EFOLD,a New Program Complex for Molecular Modeling: The Use of a Flexible Weighting Coefficient Scheme and the Standard Valence Geometry in Modeling the Enzyme Active Sites

An algorithm was proposed for the representation of biopolymer structures in an internal coordinate system (so-called structure regularization) by minimizing the target function using a flexible weighting coefficient scheme with three components that determine the reliability of deviations of each atom. For the structure regularization, an algorithm for taking into account the temperature factor was suggested for the first time. It was shown by the example of the aspartyl protease rhizopuspepsin that the representation in the internal coordinate system may result in an accurate reproduction of the structural details of separate molecule fragments, such as the enzyme active site region. This algorithm was implemented as one of the modules of EFOLD.     

Inference of biological S-system using the separable estimation method and the genetic algorithm

Reconstruction of a biological system from its experimental time series data is a challenging task in systems biology. The S-system which consists of a group of nonlinear ordinary differential equations (ODEs) is an effective model to characterize molecular biological systems and analyze the system dynamics. However, inference of S-systems without the knowledge of system structure is not a trivial task due to its nonlinearity and complexity. In this paper, a pruning separable parameter estimation algorithm (PSPEA) is proposed for inferring S-systems. This novel algorithm combines the separable parameter estimation method (SPEM) and a pruning strategy, which includes adding an l? regularization term to the objective function and pruning the solution with a threshold value. Then, this algorithm is combined with the continuous genetic algorithm (CGA) to form a hybrid algorithm that owns the properties of these two combined algorithms. The performance of the pruning strategy in the proposed algorithm is evaluated from two aspects: the parameter estimation error and structure identification accuracy. The results show that the proposed algorithm with the pruning strategy has much lower estimation error and much higher identification accuracy than the existing method.     

Fast flexible modeling of RNA structure using internal coordinates

Modeling the structure and dynamics of large macromolecules remains a critical challenge. Molecular dynamics (MD) simulations are expensive because they model every atom independently, and are difficult to combine with experimentally derived knowledge. Assembly of molecules using fragments from libraries relies on the database of known structures and thus may not work for novel motifs. Coarse-grained modeling methods have yielded good results on large molecules but can suffer from difficulties in creating more detailed full atomic realizations. There is therefore a need for molecular modeling algorithms that remain chemically accurate and economical for large molecules, do not rely on fragment libraries, and can incorporate experimental information. RNABuilder works in the internal coordinate space of dihedral angles and thus has time requirements proportional to the number of moving parts rather than the number of atoms. It provides accurate physics-based response to applied forces, but also allows user-specified forces for incorporating experimental information. A particular strength of RNABuilder is that all Leontis-Westhof basepairs can be specified as primitives by the user to be satisfied during model construction. We apply RNABuilder to predict the structure of an RNA molecule with 160 bases from its secondary structure, as well as experimental information. Our model matches the known structure to 10.2 Angstroms RMSD and has low computational expense.     

3D TOF-PET image reconstruction using total variation regularization

In this paper we introduce a semi-analytic algorithm for 3-dimensional image reconstruction for positron emission tomography (PET). The method consists of the back-projection of the acquired data into the most likely image voxel according to time-of-flight (TOF) information, followed by the filtering step in the image space using an iterative optimization algorithm with a total variation (TV) regularization. TV regularization in image space is more computationally efficient than usual iterative optimization methods for PET reconstruction with full system matrix that use TV regularization. The efficiency comes from the one-time TOF back-projection step that might also be described as a reformatting of the acquired data. An important aspect of our work concerns the evaluation of the filter operator of the linear transform mapping an original radioactive tracer distribution into the TOF back-projected image. We obtain concise, closed-form analytical formula for the filter operator. The proposed method is validated with the Monte Carlo simulations of the NEMA IEC phantom using a one-layer, 50 cm-long cylindrical device called Jagiellonian PET scanner. The results show a better image quality compared with the reference TOF maximum likelihood expectation maximization algorithm.     

Distributed modeling of human influenza a virus–host cell interactions during vaccine production

This contribution is concerned with population balance modeling of virus–host cell interactions during vaccine production. Replication of human influenza A virus in cultures of adherent Madin–Darby canine kidney (MDCK) cells is considered as a model system. The progress of infection can be characterized by the intracellular amount of viral nucleoprotein (NP) which is measured via flow cytometry. This allows the differentiation of the host cell population and gives rise to a distributed modeling approach. For this purpose a degree of fluorescence is introduced as an internal coordinate which is linearly linked to the intracellular amount of NP. Experimental results for different human influenza A subtypes reveal characteristic dynamic phenomena of the cell distribution like transient multimodality and reversal of propagation direction. The presented population balance model provides a reasonable explanation for these dynamic phenomena by the explicit consideration of different states of infection of individual cells. Kinetic parameters are determined from experimental data. To translate the emerging infinite dimensional parameter estimation problem to a finite dimension the parameters are assumed to depend linearly on the internal coordinate. As a result, the model is able to reproduce all characteristic dynamic phenomena of the considered process for the two examined virus strains and allows deeper insight into the underlying kinetic processes. Thus, the model is an important contribution to the understanding of the intracellular virus replication and virus spreading in cell cultures and can serve as a stepping stone for optimization in vaccine production. Biotechnol. Bioeng. 2013; 110: 2252–2266. © 2013 Wiley Periodicals, Inc.     

Computer modeling of polysaccharide-polysaccharide interactions: an approach to the kappa-carrageenan-mannan case.

A computer program SAINT has been developed for the investigation of the structure and for the prediction of minimum-energy structure of polysaccharide-polysaccharide complexes. The energy minimization is carried out on internal geometrical parameters--namely bond angles, torsional angles, and five parameters describing the mutual orientations of polysaccharide chains. For this purpose, the nonderivative method of conjugated directions is used. This procedure was applied to computer modeling of an idealized model of the binary gelling kappa-carrageenan and galactomannan system. It is shown that the interaction between two chains influences the structure of the individual polysaccharide molecule and that in the minimum-energy structures of the complex, the conformation of the chains does not correspond to the lowest energy.     

Adaptive local regularization methods for the inverse ECG problem

One of the fundamental problems in theoretical electrocardiography can be characterized by an inverse problem. We present new methods for achieving better estimates of heart surface potential distributions in terms of torso potentials through an inverse procedure. First, we outline an automatic adaptive refinement algorithm that minimizes the spatial discretization error in the transfer matrix, increasing the accuracy of the inverse solution. Second, we introduce a new local regularization procedure, which works by partitioning the global transfer matrix into sub-matrices, allowing for varying amounts of smoothing. Each submatrix represents a region within the underlying geometric model in which regularization can be specifically ‘tuned’ using an a priori scheme based on the L-curve method. This local regularization method can provide a substantial increase in accuracy compared to global regularization schemes. Within this context of local regularization, we show that a generalized version of the singular value decomposition (GSVD) can further improve the accuracy of ECG inverse solutions compared to standard SVD and Tikhonov approaches. We conclude with specific examples of these techniques using geometric models of the human thorax derived from MRI data.     

Structural study of homeodomain protein-DNA complexes using a homology modeling approach

The homeodomain is a conserved protein motif that binds to DNA and plays a central role in gene regulation. We use homeodomain as a model system to study the specific interactions between protein and DNA in a complex. Following the fundamental concept of homology modeling, we have developed an algorithm for predicting structures of both protein and DNA using the known structure of a similar complex as the template. The accuracies of the algorithm in predicting the complex structures are evaluated when two of the homeodomain protein-DNA complexes with known structures (antennapedia and MATalpha2) are selected as test systems. This algorithm allows structural studies of homeodomain binds to DNA with different sequences.     

Consensus alignment for reliable framework prediction in homology modeling

MOTIVATION: Even the best sequence alignment methods frequently fail to correctly identify the framework regions for which backbones can be copied from the template into the target structure. Since the underprediction and, more significantly, the overprediction of these regions reduces the quality of the final model, it is of prime importance to attain as much as possible of the true structural alignment between target and template. RESULTS: We have developed an algorithm called Consensus that consistently provides a high quality alignment for comparative modeling. The method follows from a benchmark analysis of the 3D models generated by ten alignment techniques for a set of 79 homologous protein structure pairs. For 20-to-40% of the targets, these methods yield models with at least 6 A root mean square deviation (RMSD) from the native structure. We have selected the top five performing methods, and developed a consensus algorithm to generate an improved alignment. By building on the individual strength of each method, a set of criteria was implemented to remove the alignment segments that are likely to correspond to structurally dissimilar regions. The automated algorithm was validated on a different set of 48 protein pairs, resulting in 2.2 A average RMSD for the predicted models, and only four cases in which the RMSD exceeded 3 A. The average length of the alignments was about 75% of that found by standard structural superposition methods. The performance of Consensus was consistent from 2 to 32% target-template sequence identity, and hence it can be used for accurate prediction of framework regions in homology modeling.     

Assignment and modeling of the Rev Response Element RNA bound to a Rev peptide using 13C-heteronuclear NMR

Summary The Rev Response Element (RRE) RNA-Rev protein interaction is important for regulation of gene expression in the human immunodeficiency virus. A model system for this interaction, which includes stem IIB of the RRE RNA and an arginine-rich peptide from the RNA-binding domain of Rev, was studied using multidimensional heteronuclear NMR. Assignment of the RNA when bound to the peptide was obtained from NMR experiments utilizing uniformly and specifically ¹³C-labeled RNA. Isotopic filtering experiments on the specifically labeled RNA enabled unambiguous assignment of unusual nonsequential NOE patterns present in the internal loop of the RRE. A three-dimensional model of the RNA in the complex was obtained using restrained molecular dynamics calculations. The internal loop contains two purine-purine base pairs, which are stacked to form one continuous helix flanked by two A-form regions. The formation of a G-G base pair in the internal loop requires an unusual structure of the phosphate backbone. This structural feature is consistent with mutational data as being important for the binding of Rev to the RRE. The G-G base pair may play an important role in opening the normally narrow major groove of A-form RNA to permit binding of the Rev basic domain.     

Molecular modeling of p-chlorophenoxyacetic acid binding to the CLC-0 channel

Molecular simulation techniques were applied to predict the interaction of the CLC-0 Cl(-) channel and the channel-blocking molecule p-chlorophenoxyacetic acid (CPA). A three-dimensional model of the CLC-0 channel was constructed on the basis of the homology with the bacterial Cl(-) channel StCLC, the structure of which has been solved by X-ray crystallography. Docking of the CPA molecule was obtained by using a geometric recognition algorithm, yielding 5000 possible conformations. By restraining the simulation to those conformations in which CPA is near the intracellular mouth of the channel, the CPA-protein complex models were reduced to three sets of conformations, which are interconvertible within 2 ns when molecular dynamics is applied to the system. Point mutations of CLC-0 at three different positions predicted to interact with CPA in these configurations did, however, not greatly alter CPA inhibition, suggesting a deeper final binding location. In the model, binding of CPA to a more internal position in the ionic pathway was obtained by applying a constant force vector to CPA, pushing it toward the center of the channel. This technique allowed us to outline the possible intrachannel pathway of CPA and to describe qualitatively the binding sites and energy barriers of this pathway. The consistency of the obtained models and the experimental data indicates that the CLC-0-CPA complex model is reasonable and can be used in further biological studies, such as rational design of blocking agents of and mutagenesis of CLC Cl(-) channels.     

Torsion angle dynamics: Reduced variable conformational sampling enhances crystallographic structure refinement

A reduced variable conformational sampling strategy for macromolecules based on molecular dynamics in torsion angle space is evaluated using crystallographic refinement as a prototypical search problem. Bae and Haug's algorithm for constrained dynamics [Bae, D. S., Haug, E. J. A recursive formulation for constrained mechanical system dynamics. Mech. Struct. Mach. 15:359–382, 1987], originally developed for robotics, was used. Their formulation solves the equations of motion exactly for arbitrary holonomic constraints, and hence differs from commonly used approximation algorithms. It uses gradients calculated in Cartesian coordinates, and thus also differs from internal coordinate formulations. Molecular dynamics can be carried out at significantly higher temperatures due to the elimination of the high frequency bond and angle vibrations. The sampling strategy presented here combines high temperature torsion angle dynamics with repeated trajectories using different initial velocities. The best solutions can be identified by the free R value, or the R value if experimental phase information is appropriately included in the refinement. Applications to crystallographic refinement show a significantly increased radius of convergence over conventional techniques. For a test system with diffraction data to 2 Å resolution, slow-cooling protocols fail to converge if the backbone atom root mean square (rms) coordinate deviation from the crystal structure is greater than 1.25 Å, but torsion angle refinement can correct backbone atom rms coordinate deviations up to approximately 1.7 Å. © 1994 Wiley-Liss, Inc.     

Musculoskeletal-see-through mirror: Computational modeling and algorithm for whole-body muscle activity visualization in real time

In this paper, we present a system that estimates and visualizes muscle tensions in real time using optical motion capture and electromyography (EMG). The system overlays rendered musculoskeletal human model on top of a live video image of the subject. The subject therefore has an impression that he/she sees the muscles with tension information through the cloth and skin. The main technical challenge lies in real-time estimation of muscle tension. Since existing algorithms using mathematical optimization to distribute joint torques to muscle tensions are too slow for our purpose, we develop a new algorithm that computes a reasonable approximation of muscle tensions based on the internal connections between muscles known as neuronal binding. The algorithm can estimate the tensions of 274 muscles in only 16 ms, and the whole visualization system runs at about 15 fps. The developed system is applied to assisting sport training, and the user case studies show its usefulness. Possible applications include interfaces for assisting rehabilitation.     

Analysis of conformational motions and related key residue interactions responsible for a specific function of proteins with elastic network model

Protein collective motions play a critical role in many biochemical processes. How to predict the functional motions and the related key residue interactions in proteins is important for our understanding in the mechanism of the biochemical processes. Normal mode analysis (NMA) of the elastic network model (ENM) is one of the effective approaches to investigate the structure-encoded motions in proteins. However, the motion modes revealed by the conventional NMA approach do not necessarily correspond to a specific function of protein. In the present work, a new analysis method was proposed to identify the motion modes responsible for a specific function of proteins and then predict the key residue interactions involved in the functional motions by using a perturbation approach. In our method, an internal coordinate that accounts for the specific function was introduced, and the Cartesian coordinate space was transformed into the internal/Cartesian space by using linear approximation, where the introduced internal coordinate serves as one of the axes of the coordinate space. NMA of ENM in this internal/Cartesian space was performed and the function-relevant motion modes were identified according to their contributions to the specific function of proteins. Then the key residue interactions important for the functional motions of the protein were predicted as the interactions whose perturbation largely influences the fluctuation along the internal coordinate. Using our proposed methods, the maltose transporter (MalFGK₂) from E. Coli was studied. The functional motions and the key residue interactions that are related to the channel-gating function of this protein were successfully identified.     

Exploring the control circuit of cell migration by mathematical modeling

We have developed a top-down, rule-based mathematical model to explore the basic principles that coordinate mechanochemical events during animal cell migration, particularly the local-stimulation-global-inhibition model suggested originally for chemotaxis. Cells were modeled as a shape machine that protrudes or retracts in response to a combination of local protrusion and global retraction signals. Using an optimization algorithm to identify parameters that generate specific shapes and migration patterns, we show that the mechanism of local stimulation global inhibition can readily account for the behavior of Dictyostelium under a large collection of conditions. Within this collection, some parameters showed strong correlation, indicating that a normal phenotype may be maintained by complementation among functional modules. In addition, comparison of parameters for control and nocodazole-treated Dictyostelium identified the most prominent effect of microtubules as regulating the rates of retraction and protrusion signal decay, and the extent of global inhibition. Other changes in parameters can lead to profound transformations from amoeboid cells into cells mimicking keratocytes, neurons, or fibroblasts. Thus, a simple circuit of local stimulation-global inhibition can account for a wide range of cell behaviors. A similar top-down approach may be applied to other complex problems and combined with molecular manipulations to define specific protein functions.     

Defining the assumptions underlying modeling of epistatic QTL using variance component methods

Variance component models are commonly used to detect quantitative trait loci (QTL) in general pedigrees. The variance-covariance structure of the random QTL effect is given by the identity by descent (IBD) between genotypes. Epistatic effects have previously been modeled, both for unlinked and linked loci, as a random effect with a variance-covariance structure given by the Hadamard product between the IBD matrices of the direct QTL effects. In the original papers, the model was given but not derived. Here, we identify the underlying assumptions of this previously proposed model. It assumes that either an unlinked QTL or a fully informative marker (i.e., all marker alleles are unique in the base generation) is located between the loci. We discuss the need of developing a general algorithm to estimate the variance-covariance structure of the random epistatic effect for linked loci.     

Coarse-grained modeling of the actin filament derived from atomistic-scale simulations

A coarse-grained (CG) procedure that incorporates the information obtained from all-atom molecular dynamics (MD) simulations is presented and applied to actin filaments (F-actin). This procedure matches the averaged values and fluctuations of the effective internal coordinates that are used to define a CG model to the values extracted from atomistic MD simulations. The fluctuations of effective internal coordinates in a CG model are computed via normal-mode analysis (NMA), and the computed fluctuations are matched with the atomistic MD results in a self-consistent manner. Each actin monomer (G-actin) is coarse-grained into four sites, and each site corresponds to one of the subdomains of G-actin. The potential energy of a CG G-actin contains three bonds, two angles, and one dihedral angle; effective harmonic bonds are used to describe the intermonomer interactions in a CG F-actin. The persistence length of a CG F-actin was found to be sensitive to the cut-off distance of assigning intermonomer bonds. Effective harmonic bonds for a monomer with its third nearest neighboring monomers are found to be necessary to reproduce the values of persistence length obtained from all-atom MD simulations. Compared to the elastic network model, incorporating the information of internal coordinate fluctuations enhances the accuracy and robustness for a CG model to describe the shapes of low-frequency vibrational modes. Combining the fluctuation-matching CG procedure and NMA, the achievable time- and length scales of modeling actin filaments can be greatly enhanced. In particular, a method is described to compute the force-extension curve using the CG model developed in this work and NMA. It was found that F-actin is easily buckled under compressive deformation, and a writhing mode is developed as a result. In addition to the bending and twisting modes, this novel writhing mode of F-actin could also play important roles in the interactions of F-actin with actin-binding proteins and in the force-generation process via polymerization.     

Structural modeling extends QSAR analysis of antibody-lysozyme interactions to 3D-QSAR

This work shows that quantitative multivariate modeling is an emerging possibility for unraveling protein-protein interactions using a combination of designed mutations with sequence and structure information. Using this approach, it is possible to stereochemically determine which residue properties contribute most to the interaction. This is illustrated by results from modeling of the interaction of the wild-type and 17 single and double mutants of a camel antibody specific for lysozyme. Linear multivariate models describing association and dissociation rates as well as affinity were developed. Sequence information in the form of amino acid property scales was combined with 3D structure information (obtained using molecular mechanics calculations) in the form of coordinates of the alpha-carbons and the center of the side chains. The results show that in addition to the amino acid properties of the mutated residues 101 and 105, the dissociation rate is controlled by the side-chain coordinate of residue 105, whereas the association is determined by the coordinates of residues 99, 100, 105 (side chain), 111, and 112. The great difference between the models for association and dissociation rates illustrates that the event of molecular recognition and the property of binding stability rely on different physical processes.