Abstract A particle-cluster treecode based on barycentric Hermite interpolation is presented for fast summation of electrostatic particle interactions in 3D. The interpolation nodes are Chebyshev points of the 2nd kind in each cluster. It is noted that barycentric Hermite interpolation is scale-invariant in a certain sense that promotes the treecode’s efficiency. Numerical results for the Coulomb and screened Coulomb potentials show that the treecode run time scales like O(N log N), where N is the number of particles in the system. The advantage of the barycentric Hermite treecode is demonstrated in comparison with treecodes based on Taylor approximation and barycentric Lagrange interpolation.
{"title":"A treecode based on barycentric Hermite interpolation for electrostatic particle interactions","authors":"R. Krasny, Lei Wang","doi":"10.1515/cmb-2019-0006","DOIUrl":"https://doi.org/10.1515/cmb-2019-0006","url":null,"abstract":"Abstract A particle-cluster treecode based on barycentric Hermite interpolation is presented for fast summation of electrostatic particle interactions in 3D. The interpolation nodes are Chebyshev points of the 2nd kind in each cluster. It is noted that barycentric Hermite interpolation is scale-invariant in a certain sense that promotes the treecode’s efficiency. Numerical results for the Coulomb and screened Coulomb potentials show that the treecode run time scales like O(N log N), where N is the number of particles in the system. The advantage of the barycentric Hermite treecode is demonstrated in comparison with treecodes based on Taylor approximation and barycentric Lagrange interpolation.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"7 1","pages":"73 - 84"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2019-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44607815","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}
A riboswitch is a type of RNA molecule that regulates important biological functions by changing structure, typically under ligand-binding. We assess the extent that these ligand-bound structural alternatives are present in the Boltzmann sample, a standard RNA secondary structure prediction method, for three riboswitch test cases. We use the cluster analysis tool RNAStructProfiling to characterize the different modalities present among the suboptimal structures sampled. We compare these modalities to the putative base pairing models obtained from independent experiments using NMR or fluorescence spectroscopy. We find, somewhat unexpectedly, that profiling the Boltzmann sample captures evidence of ligand-bound conformations for two of three riboswitches studied. Moreover, this agreement between predicted modalities and experimental models is consistent with the classification of riboswitches into thermodynamic versus kinetic regulatory mechanisms. Our results support cluster analysis of Boltzmann samples by RNAStructProfiling as a possible basis for de novo identification of thermodynamic riboswitches, while highlighting the challenges for kinetic ones.
{"title":"Towards an understanding of RNA structural modalities: a riboswitch case study.","authors":"Hee Rhang Yoon, Aaztli Coria, Alain Laederach, Christine Heitsch","doi":"10.1515/cmb-2019-0004","DOIUrl":"https://doi.org/10.1515/cmb-2019-0004","url":null,"abstract":"<p><p>A riboswitch is a type of RNA molecule that regulates important biological functions by changing structure, typically under ligand-binding. We assess the extent that these ligand-bound structural alternatives are present in the Boltzmann sample, a standard RNA secondary structure prediction method, for three riboswitch test cases. We use the cluster analysis tool RNAStructProfiling to characterize the different modalities present among the suboptimal structures sampled. We compare these modalities to the putative base pairing models obtained from independent experiments using NMR or fluorescence spectroscopy. We find, somewhat unexpectedly, that profiling the Boltzmann sample captures evidence of ligand-bound conformations for two of three riboswitches studied. Moreover, this agreement between predicted modalities and experimental models is consistent with the classification of riboswitches into thermodynamic versus kinetic regulatory mechanisms. Our results support cluster analysis of Boltzmann samples by RNAStructProfiling as a possible basis for de novo identification of thermodynamic riboswitches, while highlighting the challenges for kinetic ones.</p>","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"7 1","pages":"48-63"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2019-0004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39083785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A new CBSF empirical scoring function for the estimation of binding energies between proteins and small molecules is proposed in this report. The final score is obtained as a sum of three energy terms calculated using descriptors based on a simple counting of the interacting protein-ligand atomic pairs. All the required weighting coefficients for this method were derived from a pretrained neural network. The proposed method demonstrates a high accuracy and reproduces binding energies of protein-ligand complexes from the CASF-2016 test set with a standard deviation of 2.063 kcal/mol (1.511 log units) and an average error of 1.682 kcal/mol (1.232 log units). Thus, CBSF has a significant potential for the development of rapid and accurate estimates of the protein-ligand interaction energies.
{"title":"CBSF: A New Empirical Scoring Function for Docking Parameterized by Weights of Neural Network","authors":"R. Syrlybaeva, M. Talipov","doi":"10.1515/cmb-2019-0009","DOIUrl":"https://doi.org/10.1515/cmb-2019-0009","url":null,"abstract":"Abstract A new CBSF empirical scoring function for the estimation of binding energies between proteins and small molecules is proposed in this report. The final score is obtained as a sum of three energy terms calculated using descriptors based on a simple counting of the interacting protein-ligand atomic pairs. All the required weighting coefficients for this method were derived from a pretrained neural network. The proposed method demonstrates a high accuracy and reproduces binding energies of protein-ligand complexes from the CASF-2016 test set with a standard deviation of 2.063 kcal/mol (1.511 log units) and an average error of 1.682 kcal/mol (1.232 log units). Thus, CBSF has a significant potential for the development of rapid and accurate estimates of the protein-ligand interaction energies.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"7 1","pages":"121 - 134"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2019-0009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45555014","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}
F. Atici, M. Atici, Ngoc Nguyen, Tilekbek Zhoroev, G. Koch
Abstract We study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale hℕ0h$hmathbb{N}_0^h$, where h > 0. Since the measurements of the tumor volume in mice were taken daily, we consider h = 1 and obtain the model in discrete time (i.e. daily). We then continue with fractionalizing the discrete nabla operator to obtain the model as a system of nabla fractional difference equations. The nabla fractional difference operator is considered in the sense of Riemann-Liouville definition of the fractional derivative. In order to solve the fractional discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. For the data fitting purpose, we use a new developed method which is known as an improved version of the partial sum method to estimate the parameters for discrete and discrete fractional models. Sensitivity analysis is conducted to incorporate uncertainty/noise into the model. We employ both frequentist approach and Bayesian method to construct 90 percent confidence intervals for the parameters. Lastly, for the purpose of practicality, we test the discrete models for their efficiency and illustrate their current limitations for application.
{"title":"A study on discrete and discrete fractional pharmacokinetics-pharmacodynamics models for tumor growth and anti-cancer effects","authors":"F. Atici, M. Atici, Ngoc Nguyen, Tilekbek Zhoroev, G. Koch","doi":"10.1515/cmb-2019-0002","DOIUrl":"https://doi.org/10.1515/cmb-2019-0002","url":null,"abstract":"Abstract We study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale hℕ0h$hmathbb{N}_0^h$, where h > 0. Since the measurements of the tumor volume in mice were taken daily, we consider h = 1 and obtain the model in discrete time (i.e. daily). We then continue with fractionalizing the discrete nabla operator to obtain the model as a system of nabla fractional difference equations. The nabla fractional difference operator is considered in the sense of Riemann-Liouville definition of the fractional derivative. In order to solve the fractional discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. For the data fitting purpose, we use a new developed method which is known as an improved version of the partial sum method to estimate the parameters for discrete and discrete fractional models. Sensitivity analysis is conducted to incorporate uncertainty/noise into the model. We employ both frequentist approach and Bayesian method to construct 90 percent confidence intervals for the parameters. Lastly, for the purpose of practicality, we test the discrete models for their efficiency and illustrate their current limitations for application.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"7 1","pages":"10 - 24"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2019-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44645599","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}
Abhijeet R. Patil, Jongwha Chang, M. Leung, Sangjin Kim
Abstract The Illumina Infinium HumanMethylation27 (Illumina 27K) BeadChip assay is a relatively recent high-throughput technology that allows over 27,000 CpGs to be assayed. The Illumina 27K methylation data is less commonly used in comparison to gene expression in bioinformatics. It provides a critical need to find the optimal feature ranking (FR) method for handling the high dimensional data. The optimal FR method on the classifier is not well known, and choosing the best performing FR method becomes more challenging in high dimensional data setting. Therefore, identifying the statistical methods which boost the inference is of crucial importance in this context. This paper describes the detailed performances of FR methods such as fisher score, information gain, chi-square, and minimum redundancy and maximum relevance on different classification methods such as Adaboost, Random Forest, Naive Bayes, and Support Vector Machines. Through simulation study and real data applications, we show that the fisher score as an FR method, when applied on all the classifiers, achieved best prediction accuracy with significantly small number of ranked features.
{"title":"Analyzing high dimensional correlated data using feature ranking and classifiers","authors":"Abhijeet R. Patil, Jongwha Chang, M. Leung, Sangjin Kim","doi":"10.1515/cmb-2019-0008","DOIUrl":"https://doi.org/10.1515/cmb-2019-0008","url":null,"abstract":"Abstract The Illumina Infinium HumanMethylation27 (Illumina 27K) BeadChip assay is a relatively recent high-throughput technology that allows over 27,000 CpGs to be assayed. The Illumina 27K methylation data is less commonly used in comparison to gene expression in bioinformatics. It provides a critical need to find the optimal feature ranking (FR) method for handling the high dimensional data. The optimal FR method on the classifier is not well known, and choosing the best performing FR method becomes more challenging in high dimensional data setting. Therefore, identifying the statistical methods which boost the inference is of crucial importance in this context. This paper describes the detailed performances of FR methods such as fisher score, information gain, chi-square, and minimum redundancy and maximum relevance on different classification methods such as Adaboost, Random Forest, Naive Bayes, and Support Vector Machines. Through simulation study and real data applications, we show that the fisher score as an FR method, when applied on all the classifiers, achieved best prediction accuracy with significantly small number of ranked features.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"7 1","pages":"98 - 120"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2019-0008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44722830","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}
Matthew Conover, Max Staples, Dong Si, Miao Sun, Renzhi Cao
Abstract Quality Assessment (QA) plays an important role in protein structure prediction. Traditional multimodel QA method usually suffer from searching databases or comparing with other models for making predictions, which usually fail when the poor quality models dominate the model pool. We propose a novel protein single-model QA method which is built on a new representation that converts raw atom information into a series of carbon-alpha (Cα) atoms with side-chain information, defined by their dihedral angles and bond lengths to the prior residue. An LSTM network is used to predict the quality by treating each amino acid as a time-step and consider the final value returned by the LSTM cells. To the best of our knowledge, this is the first time anyone has attempted to use an LSTM model on the QA problem; furthermore, we use a new representation which has not been studied for QA. In addition to angles, we make use of sequence properties like secondary structure parsed from protein structure at each time-step without using any database, which is different than all existed QA methods. Our model achieves an overall correlation of 0.651 on the CASP12 testing dataset. Our experiment points out new directions for QA problem and our method could be widely used for protein structure prediction problem. The software is freely available at GitHub: https://github.com/caorenzhi/AngularQA
{"title":"AngularQA: Protein Model Quality Assessment with LSTM Networks","authors":"Matthew Conover, Max Staples, Dong Si, Miao Sun, Renzhi Cao","doi":"10.1101/560995","DOIUrl":"https://doi.org/10.1101/560995","url":null,"abstract":"Abstract Quality Assessment (QA) plays an important role in protein structure prediction. Traditional multimodel QA method usually suffer from searching databases or comparing with other models for making predictions, which usually fail when the poor quality models dominate the model pool. We propose a novel protein single-model QA method which is built on a new representation that converts raw atom information into a series of carbon-alpha (Cα) atoms with side-chain information, defined by their dihedral angles and bond lengths to the prior residue. An LSTM network is used to predict the quality by treating each amino acid as a time-step and consider the final value returned by the LSTM cells. To the best of our knowledge, this is the first time anyone has attempted to use an LSTM model on the QA problem; furthermore, we use a new representation which has not been studied for QA. In addition to angles, we make use of sequence properties like secondary structure parsed from protein structure at each time-step without using any database, which is different than all existed QA methods. Our model achieves an overall correlation of 0.651 on the CASP12 testing dataset. Our experiment points out new directions for QA problem and our method could be widely used for protein structure prediction problem. The software is freely available at GitHub: https://github.com/caorenzhi/AngularQA","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"7 1","pages":"1 - 9"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48729707","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}
Abstract We develop a computational method for simulating the nonlinear dynamics of an elastic tumor-host interface. This work is motivated by the recent linear stability analysis of a two-phase tumor model with an elastic membrane interface in 2D [47]. Unlike the classic tumor model with surface tension, the elastic interface condition is numerically challenging due to the 4th order derivative from the Helfrich bending energy. Here we are interested in exploring the nonlinear interface dynamics in a sharp interface framework. We consider a curvature dependent bending rigidity (curvature weakening [22]) to investigate metastasis patterns such as chains or fingers that invade the host environment. We solve the nutrient field and the Stokes flow field using a spectrally accurate boundary integral method, and update the interface using a nonstiff semi-implicit approach. Numerical results suggest curvature weakening promotes the development of branching patterns instead of encapsulated morphologies in a long period of time. For non-weakened bending rigidity, we are able to find self-similar shrinking morphologies based on marginally stable value of the apoptosis rate.
{"title":"Nonlinear simulation of an elastic tumor-host interface","authors":"Min-Jhe Lu, Chongxing Liu, Shuwang Li","doi":"10.1515/cmb-2019-0003","DOIUrl":"https://doi.org/10.1515/cmb-2019-0003","url":null,"abstract":"Abstract We develop a computational method for simulating the nonlinear dynamics of an elastic tumor-host interface. This work is motivated by the recent linear stability analysis of a two-phase tumor model with an elastic membrane interface in 2D [47]. Unlike the classic tumor model with surface tension, the elastic interface condition is numerically challenging due to the 4th order derivative from the Helfrich bending energy. Here we are interested in exploring the nonlinear interface dynamics in a sharp interface framework. We consider a curvature dependent bending rigidity (curvature weakening [22]) to investigate metastasis patterns such as chains or fingers that invade the host environment. We solve the nutrient field and the Stokes flow field using a spectrally accurate boundary integral method, and update the interface using a nonstiff semi-implicit approach. Numerical results suggest curvature weakening promotes the development of branching patterns instead of encapsulated morphologies in a long period of time. For non-weakened bending rigidity, we are able to find self-similar shrinking morphologies based on marginally stable value of the apoptosis rate.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"7 1","pages":"25 - 47"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2019-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43638869","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}
Abstract The wiring diagram of the mouse brain has recently been mapped at a mesoscopic scale in the Allen Mouse Brain Connectivity Atlas. Axonal projections from brain regions were traced using green fluoresent proteins. The resulting data were registered to a common three-dimensional reference space. They yielded a matrix of connection strengths between 213 brain regions. Global features such as closed loops formed by connections of similar intensity can be inferred using tools from persistent homology. We map the wiring diagram of the mouse brain to a simplicial complex (filtered by connection strengths). We work out generators of the first homology group. Some regions, including nucleus accumbens, are connected to the entire brain by loops, whereas no region has non-zero connection strength to all brain regions. Thousands of loops go through the isocortex, the striatum and the thalamus. On the other hand, medulla is the only major brain compartment that contains more than 100 loops.
{"title":"Topology of the mesoscale connectome of the mouse brain","authors":"Pascal Grange","doi":"10.1515/cmb-2020-0106","DOIUrl":"https://doi.org/10.1515/cmb-2020-0106","url":null,"abstract":"Abstract The wiring diagram of the mouse brain has recently been mapped at a mesoscopic scale in the Allen Mouse Brain Connectivity Atlas. Axonal projections from brain regions were traced using green fluoresent proteins. The resulting data were registered to a common three-dimensional reference space. They yielded a matrix of connection strengths between 213 brain regions. Global features such as closed loops formed by connections of similar intensity can be inferred using tools from persistent homology. We map the wiring diagram of the mouse brain to a simplicial complex (filtered by connection strengths). We work out generators of the first homology group. Some regions, including nucleus accumbens, are connected to the entire brain by loops, whereas no region has non-zero connection strength to all brain regions. Thousands of loops go through the isocortex, the striatum and the thalamus. On the other hand, medulla is the only major brain compartment that contains more than 100 loops.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"126 - 140"},"PeriodicalIF":0.0,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0106","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46730441","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}
Abstract Single channel dynamics can be modeled using stochastic differential equations, and the dynamics of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel, it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions (PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT) channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is to show that it is possible to optimize the parameters of a given drug such that the solution of theMTD model is very close to that of the WT: the mutation’s effect is, theoretically, reduced significantly.We will present the mathematical framework underpinning this methodology and apply it to several examples. In particular, we will show that it is possible to use the method to, theoretically, improve the properties of some well-known existing drugs.
{"title":"Computing Optimal Properties of Drugs Using Mathematical Models of Single Channel Dynamics","authors":"A. Tveito, M. Maleckar, G. Lines","doi":"10.1515/cmb-2018-0004","DOIUrl":"https://doi.org/10.1515/cmb-2018-0004","url":null,"abstract":"Abstract Single channel dynamics can be modeled using stochastic differential equations, and the dynamics of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel, it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions (PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT) channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is to show that it is possible to optimize the parameters of a given drug such that the solution of theMTD model is very close to that of the WT: the mutation’s effect is, theoretically, reduced significantly.We will present the mathematical framework underpinning this methodology and apply it to several examples. In particular, we will show that it is possible to use the method to, theoretically, improve the properties of some well-known existing drugs.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"6 1","pages":"41 - 64"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2018-0004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43952190","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}
Abstract In this work, we consider ionic flow through ion channels for an ionic mixture of a cation species (positively charged ions) and an anion species (negatively charged ions), and examine effects of a positive permanent charge on fluxes of the cation species and the anion species. For an ion species, and for any given boundary conditions and channel geometry,we introduce a ratio _(Q) = J(Q)/J(0) between the flux J(Q) of the ion species associated with a permanent charge Q and the flux J(0) associated with zero permanent charge. The flux ratio _(Q) is a suitable quantity for measuring an effect of the permanent charge Q: if _(Q) > 1, then the flux is enhanced by Q; if _ < 1, then the flux is reduced by Q. Based on analysis of Poisson-Nernst-Planck models for ionic flows, a universal property of permanent charge effects is obtained: for a positive permanent charge Q, if _1(Q) is the flux ratio for the cation species and _2(Q) is the flux ratio for the anion species, then _1(Q) < _2(Q), independent of boundary conditions and channel geometry. The statement is sharp in the sense that, at least for a given small positive Q, depending on boundary conditions and channel geometry, each of the followings indeed occurs: (i) _1(Q) < 1 < _2(Q); (ii) 1 < _1(Q) < _2(Q); (iii) _1(Q) < _2(Q) < 1. Analogous statements hold true for negative permanent charges with the inequalities reversed. It is also shown that the quantity _(Q) = |J(Q) − J(0)| may not be suitable for comparing the effects of permanent charges on cation flux and on anion flux. More precisely, for some positive permanent charge Q, if _1(Q) is associated with the cation species and _2(Q) is associated with the anion species, then, depending on boundary conditions and channel geometry, each of the followings is possible: (a) _1(Q) > _2(Q); (b) _1(Q) < _2(Q).
{"title":"A Flux Ratio and a Universal Property of Permanent Charges Effects on Fluxes","authors":"Weishi Liu","doi":"10.1515/cmb-2018-0003","DOIUrl":"https://doi.org/10.1515/cmb-2018-0003","url":null,"abstract":"Abstract In this work, we consider ionic flow through ion channels for an ionic mixture of a cation species (positively charged ions) and an anion species (negatively charged ions), and examine effects of a positive permanent charge on fluxes of the cation species and the anion species. For an ion species, and for any given boundary conditions and channel geometry,we introduce a ratio _(Q) = J(Q)/J(0) between the flux J(Q) of the ion species associated with a permanent charge Q and the flux J(0) associated with zero permanent charge. The flux ratio _(Q) is a suitable quantity for measuring an effect of the permanent charge Q: if _(Q) > 1, then the flux is enhanced by Q; if _ < 1, then the flux is reduced by Q. Based on analysis of Poisson-Nernst-Planck models for ionic flows, a universal property of permanent charge effects is obtained: for a positive permanent charge Q, if _1(Q) is the flux ratio for the cation species and _2(Q) is the flux ratio for the anion species, then _1(Q) < _2(Q), independent of boundary conditions and channel geometry. The statement is sharp in the sense that, at least for a given small positive Q, depending on boundary conditions and channel geometry, each of the followings indeed occurs: (i) _1(Q) < 1 < _2(Q); (ii) 1 < _1(Q) < _2(Q); (iii) _1(Q) < _2(Q) < 1. Analogous statements hold true for negative permanent charges with the inequalities reversed. It is also shown that the quantity _(Q) = |J(Q) − J(0)| may not be suitable for comparing the effects of permanent charges on cation flux and on anion flux. More precisely, for some positive permanent charge Q, if _1(Q) is associated with the cation species and _2(Q) is associated with the anion species, then, depending on boundary conditions and channel geometry, each of the followings is possible: (a) _1(Q) > _2(Q); (b) _1(Q) < _2(Q).","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"6 1","pages":"28 - 40"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2018-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42702166","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}
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