapes of phosphoglycerate kinase

Partitioning of polypeptides between protein folding and amyloid formation is of outstanding pathophysiological importance. Using yeast phosphoglycerate kinase as model, here we identify the features of the energy landscape that decide the fate of the protein: folding or amyloidogenesis. Structure formation was initiated from the acid-unfolded state, and monitored by fluorescence from 10 ms to 20 days. Solvent conditions were gradually shifted between folding and amyloidogenesis, and the properties of the energy landscape governing structure formation were reconstructed. A gradual transition of the energy landscape between folding and amyloid formation was observed. In the early steps of both folding and misfolding, the protein searches through a hierarchically structured energy landscape to form a molten globule in a few seconds. Depending on the conditions, this intermediate either folds to the native state in a few minutes, or forms amyloid fibers in several days. As conditions are changed from folding to misfolding, the barrier separating the molten globule and native states increases, although the barrier to the amyloid does not change. In the meantime, the native state also becomes more unstable and the amyloid more stable. We conclude that the lower region of the energy landscape determines the final protein structure.     

Heterogeneous folding of the trpzip hairpin: full atom simulation and experiment

The beta-hairpin trpzip2 can be tuned continuously from a two-state folder to folding on a rough energy landscape without a dominant refolding barrier. At high denaturant concentration, this extremely stable peptide exhibits a single apparent "two-state" transition temperature when monitored by different spectroscopic techniques. However, under optimal folding conditions the hairpin undergoes an unusual folding process with three clusters of melting transitions ranging from 15 degrees C to 160 degrees C, as monitored by 12 different experimental and computational observables. We explain this behavior in terms of a rough free energy landscape of the unfolded peptide caused by multiple tryptophan interactions and alternative backbone conformations. The landscape is mapped out by potentials of mean force derived from replica-exchange molecular dynamics simulations. Implications for deducing cooperativity from denaturant titrations, for the origin of folding cooperativity, and for the folding of thermophilic proteins are pointed out. trpzip is an excellent small tunable model system for the glass-like folding transitions predicted by landscape theory.     

Energy barriers, cooperativity, and hidden intermediates in the folding of small proteins

Current theoretical views of the folding process of small proteins (< approximately 100 amino acids) postulate that the landscape of potential mean force (PMF) for the formation of the native state has a funnel shape and that the free energy barrier to folding arises from the chain configurational entropy only. However, recent theoretical studies on the formation of hydrophobic clusters with explicit water suggest that a barrier should exist on the PMF of folding, consistent with the fact that protein folding generally involves a large positive activation enthalpy at room temperature. In addition, high-resolution structural studies of the hidden partially unfolded intermediates have revealed the existence of non-native interactions, suggesting that the correction of the non-native interactions during folding should also lead to barriers on PMF. To explore the effect of a PMF barrier on the folding behavior of proteins, we modified Zwanzig's model for protein folding with an uphill landscape of PMF for the formation of transition states. We found that the modified model for short peptide segments can satisfy the thermodynamic and kinetic criteria for an apparently two-state folding. Since the Levinthal paradox can be solved by a stepwise folding of short peptide segments, a landscape of PMF with a locally uphill search for the transition state and cooperative stabilization of folding intermediates/native state is able to explain the available experimental results for small proteins. We speculate that the existence of cooperative hidden folding intermediates in small proteins could be the consequence of the highly specific structures of the native state, which are selected by evolution to perform specific functions and fold in a biologically meaningful time scale.     

Determination of barrier heights and prefactors from protein folding rate data

We determine both barrier heights and prefactors for protein folding by applying constraints determined from experimental rate measurements to a Kramers theory for folding rate. The theoretical values are required to match the experimental values at two conditions of temperature and denaturant that induce the same stability. Several expressions for the prefactor in the Kramers rate equation are examined: a random energy approximation, a correlated energy approximation, and an approximation using a single Arrhenius activation energy. Barriers and prefactors are generally found to be large as a result of implementing this recipe, i.e., the folding landscape is cooperative and smooth. Interestingly, a prefactor with a single Arrhenius activation energy admits no formal solution.     

The folding landscape of an alpha-lytic protease variant reveals the role of a conserved beta-hairpin in the development of kinetic stability

Most secreted bacterial proteases, including alpha-lytic protease (alphaLP), are synthesized with covalently attached pro regions necessary for their folding. The alphaLP folding landscape revealed that its pro region, a potent folding catalyst, is required to circumvent an extremely large folding free energy of activation that appears to be a consequence of its unique unfolding transition. Remarkably, the alphaLP native state is thermodynamically unstable; a large unfolding free energy barrier is solely responsible for the persistence of its native state. Although alphaLP folding is well characterized, the structural origins of its remarkable folding mechanism remain unclear. A conserved beta-hairpin in the C-terminal domain was identified as a structural element whose formation and positioning may contribute to the large folding free energy barrier. In this article, we characterize the folding of an alphaLP variant with a more favorable beta-hairpin turn conformation (alphaLP(beta-turn)). Indeed, alphaLP(beta-turn) pro region-catalyzed folding is faster than that for alphaLP. However, instead of accelerating spontaneous folding, alphaLP(beta-turn) actually unfolds more slowly than alphaLP. Our data support a model where the beta-hairpin is formed early, but its packing with a loop in the N-terminal domain happens late in the folding reaction. This tight packing at the domain interface enhances the kinetic stability of alphaLP(beta-turn), to nearly the same degree as the change between alphaLP and a faster folding homolog. However, alphaLP(beta-turn) has impaired proteolytic activity that negates the beneficial folding properties of this variant. This study demonstrates the evolutionary limitations imposed by the simultaneous optimization of folding and functional properties.     

Analyzing the effect of homogeneous frustration in protein folding

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a C_α structure‐based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well‐separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non‐native contact interactions in different folding scenarios. These findings strongly correlate with the protein free‐energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins.Proteins 2013; 81:1727–1737. © 2013 Wiley Periodicals, Inc.     

Mapping the transition state of the WW domain beta-sheet

The folding kinetics of a three-stranded antiparallel beta-sheet (WW domain) have been measured by temperature jump relaxation. Folding and activation free energies were determined as a function of temperature for both the wild-type and the mutant domain, W39F, which modifies the beta(2)-beta(3) hydrophobic interface. The folding rate decreases at higher temperatures as a result of the increase in the activation free energy for folding. Phi-Values were obtained for thermal perturbations allowing the primary features of the folding free energy surface to be determined. The results of this analysis indicate a significant shift from an "early" (Phi(T)=0. 4) to a "late" (Phi(T)=0.8) transition state with increasing temperature. The temperature-dependent Phi-value analysis of the wild-type WW domain and of its more stable W39F hydrophobic cluster mutant reveals little participation of residue 39 in the transition state at lower temperature. As the temperature is raised, hydrophobic interactions at the beta(2)-beta(3) interface gain importance in the transition state and the barrier height of the wild-type, which contains the larger tryptophan residue, increases more slowly than the barrier height of the mutant.     

Calculations of free energy profiles for the staphylococcal nuclease catalyzed reaction

Calculations of the free energy profile for the first two (rate-limiting) steps of the staphylococcal nuclease catalyzed reaction are reported. The calculations are based on the empirical valence bond method in combination with free energy perturbation molecular dynamics simulations. The calculated activation free energy is in good agreement with experimental kinetic data, and the catalytic effect of the enzyme is reproduced without any arbitrary adjustment of parameters. The enormous reduction of the activation barrier (relative to the reference reaction in water) appears to be largely associated with the strong electrostatic effect of the Ca2+ ion and the two arginine residues in the active site. This favorable electrostatic environment reduces the cost of the general-base catalysis step by almost 15 kcal/mol (by stabilizing the OH- nucleophile) and then stabilizes the developing negative charge on the 5'-phosphate group in the second step of the reaction by about 19 kcal/mol. The basic features of the originally postulated enzyme mechanism (Cotton et al., 1979) are found to be compatible with the observed activation free energy. However, the proposed modification of the mechanism (Sepersu et al., 1987), in which Arg 87 interacts only with the pentacoordinated transition state, is supported by the simulations. Further calculations on the D21E mutant also give results in good agreement with kinetic data.     

Temperature dependence of the free energy landscape of the src-SH3 protein domain

The temperature dependence of the free energy landscape of the src-SH3 protein domain is investigated through fully atomic simulations in explicit solvent. Simulations are performed above and below the folding transition temperature, enabling an analysis of both protein folding and unfolding. The transition state for folding and unfolding, identified from the free energy surfaces, is found to be very similar, with structure in the central hydrophobic sheet and little structure throughout the rest of the protein. This is a result of a polarized folding (unfolding) mechanism involving early formation (late loss) of the central hydrophobic sheet at the transition state. Unfolding simulations map qualitatively well onto low-temperature free energy surfaces but appear, however, to miss important features observed in folding simulations. In particular, details of the folding mechanism involving the opening and closing of the hydrophobic core are not captured by unfolding simulations performed under strongly denaturing conditions. In addition, free energy surfaces at high temperatures do not display a desolvation barrier found at lower temperatures, involving the expulsion of water molecules from the hydrophobic core.     

Reading the three-dimensional structure of lattice model-designed proteins from their amino acid sequence.

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the detailed, biological active, three-dimensional structure of a protein whose sequence is known. Using insight obtained from lattice model simulations of the folding of small proteins (fewer than 100 residues), in particular of the fact that this phenomenon is essentially controlled by conserved contacts (Mirny et al., Proc Natl Acad Sci USA 1995;92:1282) among (few) strongly interacting ("hot") amino acids (Tiana et al., J Chem Phys 1998;108:757-761), which also stabilize local elementary structures formed early in the folding process and leading to the (postcritical) folding core when they assemble together (Broglia et al., Proc Natl Acad Sci USA 1998;95:12930, Broglia & Tiana, J Chem Phys 2001;114:7267), we have worked out a successful strategy for reading the three-dimensional structure of lattice model-designed proteins from the knowledge of only their amino acid sequence and of the contact energies among the amino acids.     

How cooperative are protein folding and unfolding transitions?

A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two‐state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non‐cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier‐less “downhill” folding, as well as for continuous “uphill” unfolding transitions, indicate that gradual non‐cooperative processes may be ubiquitous features on the free energy landscape of protein folding.     

154 Protein folding and binding funnels: a common driving force and a common mechanism

Under the free energy landscape theory, both the protein-folding and protein–ligand binding processes are driven by the decrease in total Gibbs free energy of the protein-solvent or protein–ligand-solvent system, which involves the non-complementary changes between the entropy and enthalpy, ultimately leading to a global free energy minimization of these thermodynamic systems (Ji & Liu, 2011; Liu et al., 2012; Yang, Ji & Liu, 2012). In the case of protein folding, the lowering of the system free energy coupled with the gradual reduction in conformational degree of freedom of the folding intermediates determines that the shape of the free energy landscape for protein folding must be funnel-like (Dill & Chan, 1997), rather than non-funneled shapes (Ben-Naim, 2012). In the funnel-like free energy landscape, protein folding can be viewed as going down the hill via multiple parallel routes from a vast majority of individual non-native states on surface outside the funnel to the native states located around the bottom of the funnel. The first stage of folding, i.e. the rapid hydrophobic collapse process, is driven by the solvent entropy maximization. Concretely, the water molecules squeeze and sequestrate the hydrophobic amino acid side chains within the interior of the folding intermediates while exposing the polar and electrostatically charged side chains on the intermediate surface so as to minimize the solvent-accessible surface area of the solute and thus, the minimal contacts between the folding intermediates and the water molecules. This will maximize the entropy of the solvent, thus contributing substantially to lowering of the system free energy due to an absolute advantage of the solvent in both quantity and mass (Yang, Ji & Liu, 2012). The resulting molten globule states (Ohgushi & Wada, 1983), within which a few transient secondary structural components and tertiary contacts have been formed but many native contacts or close residue–residue interactions has yet to form, need to be further sculptured into the native states. This is a relatively slow “bottleneck” process because the competitive interactions between protein residues within the folding intermediates and between residues and water molecules may repeat many rounds to accumulate a large enough number of stable noncovalent bonds capable of counteracting the conformational entropy loss of the intermediates, thus putting this bottleneck stage under the enthalpy control (i.e. negative enthalpy change), contributing further to the lowering of the system free energy. Although the protein–ligand association occurs around the rugged bottom of the free energy landscape, the exclusion of water from the binding interfaces and the formation of noncovalent bonds between the two partners can still lower the system free energy. In conjunction with the loss of the rotational and translational degrees of freedom of the two partners as well as the loss of the conformational entropy of the protein, these processes could merge, downwards expand, and further narrow the free energy wells within which the protein–ligand binding process takes place, thereby making them look like a funnel, which we term the binding funnel. In this funnel, the free energy downhill process follows a similar paradigm to the protein-folding process. For example, if the initial collisions/contacts occur between the properly complementary interfaces of the protein and ligand, a large amount of water molecules (which usually form a water network around the solute surface) will be displaced to suit the need for maximizing the solvent entropy. This process is similar to that of the hydrophobic collapse during protein folding, resulting in a loosely associated protein–ligand complex that needs also to be further adapted into a tight complex, i.e. the second step which is mainly driven by the negative enthalpy change through intermolecular competitive interactions to gradually accumulate the noncovalent bonds and ultimately, to stabilize the complex at a tightly bound state. Taken together, we conclude that whether in the protein-folding or in the protein–ligand binding process, both the entropy-driven first step and the enthalpy-driven second step contribute to the lowering of the system free energy, resulting in the funnel-like folding or binding free energy landscape.     

Exhaustive mutagenesis in silico: multicoordinate free energy calculations on proteins and peptides

We have extended and applied a multicoordinate free energy method, chemical Monte Carlo/Molecular Dynamics (CMC/MD), to calculate the relative free energies of different amino acid side-chains. CMC/MD allows the calculation of the relative free energies for many chemical species from a single free energy calculation. We have previously shown its utility in host:guest chemistry (Pitera and Kollman, J Am Chem Soc 1998;120:7557-7567)1 and ligand design (Eriksson et al., J Med Chem 1999;42:868-881)2, and here demonstrate its utility in calculations of amino acid properties and protein stability. We first study the relative solvation free energies of N-methylated and acetylated alanine, valine, and serine amino acids. With careful inclusion of rotameric states, internal energies, and both the solution and vacuum states of the calculation, we calculate relative solvation free energies in good agreement with thermodynamic integration (TI) calculations. Interestingly, we find that a significant amount of the unfavorable solvation of valine seen in prior work (Sun et al., J Am Chem Soc 1992;114:6798-6801)3 is caused by restraining the backbone in an extended conformation. In contrast, the solvation free energy of serine is calculated to be less favorable than expected from experiment, due to the formation of a favorable intramolecular hydrogen bond in the vacuum state. These monomer calculations emphasize the need to accurately consider all significant conformations of flexible molecules in free energy calculations. This development of the CMC/MD method paves the way for computations of protein stability analogous to the biochemical technique of "exhaustive mutagenesis." We have carried out just such a calculation at position 133 of T4 lysozyme, where we use CMC/MD to calculate the relative stability of eight different side-chain mutants in a single free energy calculation. Our T4 calculations show good agreement with the prior free energy calculations of Veenstra et al. (Prot Eng 1997;10:789-807)4 and excellent agreement with the experiments of Mendel et al. (Science 1992;256:1798-1802).