Collective Behavior in Systems Biology: A Primer on Modeling Infrastructure

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Collective Behavior in Systems Biology: A Primer on Modeling Infrastructure
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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
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