The protein folding network

The conformation space of a 20 residue antiparallel beta-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Snapshots saved along the trajectory are grouped according to secondary structure into nodes of the network and the transitions between them are links. The conformation space network describes the significant free energy minima and their dynamic connectivity without requiring arbitrarily chosen reaction coordinates. As previously found for the Internet and the World-Wide Web as well as for social and biological networks, the conformation space network is scale-free and contains highly connected hubs like the native state which is the most populated free energy basin. Furthermore, the native basin exhibits a hierarchical organization, which is not found for a random heteropolymer lacking a predominant free-energy minimum. The network topology is used to identify conformations in the folding transition state (TS) ensemble, and provides a basis for understanding the heterogeneity of the TS and denatured state ensemble as well as the existence of multiple pathways.     

Molecular Dynamics/Free Energy Perturbation Studies of the Thermostable V74I Mutant of Ribonuclease HI

Abstract

Recent site-directed mutagenesis and thermodynamic studies have shown that the V74I mutant of Escherichia coli ribonuclease HI (RNase HI) is more stable than the wild type protein [Ishikawa et al., Biochemistry 32, 6171 (1993)]. In order to clarify the stabilization mechanism of this mutant, we calculated the free energy change due to the mutation Val 74→Ile in both the native and denatured states by free energy perturbations based on molecular dynamics (MD) simulations. We carried out inclusive MD simulations for the protein in water; i.e., fully solvated, no artificial constraints applied, and all long-range Coulomb interactions included. We found that the free energy of the mutant increased slightly relative to the wild type, in the native state by 1.60 kcal/mol, and in the denatured state by 2.25 kcal/mol. The unfolding free energy increment of the mutant (0.66 ± 0.19 kcal/mol) was in good agreement with the experimental value (0.6 kcal/mol). The hysteresis error in the free energy calculations, i.e., forward and reverse perturbations, was only ±0.19 kcal/mol. These results show that the V74I mutant is stabilized relative to the wild type by the increased free energy of the denatured state and not by a decrease in the free energy of the native state as had been proposed earlier based on the mutant X-ray structure. It was found that the stabilization was caused by a loss of solvation energy in the mutant denatured state and not by improved packing interactions inside the native protein.     

Kinetic analysis of molecular dynamics simulations reveals changes in the denatured state and switch of folding pathways upon single-point mutation of a beta-sheet miniprotein

The effects of a single-point mutation on folding thermodynamics and kinetics are usually interpreted by focusing on the native structure and the transition state. Here, the entire conformational spaces of a 20-residue three-stranded antiparallel beta-sheet peptide (double hairpin) and of its single-point mutant W10V are sampled close to the melting temperature by equilibrium folding-unfolding molecular dynamics simulations for a total of 40 micros. The folded state as well as the most populated free energy basins in the denatured state are isolated by grouping conformations according to fast relaxation at equilibrium. Such kinetic analysis provides more detailed and useful information than a simple projection of the free energy. The W10V mutant has the same native structure as the wild type peptide, and similar folding rate and stability. In the denatured state, the N-terminal hairpin is about 20% more structured in W10V than the wild type mainly because of van der Waals interactions. Notably, the W10V mutation influences also the van der Waals energy at the transition state ensemble causing a shift in the ratio of fluxes between two different transition state regions on parallel folding pathways corresponding to nucleation at either of the two beta-hairpins. Previous experimental studies have focused on the effects of denaturant-dependent or temperature-dependent changes in the structure of the denatured state. The atomistic simulations show that a single-point mutation in the central strand of a beta-sheet peptide results in remarkable changes in the topography of the denatured state ensemble. These changes modulate the relative accessibility of parallel folding pathways because of kinetic partitioning of the denatured state. Therefore, the observed dependence of the folding process on the starting ensemble raises questions on the biological significance of in vitro folding studies under strongly denaturing conditions.     

Structural dynamics, stability and folding of proteins

The present concepts of protein folding in vitro are reviewed. According to these concepts, amino acid sequence of protein, which has appeared a result of evolutionary selection, determines the native structure of protein, the pathway of protein folding, and the existence of free energy barrier between native and denatured states of protein. The latter means that protein macromolecule can exist in either native or denatured state. And all macromolecules in the native state are identical but for structural fluctuations due to Brownian motion of their atoms. Identity of all molecules in native state is of primary importance for their correct functioning. The dependence of protein stability, which is measured as the difference between free energy of protein in native and denatured states, on temperature and denaturant concentration is discussed. The modern approaches characterizing transition state and nucleation are regarded. The role of intermediate and misfolded states in amorphous aggregate and amyloid fibril formation is discussed.     

Dependence of protein stability on the structure of the denatured state: free energy calculations of I56V mutation in human lysozyme.

Free energy calculations were carried out to understand the effect of the I56V mutation of human lysozyme on its thermal stability. In the simulation of the denatured state, a short peptide including the mutation site in the middle is employed. To study the dependence of the stability on the denatured-state structure, five different initial conformations, native-like, extended, and three random-coil-like conformations, were examined. We found that the calculated free energy difference, DeltaDeltaGcal, depends significantly on the structure of the denatured state. When native-like structure is employed, DeltaDeltaGcal is in good agreement with the experimental free energy difference, DeltaDeltaGexp, whereas in the other four models, DeltaDeltaGcal differs sharply from DeltaDeltaGexp. It is therefore strongly suggested that the structure around the mutation site takes a native-like conformation rather than an extended or random-coil conformation. From the free energy component analysis, it has been shown that free energy components originating from Lennard-Jones and covalent interactions dominantly determine DeltaDeltaGcal. The contribution of protein-protein interactions to the nonbonded component of DeltaDeltaGcal is about the same as that from protein-water interactions. The residues that are located in a hydrophobic core (F3, L8, Y38, N39, T40, and I89) contribute significantly to the nonbonded free energy component of DeltaDeltaGcal. We also propose a general computational strategy for the study of protein stability that is equally conscious of the denatured and native states.     

Electrostatic interactions in the denatured state and in the transition state for protein folding: effects of denatured state interactions on the analysis of transition state structure

The development of electrostatic interactions during the folding of the N-terminal domain of the ribosomal protein L9 (NTL9) is investigated by pH-dependent rate equilibrium free energy relationships. We show that Asp8, among six acidic residues, is involved in non-native, electrostatic interactions with K12 in the transition state for folding as well as in the denatured state. The perturbed native state pK(a) of D8 (pK(a) = 3.0) appears to be maintained through non-native interactions in both the transition state and the denatured state. Mutational effects on the stability of the transition state for protein (un)folding are often analyzed in respect to change in ground states. Thus, the interpretation of transition state analysis critically depends on an understanding of mutational effects on both the native and denatured state. Increasing evidence for structurally biased denatured states under physiological conditions raises concerns about possible denatured state effects on folding studies. We show that the structural interpretation of transition state analysis can be altered dramatically by denatured state effects.     

Study of the compact denatured state of a protein by molecular dynamics simulation]

The native state can be considered as a unique conformation of the protein molecule with the lowest free energy of residue contacts. In this case, all other conformations correspond to the denatured state. The degree of their compactness varies significantly. Under folding conditions, the compact denatured state rather than the random coil is in equilibrium with native protein. The balance between the main forces of protein folding, the solvophobic interactions and conformational entropy, suggests that some properties of the compact denatured state are close to those of native protein, whereas other properties are close to those of the random coil. To investigate the molecular structure of the compact denatured state, the method of molecular dynamics simulation seems to be very useful.     

The osmophobic effect: natural selection of a thermodynamic force in protein folding

Intracellular organic osmolytes are present in certain organisms adapted to harsh environments and these osmolytes protect intracellular macromolecules against the denaturing environmental stress. In natural selection of organic osmolytes as protein stabilizers, it appears that the osmolyte property selected for is the unfavorable interaction between the osmolyte and the peptide backbone, a solvophobic thermodynamic force that we call the osmophobic effect. Because the peptide backbone is highly exposed to osmolyte in the denatured state, the osmophobic effect preferentially raises the free energy of the denatured state, shifting the equilibrium in favor of the native state. By focusing the solvophobic force on the denatured state, the native state is left free to function relatively unfettered by the presence of osmolyte. The osmophobic effect is a newly uncovered thermodynamic force in nature that complements the well-recognized hydrophobic interactions, hydrogen bonding, electrostatic and dispersion forces that drive protein folding. In organisms whose survival depends on the intracellular presence of osmolytes that can counteract denaturing stresses, the osmophobic effect is as fundamental to protein folding as these well-recognized forces.     

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.     

Mechanisms of the multiphasic kinetics in the folding and unfolding of globular proteins

The multiphasic kinetics of the protein folding and unfolding processes are examined for a “cluster model” with only two thermodynamically stable macroscopic states, native (N) and denatured (D), which are essentially distributions of microscopic states. The simplest kinetic schemes consistent with the model are: N-(fast) → I-(slow) → D for unfolding and N ← (fast)-D₂ ← (slow)-D₁ for refolding. The fast phase during the unfolding process can be visualized as the redistribution of the native population N to I within its free energy valley. Then, this population crosses over the free energy barrier to the denatured state D in the slow phase. Therefore, the macrostate I is a kinetic intermediate which is not stable at equilibrium. For the refolding process, the initial equilibrium distribution of the denatured state D appears to be separated into D₁ and D₂ in the final condition because of the change in position of the free energy barrier. The fast refolding species D₂ is due to the “leak” from the broadly distributed D state, while the rest is the slow refolding species D₁, which must overpass the free energy barrier to reach N. At an early stage of the folding process the amino acid chain is considered to be composed of several locally ordered regions, which we call clusters, connected by random coil chain parts. Thus, the denatured state contains different sizes and distributions of clusters depending on the external condition. A later stage of the folding process is the association of smaller clusters. The native state is expressed by a maximum-size cluster with possible fluctuation sites reflecting this association. A general discussion is given of the correlation between the kinetics and thermodynamics of proteins from the overall shape of the free energy function. The cluster model provides a conceptual link between the folding kinetics and the structural patterns of globular proteins derived from the X-ray crystallographic data.     

Statistical mechanics of protein folding by cluster distance geometry

This is our second type of model for protein folding where the configurational parameters and the effective potential energy function are chosen in such a way that all conformations are described and the canonical partition function can be evaluated analytically. Structure is described in terms of distances between pairs of sequentially contiguous blocks of eight residues, and all possible conformations are grouped into 71 subsets in terms of bounds on these distances. The energy is taken to be a sum of pairwise interactions between such blocks. The 210 energy parameters were adjusted so that the native folds of 32 small proteins are favored in free energy over the denatured state. We then found 146 proteins having negligible sequence similarity to any of the training proteins, yet the free energy of the respective correct native states were favored over the denatured state.     

Direct comparison of experimental and calculated folding free energies for hydrophobic deletion mutants of chymotrypsin inhibitor 2: free energy perturbation calculations using transition and denatured states from molecular dynamics simulations of unfolding

Previous molecular dynamics (MD) simulations of thermal denaturation of chymotrypsin inhibitor 2 (CI2) have provided transition-state models in good agreement with experiment. Unfortunately, however, the comparisons have been necessarily indirect. The simulations have provided detailed structural information but not energetics, while from experiment, structure is inferred from a ratio of free energy changes upon mutation (Phi values). Here, direct comparison with experimental free energies is obtained by performing free energy perturbation calculations of hydrophobic deletion mutants of CI2 using transition- and denatured-state structures from various denaturation MD simulations. The agreement between the calculated and experimental DeltaDeltaG and Phi values is quite good (R = 0.8-0.9). In addition, given the availability of realistic atomic models for the denatured protein, the common approach of using small peptides to represent the denatured state in stability calculations can now be evaluated. To this end, two different extended tripeptide models were used: one using the sequence from the protein with the residue to be mutated in the center and the other with this residue surrounded by Ala residues. The results for the two peptides agree neither with one another nor with the different full-length denatured-state models, which do provide results in good agreement with experiment. This finding is noteworthy because the denatured state of CI2 is very disrupted with little residual structure, such that the peptides might have been expected to serve as reasonable models. Overall the calculations presented here validate our previous MD-generated transition- and denatured-state models and therefore the simulated unfolding pathways and their relevance to refolding.     

Protein adsorption at solid-liquid interfaces: Part IV--Effects of different solid-liquid systems and various neutral salts.

Adsorption isotherms of BSA at the solid-water interfaces have been studied as a function of protein concentration, ionic strength of the medium, pH and temperature using silica, barium sulphate, carbon, alumina, chromium, ion-exchange resins and sephadex as solid interfaces. In most cases, isotherms for adsorption of BSA attained the state of adsorption saturation. In the presence of barium sulphate, carbon and alumina, two types in the isotherms are observed. Adsorption of BSA is affected by change in pH, ionic strength and temperature of the medium. In the presence of metallic chromium, adsorbed BSA molecules are either denatured or negatively adsorbed at the metallic interface. Due to the presence of pores in ion-exchange resins, adsorption of BSA is followed by preferential hydration on resin surfaces in some cases. Sometimes two steps of isotherms are also observed during adsorption of BSA on the solid resins in chloride form. Adsorption of BSA, beta-lactoglobulin, gelatin, myosin and lysozyme is negative on Sephadex surface due to the excess adsorption of water by Sephadex. The negative adsorption is significantly affected in the presence of CaCl2, KSCN, LiCl, Na2SO4, NaI, KCl and urea. The values of absolute amounts of water and protein, simultaneously adsorbed on the surface of different solids, have been evaluated in some cases on critical thermodynamic analysis. The standard free energies (delta G0) of excess positive and negative adsorption of the protein per square meter at the state of monolayer saturation have been calculated using proposed universal scale of thermodynamics. The free energy of adsorption with reference to this state is shown to be strictly comparable to each other. The magnitude of standard free energy of transfer (delta G0B) of one mole of protein or a protein mixture at any type of physiochemical condition and at any type of surface is observed to be 38.5 kJ/mole.     

Charge-charge interactions influence the denatured state ensemble and contribute to protein stability

Several recent studies have shown that it is possible to increase protein stability by improving electrostatic interactions among charged groups on the surface of the folded protein. However, the stability increases are considerably smaller than predicted by a simple Coulomb's law calculation, and in some cases, a charge reversal on the surface leads to a decrease in stability when an increase was predicted. These results suggest that favorable charge-charge interactions are important in determining the denatured state ensemble, and that the free energy of the denatured state may be decreased more than that of the native state by reversing the charge of a side chain. We suggest that when the hydrophobic and hydrogen bonding interactions that stabilize the folded state are disrupted, the unfolded polypeptide chain rearranges to compact conformations with favorable long-range electrostatic interactions. These charge-charge interactions in the denatured state will reduce the net contribution of electrostatic interactions to protein stability and will help determine the denatured state ensemble. To support this idea, we show that the denatured state ensemble of ribonuclease Sa is considerably more compact at pH 7 where favorable charge-charge interactions are possible than at pH 3, where unfavorable electrostatic repulsion among the positive charges causes an expansion of the denatured state ensemble. Further support is provided by studies of the ionic strength dependence of the stability of charge-reversal mutants of ribonuclease Sa. These results may have important implications for the mechanism of protein folding.     

Kinetic analysis of local structure formations in protein folding

The protein folding process is described by a cluster model based on the assumption that local structures or clusters are formed at an early stage in different regions of the polypeptide chain. Possible local structural elements in a globular protein are helices, bends, and hydrophobic cores whose formation is presumably determined by the interaction with the environment. Thus the tendency of local structure formation is expressed by a surface free energy of the cluster, which is assigned to the interface between the cluster and its environment. The probability of finding the chain of N residues with k clusters and m residues in the cluster is represented by a cluster distribution map. The cluster model exhibits a distinct two-state-like equilibrium transition, which can be seen on this map as well-separated native and denatured populations at the midpoint of the transition. The native population is localized at k ≈ 1 and m ≈ N, while the position of the denatured population can vary significantly depending on the surface free energy of the cluster. If the surface free energy is strong, the denatured population is localized near k = 0 and m = 0. On the other hand, if the surface free energy is weak, the denatured population is localized at high k and m values. The dynamics of the cluster model are treated as a stochastic process involving the transition from a state (k,m) to one of its six neighbors. The transition probability for each transition is determined by the free energy difference between two states; thus no activation process is assumed. However, the conversion of the two macrostates, native and denatured populations, involves the free energy activation due to the cooperative interaction of the macrosystem. The dynamics are analyzed by following the time evolution of the population profile on the cluster distribution map. Kinetic schemes are proposed to describe the multistep mechanism of protein folding and unfolding.     

Dimensions,energetics, and denaturant effects of the protein unstructured state

Determining the energetics of the unfolded state of a protein is essential for understanding the folding mechanics of ordered proteins and the structure–function relation of intrinsically disordered proteins. Here, we adopt a coil‐globule transition theory to develop a general scheme to extract interaction and free energy information from single‐molecule fluorescence resonance energy transfer spectroscopy. By combining protein stability data, we have determined the free energy difference between the native state and the maximally collapsed denatured state in a number of systems, providing insight on the specific/nonspecific interactions in protein folding. Both the transfer and binding models of the denaturant effects are demonstrated to account for the revealed linear dependence of inter‐residue interactions on the denaturant concentration, and are thus compatible under the coil‐globule transition theory to further determine the dimension and free energy of the conformational ensemble of the unfolded state. The scaling behaviors and the effective θ‐state are also discussed.     

Thermodynamic characterization of cytochrome c at low pH. Observation of the molten globule state and of the cold denaturation process.

Several reports have pointed out the existence of intermediate states (both kinetic and equilibrium intermediate) between the native and the denatured states. The molten globule state, a compact intermediate state in which the secondary structure is formed but the tertiary structure fluctuates considerably, is currently being studied intensively because of its possible implication in the folding process of several proteins. We have examined the thermal stability of horse cytochrome c at low pH between 2.0 and 3.2 and different potassium chloride concentrations by absorbance of the Soret band, far and near-ultraviolet circular dichroism (u.v. c.d.) and tryptophan fluorescence using a multidimensional spectrophotometer. The concentration of potassium chloride ranged from 0 M to 0.5 M. The experimental thermal denaturation curves show that: (1) the helical content of cytochrome c remains stable at higher temperature when the concentration of salt is increased; whereas (2) the extent of ordering of the tertiary structure is weakly dependent on salt concentration; and (3) for cytochrome c, the stabilization of the molten globule state is induced by the binding of anions. Other salts such as NaCl, LiCl, potassium ferricyanide (K3Fe(CN)6) and Na2SO4 may also be used to stabilize the molten globule state. The thermodynamic analysis of the denaturation curves of c.d. at 222 nm and c.d. at 282 nm shows that, whereas a two-state (native and denatured) transition is observed at low-salt concentration, the far and near-u.v. c.d. melting curves of cytochrome c do not coincide with each other at high-salt concentration, and a minimum of three different thermodynamic states (IIb, intermediate or IIc, and denatured) is necessary to achieve a sufficient analysis. The intermediate state (called IIc) is attributed to the molten globule state because of its high secondary structure content and the absence of tertiary structure. Therefore, at low pH, cytochrome c is present in at least four states (native, IIb, IIc and denatured) depending on the salt concentration and temperature. The thermodynamic parameters, i.e. the Gibbs free energy differences (delta G), the enthalpy differences (delta H), the midpoint temperatures (Tm) of the transition (IIb in equilibrium intermediate (IIc in equilibrium denatured) are determined. We also give estimates of the heat capacity differences (delta Cp) from the temperature dependence of the enthalpy differences. The enthalpy change and the heat capacity difference of the IIc in equilibrium denatured transition are non-zero. The number of charges (protons or chloride anions) released upon transitions are determined by analysing the pH and chloride anion concentration dependence of the Gibbs free energy.(ABSTRACT TRUNCATED AT 400 WORDS)     

Stability analysis for the cavity-filling mutations of the Myb DNA-binding domain utilizing free-energy calculations

We have analyzed the effect of cavity-filling mutations on protein stability by means of free-energy calculations based on molecular dynamics simulations to identify the factors contributing to stability changes caused by the mutations. We have studied the DNA-binding domain of Myb, which has a cavity in one of three homologous repeat units, and analyzed a series of mutations with nonnatural and natural amino acids at a single site, which change the size of the cavity. We found that the calculated free-energy changes caused by the mutations are in excellent agreement with experimental data (correlation coefficient 0.98). The free-energy changes in the native and denatured states were independently compared with the unfolding free-energy change (deltadeltaG) and cavity-volume changes (deltaV), and it was found that deltadeltaG and deltaV correlate with the native-state free-energy changes but not with the denatured-state free-energy changes. Further analyses in terms of enthalpy and entropy show that compensation between entropy and enthalpy occurs in the denatured state but not in the native state. The main contribution to the native-state free energy was found to be van der Waals interactions associated with the cavity. We estimate that the decrease in free energy per methylene group, which results from filling the cavity, is about 2 to 3 kcal/mol. These results suggest that the stabilization of a protein by cavity-filling mutations be determined primarily by the free energy associated with the cavity volume in the native state.     

Perchlorate-induced conformational transition of Staphylococcal nuclease: evidence for an equilibrium unfolding intermediate

The sodium perchlorate-induced conformational transition of Staphylococcal nuclease has been monitored by both circular dichroism (CD) and fluorescence spectroscopy. The perchlorate-induced transition is cooperative as observed by both spectroscopic signals. However, the protein loses only about one-third of its native far-UV CD signal at high perchlorate concentrations, indicating that a significant amount of secondary structure remains in the post-transition state. The remaining CD signal can be further diminished in a cooperative manner by the addition of the strong denaturant, urea. Near-UV CD spectra clearly show that the protein loses its tertiary structure in the perchlorate-induced denatured state. The perchlorate-induced transition curves were fit to the standard two-state model and the standard free energy change and m value of the transition are 2.3kcal/mol and 1.8kcal/(molM), respectively. By comparison, the urea-induced unfolding of Staphylococcal nuclease (in the absence of perchlorate) yields an unfolding free energy change, DeltaG(0,un), of 5.6kcal/mol and an m value of 2.3kcal/(molM). Thus, the thermodynamic state obtained in the post-transition region of perchlorate-induced conformation transition has a significantly lower free energy change, a high content of secondary structure, and diminished tertiary structure. These results suggest that the perchlorate-induced denatured state is a partially folded equilibrium state. Whether this intermediate is relevant to the folding/unfolding path under standard conditions is unknown at this time.     

Structural and energetic requirements for a second binding site at the dimeric β-lactoglobulin interface

Through experimental and theoretical approaches, it has been shown that bovine β-lactoglobulin (βlg) uses its hydrophobic cavity or calyx as the primary binding site for hydrophobic molecules, whereas the existence of a second ligand binding site at the dimeric interface has only been structurally identified for vitamin D3 (VD3). This binding exists even in the thermally denatured state, suggesting the prevalence of this secondary site. Although crystallographic experiments have suggested that VD3 can bind to both monomeric and dimeric states without significant structural differences, theoretical and experimental reports have proposed some structural requirements. Thus, in this study, based on known experimental data, the dynamic interaction of VD3 with the monomeric or dimeric forms of βlg was investigated through a protocol combining blind docking and 2 microsecond molecular dynamics simulations coupled with binding free energy and per-residue binding free energy decomposition analyses using the Molecular Mechanics Generalized Born Surface Area approach. Binding free energy calculations allowed us to estimate the energetic differences of coupling VD3 at the calyx and the dimeric interface for the monomeric or dimeric state, revealing that the dimeric structure is required to form a stable complex with VD3 at the dimeric interface. This also has an important impact on the dimerization process, whereas although the monomeric state also forms a stable complex with VD3 at the dimeric interface, the incorporation of the entropy component contributed to producing a marginally favorable binding free energy. Finally, the per-residue decomposition analysis provided energetic information about the most relevant residues in stabilizing the different systems.