Configurational space continuity and free energy calculations

Free energy is arguably the most importance function(al) for understanding of molecular systems. A number of rigorous and approximate free energy calculation/estimation methods have been developed over many decades. One important issue, the continuity of an interested macrostate (or path) in configurational space, has not been well articulated, however. As a matter of fact, some important special cases have been intensively discussed. In this perspective, I discuss the relevance of configurational space continuity in development of more efficient and reliable next generation free energy methodologies.Comment: 17 pages, 2 figure

Nonlinear backbone torsional pair correlations in proteins

Protein allostery requires dynamical structural correlations. Physical origin of which, however, remain elusive despite intensive studies during last two decades. Based on analysis of molecular dynamics (MD) simulation trajectories for ten proteins with different sizes and folds, we found that nonlinear backbone torsional pair (BTP) correlations, which are spatially more long-ranged and are mainly executed by loop residues, exist extensively in most analyzed proteins. Examination of torsional motion for correlated BTPs suggested that aharmonic torsional state transitions are essential for such non-linear correlations, which correspondingly occur on widely different and relatively longer time scales. In contrast, BTP correlations between backbone torsions in stable $\alpha$ helices and $\beta$ strands are mainly linear and spatially more short-ranged, and are more likely to associate with intra-well torsional dynamics. Further analysis revealed that the direct cause of non-linear contributions are heterogeneous, and in extreme cases canceling, linear correlations associated with different torsional states of participating torsions. Therefore, torsional state transitions of participating torsions for a correlated BTP are only necessary but not sufficient condition for significant non-linear contributions. These findings implicate a general search strategy for novel allosteric modulation of protein activities. Meanwhile, it was suggested that ensemble averaged correlation calculation and static contact network analysis, while insightful, are not sufficient to elucidate mechanisms underlying allosteric signal transmission in general, dynamical and time scale resolved analysis are essential.Comment: 25 pages, 8 figure

Shot Range and High Order Correlations in Proteins

The main chain dihedral angles play an important role to decide the protein conformation. The native states of a protein can be regard as an ensemble of a lot of similar conformations, in different conformations the main chain dihedral angles vary in a certain range. Each dihedral angle value can be described as a distribution, but only using the distribution can't describe the real conformation space. The reason is that the dihedral angle has correlation with others, especially the neighbor dihedral angles in primary sequence. In our study we analysis extensive molecular dynamics (MD) simulation trajectories of eleven proteins with different sizes and folds, we found that in stable second structure the correlations only exist between the dihedrals near to each other in primary sequence, long range correlations are rare. But in unstable structures (loop) long range correlations exist. Further we observed some characteristics of the short range correlations in different second structures ({\alpha}-helix, {\beta}-sheet) and we found that we can approximate good high order dihedral angle distribution good only use three order distribution in stable second structure which illustrates that high order correlations (over three order) is small in stable second structure

Entropically Dominant State of Proteins

Configurational entropy is an important factor in the free energy change of many macromolecular recognition and binding processes, and has been intensively studied. Despite great progresses that have been made, the global sampling remains to be a grand challenge in computational analysis of relevant processes. Here we propose and demonstrate an entropy estimation method that is based on physical partition of configurational space and can be readily combined with currently available methodologies. Tests with two globular proteins suggest that for flexible macromolecules with large and complex configurational space, accurate configurational entropy estimation may be achieved simply by considering the entropically most important subspace. This conclusion effectively converts an exhaustive sampling problem into a local sampling one, and defines entropically dominant state for proteins and other complex macromolecules. The conceptional breakthrough is likely to positively impact future theoretical analysis, computational algorithm development and experimental design of diverse chemical and biological molecular systems.Comment: 10 pages, 4 figure and 27 reference

Utility of potential energy span as an approximate free energy proxy

Free energy calculation is critical in predictive tasks such as protein folding, docking and design. However, rigorous calculation of free energy change is prohibitively expensive in these practical applications. The minimum potential energy is therefore widely utilized to approximate free energy. In this study, based on analysis of extensive molecular dynamics (MD) simulation trajectories of a few native globular proteins, we found that change of minimum and corresponding maximum potential energy terms exhibit similar level of correlation with change of free energy. More importantly, we demonstrated that change of span (maximum - minimum) of potential energy terms, which engender negligible additional computational cost, exhibit considerably stronger correlations with change of free energy than the corresponding change of minimum and maximum potential energy terms. Therefore, potential energy span may serve as an alternative efficient approximate free energy proxy.Comment: 18 pages, 8 figure

Configurational space discretization and free energy calculation in complex molecular systems

Trajectories provide dynamical information that is discarded in free energy calculations, for which we sought to design a scheme with the hope of saving cost for generating dynamical information. We first demonstrated that snapshots in a converged trajectory set are associated with implicit conformers that have invariant statistical weight distribution (ISWD). Based on the thought that infinite number of sets of implicit conformers with ISWD may be created through independent converged trajectory sets, we hypothesized that explicit conformers with ISWD may be constructed for complex molecular systems through systematic increase of conformer fineness, and tested the hypothesis in lipid molecule palmitoyloleoylphosphatidylcholine (POPC). Furthermore, when explicit conformers with ISWD were utilized as basic states to define conformational entropy, change of which between two given macrostates was found to be equivalent to change of free energy except a mere difference of a negative temperature factor, and change of enthalpy essentially cancels corresponding change of average intra-conformer entropy. These findings suggest that entropy enthalpy compensation is inherently a local phenomenon in configurational space. By implicitly taking advantage of entropy enthalpy compensation and forgoing all dynamical information, constructing explicit conformers with ISWD and counting thermally accessible number of which for interested end macrostates is likely to be an efficient and reliable alternative end point free energy calculation strategy.Comment: 27 pages, 8 figures, 1 tabl

Non-reciprocal Radio Frequency Transduction in a Parametric Mechanical Artificial Lattice

Generating non-reciprocal radio frequency transduction plays important roles in a wide range of research and applications, and an aspiration is to integrate this functionality into micro-circuit without introducing magnetic field, which, however, remains challenging. By designing a 1D artificial lattice structure with neighbor-interaction engineered parametrically, we predicted a non-reciprocity transduction with giant unidirectionality. We then experimentally demonstrated the phenomenon on a nano-electromechanical chip fabricated by conventional complementary metal-silicon processing. A unidirectionality with isolation as high as 24dB is achieved and several different transduction schemes are realized by programming the control voltages topology. Apart from being used as a radio frequency isolator, the system provides a way to build practical on-chip programmable device for many researches and applications in radio frequency domain.Comment: 12 pages, 4 figure

A simple neural network implementation of generalized solvation free energy for assessment of protein structural models

Rapid and accurate assessment of protein structural models is essential for protein structure prediction and design. Great progress has been made in this regard, especially by recent development of ``knowledge-based'' potentials. Various machine learning based protein structural model quality assessment was also quite successful. However, performance of traditional ``physics-based'' potentials have not been as effective. Based on analysis of computational limitations of present solvation free energy formulation, which partially underlies unsatisfactory performance of ``physics-based'' potentials, we proposed a generalized sovation free energy (GSFE) framework. GSFE is intrinsically flexible for multi-scale treatments and is amenable for machine learning implementation. In this framework, each physical comprising unit of a complex molecular system has its own specific solvent environment. One distinctive feature of GSFE is that high order correlations within selected solvent environment might be captured through machine learning, in contrast to present empirical potentials (both ``knowledge-based'' and ``physics-based'') that are mainly based on pairwise interactions. Finally, we implemented a simple example of backbone and side-chain orientation based residue level protein GSFE with neural network, which was found to have competitive performance when compared with highly complex latest ``knowledge-based'' atomic potentials in distinguishing native structures from decoys

Pathway-based feature selection algorithms identify genes discriminating patients with multiple sclerosis apart from controls

Introduction The focus of analyzing data from microarray experiments and extracting biological insight from such data has experienced a shift from identification of individual genes in association with a phenotype to that of biological pathways or gene sets. Meanwhile, feature selection algorithm becomes imperative to cope with the high dimensional nature of many modeling tasks in bioinformatics. Many feature selection algorithms use information contained within a gene set as a biological priori, and select relevant features by incorporating such information. Thus, an integration of gene set analysis with feature selection is highly desired. Significance analysis of microarray to gene-set reduction analysis (SAM-GSR) algorithm is a novel direction of gene set analysis, aiming at further reduction of gene set into a core subset. Here, we explore the feature selection trait possessed by SAM-GSR and then modify SAM-GSR specifically to better fulfill this role. Results and Conclusions Training on a multiple sclerosis (MS) microarray data using both SAM-GSR and our modification of SAM-GSR, excellent discriminative performance on an independent test set was achieved. To conclude, absorbing biological information from a gene set may be helpful for classification and feature selection. Discussion Given the fact the complete pathway information is far from completeness, a statistical method capable of constructing biologically meaningful gene networks is in demand. The basic requirement is that interplay among genes must be taken into account

Ideal gas behavior of rotamerically defined conformers in native globular proteins

Protein conformational transitions, which are essential for function, may be driven either by entropy or enthalpy when molecular systems comprising solute and solvent molecules are the focus. Revealing thermodynamic origin of a given molecular process is an important but difficult task, and general principles governing protein conformational distributions remain elusive. Here we demonstrate that when protein molecules are taken as thermodynamic systems and solvents being treated as the environment, conformational entropy is an excellent proxy for free energy and is sufficient to explain protein conformational distributions. Specifically, by defining each unique combination of side chain torsional state as a conformer, the population distribution (or free energy) on an arbitrarily given order parameter is approximately a linear function of conformational entropy. Additionally, span of various microscopic potential energy terms is observed to be highly correlated with both conformational entropy and free energy. Presently widely utilized free energy proxies, including minimum potential energy, average potential energy terms by themselves or in combination with vibrational entropy\cite, are found to correlate with free energy rather poorly. Therefore, our findings provide a fundamentally new theoretical base for development of significantly more reliable and efficient next generation computational tools, where the number of available conformers,rather than poential energy of microscopic configurations, is the central focus. We anticipate that many related research fields, including structure based drug design and discovery, protein design, docking and prediction of general intermolecular interactions involving proteins, are expected to benefit greatly.Comment: 6 figures in the main tex