Mathematical Biology And Biological Physics

Rubem P Mondaini

• Publisher: WSPC
• Year: 2017
• eBook ISBN: 9789813227897
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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This is a book on interdisciplinary topics of the Mathematical and Biological Sciences. The treatment is both pedagogical and advanced in order to motivate research students as well as to fulfill the requirements of professional practitioners. There are comprehensive reviews written by senior experts on the important problems of growth and agglomeration in biology, on the algebraic modelling of the genetic code and on multi-step biochemical pathways.

There are new results on the state of the art research in the pattern recognition of probability distribution of amino acids, on somitogenesis through reaction-diffusion models, on the mathematical modelling of infectious diseases, on the biophysical modelling of physiological disorders, on the sensitive analysis of parameters of malaria models, on the stability and hopf bifurcation of ecological and epidemiological models, on the viral infection of bee colonies and on the structure and motion of proteins. All these contributions are also strongly recommended to professionals from other scientific areas aiming to work on these interdisciplinary fields.

--> Contents:

• Preface
• Editorial Board of the BIOMAT Consortium
• Professor C A Floudas — In Memoriam
• Comprehensive Introduction to Agglomeration and Growth and Models (R Kerner)
• The Pattern Recognition of Probability Distributions of Amino Acids in Protein Families (R P Mondaini, S C de Albuquerque Neto)
• Modelling the Electrical Activity of the Heart (R A Barrio, I Dominguez-Roman, M A Quiroz-Juarez, O Jimenez-Ramirez, R Vazquez-Medina, J L Aragon)
• How the Interval Between Primary and Booster Vaccination Affects Long-Term Disease Dynamics (A Shoukat, A L Espindola, G Röst, S M Moghadas)
• Stability and Hopf Bifurcation in a Multi-Delayed Eco-Epidemiological Model (D Adak, N Bairagi)
• Propagation of Extrinsic Perturbation in Multistep Biochemical Pathways (A G Nedungadi, S Sinha)
• Catastrophic Transitions in Coral Reef Biome Under Invasion and Overfishing (S Pal, J Bhattacharyya)
• Dynamics of Hepatitis C Viral Load with Optimal Control Treatment Strategy (R Keval, S Banerjee)
• Somitogenesis and Turing Pattern (A Lemarchand, L Signon, B Nowakowski)
• An Epidemiological Model of Viral Infections in a Varroa -Infested Bee Colony: The Case of a Bee-Dependent Mite Population Size (S Bernardi, E Venturino)
• Does Sensitivity Analysis Validate Biological Relevance of Parameters in Model Development? Revisiting Two Basic Malaria Models (S Mandal, S Sinha)
• Subcortical Homeostatic Circuitry Modulates Brain Waves and Behavioral Adaptation: Relevance for the Emergent Multidiscipline of Social Neuroscience (Limei Zhang de Barrio, V S Hernández, L E Eiden)
• Protein Structure Estimation from Incomplete NMR Data (Z Li, S Lin, Y Li, Q Lei, Q Zhao)
• Decrypting How Proteins Move and Change Their Shape (E Laine)
• Deterministic and Stochastic Model for HLTV-I Infection of CD4 + T Cells (P K Srivastava)
• Study of Global Stability and Optimal Treatment for An Infectious Disease Model (A Kumar, P K Srivastava, A Yadav)
• Global Stability of a Modified HIV Infection Model with Saturation Incidence (J Yang, Q Zhang, L Wang)
• A Survey of Geometric Techniques for Pattern Recognition of Probability of Occurrence of Amino Acids in Protein Families (R P Mondaini)
• Symmetry and Minimum Principle at the Basis of the Genetic Code (A Sciarrino, P Sorba)
• Index

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--> Readership: Undergraduates, graduates, researchers and all practitioners in the interdisciplinary fields of Mathematical Biology, Biological Physics and Mathematical Modelling of Biosystems. -->
Mathematical Modelling;Mathematical Biology;Biomathematics;Biophysics;Mathematical Physics0

SYMMETRY AND MINIMUM PRINCIPLE AT THE BASIS OF THE GENETIC CODE

A. SCIARRINO

I.N.F.N., Sezione di Napoli
Complesso Universitario di Monte S. Angelo
Via Cinthia, I-80126 Napoli, Italy
E-mail: [email protected]

P. SORBA

LAPTH,Laboratoire d’Annecy-le-Vieux de Physique Théorique CNRS
Université de Savoie
Chemin de Bellevue, BP 110
F-74941 Annecy-le-Vieux, France
E-mail: [email protected]

The importance of the notion of symmetry in physics is well established: could it also be the case for the genetic code? In this spirit, a model for the Genetic Code based on continuous symmetries and entitled the “Crystal Basis Model” has been proposed a few years ago and applied to different problems, such as the elaboration and verification of sum rules for codon usage probabilities, relations between physico-chemical properties of amino-acids and some predictions. Defining in this context a “bio-spin” structure for the nucleotides and codons, the interaction between a couple of codon-anticodon can simply be represented by a (bio) spinspin potential. Then, imposing the minimum energy principle, an analysis of the evolution of the genetic code can be performed with good agreement with the generally accepted scheme. A more precise study of this interaction model provides informations on codon bias, consistent with data.

1.Introduction

The sciences of life offer an important domain of investigations for the physicist. Already about seventy years ago, Erwin Schrödinger provided in his book “What is life?”¹ some ideas about the possible role of a “new physics” in this domain, imagining for example mutations to be directly linked to quantum leads. As can be read there:

“living matter, while not eluding the “laws of physics” as established up to date, is likely to involve “other laws of physics” hitherto unknown, which however, once they have been revealed, will form just as integral a part of science as the former”.

Among the mathematical tools which played in the second part of the twentieth century and are still playing an essential role in theoretical physics, and in particular in particle physics, is the one of Group theory, this concept being usually called in physics Symmetry, or Invariance. It is this notion which is at the basis of our model for describing the genetic code and developing a theoretical approach of its biological properties.

The idea of symmetry, or invariance, can be used in different ways, but to illustrate the one we need today, let us take an example. Consider an electron e⁻. An important physical quantity attached to it is its spin. And actually, as you know, there are two states for the spin of the electron, called up and down, or + and − (or +1/2 and −1/2 following the notation you choose, and we use to say that the spin of e⁻ is 1/2). Mathematically, these two states can be seen as orthogonal vectors of the 2-dim complex Euclidean space,^a on which acts the group of 2 by 2 unitary matrices, called

(2), transforming one state into another one. It is a Lie group and considering its Lie algebra, there exists an element on it, a 2 × 2 matrix with eigenvalues +1/2 and −1/2 associated to the eigenvectors which are the states up and down. If you consider a vector boson, (e.g. the W boson which mediates the weak interaction) there are three states of spin, denoted +1, 0, −1 and we can represent the elements of the group

(2) by 3 × 3 matrices acting on a 3-dim Hilbert space. It is this notion that we will use to construct our model describing the genetic code.

At this point, let us mention two essential aspects of genetics on which we propose to use our model: the DNA structure on one hand and the mechanism of polypeptide fixation from codons on the other hand. But, it might be good to start by reminding some essential features on the genetic code. First, as well known, the DNA macromolecule is constituted by two chains of nucleotides wrapped in a double helix shape. There are four different nucleotides, characterized by their bases: adenine (A) and guanine (G) deriving from purine, and cytosine (C) and thymine (T) coming from pyrimid...

Table of contents

• Cover Page
• Title
• Copyright
• Contents
• Preface
• Editorial Board of the BIOMAT Consortium
• Professor C.A. Floudas — In Memoriam
• Comprehensive Introduction to Agglomeration and Growth and Models
• The Pattern Recognition of Probability Distributions of Amino Acids in Protein Families
• Modelling the Electrical Activity of the Heart
• How the Interval Between Primary and Booster Vaccination Affects Long-Term Disease Dynamics
• Stability and Hopf Bifurcation in a Multi-delayed Eco-epidemiological Model
• Propagation of Extrinsic Perturbation in Multistep Biochemical Pathways
• Catastrophic Transitions in Coral Reef Biome under Invasion and Overfishing
• Dynamics of Hepatitis C Viral Load with Optimal Control Treatment Strategy
• Somitogenesis and Turing Pattern
• An Epidemiological Model of Viral Infections in a Varroa-infested Bee Colony: The Case of a Bee-dependent Mite Population Size
• Does Sensititivity Analysis Validate Biological Relevance of Parameters in Model Development? Revisiting Two Basic Malaria Models
• Subcortical Homeostatic Circuitry Modulates Brain Waves and Behavioral Adaptation: Relevance for the Emerging Multidiscipline of Social Neuroscience
• Protein Structure Estimation from Incomplete NMR Data
• Decrypting How Proteins Move and Change their Shape
• Deterministic and Stochastic Model for HLTV-I Infection of CD4+ T Cells
• Study of Global Stability and Optimal Treatment for An Infectious Disease Model
• Global Stability of a Modified HIV Infection Model with Saturation Incidence
• A Survey of Geometric Techniques for Pattern Recognition of Probability of Occurrence of Amino Acids in Protein Families
• Symmetry and Minimum Principle at the Basis of the Genetic Code
• Index