Maximum Margin Clustering for State Decomposition of Metastable Systems

When studying a metastable dynamical system, a prime concern is how to decompose the phase space into a set of metastable states. Unfortunately, the metastable state decomposition based on simulation or experimental data is still a challenge. The most popular and simplest approach is geometric clustering which is developed based on the classical clustering technique. However, the prerequisites of this approach are: (1) data are obtained from simulations or experiments which are in global equilibrium and (2) the coordinate system is appropriately selected. Recently, the kinetic clustering approach based on phase space discretization and transition probability estimation has drawn much attention due to its applicability to more general cases, but the choice of discretization policy is a difficult task. In this paper, a new decomposition method designated as maximum margin metastable clustering is proposed, which converts the problem of metastable state decomposition to a semi-supervised learning problem so that the large margin technique can be utilized to search for the optimal decomposition without phase space discretization. Moreover, several simulation examples are given to illustrate the effectiveness of the proposed method

Simulating rare events using a Weighted Ensemble-based string method

We introduce an extension to the Weighted Ensemble (WE) path sampling method to restrict sampling to a one dimensional path through a high dimensional phase space. Our method, which is based on the finite-temperature string method, permits efficient sampling of both equilibrium and non-equilibrium systems. Sampling obtained from the WE method guides the adaptive refinement of a Voronoi tessellation of order parameter space, whose generating points, upon convergence, coincide with the principle reaction pathway. We demonstrate the application of this method to several simple, two-dimensional models of driven Brownian motion and to the conformational change of the nitrogen regulatory protein C receiver domain using an elastic network model. The simplicity of the two-dimensional models allows us to directly compare the efficiency of the WE method to conventional brute force simulations and other path sampling algorithms, while the example of protein conformational change demonstrates how the method can be used to efficiently study transitions in the space of many collective variables

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.Comment: 97 pages, 30 figure

Functional dynamics of the folded ankyrin repeats of I kappa B alpha revealed by nuclear magnetic resonance.

Inhibition of nuclear factor kappaB (NF-kappaB) is mainly accomplished by IkappaB alpha, which consists of a signal response sequence at the N-terminus, a six-ankyrin repeat domain (ARD) that binds NF-kappaB, and a C-terminal PEST sequence. Previous studies with the ARD revealed that the fifth and sixth repeats are only partially folded in the absence of NF-kappaB. Here we report NMR studies of a truncated version of IkappaB alpha, containing only the first four ankyrin repeats, IkappaB alpha(67-206). This four-repeat segment is well-structured in the free state, enabling full resonance assignments to be made. H-D exchange, backbone dynamics, and residual dipolar coupling (RDC) experiments reveal regions of flexibility. In addition, regions consistent with the presence of micro- to millisecond motions occur periodically throughout the repeat structure. Comparison of the RDCs with the crystal structure gave only moderate agreement, but an ensemble of structures generated by accelerated molecular dynamics gave much better agreement with the measured RDCs. The regions showing flexibility correspond to those implicated in entropic compensation for the loss of flexibility in ankyrin repeats 5 and 6 upon binding to NF-kappaB. The regions showing micro- to millisecond motions in the free protein are the ends of the beta-hairpins that directly interact with NF-kappaB in the complex

Fourier transform microwave spectroscopy of Ac-Ser-NH2: the role of side chain interactions in peptide folding

Serine capped dipeptide N-acetyl-L-serinamide (Ac-Ser-NH2) has been investigated using Fourier transform microwave spectroscopic techniques combined with laser ablation sources. Spectral signatures originating from one dominant species have been detected in the supersonic expansion. Rotational and nuclear quadrupole coupling constants of the two 14N nuclei have been used in the characterization of a Ceq/g-turn structure, which is stabilized by a C7O·· ·HN intramolecular hydrogen bond closing a seven-membered ring. Two extra hydrogen bonds involving the polar side chain (–CH2OH) further stabilize the structure. The non-observation of C5 species, attributed to the presence of the polar side chain, is in contrast with the previous gas phase observation of the related dipeptides containing glycine or alanine residues. The A–E splitting pattern arising from the internal rotation of the methyl group has been analyzed and the internal rotation barrier has been determined

Moving College Students to a Better Understanding of Substrate Specificity of Enzymes Through Utilizing Multimedia Pre-Training and an Interactive Enzyme Model

Scientists’ progress in understanding enzyme specificity uncovered a complex natural phenomenon. However, not all of the currently available biology textbooks seem to be up to date on this progress. Students’ understanding of how enzymes work is a core requirement in biochemistry and biology tertiary education. Nevertheless, current pre-college science education does not provide students with enough biochemical background to enable them to understand complex material such as this. To bridge this gap, a multimedia pre-training presentation was prepared to fuel the learner’s prior knowledge with discrete facts necessary to understand the presented concept. This treatment is also known to manage intrinsic cognitive load during the learning process. An interactive instructional enzyme model was also built to motivate students to learn about substrate specificity of enzymes. Upon testing the effect of this combined treatment on 111 college students, desirable learning outcomes were found in terms of cognitive load, motivation, and achievement. The multimedia pre-training group reported significantly less intrinsic cognitive load, higher motivation, and demonstrated higher transfer performance than the control and post-training groups. In this study, a statistical mediation model is also proposed to explain how cognitive load and motivation work in concert to foster learning from multimedia pre-training. This type of research goes beyond simple forms of “what works” to a deeper understanding of “how it works,” thus enabling informed decisions for multimedia instructional design. Multimedia learning plays multiple roles in science education. Therefore, science learners would be some of the first to benefit from improving multimedia instructional design. Accordingly, complex scientific phenomena can be introduced to college students in a motivating, informative, and cognitively efficient learning environment

Integrating Protein Dynamics And Enhanced Conformational Ensembles To Better Understand Their Role In Biomolecular Function

Proteins have been termed the building blocks of life due to their involvement in practically every biological process that occurs in a living organism. For years now, researchers have sought to uncover the underlying mechanisms employed by biomolecules to carry out such tasks and functions. Initial understanding of proteins and how they function, at the atomic level, was revolutionized by the generation of numerous average static structures via X-ray crystallographic methods. Nevertheless, although one or multiple three-dimensional structures exist for many proteins, biological activity cannot be solely explained by relatively rigid structures. Proteins are dynamic entities governed by their dynamic personalities where biological function is rooted in their internal motions, fluctuations, and conformational changes. However, despite many experimental and computational efforts, how protein motions or dynamics couple protein function remains poorly understood. Here, in this work, we employ standard molecular dynamics (MD) simulations and enhanced sampling methods (Rotatable accelerated MD-dual boost (RaMD-db)) to try and capture a more accurate representation of the dynamic nature of two enzymes, cyclophilin A and choline oxidase. We show that molecular dynamics is a powerful method and is more than capable of acquiring a more accurate representation of the dynamic nature of the enzymes, in comparison to experimental techniques. More so, RaMD-db, because it was able to sample conformational states that were never observed in standard MD. Furthermore, we showed, at an atomic level, how protein motions facilitate and are coupled to biological function in both cyclophilin A (CypA) and choline oxidase. Ultimately, an atomic level description of how protein motions facilitate function, provided by the results in this work, can be utilized for drug design advancement, protein engineering, and to gain a better understanding of protein participation in disease

A biologically-validated HCV E1E2 heterodimer structural model

The design of vaccine strategies and the development of drugs targeting the early stages of Hepatitis C virus (HCV) infection are hampered by the lack of structural information about its surface glycoproteins E1 and E2, the two constituents of HCV entry machinery. Despite the recent crystal resolution of limited versions of both proteins in truncated form, a complete picture of the E1E2 complex is still missing. Here we combined deep computational analysis of E1E2 secondary, tertiary and quaternary structure with functional and immunological mutational analysis across E1E2 in order to propose an in silico model for the ectodomain of the E1E2 heterodimer. Our model describes E1-E2 ectodomain dimerization interfaces, provides a structural explanation of E1 and E2 immunogenicity and sheds light on the molecular processes and disulfide bridges isomerization underlying the conformational changes required for fusion. Comprehensive alanine mutational analysis across 553 residues of E1E2 also resulted in identifying the epitope maps of diverse mAbs and the disulfide connectivity underlying E1E2 native conformation. The predicted structure unveils E1 and E2 structures in complex, thus representing a step towards the rational design of immunogens and drugs inhibiting HCV entry