Index

A

ABM. see Agent-based model (ABM)
Action potentials
electrical and chemical processes, 180–181
firing patterns, 181, 183, 205, 209
incoming signals, 181
membrane potential, 181
seminal model, 183
Acyclic digraphs, 190
Agent-based model (ABM)
basic movement function, 171
biological systems, 145
differential equations, 144
downhill movement, 173
game of life, 145
heuristic approach, 163–164
optimal control, 152
optimization problems, 152
polynomial dynamical systems (PDSs), 167–168, 171
uphill movement, 173
Agent-based model, cholera, 119
description, 120
environmental contamination, 120–122
model experiment, 119–120
NetLogo platform for, 123
probability of infection, 122–123
unknown parameters, 122
Agent-based model, computation history, 109
flocking model, 112
NetLogo platform (ABM), 108
segregation model, 110
tipping model, 109–110
zero player game, 109 see also Game of life
Agent-based model, tick-borne disease. see also TICKSIM model
causes, 128
life stages, 129
modeling, 129
ODD protocol, 129–130
Algebraic approach. see also Reverse engineering
graded lexicographic ordering (grlex), 83
graded reverse lexicographic ordering (grevlex), 83
lexicographic ordering (lex), 83
linear, 82
multivariate polynomials, 82
Anabolism, 3
Axon guidance, neuron development, 113–114
agent’s interaction, 116
model construction, 117
neuron components of, 114

B

Basic movement function
in agent-based model, 171
Baum-Welch algorithm
HMM parameters, 296
maximum likelihood estimates, 295–296
training sequence, 295
Bayesian inference methods, phylogenetic method, 308
Biochemical reaction network
metabolic pathways, 242
modeling of, 257–258
through graphs, 247–248
>through hypergraphs, 257–258
Biological systems model
agent-based, 145
differential equations, 144
discrete model, 171
individual-based, 145
Bistability, 37
irreversible, 37–38
reversible, 37–38
BME cone, 310, 339
BME vector, 310
BME (Balanced minimum evolution) principle
distance-based method, 310, 320, 334
linear function, 310
phylogenetic tree reconstruction, 337
softwares for, 310
Boolean model
below-calculus level, 33
in biology, 2, 33
complexity levels, 6–7
construction, 2
deficiency, 21
Discrete Visualizer of Dynamics (DVD) in, 17
equations, lac operon, 16
fixed-point property, 26
lacoperon, 1, 3, 9–10
molecular concentration, 57
networks dynamics, 11
qualitative behavior, 76
single time-steps, limitations, 58
state space transition diagram, 12, 58
time-delays, 59
transition functions, 14–15, 58
update functions, 57–58
variables, 57
Boolean networks see Boolean model

C

cAMP
model parameters, 8
production, 5–6
CAP (catabolite activator protein), 5
CAP-cAMP
complexity, 5–6
positive control mechanism, 8, 23
Catabolism, 3, 5–6
Catabolite repression, 5–6, 9, 23
Cellular automation, 145, 170
see also Game of Life
Cellular metabolism, 239–241, 247
Cellular systems, 37
Central Limit Theorem, 202
CGI identification
alternative methods, 273
CpG Educate suite, 299
HHMs applications, 274, 282, 301–302
sliding window algorithms, 301
Complete loop-free digraphs, 193
Computation history, Agent-based model, 109
flocking model, 112
NetLogo platform (ABM), 108
segregation model, 110
tipping model, 109
zero player game, 109 see also Game of life
Continuous-time Markov chains, 308
CpG Educate suite
CGI identification, 299
Dishonest Casino application, 287–288, 294, 297–298
Viterbi algorithm, 287
Viterbi decoding, 287
Hidden Markov Models (HMMs), 302
sliding window algorithm, 271
CpG island
algorithms, 271
defined, 267
in human chromosomes, 301–302
promoter-associated, 267
unmethylated, 270

D

Dependency graph, 7–8see also Wiring Diagram
Differential equations
in agent-based models, 146
bi-molecular reaction, 41
biochemical reactions, 40
collision orientation, 40
mass-action kinetics, 40
ordinary, 150
uni-molecular reaction, 41
Differential equation, Yildirim-Mackey, lac operon
allolactose dynamics, 50–51
bacterial system, modeling, 47
basal transcription rate, 50
delay differential equation models, 47
internal lactose dynamics, 51–52
permease dynamics, 51
repressor protein, 48
Directed cycle graphs, 191
Directed cycle, network connectivity, 195
Discrete model
acyclic digraphs, 190
complete loop-free digraphs, 193
directed cycle graphs, 191
directed cycle, network connectivity, 195
discretizations, 97
in gene regulatory network, 76
neuronal network, 183–184
Discrete-time model, 2
Discrete Visualizer of Dynamics (DVD), 17
Disease dynamics, neuronal network model
dynamic clustering, 205
mathematical model vs. natural system 202
natural systems, 202
SIR models, 202–203
Dissimilarity map
BME principle, 337, 339–340
edge-weighted tree, 323, 327
Hamming distance, 319
mathematical formulations, 320
Neighbor-Joining (NJ) Algorithm, 329–331, 333
pairwise distances, 309
Q-criterion, 340
tree metrices, 324–325
Distance-based methods
BME methods, 334
geometrical approaches, 309
NJ algorithm, 310
phylogenetic tree reconstruction, 309, 339
polynomial time algorithms, 340
Distance matrix, 309 see also Dissimilarity map
DNA
binding of proteins, 1
CAP (forcatabolite activator protein) and, 5–6
E.coli’s role, 3
DNA methylation
in cancer, 270
dinucleotide replication, 268
DNA sequence
dinucleotides, 270–271
HMMs application, 279–280, 282
methylated cytosines, 267–268
multicellular organism, 267
sliding window algorithms, 271–273
Downhill movement
in agent based models, 173
Dynamic clustering, 181
firing Patterns, 181
olfaction, 182

E

E. coli (Escherichia coli)
bistable behavior, 52
gene regulation, 1
hysteresis effect, 38
metabolic pathway, 239
LacOperon and, 3–6
lactose concentration, 32
lactose metabolism, 2
life span, 8
Eigenvalue
algebraic dimension, 228
biological information, 234–235
charactristics, 227
dominant, 232–233
equation, 227
geometric dimension, 228
MATLAB calculation, 234–235
Perron-Frobenius Theorem, 228
R command, 236
stable distribution, individuals, 231
Eigenvector
algebraic dimension, 227–228
biological information, 234–235
dominant, 232
dominant eigenvalue and, 232–233
MATLAB calculation, 235
multiplication, 227
Perron-Frobenius Theorem, 228, 231
R command, 236
Evolutionary model, 308–309, 320
Exons, genomic sequence, 268

F

Finite dynamical systems (FDS), 33
Firing patterns
dynamic clustering, 181
neurons, 181
Parkinson’s disease, 208
thalamus, during sleep, 209
Fixed points, Boolean network, 1
determining factors, 25–26
Forward-backward algorithm
posterior decoding, 292

G

Game of Life
in agent-based model, 145
black or white cell, 145
features, 146
polynomial dynamical system, 171
Gene expression
mechanisms, 1
transcription level, 1
Gene regulation. see also Gene regulatory network
defined, 75–76
lac operon, 76
Gene regulatory network
binary discretizations, 96
discrete dynamical system, 179
molecular biology, 75
neuronal network model, 180
regulatory interactions, 75–76
reverse engineering, 76
Genetic algorithms
in heuristic approach, 167
process, 164
Global dynamics, 146
Graded lexicographic ordering (grlex), 83
Graded reverse lexicographic ordering (grevlex), 83
Graphs
biochemical reaction systems by, 257–258
modeling decision, 260
Greedy algorithm, 339
Gröbner(Groebner) bases
model selection, 93
monomial ordering, 84, 89, 93
polynomial equations, 3, 26
Gröbner Fan Method, post processing, 93

H

Hamming distance, 319
Heuristic approach
in agent based model (ABM), 163
other types, 167
standard procedure, 165
Hidden Markov Models (HMMs)
Baum-Welch algorithm, 296
canonical problems, 282, 287
CGI identification, 271–274, 301
comma separated value (CSV) parameters, 288–289
CpG Educate, 302
DNA sequence, 271–274, 279–280
hybrid visualization, 301–302
maximum likelyhood estimates, 295–296
model parameters, 295
post-processing, 299
process, description, 274
training sequence, 295
Hill equations, 274
Hodgkin-Huxley model
membrane potential evolution, 183
neuron interaction, 183
Housekeeping genes, 1
Hypergraphs, 257–258
Hysteresis, 37

I

Immunocompetent cells, 143
Inducible proteins, 4
Interior vertex, 310–311
Introns, genomic sequence, 268

L

Lac operon
defined, 16
E. coli (Escherichia coli)and, 3–6
equations, 16–17
mathematical model 38–39
molecular mechanism, 39
positive feedback mechanism, 40
regulatory components, 39
Lactose, maintenance concentration, 38
Lexicographic ordering (lex), 83
Life cycles
ginseng example, 215
irreducible matrix, 229
multiple stages of, 214
number of stages, 215
population growth, 214
stage, determination in, 215
transitions, tracking, 214
Linear algebra
biochemical reaction network, 241
metabolite conservation, 257–258

M

Maintenance concentration, lactose, 38
Maintenance methylases, 267–268
Mathematical models
algebraic, 2
Boolean network models, 38–39
deterministic, 2
differential equation model, 38–39
discrete-time, 2
Minimal Sets Algorithm (MSA), 91
space-continuous, 2
space-discrete, 2
static, 2
stochastic, 2
time-continuous, 2
time-discrete, 2
Matrix algebra
Perron-Frobenius Theorem, 228
population growth, 214
stable distribution, 214
Maximum-likelihood (ML) method, 308–309
Metabolic engineering, 241
Metabolic pathways
biochemical production methods, 241
for E.coli257–258
enzymatic reactions, 239
stoichiometry matrix, 242
Metabolism
cellular, 239–241
defined, 239
modeling decision, 260–261
5-Methyl cytosine, 267–268
Michaelis-Menten Equation
defined, 43
enzymatic reactions, 42
enzyme-substrate complex, 42
individual reactions, 42
single enzyme single substrate reaction, 42
Model selection, 257
Gröbner bases, 93
in gene regulatory network, 77–78
monomial ordering, 89
Monomial ordering
classification, 83
defined, 83–84
graded lexicographic (grlex), 83
graded reverse lexicographic (grevlex), 83
Gröbner bases, 84, 89, 93
mRNA
Boolean functions, 15
defficient ,model, 21–22
model parameters, 8
On and Off states, 15–16
production levels, 5
Multiple alignment, phylogenetic tree reconstruction, 307
Multi-molecule binding
enzymatic reactions, 44
individual reactions, 44
Multivariate polynomial, 84
Mycobacterium tuberculosis, 241

N

Neighbor-joining (NJ algorithm), 309, 337, 340
cherry-picking order, 333
NJ cones, 334
Q-criterion, 330–331
set of instructions, 329
Netlogo
introduction, 148
uphill and downhill movement, 173
website, 165
Network connectivity
acyclic digraphs, 190
complete loop-free digraphs, 193
cycle graphs, 191
directed cycle, 195
typical dynamics, 197
Network dynamics
defined, 77
Network topology
reverse engineering, 77
wiring diagram, 79
Neuronal system
action potentials, 209
firing pattern, 209
functional role, 209
synchronous activities, 209
Neurons
electoral activities, 180–181
membrane potential, 181
schematic drawing, 181
sequential activation, 182
Nodes. see Boolean model, network dynamics
Numerical simulation, Yildirim-Mackey,
allolactose dynamics, 54–55
bistable behavior, 52–53
lactose concentration, 52, 54–55
MATLAB starter code, 54
nonlinear equations, 55
Steady state analysis, 52, 54–55
time-series simulations, 55–56

O

ODE model
biophysical mechanisms of AL and OB, 206
discrete-time system, 205–206
Olfaction
firing patterns, 182
intrinsic properties, 182
network architecture, 182
spatiotemporal firing patterns, 182
Operator
Boolean models, 10
lacgenes, 7–8
lacrepressor, 4–5
transition function, 14–15
Optimal control
goal of, 154
in agent agent-based (ABM), 153
Optimization problems
in agent-based model, 152–153, 156

P

Parsimony methods, phylogenetic tree reconstruction, 307–309
Pauplin’s formula, 310, 335
Perron-Frobenius Theorem, 228–231
Phylogenetic tree
alignment methods, 308
biological perspectives, 307
BME principle, 310, 335, 339
branching processes, 310–311
continuous-time Markov chains, 308–309
distance-based methods, 308–309
edge-weighted, 324, 327
isomorphism of, 315
Newick format, 310–311
unrooted, 316
Phylogenetic tree reconstruction
basics, 310
BME method, 334, 337–338
continuous-time Markov process, 309
distance-based approach, 320, 334
edges labeling, 318
genomic data set, 307
as multi-layered process, 307
linear function, 310
NJ algorithms, 334
softwares for, 310
Polyhedral cones, 309
Polyhedral geometry, 309–310
Polynomial dynamical system (PDSs)
in agent based models, 167–168, 171
in gene regulatory network, 78
reverse engineering, 85, 93
Population growth
dominant eigenvalues, 234–235
life cycles, 214
linear algebra, 216
Perron-Frobenius Theorem, 228
projection matrices, 213, 237–239
stable distribution, 234–235
stage, determinations, 215
stage-structured model, 214
Posterior decoding
forward-backward algorithm, 289
post-processing, 299
Viterbi decoding, 293
Projection matrices
construction of, 217
eigenvalue, 213, 233
eigenvector, 234
life stages, 213
Perron-Frobenius Theorem, 228–231
population growth, 234–235, 237–239
stable distribution, individual stages, 226
through MATLAB, 235, 236
transition models, 213

R

Random connectivities, network
Central Limit Theorem, 202
Erdös-Rényi digraphs, 202
power law distributions, 202
typical dynamics, 197
Regulated genes, 1
Reverse engineering
discretization, 96
in gene regulatory network, 76–77
PDSs construction, 85, 93
RNA polymerase
gene transcription, 1
in E. coli, 4
lac operon mechanism, 5

S

Saccharomyces cerevisiae (yeast), 241
Segregation model, 110
Sliding window algorithm
CIG identification, different interpretations, 271–273, 301
CpG Educate suite, 271
quantitative characteristics, 270–271
Stoichiometry matrix, 242
biochemical reaction network, 242
nullspace, 242
State space graph, 22, 79
Sugar transport proteins, 3, 4
Synapses
cellular automata, 182
>neuron communication, 180–181

T

T-cells, 143, 144
Terminal vertex, 310–311
TICKSIM model, 130
design concept, 131–132
input, 132
RMSF-SIM model, 130
scheduling process, 130
simulation experiments, 132–133
variables and scales, 130
Tipping model, 109
Training algorithm
Baum-Welch algorithm, 295
HMM parameters, 295–296, 301–302
post-processing, 283
Training sequence
Baum-Welch algorithm, 295
Transcription control
E.coli in, 3
gene expression, 1
variables and parameters, 8
Tree topology, 309–310, 334

U

Uphill movement
in agent based models, 173

V

Viterbi algorithm
computational complexity, 286
CpG Educate, 287
decoding, 283, 288–289
forward alogorithm, 283, 288–289
trellis diagram, 286
Viterbi decoding
CpG Educate, 287
posterior probabilities, 293

W

Wiring diagram
Boolean model, 10, 14–15, 23, 25
Discrete Visualizer of Dynamics (DVD), 17–18
variables and parameters, 9, 23

Y

Yildirim-Mackey differential equation, lactose operon
allolactose dynamics, 50–51
bacterial system, modeling, 47
basal transcription rate, 50
delay differential equation models, 47
internal lactose dynamics, 51–52
permease dynamics, 51
repressor protein, 48
Yildirim-Mackey 3-variable model, 51
allolactose dynamics, 62–63
bistable behavior, 53
Boolean variants of, 60
DVD software application, 62
translation and transcription, 61
variables, comparative order, 60–61
Yildirim-Mackey 5-variable model, 52
bistable behavior, 55
Boolean variants of, concentration level, 65–66
degradation constants, 65
parameters, 65
Yildirim-Mackey, numerical simulation
allolactose dynamics, 54–55
bistable behavior, 52–53
lactose concentration, 52, 54–55
MATLAB starter code, 54
nonlinear equations, 55
Steady state analysis, 52, 54–55
time-series simulations, 55–56

Z

Zero player game, 109 see also Game of life
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