Multiscale Modeling & Simulation最新文献

{"title":"A MATHEMATICAL FRAMEWORK FOR EXACT MILESTONING.","authors":"David Aristoff,&nbsp;Juan M Bello-Rivas,&nbsp;Ron Elber","doi":"10.1137/15M102157X","DOIUrl":"https://doi.org/10.1137/15M102157X","url":null,"abstract":"<p><p>We give a mathematical framework for Exact Milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process that can be efficiently simulated and analyzed. We generalize the setting of Exact Milestoning and give explicit error bounds for the error in the Milestoning equation for mean first passage times.</p>","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/15M102157X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34594412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"COARSE-GRAINED MODELING OF PROTEIN UNFOLDING DYNAMICS.","authors":"Mingge Deng,&nbsp;George Em Karniadakis","doi":"10.1137/130921519","DOIUrl":"https://doi.org/10.1137/130921519","url":null,"abstract":"<p><p>We present a new <i>dynamic elastic network model</i> (DENM) that describes the unfolding process of a force-loaded protein. The protein interaction network and its potentials are constructed based on information of its native-state structure obtained from the Protein Data Bank, with network nodes positioned at the <i>C_α</i> coordinates of the protein backbone. Specifically, to mimic the unfolding process, i.e., to simulate the process of overcoming the local energy barrier on the free energy landscape with force loading, the noncovalent protein network bonds (i.e., hydrogen bonds, salt bridges, hydrophobic contacts, etc.) are broken one-by-one with a certain probability, while the strong covalent bonds along the backbone (i.e., peptide bonds, disulfide bonds, etc.) are kept intact. The jumping event from local energy minima (bonds breaking rate) are chosen according to Kramer's theory and the Bell model. Moreover, we exploit the self-similar structure of proteins at different scales to design an effective coarse-graining procedure for DENM with optimal parameter selection. The robustness of DENM is validated by coarse-grained molecular dynamics (MD) simulation against atomistic MD simulation of force-extension processes of the Fibrinogen and Titin Immunoglobulin proteins. We observe that the native structure of the proteins determines the <i>total</i> unfolding dynamics (including large deviations) and not just the fluctuations around the native state.</p>","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/130921519","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32818356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Low Mach Number Fluctuating Hydrodynamics of Diffusively Mixing Fluids","authors":"A. Donev, A. Nonaka, Yifei Sun, T. Fai, Alejandro L. Garcia, J. Bell","doi":"10.2140/camcos.2014.9.47","DOIUrl":"https://doi.org/10.2140/camcos.2014.9.47","url":null,"abstract":"We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fluctuations in pressure associated with the propagation of sound waves by replacing the equation of state with a local thermodynamic constraint. We demonstrate that the low Mach number model preserves the spatio-temporal spectrum of the slower diffusive fluctuations. We develop a strictly conservative finite-volume spatial discretization of the low Mach number fluctuating equations in both two and three dimensions and construct several explicit Runge-Kutta temporal integrators that strictly maintain the equation of state constraint. The resulting spatio-temporal discretization is second-order accurate deterministically and maintains fluctuation-dissipation balance in the linearized stochastic equations. We apply our algorithms to model the development of giant concentration fluctuations in the presence of concentration gradients, and investigate the validity of common simplifications such as neglecting the spatial non-homogeneity of density and transport properties. We perform simulations of diffusive mixing of two fluids of different densities in two dimensions and compare the results of low Mach number continuum simulations to hard-disk molecular dynamics simulations. Excellent agreement is observed between the particle and continuum simulations of giant fluctuations during time-dependent diffusive mixing.","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2012-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/camcos.2014.9.47","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68005154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cell-Based Modeling","authors":"Roeland M. H. Merks, B. Enquist","doi":"10.1007/978-3-540-70529-1_70","DOIUrl":"https://doi.org/10.1007/978-3-540-70529-1_70","url":null,"abstract":"","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/978-3-540-70529-1_70","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51061334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A computational model of cell polarization and motility coupling mechanics and biochemistry.","authors":"Ben Vanderlei,&nbsp;James J Feng,&nbsp;Leah Edelstein-Keshet","doi":"10.1137/100815335","DOIUrl":"https://doi.org/10.1137/100815335","url":null,"abstract":"<p><p>The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time scales, with reaction kinetics on the order of seconds, and the deformation and motion of the cell occurring on the order of minutes. The computational difficulty, even in 2D, resides in the fact that the problem is inherently one of deforming, non-stationary domains, bounded by an elastic perimeter, inside of which there is redistribution of biochemical signaling substances. Here we report the results of a computational scheme using the immersed boundary method to address this problem. We adopt a simple reaction-diffusion system that represents an internal regulatory mechanism controlling the polarization of a cell, and determining the strength of protrusion forces at the front of its elastic perimeter. Using this computational scheme we are able to study the effect of protrusive and elastic forces on cell shapes on their own, the distribution of the reaction-diffusion system in irregular domains on its own, and the coupled mechanical-chemical system. We find that this representation of cell crawling can recover important aspects of the spontaneous polarization and motion of certain types of crawling cells.</p>","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2011-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/100815335","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"30843772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"P-SPLINES USING DERIVATIVE INFORMATION.","authors":"Christopher P Calderon, Josue G Martinez, Raymond J Carroll, Danny C Sorensen","doi":"10.1137/090768102","DOIUrl":"10.1137/090768102","url":null,"abstract":"<p><p>Time series associated with single-molecule experiments and/or simulations contain a wealth of multiscale information about complex biomolecular systems. We demonstrate how a collection of Penalized-splines (P-splines) can be useful in quantitatively summarizing such data. In this work, functions estimated using P-splines are associated with stochastic differential equations (SDEs). It is shown how quantities estimated in a single SDE summarize fast-scale phenomena, whereas variation between curves associated with different SDEs partially reflects noise induced by motion evolving on a slower time scale. P-splines assist in \"semiparametrically\" estimating nonlinear SDEs in situations where a time-dependent external force is applied to a single-molecule system. The P-splines introduced simultaneously use function and derivative scatterplot information to refine curve estimates. We refer to the approach as the PuDI (P-splines using Derivative Information) method. It is shown how generalized least squares ideas fit seamlessly into the PuDI method. Applications demonstrating how utilizing uncertainty information/approximations along with generalized least squares techniques improve PuDI fits are presented. Although the primary application here is in estimating nonlinear SDEs, the PuDI method is applicable to situations where both unbiased function and derivative estimates are available.</p>","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3117255/pdf/nihms272821.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"29952270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Easy Path Wavelet Transform: A New Adaptive Wavelet Transform for Sparse Representation of Two-Dimensional Data","authors":"G. Plonka","doi":"10.1137/080719248","DOIUrl":"https://doi.org/10.1137/080719248","url":null,"abstract":"We introduce a new locally adaptive wavelet transform, called easy path wavelet transform (EPWT), that works along pathways through the array of function values and exploits the local correlations of the data in a simple appropriate manner. The usual discrete orthogonal and biorthogonal wavelet transform can be formulated in this approach. The EPWT can be incorporated into a multiresolution analysis structure and generates data dependent scaling spaces and wavelet spaces. Numerical results show the enormous efficiency of the EPWT for representation of two-dimensional data.","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2009-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/080719248","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64019023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BLOOD FLOW IN THE CIRCLE OF WILLIS: MODELING AND CALIBRATION.","authors":"Kristen Devault,&nbsp;Pierre A Gremaud,&nbsp;Vera Novak,&nbsp;Mette S Olufsen,&nbsp;Guillaume Vernières,&nbsp;Peng Zhao","doi":"10.1137/07070231X","DOIUrl":"https://doi.org/10.1137/07070231X","url":null,"abstract":"<p><p>A numerical model based on one-dimensional balance laws and ad hoc zero-dimensional boundary conditions is tested against experimental data. The study concentrates on the circle of Willis, a vital subnetwork of the cerebral vasculature. The main goal is to obtain efficient and reliable numerical tools with predictive capabilities. The flow is assumed to obey the Navier-Stokes equations, while the mechanical reactions of the arterial walls follow a viscoelastic model. Like many previous studies, a dimension reduction is performed through averaging. Unlike most previous work, the resulting model is both calibrated and validated against in vivo data, more precisely transcranial Doppler data of cerebral blood velocity. The network considered has three inflow vessels and six outflow vessels. Inflow conditions come from the data, while outflow conditions are modeled. Parameters in the outflow conditions are calibrated using a subset of the data through ensemble Kalman filtering techniques. The rest of the data is used for validation. The results demonstrate the viability of the proposed approach.</p>","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2008-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/07070231X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"27868871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Application of new multi-resolution methods for the comparison of biomolecular electrostatic properties in the absence of global structural similarity.","authors":"Xiaoyu Zhang, Chandrajit L Bajaj, Bongjune Kwon, Todd J Dolinsky, Jens E Nielsen, Nathan A Baker","doi":"10.1137/050647670","DOIUrl":"10.1137/050647670","url":null,"abstract":"<p><p>In this paper we present a method for the multi-resolution comparison of biomolecular electrostatic potentials without the need for global structural alignment of the biomolecules. The underlying computational geometry algorithm uses multi-resolution attributed contour trees (MACTs) to compare the topological features of volumetric scalar fields. We apply the MACTs to compute electrostatic similarity metrics for a large set of protein chains with varying degrees of sequence, structure, and function similarity. For calibration, we also compute similarity metrics for these chains by a more traditional approach based upon 3D structural alignment and analysis of Carbo similarity indices. Moreover, because the MACT approach does not rely upon pairwise structural alignment, its accuracy and efficiency promises to perform well on future large-scale classification efforts across groups of structurally-diverse proteins. The MACT method discriminates between protein chains at a level comparable to the Carbo similarity index method; i.e., it is able to accurately cluster proteins into functionally-relevant groups which demonstrate strong dependence on ligand binding sites. The results of the analyses are available from the linked web databases http://ccvweb.cres.utexas.edu/MolSignature/ and http://agave.wustl.edu/similarity/. The MACT analysis tools are available as part of the public domain library of the Topological Analysis and Quantitative Tools (TAQT) from the Center of Computational Visualization, at the University of Texas at Austin (http://ccvweb.csres.utexas.edu/software). The Carbo software is available for download with the open-source APBS software package at http://apbs.sf.net/.</p>","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2561295/pdf/nihms50731.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"27716873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PREDICTED EFFECTS OF LOCAL CONFORMATIONAL COUPLING AND EXTERNAL RESTRAINTS ON THE TORSIONAL PROPERTIES OF SINGLE DNA MOLECULES.","authors":"Atsushi Matsumoto,&nbsp;Wilma K Olson","doi":"10.1137/060663040","DOIUrl":"https://doi.org/10.1137/060663040","url":null,"abstract":"<p><p>A newly developed, coarse-grained treatment of the low-frequency normal modes of DNA has been adapted to study the torsional properties of fully extended, double-helical molecules. Each base pair is approximated in this scheme as a rigid body, and molecular structure is described in terms of the relative position and orientation of successive base pairs. The torsional modulus C is computed from the lowest-frequency normal twisting mode using expressions valid for a homogeneous, naturally straight elastic rod. Fluctuations of local dimeric structure, including the coupled variation of conformational parameters, are based on the observed arrangements of neighboring base pairs in high-resolution structures. Chain ends are restrained by an elastic energy term. The calculations show how the end-to-end constraints placed on a naturally straight DNA molecule, in combination with the natural conformational features of the double helix, can account for the substantially larger torsional moduli determined with state-of-the-art, single-molecule experiments compared to values extracted from solution measurements and/or incorporated into theories to account for the force-extension properties of single molecules. The computed normal-mode frequencies and torsional moduli increase substantially if base pairs are inclined with respect to the double-helical axis and the deformations of selected conformational variables follow known interdependent patterns. The changes are greatest if the fluctuations in dimeric twisting are coupled with parameters that directly alter the end-to-end displacement. Imposed restraints that mimic the end-to-end conditions of single-molecule experiments then impede the twisting of base pairs and increase the torsional modulus. The natural inclination of base pairs concomitantly softens the Young's modulus, i.e., ease of duplex stretching. The analysis of naturally curved DNA points to a drop in the torsional modulus upon imposed extension of the double-helical molecule.</p>","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/060663040","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"27899248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}