Free-energy barriers in MbCO rebinding

The rebinding of CO to myoglobin (Mb) from locations around the active site is studied using a combination of molecular dynamics and stochastic simulations for native and L29F mutant Mb. The interaction between the dissociated ligand and the protein environment is described by the recently developed fluctuating three-point charge model for the CO molecule. Umbrella sampling along trajectories, previously found to sample the binding site (B) and the Xe4 pocket, is used to construct free-energy profiles for the ligand escape. On the basis of the Smoluchowski equation, the relaxation of different initial population distributions is followed in space and time. For native Mb at room temperature, the calculated rebinding times are in good agreement with experimental values and give an inner barrier of 4.3 kcal/mol between the docking site B (Mb...CO) and the A state (bound MbCO), compared to an effective barrier, Heff, of 4.5 kcal/mol and barriers into the majority conformation A1 and the minority conformation A3 of 2.4 and 4.3 kcal/mol, respectively. In the case of the L29F mutant, the free-energy surface is flatter and the dynamics is much more rapid. As was found in experiment, escape to the Xe4 pocket is facile for L29F whereas, for native Mb, the barriers to this site are larger. At lower temperatures, the rebinding dynamics is delayed by orders of magnitude also due to increased barriers between the docking sites.     

Temperature-dependent studies of NO recombination to heme and heme proteins

The rebinding kinetics of NO to the heme iron of myoglobin (Mb) is investigated as a function of temperature. Below 200 K, the transition-state enthalpy barrier associated with the fastest (approximately 10 ps) recombination phase is found to be zero and a slower geminate phase (approximately 200 ps) reveals a small enthalpic barrier (approximately 3 +/- 1 kJ/mol). Both of the kinetic rates slow slightly in the myoglobin (Mb) samples above 200 K, suggesting that a small amount of protein relaxation takes place above the solvent glass transition. When the temperature dependence of the NO recombination in Mb is studied under conditions where the distal pocket is mutated (e.g., V68W), the rebinding kinetics lack the slow phase. This is consistent with a mechanism where the slower (approximately 200 ps) kinetic phase involves transitions of the NO ligand into the distal heme pocket from a more distant site (e.g., in or near the Xe4 cavity). Comparison of the temperature-dependent NO rebinding kinetics of native Mb with that of the bare heme (PPIX) in glycerol reveals that the fast (enthalpically barrierless) NO rebinding process observed below 200 K is independent of the presence or absence of the proximal histidine ligand. In contrast, the slowing of the kinetic rates above 200 K in MbNO disappears in the absence of the protein. Generally, the data indicate that, in contrast to CO, the NO ligand binds to the heme iron through a "harpoon" mechanism where the heme iron out-of-plane conformation presents a negligible enthalpic barrier to NO rebinding. These observations strongly support a previous analysis (Srajer et al. J. Am. Chem. Soc. 1988, 110, 6656-6670) that primarily attributes the low-temperature stretched exponential rebinding of MbCO to a quenched distribution of heme geometries. A simple model, consistent with this prior analysis, is presented that explains a variety of MbNO rebinding experiments, including the dependence of the kinetic amplitudes on the pump photon energy.     

CO rebinding to protoheme: investigations of the proximal and distal contributions to the geminate rebinding barrier

The rebinding kinetics of CO to protoheme (FePPIX) in the presence and absence of a proximal imidazole ligand reveals the magnitude of the rebinding barrier associated with proximal histidine ligation. The ligation states of the heme under different solvent conditions are also investigated using both equilibrium and transient spectroscopy. In the absence of imidazole, a weak ligand (probably water) is bound on the proximal side of the FePPIX-CO adduct. When the heme is encapsulated in micelles of cetyltrimethylammonium bromide (CTAB), photolysis of FePPIX-CO induces a complicated set of proximal ligation changes. In contrast, the use of glycerol-water solutions leads to a simple two-state geminate kinetic response with rapid (10-100 ps) CO recombination and a geminate amplitude that can be controlled by adjusting the solvent viscosity. By comparing the rate of CO rebinding to protoheme in glycerol solution with and without a bound proximal imidazole ligand, we find the enthalpic contribution to the proximal rebinding barrier, H(p), to be 11 +/- 2 kJ/mol. Further comparison of the CO rebinding rate of the imidazole bound protoheme with the analogous rate in myoglobin (Mb) leads to a determination of the difference in their distal free energy barriers: DeltaG(D) approximately 12 +/- 1 kJ/mol. Estimates of the entropic contributions, due to the ligand accessible volumes in the distal pocket and the xenon-4 cavity of myoglobin ( approximately 3 kJ/mol), then lead to a distal pocket enthalpic barrier of H(D) approximately 9 +/- 2 kJ/mol. These results agree well with the predictions of a simple model and with previous independent room-temperature measurements of the enthalpic MbCO rebinding barrier (18 +/- 2 kJ/mol).     

Mechanism of the hydration of carbon dioxide: direct participation of H2O versus microsolvation

Thermochemical parameters of carbonic acid and the stationary points on the neutral hydration pathways of carbon dioxide, CO 2 + nH 2O --> H 2CO 3 + ( n - 1)H 2O, with n = 1, 2, 3, and 4, were calculated using geometries optimized at the MP2/aug-cc-pVTZ level. Coupled-cluster theory (CCSD(T)) energies were extrapolated to the complete basis set limit in most cases and then used to evaluate heats of formation. A high energy barrier of approximately 50 kcal/mol was predicted for the addition of one water molecule to CO 2 ( n = 1). This barrier is lowered in cyclic H-bonded systems of CO 2 with water dimer and water trimer in which preassociation complexes are formed with binding energies of approximately 7 and 15 kcal/mol, respectively. For n = 2, a trimeric six-member cyclic transition state has an energy barrier of approximately 33 (gas phase) and a free energy barrier of approximately 31 (in a continuum solvent model of water at 298 K) kcal/mol, relative to the precomplex. For n = 3, two reactive pathways are possible with the first having all three water molecules involved in hydrogen transfer via an eight-member cycle, and in the second, the third water molecule is not directly involved in the hydrogen transfer but solvates the n = 2 transition state. In the gas phase, the two transition states have comparable energies of approximately 15 kcal/mol relative to separated reactants. The first path is favored over in aqueous solution by approximately 5 kcal/mol in free energy due to the formation of a structure resembling a (HCO 3 (-)/H 3OH 2O (+)) ion pair. Bulk solvation reduces the free energy barrier of the first path by approximately 10 kcal/mol for a free energy barrier of approximately 22 kcal/mol for the (CO 2 + 3H 2O) aq reaction. For n = 4, the transition state, in which a three-water chain takes part in the hydrogen transfer while the fourth water microsolvates the cluster, is energetically more favored than transition states incorporating two or four active water molecules. An energy barrier of approximately 20 (gas phase) and a free energy barrier of approximately 19 (in water) kcal/mol were derived for the CO 2 + 4H 2O reaction, and again formation of an ion pair is important. The calculated results confirm the crucial role of direct participation of three water molecules ( n = 3) in the eight-member cyclic TS for the CO 2 hydration reaction. Carbonic acid and its water complexes are consistently higher in energy (by approximately 6-7 kcal/mol) than the corresponding CO 2 complexes and can undergo more facile water-assisted dehydration processes.     

Determination of the Fe-CO bond energy in myoglobin using heterodyne-detected transient thermal phase grating spectroscopy

The bond energies at active sites of proteins are intimately coupled to the structure-function relationship in biological systems. Due to the unknown nature of the protein relaxation along a reaction coordinate, it has not been possible to directly determine bond energies relevant to protein function. By embedding proteins in trehalose glasses, it is possible to freeze out protein relaxation on short time scales and determine the bond energies of photolabile ligands using photothermal spectroscopies. As a prototypical example, the photodissociation dynamics and energetics of carboxy-myoglobin (MbCO) in a trehalose glass matrix at room temperature were studied by transient absorption (or pump-probe) and transient thermal phase grating spectroscopy to determine the CO recombination dynamics and associated energetics, respectively. Both the initial energetics of the bond breaking and the energy released upon bond reformation could be used, on a time scale faster than significant protein relaxation, to determine the Fe-CO bond energy as 34 +/- 4 kcal/mol. This bond energy is significantly larger than that typically cited (25 kcal/mol) on the basis of indirect measurements but is in good agreement with recent theoretical predictions (35 kcal/mol) (Rovira, C.; Parrinello, M. Int. J. Quantum Chem. 2000, 80, 1172). This result in combination with the theoretical study suggests that protein structure plays a significant role in the bond energies at active sites which in turn provides a tuning element of the effective barrier heights independent to the transition state region.     

Free energy profiles for monomer capture in Grubbs- and SHOP-type olefin polymerization catalysts: a constraint ab initio molecular dynamics study

Density functional theory together with Car-Parrinello ab initio molecular dynamics simulation has been used to investigate the free energy profiles (FEP) of monomer capture in Grubbs- and SHOP-type olefin polymerization catalysts. The FEPs along the reaction coordinates at 300 K were determined directly by a point wise thermodynamic integration technique. Comparison between potential energy profile (PEP) and the FEP has been made. The results show that, for both catalysts, the PEP for the monomer ethylene uptake by the metal center is a typical Morse curve without energy barrier. However, a small barrier (1.8 kcal/mol for Grubbs catalyst and 2.4 kcal/mol for SHOP catalyst) exists on the FEP. The pi complexation energy on the FES at 300 K is higher by 10-12 kcal/mol over that on the PES. The differences between FES and PES are due to entropy contribution. Slow growth simulations on the ethylene capture process show that the ethylene attacks the metal center by an asynchronous mode. This indicates that the forming of the pi-bonding between the metal and ethylene is initiated by electrophilic attack of the metal to one of the ethylene carbons.     

Confinement in nanopores can destabilize α-helix folding proteins and stabilize the β structures

Protein folding in confined media has attracted wide attention over the past decade due to its importance in both in vivo and in vitro applications. Currently, it is generally believed that protein stability increases by decreasing the size of the confining medium, if its interaction with the confining walls is repulsive, and that the maximum folding temperature in confinement occurs for a pore size only slightly larger than the smallest dimension of the folded state of a protein. Protein stability in pore sizes, very close to the size of the folded state, has not however received the attention that it deserves. Using detailed, 0.3-ms-long molecular dynamics simulations, we show that proteins with an α-helix native state can have an optimal folding temperature in pore sizes that do not affect the folded-state structure. In contradiction to the current theoretical explanations, we find that the maximum folding temperature occurs in larger pores for smaller α-helices. In highly confined pores the free energy surface becomes rough, and a new barrier for protein folding may appear close to the unfolded state. In addition, in small nanopores the protein states that contain the β structures are entropically stabilized, in contrast to the bulk. As a consequence, folding rates decrease notably and the free energy surface becomes rougher. The results shed light on many recent experimental observations that cannot be explained by the current theories, and demonstrate the importance of entropic effects on proteins' misfolded states in highly confined environments. They also support the concept of passive effect of chaperonin GroEL on protein folding by preventing it from aggregation in crowded environment of biological cells, and provide deeper clues to the α → β conformational transition, believed to contribute to Alzheimer's and Parkinson's diseases. The strategy of protein and enzyme stabilization in confined media may also have to be revisited in the case of tight confinement. For in silico studies of protein folding in confined media, use of non-Go potentials may be more appropriate.     

Disproportionation of Gold(II) complexes. A density functional study of ligand and solvent effects

A computational study of gold(II) disproportionation is presented for the atomic ion as well as complexes with chloride and neutral ligands. The Au2+ atomic ion is stable to disproportionation, but the barrier is more than halved to 119 kcal/mol in an aqueous environment vs 283 kcal/mol in the gas phase. For dissociative disproportionation of chloride complexes, the loss of chlorine, either as an atom (Delta G(aq) = +20 kcal/mol) or as an anion (Delta G(aq) = +15 kcal/mol) represents the largest calculated barrier. The calculated transition state for associative disproportionation is only 9 kcal/mol above separated Au(II)Cl3(-) anions. For the disproportionation of Au(II)L3 complexes with neutral ligands, disproportionation is highly endergonic in the gas phase. Calculations imply that for synthesis of a monometallic Au(II) complex, a nonpolar solvent is preferred. With the exception of [Au(CO)3]2+, disproportionation of Au(II)L3 complexes to Au(I)L and Au(III)L3 is exergonic in solution phase for the ligands investigated. The driving force is provided by the very favorable solvation free energy of the trivalent gold complex. The solvation free energy contribution to the reaction (Delta G(solv)) is very large for small and polar ligands such as ammonia and water. Furthermore, calculations imply that choosing ligands that would yield neutral species upon disproportionation may provide an effective route to thwart this decomposition pathway for Au(II) complexes. Likewise, bulkier ligands that yield larger, more weakly solvated complex ions would appear to be desirable.     

Geminate rebinding in R-state hemoglobin: kinetic and computational evidence for multiple hydrophobic pockets

Biphasic geminate rebinding of CO to myoglobin upon flash photolysis has been associated to ligand distribution in hydrophobic cavities, structurally detected by time-resolved crystallography, xenon occupancy, and molecular simulations. We show that the time course of CO rebinding to human hemoglobin also exhibits a biphasic geminate rebinding when the protein is entrapped in wet nanoporous silica gel. A simple branched kinetic scheme, involving the bound state A, the primary docking site C, and a secondary binding site B was used to calculate the microscopic rates and the time-dependent population of the intermediate species. The activation enthalpies of the associated transitions were determined in the absence and presence of 80% glycerol. Potential hydrophobic docking cavities within the alpha and beta chains of hemoglobin were identified by computational modeling using xenon as a probe. A hydrophobic pocket on the distal side of the heme, corresponding to Xe4 in Mb, and a nearby site that does not have a correspondence in Mb were detected. Neither potential xenon sites on the proximal side nor a migration channel from the distal to proximal site was located. The small enthalpic barriers between states B and C are in very good agreement with the location of the xenon sites on the distal side. Furthermore, the connection between the two xenon sites is relatively open, explaining why the decreased mobility of the protein with viscosity only slightly perturbs the energetics of ligand migration between the two sites.     

Myoglobin-CO substate structures and dynamics: multidimensional vibrational echoes and molecular dynamics simulations

Spectrally resolved infrared stimulated vibrational echo data were obtained for sperm whale carbonmonoxymyoglobin (MbCO) at 300 K. The measured dephasing dynamics of the CO ligand are in agreement with dephasing dynamics calculated with molecular dynamics (MD) simulations for MbCO with the residue histidine-64 (His64) having its imidazole epsilon nitrogen protonated (N(epsilon)-H). The two conformational substate structures B(epsilon) and R(epsilon) observed in the MD simulations are assigned to the spectroscopic A(1) and A(3) conformational substates of MbCO, respectively, based on the agreement between the experimentally measured and calculated dephasing dynamics for these substates. In the A(1) substate, the N(epsilon)-H proton and N(delta) of His64 are approximately equidistant from the CO ligand, while in the A(3) substate, the N(epsilon)-H of His64 is oriented toward the CO, and the N(delta) is on the surface of the protein. The MD simulations show that dynamics of His64 represent the major source of vibrational dephasing of the CO ligand in the A(3) state on both femtosecond and picosecond time scales. Dephasing in the A(1) state is controlled by His64 on femtosecond time scales, and by the rest of the protein and the water solvent on longer time scales.     

Oxygen Migration Pathways in NO‐bound Truncated Hemoglobin

Atomistic simulations of dioxygen (O₂) dynamics and migration in nitric oxide‐bound truncated Hemoglobin N (trHbN) of Mycobacterium tuberculosis are reported. From more than 100 ns of simulations the connectivity network involving the metastable states for localization of the O₂ ligand is built and analyzed. It is found that channel I is the primary entrance point for O₂ whereas channel II is predominantly an exit path although access to the protein active site is also possible. For O₂ a new site compared to nitric oxide, from which reaction with the heme group can occur, was found. As this site is close to the heme iron, it could play an important role in the dioxygenation mechanism as O₂ can remain there for hundreds of picoseconds after which it can eventually leave the protein, while NO is localized in Xe2. The present study supports recent experimental work which proposed that O₂ docks in alternative pockets than Xe close to the reactive site. Similar to other proteins, a phenylalanine residue (Phe62) plays the role of a gate along the access route in channel I. The most highly connected site is the Xe3 pocket which is a “hub” and free energy barriers between the different metastable states are ≈1.5 kcal mol^?1 which allows facile O₂ migration within the protein.     

Exciplex Formation in Lipid-bound Escherichia coli Flavohemoglobin

Flavohemoglobins have the particular capability of binding unsaturated and cyclopropanated fatty acids as free acids or phospholipids. Fatty acid binding to the ferric heme results in a weak but direct bonding interaction. Ferrous and ferric protein, in presence or absence of a bound lipid molecule, have been characterized by transient absorption spectroscopy. Measurements have been also carried out both on the ferrous deoxygenated and on the CO bound protein to investigate possible long-range interaction between the lipid acyl chain moiety and the ferrous heme. After excitation of the deoxygenated derivatives the relaxation process reveals a slow dynamics (350 ps) in lipid-bound protein but is not observed in the lipid-free protein. The latter feature and the presence of an extra contribution in the absorption spectrum, indicates that the interaction of iron heme with the acyl chain moiety occurs only in the excited electronic state and not in the ground electronic state. Data analysis highlights the formation of a charge-transfer complex in which the iron ion of the lipid-bound protein in the expanded electronic excited state, possibly represented by a high spin Fe III intermediate, is able to bind to the sixth coordination ligand placed at a distance of at 3.5 Å from the iron. A very small nanosecond geminate rebinding is observed for CO adduct in lipid-free but not in the lipid-bound protein. The presence of the lipid thus appears to inhibit the mobility of CO in the heme pocket.     

Ab initio quantum mechanical/molecular mechanical molecular dynamics simulation of enzyme catalysis: the case of histone lysine methyltransferase SET7/9

To elucidate enzyme catalysis through computer simulation, a prerequisite is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio quantum mechanical/molecular mechanical approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9 and its corresponding uncatalyzed reaction in aqueous solution, respectively. Our calculated activation free energy barrier for the enzyme catalyzed reaction is 22.5 kcal/mol, which agrees very well with the experimental value of 20.9 kcal/mol. The difference in potential of mean force between a corresponding prereaction state and the transition state for the solution reaction is computed to be 30.9 kcal/mol. Thus, our simulations indicate that the enzyme SET7/9 plays an essential catalytic role in significantly lowering the barrier for the methyl-transfer reaction step. For the reaction in solution, it is found that the hydrogen bond network near the reaction center undergoes a significant change, and there is a strong shift in electrostatic field from the prereaction state to the transition state, whereas for the enzyme reaction, such an effect is much smaller and the enzyme SET7/9 is found to provide a preorganized electrostatic environment to facilitate the methyl-transfer reaction. Meanwhile, we find that the transition state in the enzyme reaction is a little more dissociative than that in solution.     

Catalytic mechanism and product specificity of the histone lysine methyltransferase SET7/9: an ab initio QM/MM-FE study with multiple initial structures

Histone lysine methylation is emerging as an important mechanism to regulate chromatin structure and gene activity. To provide theoretical understanding of its reaction mechanism and product specificity, ab initio quantum mechanical/molecular mechanical free energy (QM/MM-FE) calculations and molecular dynamics simulations have been carried out to investigate the histone lysine methyltransferase SET7/9. It is found that the methyl-transfer reaction catalyzed by SET7/9 is a typical in-line S(N)2 nucleophilic substitution reaction with a transition state of 70% dissociative character. The calculated average free energy barrier at the MP2(6-31+G) QM/MM level is 20.4 +/- 1.1 kcal/mol, consistent with the activation barrier of 20.9 kcal/mol estimated from the experimental reaction rate. The barrier fluctuation has a strong correlation with the nucleophilic attack distance and angle in the reactant complex. The calculation results show that the product specificity of SET7/9 as a monomethyltransferase is achieved by disrupting the formation of near-attack conformations for the dimethylation reaction.     

Molecular dynamics simulations of the catalytic pathway of a cysteine protease: a combined QM/MM study of human cathepsin K

Molecular dynamics simulations using a combined QM/MM potential have been performed to study the catalytic mechanism of human cathepsin K, a member of the papain family of cysteine proteases. We have determined the two-dimensional free energy surfaces of both acylation and deacylation steps to characterize the reaction mechanism. These free energy profiles show that the acylation step is rate limiting with a barrier height of 19.8 kcal/mol in human cathepsin K and of 29.3 kcal/mol in aqueous solution. The free energy of activation for the deacylation step is 16.7 kcal/mol in cathepsin K and 17.8 kcal/mol in aqueous solution. The reduction of free energy barrier is achieved by stabilization of the oxyanion in the transition state. Interestingly, although the "oxyanion hole" has been formed in the Michaelis complex, the amide units do not donate hydrogen bonds directly to the carbonyl oxygen of the substrate, but they stabilize the thiolate anion nucleophile. Hydrogen-bonding interactions are induced as the substrate amide group approaches the nucleophile, moving more than 2 A and placing the oxyanion in contact with Gln19 and the backbone amide of Cys25. The hydrolysis of peptide substrate shares a common mechanism both for the catalyzed reaction in human cathepsin K and for the uncatalyzed reaction in water. Overall, the nucleophilic attack by Cys25 thiolate and the proton-transfer reaction from His162 to the amide nitrogen are highly coupled, whereas a tetrahedral intermediate is formed along the nucleophilic reaction pathway.     

Ab initio molecular dynamics study of carbon dioxide and bicarbonate hydration and the nucleophilic attack of hydroxide on CO2

We apply ab initio molecular dynamics (AIMD) to study the hydration structures of the carbon dioxide molecule and the bicarbonate and carbonate anions in liquid water. We also compute the free energy change associated with the nucleophilic attack of the hydroxide ion on carbon dioxide. CO2 behaves like a hydrophobic species and exhibits weak interactions with water molecules. The bicarbonate and carbonate ions are strongly hydrated and coordinate to an average of 6.9 and 8.7 water molecules, respectively. The energetics for the reaction in the gas phase are investigated using density functional theory and second-order M?ller-Plesset perturbation theory (MP2) in conjunction with high-quality basis sets. Using umbrella sampling techniques, we compute the standard state, aqueous phase free energy difference associated with the reaction CO2+OH--->HCO3- after correcting AIMD energies with MP2 results. Our predictions are in good agreement with experiments. The hydration structures along the reaction coordinate, which give rise to a predicted 9.7 kcal/mol standard state free energy barrier, are further analyzed.     

Two-state folding observed in individual protein molecules

The folding dynamics of small proteins are often described in terms of a simple two-state kinetic model. Within this notion, the behavior of individual molecules is expected to be stochastic, with a protein molecule residing in either the unfolded or the folded state for extended periods of time, with intermittent rapid jumps across the free energy barrier. However, a direct observation of this bistable behavior has not been made to date. Rather, previous reports of folding trajectories of individual proteins have shown an unexpected degree of complexity. This raises the question whether the simple kinetic properties derived from classical experiments on large ensembles of molecules are reflected in the folding paths taken by individual proteins. Here we report single-molecule folding/unfolding trajectories observed by fluorescence resonance energy transfer for a protein that meets all criteria of a two state-system. The trajectories, measured on molecules immobilized in lipid vesicles, demonstrate the anticipated bistable behavior, with steplike transitions between folded and unfolded conformations. They further allow us to put an upper bound on the barrier crossing time.     

Theoretical analysis of concerted and stepwise mechanisms of Diels-Alder reactions of butadiene with silaethylene and disilene

The concerted and the stepwise mechanisms of the Diels-Alder reactions of butadiene with silaethylene and disilene were studied by ab initio MO methods. For the reaction of butadiene and silaethylene, an asymmetric concerted process that is almost stepwise and two stepwise processes were located. For the first step of the stepwise process, the C-Si bond formation is more favorable than the C-C bond formation. The activation energy barrier of the concerted transition state is only 0.89 kcal/mol lower than that of the first-step transition state of the C-Si bond formation for the stepwise process by the CASPT2 calculation level. For the reaction of butadiene and disilene, the activation energy barrier of the concerted-type transition state constrained with Cs symmetry is about 9 kcal/mol higher than that of the stepwise transition state by the CASSCF method. The energy barrier of the first step of the stepwise reaction disappears at the CASPT2/6-311++G(d,p) calculation level including the nondynamical correlation energy, although the reaction of the butadiene with disilene occurs through the stepwise-like process.     

Dynamics of proteins encapsulated in silica sol-gel glasses studied with IR vibrational echo spectroscopy

Spectrally resolved infrared stimulated vibrational echo spectroscopy is used to measure the fast dynamics of heme-bound CO in carbonmonoxy-myoglobin (MbCO) and -hemoglobin (HbCO) embedded in silica sol-gel glasses. On the time scale of approximately 100 fs to several picoseconds, the vibrational dephasing of the heme-bound CO is measurably slower for both MbCO and HbCO relative to that of aqueous protein solutions. The fast structural dynamics of MbCO, as sensed by the heme-bound CO, are influenced more by the sol-gel environment than those of HbCO. Longer time scale structural dynamics (tens of picoseconds), as measured by the extent of spectral diffusion, are the same for both proteins encapsulated in sol-gel glasses compared to that in aqueous solutions. A comparison of the sol-gel experimental results to viscosity-dependent vibrational echo data taken on various mixtures of water and fructose shows that the sol-gel-encapsulated MbCO exhibits dynamics that are the equivalent of the protein in a solution that is nearly 20 times more viscous than bulk water. In contrast, the HbCO dephasing in the sol-gel reflects only a 2-fold increase in viscosity. Attempts to alter the encapsulating pore size by varying the molar ratio of silane precursor to water (R value) used to prepare the sol-gel glasses were found to have no effect on the fast or steady-state spectroscopic results. The vibrational echo data are discussed in the context of solvent confinement and protein-pore wall interactions to provide insights into the influence of a confined environment on the fast structural dynamics experienced by a biomolecule.     

The protein folding transition-state ensemble from a Gō-like model

Characterizing the structure of transition states (TS) is a first step towards understanding two-state protein folding mechanisms. However, a direct experimental characterization of these states is challenging and indirect information derived from protein engineering methodologies (?-value analysis) is often difficult to interpret. We present here a theoretical study on the nature of the transition state ensemble for three representative proteins covering the major structural classes using a mean-field C(α)-based Gō-model. We identify that transition state ensembles are dominated by local contacts, indicating that most non-local contacts form only upon crossing the macroscopic folding free energy barrier. We demonstrate that the mean ?-value corresponds to the fraction of stabilization energy gained at the barrier-top in two-state-like systems, and that it depends monotonically on the stability conditions. Furthermore, we show that there is a fundamental connection between small destabilization and large ?-values that in turn depends on the location of the mutated residue in the structure. These results that are in agreement with the recent empirical findings highlight the importance of local energetics in determining folding mechanisms.