Session D26: Focus Session: Protein Folding: Theory and Simulations III

Mechanisms of Protein Assembly and Folding: Lessons from Minimalist Models

Globally the energy landscape of a folding protein resembles a partially rough funnel. The local roughness of the funnel reflects transient trapping of the protein configurations in local free energy minima. The overall funnel shape of the landscape, superimposed on this roughness, arises because the interactions present in the native structure of natural proteins conflict with each other much less than expected if there were no constraints of evolutionary design to achieve reliable and relatively fast folding (minimal energetic frustration). A consequence of minimizing energetic frustration is that the topology of the native fold also plays a major role in the folding mechanism. Topological effects go beyond the structure of the TSE. The overall structure of the on-route and off-route (traps) intermediates for the folding of more complex proteins is also strongly influenced by topology. Going beyond folding, the power of reduced models to study the physics of protein assembly will be discussed. Since energetic frustration is sufficiently small, native topology-based models have shown that binding mechanisms are robust and governed primarily by the protein's native topology. These models impressively capture many of the binding characteristics found in experiments and highlight the fundamental role of flexibility in binding.   

Direct application of a simple model to the quantitative analysis of experiments on an ultrafast folding protein

A simple Ising-like statistical-mechanical model for protein folding (Henry and Eaton, \textit{Chem. Phys.} {\bf 307}, 163-185, 2004) is used to analyze a broad set of experimental data on the ultrafast folding villin subdomain. In this model each residue in the protein sequence can adopt one of two possible microscopic states corresponding to native and non-native conformations; model protein states are identified with distinct sequences of native/non-native residues. The folding properties of the protein are determined entirely by the map of inter-residue contacts in the native structure. To compute partition functions by complete enumeration of all protein states, only those states are included that contain at most two contiguous sequences of native residues. Native contacts are only permitted between residues lying in such contiguous sequences. The stability of any state of the chain is determined by the offsetting effects of the stabilizing native contacts and the destabilizing entropy losses associated with fixing residues in the native conformation and with closing loops of nonnative residues created by contacts between distinct native sequences. In a least-squares fitting analysis, the temperature-dependent populations predicted by the model for all the protein states, combined with a simple description of the spectroscopic properties of individual states, are used to model the results of spectroscopic and thermodynamic experiments. The model reproduces the temperature dependence of the excess heat capacity, tryptophan fluorescence quantum yield, circular dichroism, and relaxation rates and amplitudes, as well as the effects of site-directed mutants on the folding rates and equilibrium constants.   

Desolvation effects and topology-dependent protein folding

As a protein folds, water molecules must be excluded from the hydrophobic core, and thus desolvation barriers between the protein's constituents must be crossed in order to reach the final folded state. Previous research on continuum G$\bar{o}$-like protein models has demonstrated that pairwise-additive desolvation potentials lead to more thermodynamically and kinetically cooperative folding/unfolding transitions (Z. Liu and H. S. Chan, Phys. Biol. \textbf{2}, S75-S85, \textit{2005}). The present work focuses on the role of this elementary desolvation potential in improving predictions of the well-known topology-folding rate relationship (K. W. Plaxco \textit{et al}, J. Mol. Biol. \textbf{277}, 985-994, \textit{1998}) of small single-domain proteins. Recent computational studies without desolvation barriers have shown (S. Wallin and H. S. Chan, J. Phys.: Condens. Matt. \textbf{18}, S307-S328, \textit{2006}) that the observed correlation between topological parameters and folding rates is because these parameters may be proxies for rate-determining properties of the transition state, such as the activation free energy $\Delta G^{\ddagger}$ and activation conformational entropy $\Delta S^{\ddagger}$. Including the desolvation barrier in the model results in stronger correlations between measures of topology and simulated folding rates / transition state properties, reinforcing the theory that even simple representations of the desolvation effect are important for understanding crucial features of protein folding.   

Networks in Protein Folding

We take a networks approach to protein folding by identifying different protein conformations with nodes, while an elementary step of the system (rotation around a bond) that takes one configuration to another is defined as a link. The energies of configurations are scalar quantities associated with each node. Using this approach we can show that the scale-free nature of the observed protein conformation networks can be explained by simple results obtained on gradient networks.   

Intramolecular Vibrational Preparation of the Unfolding Transition State of Zn$^{\rm II}$-substituted Cytochrome \emph{c}: Picosecond Time-Resolved Fluorescence and Dynamic Stokes Shift Studies

We show that an intramolecular vibrational excitation provided by the radiationless decay of a covalently bound electronic chromophore can be exploited to drive a protein from its native folded state to the transition state for unfolding. Using this approach, we examine the effect of the polarity and viscosity of the solvent medium on the unfolding and refolding reactions of Zn$^{\rm II}$-substituted cytochrome \emph{c} at room temperature. The dynamic Stokes shift of the S$_1$-state Zn$^{\rm II}$--porphyrin is monitored using picosecond time-resolved fluorescence spectroscopy as a probe of the protein and solvent dynamics that are associated with the crossing of the unfolding transition state and with the subsequent unfolding and refolding trajectories. The results show that the solvent polarity controls the activation energy for the unfolding and refolding reactions; the solvent viscosity further controls the rate by frictionally hindering the moving polypeptide. These findings suggest an important role for the solvent in the kinetic control of protein-folding trajectories on the energy landscape.   

Single Mutation Effect on Lysozyme Stability and Misfolding

We propose a mechanism, based on an unprecedended 10+ microsecond molecular dynamics simulation, for the surprising misfolding of hen lysozyme caused by a single mutation (W62G). Our simulations of the wild-type and the mutant lysozyme in 8M urea solution at biological temperature (with both pH = 2 and pH = 7) reveal that the mutant structure is much less stable than the wild-type, with the mutant showing larger fluctuations and less native-like contacts. Analysis of local contacts reveals that the Trp62 residue is the key to a cooperative long-range interaction within the wild-type where it acts like a bridge between two neighboring basic residues. A native-like cluster or nucleation site can thus form near these residues in the wild-type, but not in the mutant. These findings, while supporting the general conclusions of a recent experimental study by Dobson and coworkers, provide a detailed but different molecular picture of the misfolding mechanism.   

On the Mechanism of Protein Unfolding by Pressure A Molecular Dynamics Simulation Study

Proteins are denaturized at high pressure and the mechanism of such a denaturation is still on debate. We have studied lyzozyme and apomyoglobin, under pressure up to 0.3GPa using molecular dynamics simulation. Lysozyme shows more stability, although it cannot retain the native structure. On the other hand apomyoglobin shows a continuing unfolding process during the 180 ns simulation time. The analysis of the hydrophilic and hydrophobic proteins Solvent Accessed Surface clearly shows the increment of the hydrophobic exposed area in the formation of crevices and in the appearing of hydrophobic `spikes' around the overall surface. The observation of the final state, within the simulation time, shows a clear effect on the conformational state of the proteins. Comparing the behavior of the proteins with de aggregation state of simple non-polar solutes at different pressures we have been able to conclude that the driving force of the denaturation is the change in the hydrophobic contribution to the native folding due to the changes of water structure under pressure, which have been shown both experimental and by computer simulation.   

Free Energy Landscape - Settlements of Key Residues.

FEL perspective in studies of protein folding transitions reflects notion that since there are $\sim $10$^{N}$ conformations to scan in search of lowest free energy state, random search is beyond biological timescale. Protein folding must follow certain fel pathways and folding kinetics of evolutionary selected proteins dominates kinetic traps. Good model for functional robustness of natural proteins - coarse-grained model protein is not very accurate but affords bringing simulations closer to biological realm; Go-like potential secures the fel funnel shape; biochemical contacts signify the funnel bottleneck. Boltzmann-weighted ensemble of protein conformations and histogram method are used to obtain from MC sampling of protein conformational space the approximate probability distribution. The fel is F(\textit{rmsd}) = -1/$\beta $\textbullet Ln[Hist(\textit{rmsd})], \textit{$\beta $}=k$_{B}$T and\textit{ rmsd} is root-mean-square-deviation from native conformation. The sperm whale myoglobin has rich dynamic behavior, is small and large - on computational scale, has a symmetry in architecture and unusual sextet of residue pairs. Main idea: there is a mathematical relation between protein fel and a key residues set providing stability to folding transition. Is the set evolutionary conserved also for functional reasons? Hypothesis: primary sequence determines the key residues positions conserved as stabilizers and the fel is the battlefield for the folding stability. Preliminary results: primary sequence - not the architecture, is the rule settler, indeed.   

Interplay between secondary and tertiary structure formation in a lattice model alpha helical hairpin peptide

We present results from Monte Carlo simulations of folding dynamics of a model alpha helical hairpin peptide. The dynamics shows that the peptide chain folds in a two step fashion that involves the formation of partial helical segments followed by the formation of a stable tertiary structure by joining these semi-stable helical segments. The interplay between the formation of secondary and tertiary structures during the folding process was investigated by calculating the heat capacity and other thermodynamic quantities at various simulation temperatures. In addition to a sharp peak in the heat capacity curve for the transition between unfolded state and folded native state, the helix-random coil transition in the unfolded state is also cooperative.   

First Principles Study of the Reaction Mechanism for Intein C-terminal Cleavage

Protein splicing, consisting of the excision and ligation of two flanking sequences (the exteins), is auto-catalyzed by the internal sequence (the intein). It has been shown experimentally that by mutating the critical first residue of the intein, the first step of splicing is inhibited, although intein C-terminal cleavage can still occur independently. Using a tripeptide model system with QM methods, we have investigated the effect of different mutants in order to provide an atomic level understanding of this mechanism. We find that the reaction energy barrier for asparagine cyclization can be controlled by mutation of non-essential residues: specifically we found that the barrier with a methionine mutant is larger than to the barrier for cysteine, resulting in slower C-terminal cleavage in agreement with experiment. The accuracy of our model system is further confirmed by comparing results with that of a combined quantum mechanics and molecular mechanics (QM/MM) approach. These results suggest that certain mutations in inteins could be used to control the reaction rate without affecting the overall reaction mechanism and could exploited for many applications including molecular switches, sensors and controlled drug delivery.