Introduction to Modeling Biological Cellular Control Systems (MS&A, 6)

✍ Scribed by Weijiu Liu

• Publisher: Springer
• Year: 2011
• Tongue: English
• Leaves: 275
• Category: Library

✦ Synopsis

This textbook contains the essential knowledge in modeling, simulation, analysis, and applications in dealing with biological cellular control systems. In particular, the book shows how to use the law of mass balance and the law of mass action to derive an enzyme kinetic model - the Michaelis-Menten function or the Hill function, how to use a current-voltage relation, Nernst potential equilibrium equation, and Hodgkin and Huxley's models to model an ionic channel or pump, and how to use the law of mass balance to integrate these enzyme or channel models into a complete feedback control system. The book also illustrates how to use data to estimate parameters in a model, how to use MATLAB to solve a model numerically, how to do computer simulations, and how to provide model predictions. Furthermore, the book demonstrates how to conduct a stability and sensitivity analysis on a model.

✦ Table of Contents

Title page
Copyright page
Preface
Table of contents
1 Overview
1.1 Examples of Biological Cellular Control Systems
1.2 Modeling Methodology
1.3 Computer Simulation
1.4 Impact
1.5 Audience
References
2 Enzyme Kinetics
2.1 The Law of Mass Balance
2.2 The Law of Mass Action
2.3 The Michaelis-Menten Equation
2.4 Bi-substrate Enzymes
2.5 Inhibitors
2.5.1 Competitive Inhibition
2.5.2 Uncompetitive Inhibition
2.5.3 Noncompetitive Inhibition
2.6 Cooperativity
2.7 Chemical Potential
2.8 The Arrhenius Formula
2.9 Effects of Energy
2.10 Effects of pH
2.11 The Ion Hopping Model
Exercises
References
3 Preliminary Systems Theory
3.1 Elementary Matrix Algebra
3.1.1 Matrix Sums
3.1.2 Scalar Multiple
3.1.3 Matrix Multiplication
3.1.4 Powers of a Matrix
3.1.5 Transpose of a Matrix
3.1.6 The Determinant
3.1.7 Eigenvalues
3.1.8 Rank of a Matrix
3.2 Stability of Equilibrium Points
3.2.1 Definition of Stability
3.2.2 Lyapunov’s Stability Theorem
3.2.3 Lyapunov’s Indirect Method
3.2.4 Invariance Principle
3.2.5 Input-output Stability
3.3 Controllability and Observability
3.4 Feedback Control
3.5 Parametric Sensitivity
Exercises
References
4 Control of Blood Glucose
4.1 A Control System of Blood Glucose
4.2 Design of Feedback Controllers
4.2.1 Insulin and Glucagon Transition
4.2.2 Glucagon Signaling Pathway
4.2.3 Insulin Signaling Pathway
4.2.3.1 Insulin Receptor Recycling Subsystem
4.2.3.2 Postreceptor Signaling Subsystem
4.2.3.3 GLUT4 Transport Subsystem
4.2.4 Dynamical Feedback Controllers
4.3 Estimation of Parameters
4.4 Simulation of Glucose and Insulin Dynamics
4.5 Model Prediction of Parametrical Sensitivity
4.6 Simulation of Glucose and Insulin Oscillations
Exercises
References
5 Control of Calcium in Yeast Cells
5.1 A Model of Aging Process
5.2 Calcium Uptake from Environment
5.3 Calcium Movement across the Vacuolar Membrane
5.4 Calcium Movement across the Golgi Membrane
5.5 Calcium Movement across the Endoplasmic Reticulum Membrane
5.6 A Calcium Control System
5.7 Design of Feedback Controllers
5.7.1 Control of Calcium Uptake from Environment
5.7.2 Control of Ca2+/H+ Exchanger Vcx1p
5.7.3 Control of Calcium Pumps Pmc1p and Pmr1p
5.7.4 Control of Channel Yvc1p
5.7.5 Control of X-induced Calcium Channel on the Vacuolar Membrane
5.7.6 Control of Calcium Homeostasis in Golgi and ER
5.8 Simulation of Calcium Shocks
5.9 Simulation of Calcium Accumulations
5.10 Prediction of Cell Cycle-dependent Oscillations of Calcium
5.11 Prediction of an Upper-limit of Cytosolic Calcium Tolerance for Cell Survival
5.12 Model Limitation
Exercises
References
6 Kinetics of Ion Pumps and Channels
6.1 The Nernst-Planck Equation
6.2 The Nernst Equilibrium Potential
6.3 Current-voltage Relations
6.4 The Potassium Channel
6.4.1 The Voltage-Gated Potassium Channel
6.4.2 The Calcium-Activated Potassium Channel
6.4.3 The ATP-Sensitive Potassium Channel
6.5 The Voltage-Gated Sodium Channel
6.6 The Voltage-Gated Calcium Channel
6.7 The IP3 Receptor
6.8 The Ryanodine Receptor
6.9 The Sarcoplasmic or Endoplasmic Reticulum Calcium ATPase
6.10 The Plasma Membrane Calcium ATPase
6.11 The Sodium/Potassium ATPase
6.12 The Sodium/Calcium Exchanger
6.13 Membrane Potential Models
6.14 The Hodgkin-Huxley Model
Exercises
References
7 Control of Intracellular Calcium Oscillations
7.1 The Chay-Keizer Feedback Control System
7.2 The BSSMAMS Feedback Control System
7.3 The FTMP Feedback Control System
Exercises
References
8 Store-Operated Calcium Entry
8.1 A Calcium Control System
8.2 Design of an Output Feedback Controller
8.3 SOCE Computer Simulation
8.4 Simulation of Rejection of Agonist Disturbances
8.5 Stability Analysis
8.6 Remarks
Exercises
References
9 Control of Mitochondrial Calcium
9.1 Respiration-driven Proton Ejection
9.2 ATP Synthesis and Proton Uptake by the F1F0-ATPase
9.3 ATP and ADP Transport by the Adenine Nucleotide Translocator
9.4 Calcium Uptake by the Uniporter
9.5 Calcium Efflux via the Sodium/Calcium Exchanger
9.6 Governing Equations of Calcium Dynamics
Exercises
References
10 Control of Phosphoinositide Synthesis
10.1 PIP Synthesis from PI
10.2 PIP2 Synthesis from PIP
10.3 PIP2 Hydrolysis
10.4 A Control System for Phosphoinositide Synthesis
Exercises
References
Appendix A Preliminary MATLAB
A.1 MATLAB Desktop
A.1.1 Command Window
A.1.2 Help Browser
A.1.3 Editor / Debugger
A.2 Creating, Writing, and Saving a MATLAB File
A.3 Simple Mathematics
A.3.1 Variables
A.3.2 Operators
A.3.3 Built-in Functions
A.3.4 Mathematical Expressions
A.4 Vectors and Matrices
A.4.1 Generating vectors
A.4.2 Generating matrices
A.4.3 Array Addressing or Indexing
A.4.4 Arithmetic Operations on Arrays
A.5 M-Files
A.5.1 Scripts
A.5.2 Functions
A.6 Basic Plotting
A.7 Relational Operators
A.8 Flow Control
A.8.1 If-Else-End Constructions
A.8.2 For Loops
A.8.3 While Loops
A.9 Logical Operators
A.10 Solving Symbolic Equations
A.11 Solving Ordinary Differential Equations
A.12 Data Fitting
A.13 Parameter Estimation
Exercises
References
Appendix B Units, Physical Constants and Formulas
B.1 Physical Formulas
B.2 Units, Unit Scale Factors and Physical Constants
References
Index