We show that the interplay between excluded volume effects, hydrophobicity, and hydrogen bonding of a tube-like representation of a polypeptide chain gives rise to free energy landscapes that exhibit a small number of metastable minima corresponding to common structural motifs observed in proteins. The complexity of the landscape increases only moderately with the length of the chain. Analysis of the temperature dependence of these landscapes reveals that the stability of specific metastable states is maximal at a temperature close to the mid-point of folding. These mestastable states are therefore likely to be of particular significance in determining the generic tendency of proteins to aggregate into potentially pathogenic agents.
We carried out dynamic force manipulations $in$ $silico$ on a variety of superhelical protein fragments from myosin, chemotaxis receptor, vimentin, fibrin, and phenylalanine zippers that vary in size and topology of their $α$-helical packing. When stretched along the superhelical axis, all superhelices show elastic, plastic, and inelastic elongation regimes, and undergo a dynamic transition from the $α$-helices to the $β$-sheets, which marks the onset of plastic deformation. Using Abeyaratne-Knowles formulation of phase transitions, we developed a theory to model mechanical and kinetic propert…
The free energy landscape responsible for crystallization can be complex even for relatively simple systems like hard sphere and charged stabilized colloids. In this work, using hard-core repulsive Yukawa model, which is known to show complex phase behavior consisting of fluid, FCC and BCC phases, we studied the interplay between the free energy landscape and polymorph selection during crystallization. When the stability of the BCC phase with respect to the fluid phase is gradually increased by changing the temperature and pressure at a fixed fluid-FCC stability, the final phase formed by crys…
The complex dynamics of an increasing number of systems is attributed to the emergence of a rugged energy landscape with an exponential number of metastable states. To develop this picture into a predictive dynamical theory I discuss how to compute the exponentially small probability of a jump from one metastable state to another. This is expressed as a path integral that can be evaluated by saddle-point methods in mean-field models, leading to a boundary value problem. The resulting dynamical equations are solved numerically by means of a Newton-Krylov algorithm in the paradigmatic spherical …
The interconversion between left- and right-handed helical folds of a polypeptide defines a dual-funneled free energy landscape. In this context, the funnel minima are connected through a continuum of unfolded conformations, evocative of the classical helix-coil transition. Physical intuition and recent conjectures suggest that this landscape can be mapped by assigning a left- or right-handed helical state to each residue. We explore this possibility using all-atom replica exchange molecular dynamics and an Ising-like model, demonstrating that the energy landscape architecture is at odds with …
Inferring intermediate states by leveraging the many-body Arrhenius law
The Institute of Mathematical Sciences（数学科学研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；University of Haifa at Oranim（奥拉尼姆海法大学）；University of Haifa（海法大学）
We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, the second on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleati…
Free-energy landscapes for short peptides -- specifically for variants of the pH Low Insertion Peptide (pHLIP) -- in the heterogeneous environment of a lipid bilayer or cell membrane are constructed, taking into account a set of dominant interactions and the conformational preferences of the peptide backbone. Our methodology interprets broken internal H-bonds along the backbone of a polypeptide as statistically interacting quasiparticles, activated from the helix reference state. The favored conformation depends on the local environment (ranging from polar to nonpolar), specifically on the ava…
Potential energy landscape picture of zero-temperature avalanche criticality governing dynamics in supercooled liquids
Toyota Central R&D Labs., Inc.（丰田中央研究所）；D3 Center, The University of Osaka（大阪大学D3中心）；Department of Physics, The University of Osaka（大阪大学物理系）；Department of Physics, Nagoya University（名古屋大学物理系）；Division of Chemical Engineering, Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科化学工程专攻）
We consider a range of model potentials with metastable states undergoing molecular dynamics coupled to a thermal bath in the high friction regime, and consider how the optimal reaction coordinate depends on the diffusion anisotropy. For this we use our recently proposed method 'Spectral gap optimization of order parameters (SGOOP)' (Tiwary and Berne, Proc. Natl. Acad. Sci. 113 2839 2016). We show how available information about dynamical observables in addition to static information can be incorporated into SGOOP, which can then be used to accurately determine the 'best' reaction coordinate f…
The relationship between short and long time relaxation dynamics is obtained for a simple solvable two-level energy landscape model of a glass. This is done through means of the Kramers transition theory, which arises in very natural manner to calculate transition rates between wells. Then the corresponding stochastic master equation is analytically solved to find the population of metastable states. A relation between the cooling rate, the characteristic relaxation time and the population of metastable states is found from the solution of such equation. From this, a relationship between the r…
The surface energy of the nucleus of a stable phase growing in the presence of several amorphous metastable phases of character intermediate between the initial and the final phases may depend non-trivially on the size of the nucleus. This size dependence is being increasingly used to explain diverse non-equilibrium phase selection, and relaxation, as in the random first-order transition (RFOT) theory of glasses. Here we develop an order parameter based Ginzburg-Landau approach that explicitly includes the rugged free energy landscape due to the metastable phases. The fractional dependence of …
As the simplest model of transition between the superhydrophobic Cassie-Baxter (CB) and Wenzel (W) states of a macroscopic droplet sitting on a microscopically rough or corrugated substrate, a substrate whose surface is covered by identical truncated or inverted truncated conical pores is considered. The free energy landscapes of the intrusion and extrusion processes of a liquid into single pore are analyzed when the liquid is compressed or stretched so that the liquid phase is either stable or metastable relative to the vapor phase. Therefore, this model is also relevant to the stability of t…
The ability to design synthesis processes that are out of equilibrium has opened the possibility of creating nanomaterials with remarkable physico-chemical properties, choosing from a much richer palette of possible atomic architectures compared to equilibrium processes in extended systems. In this work, we employ atomistic simulations to demonstrate how to control polymorph selection via cooling rate during nanoparticle freezing in the case of Ni$_3$Al, a material with a rich structural landscape. State-of-the-art free-energy calculations allow to rationalize the complex nucleation process, d…
