Potential functions are critical for computational studies of protein structure prediction, folding, and sequence design. A class of widely used potentials for coarse grained models of proteins are contact potentials in the form of weighted linear sum of pairwise contacts. However, these potentials have been shown to be unsuitable choices because they cannot stabilize native proteins against a large number of decoys generated by gapless threading. We develop an alternative framework for designing protein potential. We describe how finding optimal protein potential can be understood from two geometric viewpoints, and we derive nonlinear potentials using mixture of Gaussian kernel functions for folding and design. The optimization criterion for obtaining parameters of the potential is to minimize bounds on the generalization error of discriminating protein structures and decoys not used in training. In our experiment we use a training set of 440 protein structures repre senting a major portion of all known protein structures, and about 14 million structure decoys and sequence decoys obtained by gapless threading. We succeeded in obtaining nonlinear potential with perfect discrimination of the 440 native structures and native sequences. For the more challenging task of sequence design when decoys are obtained by gapless threading, we show that there is no linear potential with perfect discrimination of all 440 native sequences. Results on an independent test set of 194 proteins also showed that nonlinear kernel potential performs well.
Microscopic Theory of Protein Folding Rates.I: Fine Structure of the Free Energy Profile and Folding Routes from a Variational Approach
提出了一种关于最小受抑蛋白质的自由能垒和折叠路线的微观理论，大大扩展了先前概述的变分方法的介绍[J. J. Portman，S. Takada，P. G. Wolynes，Phys. Rev. Lett. { \bf 81}，5237（1998）]。我们选择的$λ$ -阻遏蛋白作为一个说明性的例子，并专注于如何聚合物链的统计影响自由能分布和部分有序的合奏结构。特别是，我们调查的自由能配置文件和折叠路线链刚度的作用。我们评估的适用性更简单的近似，其中沿着折叠路线的蛋白质分子的构象被限制有残基，要么完全折叠或展开在连续的拉伸。我们发现，从只有一个连续的折叠区域获得的折叠路线对应于一个链具有更大的持久性长度比适合于天然蛋白质链，而从两个连续的折叠区域获得的折叠路线是能够捕获的变分方法内计算的相对折叠区域。从连续序列近似获得的自由能分布有更大的障碍比更微观的变分理论，这被理解为部分有序的后果。
Contact Order Dependent Protein Folding Rates: Kinetic Consequences of a Cooperative Interplay Between Favorable Nonlocal Interactions and Local Conformational Preferences
The folding vs. adsorption behaviour of a coarse-grained off-lattice protein model near an attractive surface is presented within the frame of a Multicanonical Monte Carlo simulations. In the polymer-surface model, the Lennard-Jones potential is assumed as an interaction potential between the effective monomers and the attractive surface. Thermodynamic properties and some structural parameters for the minimum energy conformations are calculated for comparison of the folding and adsorption cases.
We develop a multi-scale approach to simulate hydrated nanobio systems under realistic condi- tions (e.g., nanoparticles and protein solutions at physiological conditions over time-scales up to hours). We combine atomistic simulations of water at bio-interfaces (e.g., proteins or membranes) and nano-interfaces (e.g., nanoparticles or graphene sheets) and coarse-grain models of hydration water for protein folding and protein design. We study protein self-assembly and crystallization, in bulk or under confinement, and the kinetics of protein adsorption onto nanoparticles, verify- ing our predict…
We study the protein folding problem on the base of the quantum approach we proposed recently by considering the model of protein chain with nine amino-acid residues. We introduced the concept of distance space and its projections on a $XY$-plane, and two characteristic quantities, one is called compactness of protein structure and another is called probability ratio involving shortest path. Our results not only confirmed the fast quantum folding time but also unveiled the existence of quantum intelligence hidden behind in choosing protein folding pathways.
We introduce a powerful iterative algorithm to compute protein folding pathways, with realistic all-atom force fields. Using the path integral formalism, we explicitly derive a modified Langevin equation which samples directly the ensemble of reactive pathways, exponentially reducing the cost of simulating thermally activated transitions. The algorithm also yields a rigorous stochastic estimate of the reaction coordinate. After illustrating this approach on a simple toy model, we successfully validate it against the results of ultra-long plain MD protein folding simulations for a fast folding …
We investigate the interplay between post-translational folding and escape of two small single-domain proteins at the ribosomal exit tunnel by using Langevin dynamics with coarse-grained models. It is shown that at temperatures lower or near the temperature of the fastest folding, folding proceeds concomitantly with the escape process, resulting in vectorial folding and enhancement of foldability of nascent proteins. The concomitance between the two processes, however, deteriorates as temperature increases. Our folding simulations as well as free energy calculation by using umbrella sampling s…
When described by a low-dimensional reaction coordinate, the rates of protein folding are determined by a subtle interplay between free-energy barriers and friction. While it is commonplace to extract free-energy profiles from molecular trajectories, a direct evaluation of friction is far more elusive, and one typically evaluates it indirectly via memoryless reaction rate theories. Here, using memory-kernel extraction methods founded on a generalised Langevin equation (GLE) formalism, we directly calculate the memory-dependent friction for eight fast-folding proteins, taken from a published se…
We propose a general theory to describe the distribution of protein-folding transition paths. We show that transition paths follow a predictable sequence of high-free-energy transient states that are separated by free-energy barriers. Each transient state corresponds to the assembly of one or more discrete, cooperative units, which are determined directly from the native structure. We show that the transition state on a folding pathway is reached when a small number of critical contacts are formed between a specific set of substructures, after which folding proceeds downhill in free energy. Th…
Focusing on a small set of proteins that i) fold in a concerted, all-or-none fashion and ii) do not contain knots or slipknots, we show that the Gauss linking integral, the torsion and the number of sequence-distant contacts provide information regarding the folding rate. Our results suggest that the global topology/geometry of the proteins shifts from right-handed to left-handed with decreasing folding rate, and that this topological change is associated with an increase in the number of more sequence-distant contacts.
Simulation, Experiment, and Evolution: Understanding Nucleation in Protein S6 Folding
在这项研究中，我们探索核和过渡态合奏的核糖体蛋白S6使用Monte Carlo Go模型结合实验的限制。结果进行了分析的背景下，广泛的实验和进化数据。单个残基在折叠核中的作用进行了鉴定，并详细探讨了S6折叠机制中的事件顺序。我们的结果的解释同意，并扩展了效用，通过调节变性剂浓度的实验，改变f值，并提出了强有力的证据，为现实主义的机械细节在我们的蒙特卡罗围棋模型和结构的解释实验f值。我们还观察到支持特定核的疏水核心的接触的可塑性。对于S6，它在折叠后与RNA和蛋白质结合，这种可塑性可能来自实现生物功能所需的构象灵活性。这些结果提出了一个理论和概念的图片，是相关的理解成核机制的蛋白质折叠。
