Session J39: Physics of Proteins III: Folding, Structure and Stability

The Speed Limit of Protein Folding: Alpha-Helix Initiation Modeled and Observed

As a primary event of protein folding, alpha-helix initiation is the starting point of macromolecular complexity. In this work, an analytic coarse-grained model which predicts the initiation rate as a function of temperature, is presented. Helix initiation was measured via ultrafast temperature-jump fluorescence refolding experiments on two penta-peptides, and the measured rates agreed well with those of the model. In addition, the temporal separation of rate-limiting diffusion from fast annealing stipulated by the model was confirmed via ensemble-converging all-atom molecular dynamics simulations, which reproduced both the diffusion and the picosecond annealing processes and rates observed experimentally. Some of these results were published in: Mohammed OF, Jas GS, Lin MM, Ma H, Zewail AH (2009) Primary peptide folding dynamics observed with ultrafast temperature jump. Angew Chem 48: 5628-5632.   

Protein folding microenvironments within the cytoplasm of living cells

The protein folding kinetics in a living cell strongly depends on the local environment. Viscosity of cytoplasm and crowding by macromolecules modulate stability, folding rates and folding mechanism in the folding progresses. We use Fast Relaxation Imaging (FReI) to map out the stability and folding kinetics of a FRET-labeled phosphoglycerate kinase (PGK) in the cytoplasm of individual eukaryotic cells with 500 nm spatial resolution. It shows that this modulation results in large variation of folding mechanism compared to in vitro experiment. We have developed the folding-diffusion model of protein folding in cell with hetergenous microenvironment, which includes spatial hetergenous of folding rates of the multiple-state folding of PGK and diffusion between pixels. It is shown that diffusion contributes little to the large variation of folding kinetics, which can only result from the change of folding mechanism due to microenvironment.   

First step in folding of nonconstitutive membrane proteins: spontaneous insertion of a polypeptide into a lipid bilayer and formation of helical structure

There are two questions we would like to address: 1) what is the molecular mechanism of a polypeptide insertion into a lipid bilayer and formation of transmembrane helix? 2) Are there any transient changes of a lipid bilayer in process of a polypeptide insertion and folding? As a convenient system we are studying pHLIP (pH (Low) Insertion Peptide) insertion into a membrane and folding, which is modulated by pH. The insertion of pHLIP occurs with rapid (0.1 sec) interfacial helix formation followed by a much slower (100 sec) insertion pathway to form a transmembrane helix. The reverse process of unfolding and peptide exit from the bilayer core proceeds much faster than folding/insertion and through different intermediate states. Our kinetic studies with pHLIP variants indicate that insertion can occur 100 times faster and with less number of intermediate states. To study changes, which might occur with a lipid bilayer in a process of peptide insertion and folding, we employed stopped-flow SAXS.   

Protein barrel fluctuations and the barrel permeability: A comparison between Green and Red Fluorescent proteins

As compared to the Green Fluorescent Proteins (GFP), the monomeric variants of the Red Fluorescent Proteins (RFP), also known as mFruits, are substantially less photostable, possibly due to the barrel permeability for molecular oxygen into the protein barrel. We performed molecular dynamics simulations to compare the protein barrel fluctuations of the GFP as well as a monomeric variant of the RFP. We also performed implicit ligand sampling for uncovering the pathways for molecular oxygen entry into the barrels. We found that, as compared to the GFP barrel, the RFP barrel has significantly larger structural fluctuations and these large barrel fluctuations lead to clear pathways through which molecular oxygen or other ions can enter the barrel more easily.   

Heterogeneous helical propensity and its effects on dimerization and the stability of a model protein dimer

We will present the results of Monte Carlo simulations of the dimerization and unfolding of a helical protein dimer. Using a three dimensional lattice model, we investigate the role of including sections of amino acids with strong alpha-helix propensity at different locations along the helices on the dimerization kinetics and the dimer stability. Specifically, we focus on the rate limiting steps in both folding and unfolding processes. We find that these processes can be optimized by tuning the ease of access through diffusion to the metastable intermediate state and its stability. The kinetics and thermodynamical stability is tuned by a combination of the locations of the amino acids with the high helical propensity and the salt bridges.   

Protein-like folding and free energy landscape of a homopolymer chain

Many small proteins fold via a first-order ``all-or-none'' transition directly from an expanded coil to a compact native state. We have recently reported an analogous direct coil-to-crystallite transition for a flexible homopolymer [1]. Wang-Landau sampling was used to construct the 1D density of states for square-well chains up to length 256 and a microcanonical analysis shows that for short-range interactions the usual polymer collapse transition is preempted by a direct freezing transition. A 2D configurational probability landscape, built via multi-canonical sampling, reveals a dominant folding pathway and an inherent configurational barrier to folding. Despite the non-unique homopolymer ground state, the thermodynamics of this direct freezing transition are identical to those of two-state protein folding. Homopolymer folding proceeds over a free energy barrier via a transition state folding nucleus, displays a protein-like Chevron plot, and satisfies the van't Hoff two-state criterion.\\[4pt][1] Phys. Rev. E 79, 050801(R) (2009); J. Chem. Phys. 131, 114907 (2009).   

Unfolding Kinetics of Egg Protein

This study explores denaturing kinetics of egg white using high resolution calorimetric technique. Fresh egg was scanned fro heating and cooling to see the thermodynamics 10$^{\circ}$ C to 100$^{\circ}$ C at different heating ramp rates varying from 1 to 20$^{\circ}$ C/min. An endothermic peak was found on heating scan showing denaturing of protein which was found absent at the cooling indicating the absence of any residue after heating. The denature peak shifted towards higher temperature as ramp rate increases following Arrhenius behavior and shows an activated denaturing kinetics of the egg protein. This peak was also compared with the water to avoid water effects. Behavior of denaturing peak can be explained in terms of Arrhenius theory.   

Probing the dynamics of biomolecules in liquid water by terahertz spectroscopy

Decades of molecular dynamics and normal mode calculations suggest that proteins are rife with collective vibrational modes with ps to ns time constants. Given that proteins are ``decorated'' with charged groups, these motions should lead to oscillating dipoles that, in turn, will lead to strong gigahertz to terahertz absorption. Investigation of these harmonic motions by absorption spectroscopy, however, is extremely challenging due to the strong absorption of water. In response, we have developed a sensitive Vector Network Analyzer based spectrometer that operates from 65 to 700 GHz and can measure both the absorbance and refractive index of protein solutions. In order to extract the complex dielectric response of the protein in solution we employ an effective medium approximation for the mixture of the protein and aqueous buffer. The extracted dielectric response suggests that each protein molecule is surrounded by a tightly held layer of 164 +/- 5 water molecules that behave as if they are an integral part of the protein. The size of this hydration shell and the dielectric response of the solvated protein are all independent of protein concentration. Our measured dielectric response, however, does not agree with published computation models of the protein: the measurements indicate a low frequency cutoff in the density of modes of $\sim$250 GHz.   

MD-simulations of Beta-Amyloid Protein Insertion Efficiency and Kinetics into Neuronal Membrane Mimics

Early interaction events of beta-amyloid (A$\beta )$ peptides with the neuronal membranes play a key role in the pathogenesis of Alzheimer's disease. We have used all-atom MD simulations to study the protein insertion efficiency and kinetics of monomeric A$\beta _{40}$ and A$\beta _{42}$ into phosphatidylcholine lipid bilayers (PC) with and without 40 mole{\%} cholesterol (CHOL) that mimic the cholesterol-enriched and depleted lipid nanodomains of the neuronal plasma membranes. Independent replicates of 200-ns simulations of each protein pre-inserted in the upper lipid layer were generated. In PC bilayers, only 25{\%} of A$\beta _{40}$ and 50{\%} of A$\beta _{42}$ in the replicates showed complete insertion into the lower lipid layer, whereas the percentages increased to 50{\%} and 100{\%}, respectively, in PC/CHOL bilayers, providing evidence that cholesterol improves the protein insertion efficiency into the bilayers. The rate of protein insertion was proportional to the hydrophobic, transmembrane helix length of the inserted peptide and depended on the cholesterol content. We propose that the lysine snorkeling and C-terminus anchoring of A$\beta $ to the PC headgroups at the upper and lower lipid/water interfaces represent the dual-transmembrane stabilization mechanisms of A$\beta $ in the neuronal membrane domains.   

Characterization of Polyethylene Glycol Modified Hemoglobins

Polyethylene glycol modified hemoglobins (PEGHbs) was characterized by liquid chromatography and fluorescence methods. We prepared four samples of two different molecular weight PEG, 5KDa and 20KDa, modified bovine and human hemoglobin. We studied the oxygen affinities, stabilities, and peroxidase activities of PEGHbs. We have related oxygen affinities with different degrees of modifications. The data showed that the modification on the beta subunits was less stable than that of the alpha subunits on the human Hb based samples especially. We also compared peroxidase activities among different modified PEGHbs.   

Multi-scale structure of a protein (histone H3.1) via a knowledge-based potential

A coarse-grained computer simulation model is used to investigate the multi-scale structures of a histone H3.1, a protein with 136 residues in an effective solvent medium. The protein chain consisting of residues (nodes) tethered together by fluctuating bonds on a cubic lattice where empty lattice sites constitute the effective solvent matrix. Each residue interacts with surrounding solvent sites and other residues via Lennard-Jones (LJ) potential. A knowledge-based interaction matrix is used for the residue-residue interaction coefficient of the LJ potential. Interaction between the residue and solvent sites, a measure of the solvent quality, is varied. Each residue executes its stochastic motion with the Metropolis algorithm. We examine a number of local and global physical quantities some of which include mobility and energy profiles of each residue and their local structural histogram, radius of gyration ($R_{g})$, radial distribution function, and structure factor of the protein for a range of the solvent interactions. Variation of $R_{g}$ with the solvent quality of solvent exhibits a maximum.   

Calculating the shift in pKa of the position 66 for an Staphylococcal nuclease mutant with the Replica Exchange Free Energy Perturbation method

The Experimental pKa value of Glutamate66 in a hyperstable mutant of Staph Nuclease, which has been measured by Moreno et al., shows a large shift of around 5 pKa units with respect to a glutamate in solution. In order to reproduce the large experimental shift by single structure continuum solvent computational methods, it is required that the dielectric constant of the interior of the protein be set to around ten in the simulations. The physical reason behind this is not understood as of yet and hypotheses have been produced by the Moreno group regarding solvent penetration, protein reorganization etc. We tried to resolve this inconsistency between experimental and continuum methods by introducing a four-state thermodynamic cycle that has couples conformational states with protonation state of the side chain of E66. We propose that what the experimental methods, (which are mostly sensitive to configurational changes) are measuring is actually the equilibrium constant between the two configurational states rather than between the two protonation states. In this regard we applied our recently developed Replica Exchange method Free Energy Perturbation (REFEP) in implicit solvent to calculate the pKa value of E66 for each of the configurational states as well as the mixed configuration, and our results are in almost perfect agreement with the experiments of Moreno.   

Brownian dynamics simulations of amelogenin microribbons formation

Recent advances in chemical particle synthesis have emphasized the fundamental role of surface colloidal heterogeneities and their detailed chemical composition, which is particularly significant for an important subclass of colloidal systems, namely, proteins. Recently, the process of self-assembly of amelogenin monomers with a hydrophobic/hydrophilic bipolar nature into ordered ribbon structures has been studied experimentally. In this work, we study this dynamical process by means of a Brownian dynamic simulation of a simple model which represents the bipolar character of the globular amelogenin molecule and the hydrophilic C-terminal tail. We monitor the kinetics of self-assembly through a study of the structure factor. We also calculate the phase diagram of the model using Gibbs ensemble Monte Carlo simulation and thermodynamic perturbation theory.   

Stability of proteins inside a hydrophobic cavity

Previous studies have shown that enclosing a protein in an athermal cavity stabilizes the protein against reversible unfolding by virtue of eliminating many open chain conformations. Examples of such confined spaces include pores in chromatographic columns, Anfinsen's cage in Chaperonins, interiors of Ribosomes or regions of steric occlusion inside cells. However, the situation is more complex inside a hydrophobic cavity. The protein has a tendency to adsorb on the surface of the hydrophobic cavity, but at the same time it loses conformational entropy because of confinement. We study this system using a simple Hydrophobic Polar (HP) lattice protein model. Canonical Monte Carlo (MC) simulations at different temperatures and surface hydrophobicity show that proteins are stabilized at low and moderate hydrophobicity upon adsorption. The range of surface hydrophobicity over which a protein is stable increases with a decrease in radius of the cavity.   

Wang-Landau sampling of protein adsorption using the HP model

We have applied Wang-Landau sampling\footnote{F. Wang and D. P. Landau, Phy. Rev. Lett. \textbf{86}, 2050 (2001).} with appropriate trial moves\footnote{T. W\"{u}st and D. P. Landau, Phy. Rev. Lett. \textbf{102}, 178101 (2009).} to investigate the thermodynamics and structural properties of lattice hydrophobic-polar heteropolymers (commonly known as the HP protein model) interacting with an attractive substrate. We estimate the density of states of the system, from which the partition function and all thermodynamic quantities, e.g. specific heat, radius of gyration, end-to-end distance and surface contacts, can be calculated. ``Transitions'' between ``phases'' are then identified based on a comprehensive analysis of these observables. Generally speaking, three transition processes are observed: adsorption-desorption, collapse (formation of hydrophobic core), and ``flattening'' of adsorbed structures. These have been confirmed by ``snapshots'' of typical states of the system. Depending on the surface attractive strength, these transitions take place in different order upon cooling, giving rise to different thermodynamic behaviors. Such dependence of folding hierarchy on the surface attraction is found to be universal for different HP sequences.