Computational and Mathematical Biophysics最新文献

{"title":"Boundary Layer Effects on Ionic Flows Via Classical Poisson-Nernst-Planck Systems","authors":"Mingji Zhang","doi":"10.1515/cmb-2018-0002","DOIUrl":"https://doi.org/10.1515/cmb-2018-0002","url":null,"abstract":"Abstract A quasi-one-dimensional steady-state Poisson-Nernst-Planck model of two oppositely charged ion species through a membrane channel is analyzed. The model problem is treated as a boundary value problem of a singularly perturbed differential system. Our analysis is based on the geometric singular perturbation theory but, most importantly, on specific structures of this concrete model. The existence and (local ) uniqueness of solutions to the boundary value problem is established. In particular, an approximation of both the individual flux and the I-V (current-voltage) relation are derived explicitly from the zeroth order approximation (in \") solutions, from which the boundary layer effects on ionic flows are studied in great details.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"6 1","pages":"14 - 27"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2018-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48083124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extension of Caspar-Klug theory to higher order pentagonal polyhedra","authors":"Farrah Sadre-Marandi, Praachi Das","doi":"10.1515/cmb-2018-0001","DOIUrl":"https://doi.org/10.1515/cmb-2018-0001","url":null,"abstract":"Abstract Many viral capsids follow an icosahedral fullerene-like structure, creating a caged polyhedral arrangement built entirely from hexagons and pentagons. Viral capsids consist of capsid proteins,which group into clusters of six (hexamers) or five (pentamers). Although the number of hexamers per capsid varies depending on the capsid size, Caspar-Klug Theory dictates there are exactly twelve pentamers needed to form a closed capsid.However, for a significant number of viruses, including viruses of the Papovaviridae family, the theory doesn’t apply. The anomaly of the Caspar-Klug Theory has raised a new question:“For which Caspar and Klug models can each hexamer be replaced with a pentamer while still following icosahedral symmetry?” This paper proposes an answer to this question by examining icosahedral viral capsid-like structures composed only of pentamers, called pentagonal polyhedra. The analysis shows that pentagonal polyhedra fall in a subclass of T, defined by P ≥ 7 and T = 1( mod 3).","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"6 1","pages":"1 - 13"},"PeriodicalIF":0.0,"publicationDate":"2018-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2018-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46735103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modification of Bikerman model with specific ion sizes","authors":"Tzyy-Leng Horng, Ping-Hsuan Tsai, Tai-Chia Lin","doi":"10.1515/mlbmb-2017-0010","DOIUrl":"https://doi.org/10.1515/mlbmb-2017-0010","url":null,"abstract":"Abstract Classical Poisson-Boltzman and Poisson-Nernst-Planck models can only work when ion concentrations are very dilute, which often mismatches experiments. Researchers have been working on the modification to include finite-size effect of ions, which is non-negelible when ion concentrations are not dilute. One of modified models with steric effect is Bikerman model, which is rather popular nowadays. It is based on the consideration of ion size by putting additional entropy term for solvent in free energy. However, ion size is non-specific in original Bikerman model, which did not consider specific ion sizes. Many researchers have worked on the extension of Bikerman model to have specific ion sizes. A direct extension of original Bikerman model by simply replacing the non-specific ion size to specific ones seems natural and has been acceptable to many researchers in this field.Herewe prove this straight forward extension, in some limiting situations, fails to uphold the basic requirement that ion occupation sites must be identical. This requirement is necessary when computing entropy via particle distribution on occupation sites.We derived a new modified Bikerman model for using specific ion sizes by fixing this problem, and obtained its modified Poisson-Boltzmann and Poisson-Nernst-Planck equations.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"5 1","pages":"142 - 149"},"PeriodicalIF":0.0,"publicationDate":"2017-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mlbmb-2017-0010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48984110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematics at the eve of a historic transition in biology","authors":"G. Wei","doi":"10.1515/mlbmb-2017-0009","DOIUrl":"https://doi.org/10.1515/mlbmb-2017-0009","url":null,"abstract":"A century ago physicists and mathematicians worked in tandem and established quantum mechanism. Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism. Currently, biology is undergoing a historic transition from qualitative, phenomenological and descriptive to quantitative, analytical and predictive. Mathematics, again, becomes a driving force behind this new transition in biology.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"5 1","pages":"138 - 141"},"PeriodicalIF":0.0,"publicationDate":"2017-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mlbmb-2017-0009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48485116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relative dielectric constants and selectivity ratios in open ionic channels","authors":"B. Eisenberg, Weishi Liu","doi":"10.1515/mlbmb-2017-0008","DOIUrl":"https://doi.org/10.1515/mlbmb-2017-0008","url":null,"abstract":"Abstract We investigate the effects of the relative dielectric coefficient on ionic flows in open ion channels, using mathematical analysis of reasonably general Poisson-Nernst-Planck type models that can include the finite sizes of ions. The value of the relative dielectric coefficient is of course a crucial parameter for ionic behavior in general. Using the powerful theory of singularly perturbed problems in applied mathematics, we show that some properties of open channels are quite insensitive to variation in the relative dielectric coefficient, thereby explaining such effects seen unexpectedly in simulations. The ratio between the total number of one ion species and that of another ion species, and the ratio between the flux of one ion species and that of another ion species do not depend significantly on the relative dielectric coefficient.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"5 1","pages":"125 - 137"},"PeriodicalIF":0.0,"publicationDate":"2017-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mlbmb-2017-0008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48570646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric singular approach to Poisson-Nernst-Planck models with excess chemical potentials: Ion size effects on individual fluxes","authors":"Mingji Zhang, Jianbao Zhang, D. Acheampong","doi":"10.1515/mlbmb-2017-0005","DOIUrl":"https://doi.org/10.1515/mlbmb-2017-0005","url":null,"abstract":"Abstract We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck model for ionic flows through membrane channels. Excess chemical potentials are included in this work to account for finite ion size effects. This is the main difference from the classical Poisson-Nernst-Planck models, which treat ion species as point charges and neglect ion-to-ion interactions. Due to the fact that most experiments (with some exceptions) can only measure the total current while individual fluxes contain much more information on channel functions, our main focus is to study the qualitative properties of ionic flows in terms of individual fluxes under electroneutrality conditions. Our result shows that, in addition to ion sizes, the property depends on multiple physical parameters such as boundary concentrations and potentials, diffusion coe-cients, and ion valences. For the relatively simple setting and assumptions of the model in this paper, we are able to characterize, almost completely, the distinct effects of the nonlinear interplay between these physical parameters. The boundaries of different parameter regions are identified through a number of critical potential values that are explicitly expressed in terms of the physical parameters.Numerical simulations are performed to detect the critical potentials and investigate the quantitative properties of ionic flows over different potential regions. In particular, a special case is studied in Section 5 without the assumption of electroneutrality conditions.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"5 1","pages":"58 - 77"},"PeriodicalIF":0.0,"publicationDate":"2017-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mlbmb-2017-0005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42540808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of Current, Charge and Mass","authors":"B. Eisenberg, X. Oriols, D. Ferry","doi":"10.1515/mlbmb-2017-0006","DOIUrl":"https://doi.org/10.1515/mlbmb-2017-0006","url":null,"abstract":"Abstract Electricity plays a special role in our lives and life. The dynamics of electrons allow light to flow through a vacuum. The equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term, the displacement current (of a vacuum). The displacement current allows electrical signals to propagate through space. Displacement current guarantees that current is exactly conserved from inside atoms to between stars, as long as current is defined as the entire source of the curl of the magnetic field, as Maxwell did.We show that the Bohm formulation of quantum mechanics allows the easy definition of the total current, and its conservation, without the dificulties implicit in the orthodox quantum theory. The orthodox theory neglects the reality of magnitudes, like the currents, during times that they are not being explicitly measured.We show how conservation of current can be derived without mention of the polarization or dielectric properties of matter. We point out that displacement current is handled correctly in electrical engineering by ‘stray capacitances’, although it is rarely discussed explicitly. Matter does not behave as physicists of the 1800’s thought it did. They could only measure on a time scale of seconds and tried to explain dielectric properties and polarization with a single dielectric constant, a real positive number independent of everything. Matter and thus charge moves in enormously complicated ways that cannot be described by a single dielectric constant,when studied on time scales important today for electronic technology and molecular biology. When classical theories could not explain complex charge movements, constants in equations were allowed to vary in solutions of those equations, in a way not justified by mathematics, with predictable consequences. Life occurs in ionic solutions where charge is moved by forces not mentioned or described in the Maxwell equations, like convection and diffusion. These movements and forces produce crucial currents that cannot be described as classical conduction or classical polarization. Derivations of conservation of current involve oversimplified treatments of dielectrics and polarization in nearly every textbook. Because real dielectrics do not behave in that simple way-not even approximately-classical derivations of conservation of current are often distrusted or even ignored. We show that current is conserved inside atoms. We show that current is conserved exactly in any material no matter how complex are the properties of dielectric, polarization, or conduction currents. Electricity has a special role because conservation of current is a universal law.Most models of chemical reactions do not conserve current and need to be changed to do so. On the macroscopic scale of life, conservation of current necessarily links far spread boundaries to each other, correlating inputs and outputs, and thereby creating devi","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"5 1","pages":"115 - 78"},"PeriodicalIF":0.0,"publicationDate":"2017-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mlbmb-2017-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45378836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions","authors":"Jinn-Liang Liu, Dexuan Xie, B. Eisenberg","doi":"10.1515/mlbmb-2017-0007","DOIUrl":"https://doi.org/10.1515/mlbmb-2017-0007","url":null,"abstract":"Abstract We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation effects important in a variety of chemical and biological systems, especially in high field or large concentration conditions found in and near binding sites, ion channels, and electrodes. Steric effects and correlations are apparent when we compare nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric double layer and to experimental measurements on the selectivity of potassium channels for K+ over Na+.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"5 1","pages":"116 - 124"},"PeriodicalIF":0.0,"publicationDate":"2017-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mlbmb-2017-0007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49153077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fatgraph models of RNA structure","authors":"F. Huang, C. Reidys, Reza Rezazadegan","doi":"10.1515/mlbmb-2017-0001","DOIUrl":"https://doi.org/10.1515/mlbmb-2017-0001","url":null,"abstract":"Abstract In this review paper we discuss fatgraphs as a conceptual framework for RNA structures. We discuss various notions of coarse-grained RNA structures and relate them to fatgraphs.We motivate and discuss the main intuition behind the fatgraph model and showcase its applicability to canonical as well as noncanonical base pairs. Recent discoveries regarding novel recursions of pseudoknotted (pk) configurations as well as their translation into context-free grammars for pk-structures are discussed. This is shown to allow for extending the concept of partition functions of sequences w.r.t. a fixed structure having non-crossing arcs to pk-structures. We discuss minimum free energy folding of pk-structures and combine these above results outlining how to obtain an inverse folding algorithm for PK structures.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"5 1","pages":"1 - 20"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mlbmb-2017-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67036072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparative Assessment of Nonlocal Continuum Solvent Models Exhibiting Overscreening","authors":"Baihua Ren, J. Bardhan","doi":"10.1515/mlbmb-2017-0004","DOIUrl":"https://doi.org/10.1515/mlbmb-2017-0004","url":null,"abstract":"Abstract Nonlocal continua have been proposed to offer a more realistic model for the electrostatic response of solutions such as the electrolyte solvents prominent in biology and electrochemistry. In this work, we review three nonlocal models based on the Landau-Ginzburg framework which have been proposed but not directly compared previously, due to different expressions of the nonlocal constitutive relationship. To understand the relationships between these models and the underlying physical insights from which they are derive, we situate these models into a single, unified Landau-Ginzburg framework. One of the models offers the capacity to interpret how temperature changes affect dielectric response, and we note that the variations with temperature are qualitatively reasonable even though predictions at ambient temperatures are not quantitatively in agreement with experiment. Two of these models correctly reproduce overscreening (oscillations between positive and negative polarization charge densities), and we observe small differences between them when we simulate the potential between parallel plates held at constant potential. These computations require reformulating the two models as coupled systems of local partial differential equations (PDEs), and we use spectral methods to discretize both problems. We propose further assessments to discriminate between the models, particularly in regards to establishing boundary conditions and comparing to explicit-solvent molecular dynamics simulations.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"5 1","pages":"40 - 57"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mlbmb-2017-0004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67036074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}