Soliton driven relaxation dynamics and protein collapse in the villin headpiece

Investigation of Phosphorylation-Induced Folding of an Intrinsically Disordered Protein by Coarse-Grained Molecular Dynamics

Apart from being the most common mechanism of regulating protein function and transmitting signals throughout the cell, phosphorylation has an ability to induce disorder-to-order transition in an intrinsically disordered protein. In particular, it was shown that folding of the intrinsically disordered protein, eIF4E-binding protein isoform 2 (4E-BP2), can be induced by multisite phosphorylation. Here, the principles that govern the folding of phosphorylated 4E-BP2 (pT37pT46 4E-BP2_18-62) are investigated by analyzing canonical and replica exchange molecular dynamics trajectories, generated with the coarse-grained united-residue force field, in terms of local and global motions and the time dependence of formation of contacts between C^αs of selected pairs of residues. The key residues involved in the folding of the pT37pT46 4E-BP2_18-62 are elucidated by this analysis. The correlations between local and global motions are identified. Moreover, for a better understanding of the physics of the formation of the folded state, the experimental structure of the pT37pT46 4E-BP2_18-62 is analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger equation. It is shown that without molecular dynamics simulations the kinks are able to identify not only the phosphorylated sites of protein, the key players in folding, but also the reasons for the weak stability of the pT37pT46 4E-BP2_18-62.

On topology and knotty entanglement in protein folding

We investigate aspects of topology in protein folding. For this we numerically simulate the temperature driven folding and unfolding of the slipknotted archaeal virus protein AFV3-109. Due to knottiness the (un)folding is a topological process, it engages the entire backbone in a collective fashion. Accordingly we introduce a topological approach to model the process. Our simulations reveal that the (un)folding of AFV3-109 slipknot proceeds through a folding intermediate that has the topology of a trefoil knot. We observe that the final slipknot causes a slight swelling of the folded AFV3-109 structure. We disclose the relative stability of the strands and helices during both the folding and unfolding processes. We confirm results from previous studies that pointed out that it can be very demanding to simulate the formation of knotty self-entanglement, and we explain how the problems are circumvented: The slipknotted AFV3-109 protein is a very slow folder with a topologically demanding pathway, which needs to be properly accounted for in a simulation description. When we either increase the relative stiffness of bending, or when we decrease the speed of ambient cooling, the rate of slipknot formation rapidly increases.

New Insights into Folding, Misfolding, and Nonfolding Dynamics of a WW Domain

Intermediate states in protein folding are associated with formation of amyloid fibrils, which are responsible for a number of neurodegenerative diseases. Therefore, prevention of the aggregation of folding intermediates is one of the most important problems to overcome. Recently, we studied the origins and prevention of formation of intermediate states with the example of the Formin binding protein 28 (FBP28) WW domain. We demonstrated that the replacement of Leu26 by Asp26 or Trp26 (in ∼15% of the folding trajectories) can alter the folding scenario from three-state folding, a major folding scenario for the FBP28 WW domain (WT) and its mutants, toward two-state or downhill folding at temperatures below the melting point. Here, for a better understanding of the physics of the formation/elimination of intermediates, (i) the dynamics and energetics of formation of β-strands in folding, misfolding, and nonfolding trajectories of these mutants (L26D and L26W) is investigated; (ii) the experimental structures of WT, L26D, and L26W are analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger equation. We show that the formation of each β-strand in folding trajectories is accompanied by the emergence of kinks in internal coordinate space as well as a decrease in local free energy. In particular, the decrease in downhill folding trajectory is ∼7 kcal/mol, while it varies between 31 and 48 kcal/mol for the three-state folding trajectory. The kink analyses of the experimental structures give new insights into formation of intermediates, which may become a useful tool for preventing aggregation.

Protein tertiary structure and the myoglobin phase diagram

We develop an effective theory approach to investigate the phase properties of globular proteins. Instead of interactions between individual atoms or localized interaction centers, the approach builds directly on the tertiary structure of a protein. As an example we construct the phase diagram of (apo)myoglobin with temperature (T) and acidity (pH) as the thermodynamical variables. We describe how myoglobin unfolds from the native folded state to a random coil when temperature and acidity increase. We confirm the presence of two molten globule folding intermediates, and we predict an abrupt transition between the two when acidity changes. When temperature further increases we find that the abrupt transition line between the two molten globule states terminates at a tricritical point, where the helical structures fade away. Our results also suggest that the ligand entry and exit is driven by large scale collective motions that destabilize the myoglobin F-helix.

Solution x-ray scattering and structure formation in protein dynamics

We propose a computationally effective approach that builds on Landau mean-field theory in combination with modern nonequilibrium statistical mechanics to model and interpret protein dynamics and structure formation in small- to wide-angle x-ray scattering (S/WAXS) experiments. We develop the methodology by analyzing experimental data in the case of Engrailed homeodomain protein as an example. We demonstrate how to interpret S/WAXS data qualitatively with a good precision and over an extended temperature range. We explain experimental observations in terms of protein phase structure, and we make predictions for future experiments and for how to analyze data at different ambient temperature values. We conclude that the approach we propose has the potential to become a highly accurate, computationally effective, and predictive tool for analyzing S/WAXS data. For this, we compare our results with those obtained previously in an all-atom molecular dynamics simulation.

Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example

We propose to combine a mean-field approach with all-atom molecular dynamics (MD) into a multistage algorithm that can model protein folding and dynamics over very long time periods yet with atomic-level precision. As an example, we investigate an isolated monomeric Myc oncoprotein that has been implicated in carcinomas including those in colon, breast, and lungs. Under physiological conditions a monomeric Myc is presumed to be an example of intrinsically disordered proteins that pose a serious challenge to existing modeling techniques. We argue that a room-temperature monomeric Myc is in a dynamical state, it oscillates between different conformations that we identify. For this we adopt the Cα backbone of Myc in a crystallographic heteromer as an initial ansatz for the monomeric structure. We construct a multisoliton of the pertinent Landau free energy to describe the Cα profile with ultrahigh precision. We use Glauber dynamics to resolve how the multisoliton responds to repeated increases and decreases in ambient temperature. We confirm that the initial structure is unstable in isolation. We reveal a highly degenerate ground-state landscape, an attractive set towards which Glauber dynamics converges in the limit of vanishing ambient temperature. We analyze the thermal stability of this Glauber attractor using room-temperature molecular dynamics. We identify and scrutinize a particularly stable subset in which the two helical segments of the original multisoliton align in parallel next to each other. During the MD time evolution of a representative structure from this subset, we observe intermittent quasiparticle oscillations along the C-terminal α helix, some of which resemble a translating Davydov's Amide-I soliton. We propose that the presence of oscillatory motion is in line with the expected intrinsically disordered character of Myc.

Thermal unfolding of myoglobin in the Landau-Ginzburg-Wilson approach

The Landau-Ginzburg-Wilson paradigm is applied to model the low-temperature crystallographic Cα backbone structure of sperm whale myoglobin. The Glauber protocol is employed to simulate its response to an increase in ambient temperature. The myoglobin is found to unfold from its native state by a succession of α-helical intermediates, fully in line with the observed folding and unfolding patterns in denaturation experiments. In particular, a molten globule intermediate is identified with experimentally correct attributes. A detailed, experimentally testable contact map is constructed to characterize the specifics of the unfolding pathway, including the formation of long-range interactions. The results reveal how the unfolding process of a protein is driven by the interplay between, and a successive melting of, its modular secondary structure components.

Aspects of structural landscape of human islet amyloid polypeptide

The human islet amyloid polypeptide (hIAPP) co-operates with insulin to maintain glycemic balance. It also constitutes the amyloid plaques that aggregate in the pancreas of type-II diabetic patients. We have performed extensive in silico investigations to analyse the structural landscape of monomeric hIAPP, which is presumed to be intrinsically disordered. For this, we construct from first principles a highly predictive energy function that describes a monomeric hIAPP observed in a nuclear magnetic resonance experiment, as a local energy minimum. We subject our theoretical model of hIAPP to repeated heating and cooling simulations, back and forth between a high temperature regime where the conformation resembles a random walker and a low temperature limit where no thermal motions prevail. We find that the final low temperature conformations display a high level of degeneracy, in a manner which is fully in line with the presumed intrinsically disordered character of hIAPP. In particular, we identify an isolated family of α-helical conformations that might cause the transition to amyloidosis, by nucleation.

Phase diagram and the pseudogap state in a linear chiral homopolymer model

The phase structure of a single self-interacting homopolymer chain is investigated in terms of a universal theoretical model, designed to describe the chain in the infrared limit of slow spatial variations. The effects of chirality are studied and compared with the influence of a short-range attractive interaction between monomers, at various ambient temperature values. In the high-temperature limit the homopolymer chain is in the self-avoiding random walk phase. At very low temperatures two different phases are possible: When short-range attractive interactions dominate over chirality, the chain collapses into a space-filling conformation. But when the attractive interactions weaken, there is a low-temperature unfolding transition and the chain becomes like a straight rod. Between the high- and low-temperature limits, several intermediate states are observed, including the θ regime and pseudogap state, which is a novel form of phase state in the context of polymer chains. Applications to polymers and proteins, in particular collagen, are suggested.

Peierls-Nabarro barrier and protein loop propagation

When a self-localized quasiparticle excitation propagates along a discrete one-dimensional lattice, it becomes subject to a dissipation that converts the kinetic energy into lattice vibrations. Eventually the kinetic energy no longer enables the excitation to cross over the minimum energy barrier between neighboring sites, and the excitation becomes localized within a lattice cell. In the case of a protein, the lattice structure consists of the C(α) backbone. The self-localized quasiparticle excitation is the elemental building block of loops. It can be modeled by a kink that solves a variant of the discrete nonlinear Schrödinger equation. We study the propagation of such a kink in the case of the protein G related albumin-binding domain, using the united residue coarse-grained molecular-dynamics force field. We estimate the height of the energy barriers that the kink needs to cross over in order to propagate along the backbone lattice. We analyze how these barriers give rise to both stresses and reliefs, which control the kink movement. For this, we deform a natively folded protein structure by parallel translating the kink along the backbone away from its native position. We release the transposed kink, and we follow how it propagates along the backbone toward the native location. We observe that the dissipative forces that are exerted on the kink by the various energy barriers have a pivotal role in determining how a protein folds toward its native state.