Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top

2014 | Book

Brief Introduction to Chemical Kinetics Read chapter Read first chapter

Chemical Kinetics, Stochastic Processes, and Irreversible Thermodynamics

Author: Moisés Santillán

Publisher: Springer International Publishing

Book Series : Lecture Notes on Mathematical Modelling in the Life Sciences

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Login to get access
insite
SEARCH

About this book

This book brings theories in nonlinear dynamics, stochastic processes, irreversible thermodynamics, physical chemistry and biochemistry together in an introductory but formal and comprehensive manner. Coupled with examples, the theories are developed stepwise, starting with the simplest concepts and building upon them into a more general framework. Furthermore, each new mathematical derivation is immediately applied to one or more biological systems. The last chapters focus on applying mathematical and physical techniques to study systems such as: gene regulatory networks and molecular motors.

The target audience of this book are mainly final year undergraduate and graduate students with a solid mathematical background (physicists, mathematicians and engineers), as well as with basic notions of biochemistry and cellular biology. This book can also be useful to students with a biological background who are interested in mathematical modeling and have a working knowledge of calculus, differential equations and a basic understanding of probability theory.

Table of Contents

Frontmatter
Chapter 1. Brief Introduction to Chemical Kinetics
Abstract
In this chapter we present a brief introduction to chemical kinetics. Key concepts like: reversibility of chemical reactions, reaction rate, reaction rate constant, and chemical equilibrium, are introduced and discussed. The most important of the results here derived is the so-called law of mass action; which we discuss from the perspective of chemical kinetics. In this chapter we follow a heuristic rather than a formal approach. We start by analyzing a few simple chemical reactions to gain insight into the chemical kinetics basic concepts. After that, we heuristically derive and discuss the corresponding results for the most general case. The interested reader can consult any of the many available books on the subject. We particularly recommend the book by Houston (Chemical kinetics and reaction dynamics. McGraw-Hill, New York, 2001).
Moisés Santillán
Chapter 2. Brief Introduction to Thermodynamics
Abstract
This chapter is devoted to introducing the basic concepts of thermodynamics, specially as applied to chemistry. The reader must be aware that the material in this chapter is rather technical and succinct. Therefore, it is quite possible that some of the results are not clear, even after carefully reading the chapter material more than once. Of course, people interested in this field can go to the specialized literature. However, one of the mayor goals of the present book is to help make these things clear through some examples. So, if things seem a bit blurry after finishing this chapter, please do not despair and keep reading. It will soon get better, promise.
Moisés Santillán
Chapter 3. Different Approaches to Analyzing a Simple Chemical Reaction
Abstract
In this chapter, the dynamics of the chemical reaction \(A \rightleftharpoons B\) are analyzed from the perspectives of macroscopic chemical kinetics, thermodynamics, and stochastic processes. The main objective is to show that all these approaches are not exclusive but complementary, and that properly combining them through a fourth unifying approach (the one I call the energy landscape approach) allows a deeper understanding of the system dynamic behavior. After finishing this chapter not only the reader shall understand the different approaches to analyzing the dynamics of a chemical reaction, but will also obtain some basic notions of stochastic processes. Namely, the chemical master equation and Gillespie’s algorithm.
Moisés Santillán
Chapter 4. Molecule Synthesis and Degradation
Abstract
The present chapter is advocated to analyzing the dynamics of a simple birth–death process from the perspectives of chemical kinetics, stochastic processes, and thermodynamics. This process is important because, under certain conditions, it constitutes a good model for the numerous biomolecule production/degradation processes taking place within cells. To facilitate the achievement of the above stated goal, a couple of simple stochastic processes are previously introduced and analyzed in detail: the Poisson process and a simple pure death process. The objectives of the present chapter are twofold. On the one hand, we will gain deeper insight into the previous chapter methods, results, and conclusions, by tackling more elaborated examples. But also, the examples here introduced shall serve as building blocks for more realistic cellular-process models to be introduced thereafter. As a bonus, we also introduce and discuss some basic concepts of irreversible thermodynamics in the context of chemical kinetics.
Moisés Santillán
Chapter 5. Enzymatic Reactions
Abstract
In this chapter we generalize the birth–death process analyzed in the previous chapter to account for enzymatic molecule synthesis, rather than simple Poissonian production. To facilitate the analysis we assume a time-scale separation in the enzymatic reactions, and use it to reduce the complexity of the complete system. With this simplification the generalized birth–death process can be separated into two different subsystems that can be studied separately, and correspond to the systems studied in Chaps. 3 and 4. The simplification procedure, introduced in Sect. 5.1, is a very useful mathematical tool way beyond the scope of the present chapter.
Moisés Santillán
Chapter 6. Receptor–Ligand Interaction
Abstract
In this chapter we study the dynamic and thermodynamic behavior of a ubiquitous biochemical process: the interaction of a receptor molecule with multiple ligands. As before, we study it from the perspectives of chemical kinetics, stochastic processes, and thermodynamics. In essence we do not introduce any new tools, but make use of the ones introduced in the previous chapters. However, as the readers will be aware by the end of the chapter, the obtained conclusions allow a deeper understanding not only of this particular system but also of the dynamic and thermodynamic behavior of biochemical systems in general. It is our goal that, by gradually increasing the complexity of the studied systems, while building up upon previous examples, the reader will develop a more profound notion of the way the different approaches are inter-related. In particular, the present chapter includes a thorough discussion about the thermodynamic behavior of the studied system and how it compares with the ones in previous chapters.
Moisés Santillán
Chapter 7. Cooperativity
Abstract
In the present chapter we generalize the results in the previous chapter to study one of the most fascinating biochemical phenomena: the cooperative interaction between two or more ligands that bind a single receptor (or simply cooperativity). Once more, we make use of our previous knowledge to carefully analyze the dynamic and thermodynamic characteristics of this phenomenon.
Moisés Santillán
Chapter 8. Gene Expression and Regulation
Abstract
In this chapter we make use of all the material studied so far to construct a few (simple but informative) models for gene expression. As before, we are interested in obtaining useful information regarding both the dynamical and thermodynamical aspects of this phenomenon.
Moisés Santillán
Chapter 9. Ion Channel Dynamics and Ion Transport Across Membranes
Abstract
In previous chapters we have employed the formalism and techniques introduced in the book to study different biological systems by conceptualizing them as chemical reactions. In all cases this conceptualization was more or less evident. However, the formalism is more versatile as it can be applied to systems that apparently have nothing to do with chemical reactions. In the present chapter we tackle a few of those systems, all of which are related to diffusion. Not only we exemplify in this chapter how to employ the formalism here introduced to study systems with no obvious connection with chemical reactions, but we also derive some classical results regarding ion transport across membranes. As in previous chapters we start with a very simple example, and gradually make it more complex to end with a more realistic model.
Moisés Santillán
Backmatter
Metadata
Title
Chemical Kinetics, Stochastic Processes, and Irreversible Thermodynamics
Author
Moisés Santillán
Copyright Year
2014
Electronic ISBN
978-3-319-06689-9
Print ISBN
978-3-319-06688-2
DOI
https://doi.org/10.1007/978-3-319-06689-9

Premium Partner

    Image Credits