Collective Behavior in Systems Biology: A Primer on Modeling Infrastructure

✍ Scribed by Assaf Steinschneider

• Publisher: Academic Pr
• Year: 2019
• Tongue: English
• Leaves: 258
• Category: Library

✦ Synopsis

Collective Behavior In Systems Biology: A Primer on Modeling Infrastructure offers a survey of established and emerging methods for quantifying process behavior in cellular systems. It introduces and applies mathematics and related abstract methods to processes in biological systems - why they are used, how they work, and what they mean. Emphasizing differential equations in an interdisciplinary approach, this book discusses infrastructure for kinetic modeling, technological system and control theories, optimization, and process behavior in cellular networks. The knowledge that the reader gains will be valuable for entering and keeping up with a rapidly developing discipline.

• Introduces basics of mathematical and abstract methods for understanding, predicting, and modifying collective behavior in cellular systems
• Targets biomedical professionals as well as computational specialists who are willing to take advantage of novel high-throughput data acquisition technologies

✦ Table of Contents

Cover
Collective Behavior in Systems Biology: A Primer on Modeling Infrastructure
Copyright
Contents
Assaf Steinschneider in memoriam
Introduction
1 Change/differential equations
Context
Assembling a statement
Collective behavior
Essentials
Model makeup
Variables
Relating the variables
Terms collectively
Format
Linear (in)dependence
Linearity and nonlinearity
A bird’s eye view
Change by differential equations
An algebraic prelude
Turning differential
Building blocks and operations
Functions
Derivatives
Integrals
Definite integral
Coefficients and time
Operators as facilitators and delimiters
Choosing a differential equation model
Options
Single variable dependent only/ordinary differential equations
Multiple variable dependent/partial differential equations
First-order partial differential equations
Second-order partial differential equations
Unity in diversity/systems of ordinary differential equations
A complex whole/no parts
The complex whole/with parts
Customized modeling
Structured modeling
Existence and uniqueness
Description into general law, interpreted
Solving equations
Solving ordinary differential equations
Taking integrals
Higher order equations into latent power
Laplace transform
Miscellaneous
Alternative and supplementary methods
Series methods
Empirical/numerical methods
Simulations
Ways with partial differential equations
The ordinary differential equation route
Other partial differential equations solution methods
Divining systems of ordinary differential equations
Customized
Structured systems
Breaking the ground
Direct integration
Prospecting for the latent
More on eigenvalues and rates
A perturbing real world
Varying systematically the internal and external makeup
A role for system parameters
Visual patterns
Quantitating the qualitative
Processes under perturbation
Stability options
Quantitative underpinnings
Local stability
Bypassing a formal solution
Being discrete/difference equations
Context
Building blocks
Making a difference/elementary units of change
Discrete equations/multiple faces
Formal solutions/process and product
Fibonacci
Joining forces/hybrid and mixed representations
Keep in mind
References
Further reading
2 Consensus/linear algebra
Context
How equations change into modules
Getting organized
Vectors
Matrices
Square matrices
Diagonal matrices
Operating by the rules
Single element
Intramatrix
Intermatrix or vector
Mergers
Matrix addition/subtraction
Matrix multiplication
Order of multiplication
Matrix division via inversion
Intervector operations
A value for a matrix or determinants
Solving equation systems
Consistency
Linear (in)dependence
Eliminating the variables the ordered way
No solution
Infinite number
Unique
Solution values
Employing determinants
Exploring the latent
Keep in mind
Reference
Further reading
3 Alternative infrastructure/series, numerical methods
Context
Value formally/series solutions
The polynomial way
Fine tuning with derivatives
Recruiting sines, cosines, and their integrals
Innate periodicity
Quest for the best
Values the practical way: numerical methods
Get in line
Calculating derivatives
Computing integrals
Values for differential equations
Tangents into curves/Euler methods
Algebraic fine tuning/Runge–Kutta
Simulation
Interfacing with machine computation
Keep in mind
Further reading
4 Systems/input into output
Context
Groundwork/descriptive/from input to output
What is at stake
The cast
The play/a process on its way
More time related
Systems with a past
Delay
A quantitative view
State variable model/the cast in full
System
Input
Output
At work
State updating
Output
Input/output model/success with less
Quantitative
Between models
Graphical aids
Block diagrams
Signal-flow graphs
Keep in mind
Further reading
5 Managing processes/control
Context
Control structure and function
Targets and immediate objectives
Schematics
Open loop
Closed loop
Quantitative views
Models
The state variable model
Input–output model
Prospects for control
Feasibility
Transparency
Evaluating control options
Open or closed loop
Sensitivity
Feedback
Contributing processes
Feedback implemented
Optimizing controlled systems
Cellular self-regulation
Metabolic control analysis
Perturbing the pathway and the membership
Control sharing
Keep in mind
References
Further reading
6 Best choices/optimization
Context
A formula for the optimum
The classical way
Constraints on reality
Variational choices
Calculus of variations
A Hamiltonian format with a maximum principle
Coda
Mathematical programming
Linear programming
Dynamic programming
Keep in mind
References
Further reading
7 Chance encounters/random processes
Context
Low copy number processes
A single cell setting
Probability
Basic notions
Chances of individual members in a population
Population profile
Journey stochastic
Gillespie’s simulation model
Interacting neighbors
A polypeptides environment
Selecting next neighbors
Energies into probabilities
Keep in mind
References
Further reading
8 Organized behavior/networks
Context
Network schematics
Graphs
The building blocks/elements
Network members with class
Refining based on functional relationships
Graphs modified
Adding value
Walks
Connected by a walk
Network facing interference
Trees
A botanical hierarchy
Rooted trees
Spanning trees
Structure by numbers
Graph statistics
Matrix representation
Similarity between graphs
Networks in action
Streaming freely/flow networks
From source to sink
Optimal flow
A maximizing algorithm
Beyond graph theory
Progress by firing squad/petri nets
Building blocks
In action (local and global)
Timings
Feasibility
Colors, chimeras, hybrids
Afterthoughts
With a little bit of logic/Boolean networks
Status and change
Logic, qualitative and quantitative
Scheduling updates
An updating process on its way
Robustness in a large network
Pairing logic with kinetics/motifs
Small regulatory devices
Integrated motif models
Exercising control
Statistical coda
The cellular ecosystem
Guilt by association
Keep in mind
References
Further reading
Index
Back Cover