Computational and Mathematical Biophysics

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.

Raulia R. Syrlybaeva

Marat R. Talipov

CBSF: A New Empirical Scoring Function for Docking Parameterized by Weights of Neural Network

CBSF：一种新的基于神经网络权重参数化的对接经验评分函数

Abstract Dengue viral capsid plays a significant role in viral life cycle of dengue, especially in vial genome protection and virus-cell fusion. Revealing mechanisms of the viral capsid protein assembly may lead to the discovery of anti-viral drugs that inhibit the assembly of the viral capsid. The E and M-proteins are arranged into heterotetramers, which consists of two copies of E and M-protein. The heterotetramers are assembled into a highly ordered capsid. While many investigations of the interactions between E and M-proteins have been performed, there are very few studies on the interactions between the heterotetramers and their roles in capsid assembly. Utilizing a series of computational approaches, this study focuses on the assembly mechanism of the heterotetramers. Our electrostatic analyses lead to the identification of four binding modes between each two dengue heterotetramers that repeat periodically throughout the virus capsid. Among these four binding modes, heterotetramers in binding modes I, II and IV are attractive. But in the binding mode III the heterotetramers repel each other, making mode III a suitable target for drug design. Furthermore, MD simulations were performed following by salt bridges analysis. This study demonstrates that using computational approaches is a promising direction to study the dengue virus.

Gicela G Saucedo Salas

Alan E Lopez Hernandez

Jiadi He

Chitra Karki

Yixin Xie

Shengjie Sun

Yuejiao Xian

Lin Li

Using computational approaches to study dengue virus capsid assembly

利用计算方法研究登革病毒衣壳组装

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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>h</m:mi> <m:msubsup> <m:mrow> <m:mi>ℕ</m:mi> </m:mrow> <m:mn>0</m:mn> <m:mi>h</m:mi> </m:msubsup> </m:mrow> </m:math> $h\mathbb{N}_0^h$ , where h &gt; 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.

Ferhan M. Atıcı

Mustafa Atıcı

Ngoc Nguyen

Tilekbek Zhoroev

Gilbert Koch

A study on discrete and discrete fractional pharmacokinetics-pharmacodynamics models for tumor growth and anti-cancer effects

肿瘤生长与抗癌效果的离散及离散分数阶药代动力学-药效学模型研究

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.

Abhijeet R Patil

Jongwha Chang

Ming-Ying Leung

Sangjin Kim

Analyzing high dimensional correlated data using feature ranking and classifiers

利用特征排序和分类器分析高维相关数据

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

Matthew Conover

Max Staples

Dong Si

Miao Sun

Renzhi Cao

AngularQA: Protein Model Quality Assessment with LSTM Networks

AngularQA：基于LSTM网络的蛋白质模型质量评估

Abstract We observed the existence of periodic orbits in immune network under transitive solvable Lie algebra. In this article, we focus to develop condition of maximal Lie algebra for immune network model and use that condition to construct a vector field of symmetry to study nonlinear pathogen model. We used two methods to obtain analytical structure of solution, namely normal generator and differential invariant function. Numerical simulation of analytical structure exhibits correlated periodic pattern growth under spatiotemporal symmetry, which is similar to the linear dynamical simulation result. We used Lie algebraic method to understand correlation between growth pattern and symmetry of dynamical system. We employ idea of using one parameter point group of transformation of variables under which linear manifold is retained. In procedure, we present the method of deriving Lie point symmetries, the calculation of the first integral and the invariant solution for the ordinary differential equation (ODE). We show the connection between symmetries and differential invariant solutions of the ODE. The analytical structure of the solution exhibits periodic behavior around attractor in local domain, same behavior obtained through dynamical analysis.

Ruma Dutta

Aurel Stan

Correlated dynamics of immune network and sl(3, R) symmetry algebra

免疫网络与sl(3, R)对称代数的关联动力学

Abstract This work builds machine learning models for the dataset generated using a numerical model developed on an idealized human artery. The model has been constructed accounting for varying blood characteristics as it flows through arteries with variable vascular properties, and it is applied to simulate blood flow in the femoral and its continued artery. For this purpose, we designed a pipeline model consisting of three components to include the major segments of the femoral artery: CFA, the common femoral artery and SFA, the superficial artery, and its continued one, the popliteal artery (PA). A notable point of this study is that the features and target variables of the former component pipe form the set of features of the latter, thus resulting in multicollinearity among the features in the third component pipe. Thus, we worked on understanding the effect of these correlated features on the target variables using regularized linear regression models, ensemble, and boosting algorithms. This study highlighted the blood velocity in CFA as the primary influential factor for wall shear stress in both CFA and SFA. Additionally, it established the blood rheology in PA as a significant factor for the same in it. Nevertheless, because the study relies on idealized conditions, these discoveries necessitate thorough clinical validation.

Debismita Nayak

Sai Lakshmi Radhika Tantravahi

On building machine learning models for medical dataset with correlated features

关于构建具有相关特征的医疗数据集的机器学习模型

Abstract We focus on the stability analysis of two types of discrete dynamic models: a discrete dynamic equation and a discrete dynamics system consisting of two equations with mutualistic interaction given by <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mi>a</m:mi> <m:mo>+</m:mo> <m:mfrac> <m:mrow> <m:mi>b</m:mi> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msup> <m:mrow> <m:mi>λ</m:mi> </m:mrow> <m:mrow> <m:mo>−</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mi>k</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:msup> </m:mrow> <m:mrow> <m:mi>c</m:mi> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mi>k</m:mi> </m:mrow> </m:msub> </m:mrow> </m:mfrac> </m:math> {x}_{n+1}=a+\frac{b{x}_{n}{\lambda }^{-\left({x}_{n-1}+{x}_{n-k})}}{c+{x}_{n-1}+{x}_{n-k}} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:msub> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:mfrac> <m:mrow> <m:msub> <m:mrow> <m:mi>b</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msup> <m:mrow> <m:mi>λ</m:mi> </m:mrow> <m:mrow> <m:mo>−</m:mo> <m:mrow> <m:mrow> <m:mo>(</m:mo> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mi>k</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:msup> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mi>k</m:mi> </m:mrow> </m:msub> </m:mrow> </m:mfrac> <m:mo>,</m:mo> <m:mspace width="1.0em" /> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:msub> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:mfrac> <m:mrow> <m:msub> <m:mrow> <m:mi>b</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msup> <m:mrow> <m:mi>λ</m:mi> </m:mrow> <m:mrow> <m:mo>−</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mi>k</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:msup> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>−</m:mo> <m:mi>k</m:mi> </m:mrow> </m:msub> </m:mrow> </m:mfrac> <m:mo>,</m:mo> </m:math> {x}_{n+1}={a}_{1}+\frac{{b}_{1}{y}_{n}{\lambda }^{-({y}_{n-1}+{x}_{n-k})}}{{c}_{1}+{y}_{n-1}+{x}_{n-k}},\hspace{1.0em}{y}_{n+1}={a}_{2}+\frac{{b}_{2}{x}_{n}{\lambda }^{-\left({x}_{n-1}+{y}_{n-k})}}{{c}_{2}+{x}_{n-1}+{y}_{n-k}}, respectively, where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo>{</m:mo> <m:mrow> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mn>3</m:mn> <m:mo>,</m:mo> <m:mrow> <m:mo>…</m:mo> </m:mrow> </m:mrow> <m:mo>}</m:mo> </m:mrow> </m:math> k\in \left\{2,3,\ldots \right\} , the constants <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>a</m:mi> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>,</m:mo> <m:mo>≥</m:mo> <m:mn>0</m:mn> </m:math> a,{a}_{1},\ge 0 , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>b</m:mi> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>b</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>&gt;</m:mo> <m:mn>0</m:mn> </m:math> b,{b}_{1}\gt 0 , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>c</m:mi> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>≥</m:mo> <m:mn>0</m:mn> </m:math> c,{c}_{1}\ge 0 be the initial densities, finite rate of increase and the limiting constant associated with the density of the species, respectively, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mo>≥</m:mo> <m:mn>0</m:mn> </m:math> {a}_{2}\ge 0 , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>b</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mo>&gt;</m:mo> <m:mn>0</m:mn> </m:math> {b}_{2}\gt 0 , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mo>≥</m:mo> <m:mn>0</m:mn> </m:math> {c}_{2}\ge 0 be the initial densities, finite rate of increase, and the limiting constant associated with the density of the mutually interacting species, respectively. <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> </m:math> k , a positive integer represents a time delay in the system and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>λ</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:math> \lambda \ge 1 shows a decay factor based on the sum of two past time step population densities. Our main objective is to understand the impact of mutualistic interactions on the stability of discrete dynamic systems. To illustrate the boundedness and stability of these models, we also provide animated plots and bifurcation diagrams.

Sibi C. Babu

D. S. Dilip

Smitha Mary Mathew

Behavior of solutions of a discrete population model with mutualistic interaction

离散种群模型中互利相互作用解的行为

Abstract Harmful algal blooms are one of the major threats to aquatic ecosystem. Some phytoplankton species produce toxins during algal bloom and affect other aquatic species as well as human beings. Thus, for the conservation of aquatic habitat, it is much needed to control such phenomenon. In the present study, we propose a mathematical model of toxin-producing phytoplankton and zooplankton species, which follows the Holling Type III functional response. We consider the effect of prey refuge and harvesting on both the species. Boundedness of the proposed model, existence of equilibria, and their stability have been discussed analytically. We also discuss the optimal harvesting policy and existence of bionomic equilibrium. The numerical simulation has also been performed. We identify the control parameters that are responsible for the system dynamics of the model. The parameter prey refuge has a great impact on the dynamics of the model system. Higher value of prey refuge leads to the stable dynamics. Also, the growth rate of phytoplankton acts as a control parameter for the dynamics of the model. The higher value of growth rate of phytoplankton is responsible for oscillatory behavior.

Poulomi Basak

Satish Kumar Tiwari

Jai Prakash Tripathi

Vandana Tiwari

Ratnesh Kumar Mishra

Plankton interaction model: Effect of prey refuge and harvesting

浮游生物相互作用模型：猎物避难所和捕捞的影响

Abstract As per the World Health Organization’s (WHO’s) suggestions, personal protection via adopting precautionary measures is one of the most effective control aspects to avoid Zika infection in the absence of suitable medical treatment. This personal protection further can be enhanced and explored by propagating information about disease prevalence. Therefore, in this study, we wish to see the effect of information on Zika transmission by formulating a compartmental mathematical model that quantifies the effect of an individual’s behavioral response as self-protection due to information. Furthermore, the basic reproduction number was calculated using the next-generation matrix technique. The model analysis was carried out to determine the local and global stability properties of equilibrium points. In addition, the model shows the occurrence of forward bifurcation when the reproduction number crosses unity. To understand the impact of various model parameters, we conducted a sensitivity analysis using both the normalized sensitivity index and the partial rank correlation coefficient methods. Moreover, we performed numerical simulations to assess the influence of important parameters on the model’s behavior for Zika prevalence. Our study accentuates that as information-induced self-protection increases, the prevalence of Zika infection will be at a very minimum level, and this observation is in line with WHO suggestions.

None Manisha

None Nidhi

Anuj Kumar

Assessing the impact of information-induced self-protection on Zika transmission: A mathematical modeling approach

评估信息诱导自我保护对寨卡传播的影响：一种数学建模方法

ISSN	2544-7297
h-index	13

涉及主题	数学物理生物化学计算机科学量子力学工程类生物化学医学遗传学材料科学数学分析热力学内科学几何学基因有机化学社会学电气工程统计病理
出版信息	出版商: Walter de Gruyter GmbH，出版周期: ，期刊类型: journal，开源期刊: 是
基本数据	创刊年份: 2012，原创研究文献占比: 0.00%，自引率:N.A.， Gold OA占比: 0.00%
期刊费用	$详情
平均审稿周期	30 weeks

Computational and Mathematical Biophysics

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