Index
A
ABM. see Agent-based model (ABM)
Action potentials
electrical and chemical processes,
180–
181
Agent-based model (ABM)
basic movement function,
171
differential equations,
144
optimization problems,
152
polynomial dynamical systems (PDSs),
167–
168,
171
Agent-based model, cholera,
119
environmental contamination,
120–
122
NetLogo platform for,
123
probability of infection,
122–
123
Agent-based model, computation history,
109
NetLogo platform (ABM),
108
zero player game,
109 see also Game of life
Agent-based model, tick-borne disease. see also TICKSIM model
Algebraic approach. see also Reverse engineering
graded lexicographic ordering (grlex),
83
graded reverse lexicographic ordering (grevlex),
83
lexicographic ordering (lex),
83
multivariate polynomials,
82
Anabolism,
Axon guidance, neuron development,
113–
114
neuron components of,
114
B
Basic movement function
in agent-based model,
171
Baum-Welch algorithm
maximum likelihood estimates,
295–
296
Bayesian inference methods, phylogenetic method,
308
Biochemical reaction network
Biological systems model
differential equations,
144
BME (Balanced minimum evolution) principle
phylogenetic tree reconstruction,
337
Boolean model
complexity levels, –
construction,
Discrete Visualizer of Dynamics (DVD) in,
17
equations,
lac operon,
16
molecular concentration,
57
single time-steps, limitations,
58
state space transition diagram,
12,
58
transition functions,
14–
15,
58
Boolean networks see Boolean model
C
cAMP
model parameters,
production, –
CAP (catabolite activator protein),
CAP-cAMP
complexity, –
positive control mechanism, ,
23
Catabolism, , –
Catabolite repression, –, ,
23
see also Game of Life
Central Limit Theorem,
202
CGI identification
sliding window algorithms,
301
Complete loop-free digraphs,
193
Computation history, Agent-based model,
109
NetLogo platform (ABM),
108
zero player game,
109 see also Game of life
Continuous-time Markov chains,
308
CpG Educate suite
Hidden Markov Models (HMMs),
302
sliding window algorithm,
271
CpG island
D
Dependency graph, –see also Wiring Diagram
Differential equations
in agent-based models,
146
bi-molecular reaction,
41
biochemical reactions,
40
collision orientation,
40
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
Directed cycle graphs,
191
Directed cycle, network connectivity,
195
Discrete model
complete loop-free digraphs,
193
directed cycle graphs,
191
directed cycle, network connectivity,
195
in gene regulatory network,
76
Discrete-time model,
Discrete Visualizer of Dynamics (DVD),
17
Disease dynamics, neuronal network model
mathematical model vs. natural system 202
Dissimilarity map
mathematical formulations,
320
Neighbor-Joining (NJ) Algorithm,
329–
331,
333
Distance-based methods
geometrical approaches,
309
phylogenetic tree reconstruction,
309,
339
polynomial time algorithms,
340
Distance matrix,
309 see also Dissimilarity map
DNA
binding of proteins,
CAP (forcatabolite activator protein) and, –
E.coli’s role,
DNA methylation
dinucleotide replication,
268
DNA sequence
multicellular organism,
267
sliding window algorithms,
271–
273
Downhill movement
in agent based models,
173
E
E. coli (Escherichia coli)
gene regulation,
LacOperon and, –
lactose concentration,
32
lactose metabolism,
life span,
Eigenvalue
biological information,
234–
235
Perron-Frobenius Theorem,
228
stable distribution, individuals,
231
Eigenvector
biological information,
234–
235
dominant eigenvalue and,
232–
233
Perron-Frobenius Theorem,
228,
231
Exons, genomic sequence,
268
F
Finite dynamical systems (FDS),
33
Firing patterns
thalamus, during sleep,
209
Fixed points, Boolean network,
determining factors,
25–
26
Forward-backward algorithm
G
Game of Life
in agent-based model,
145
polynomial dynamical system,
171
Gene expression
mechanisms,
transcription level,
Gene regulation. see also Gene regulatory network
Gene regulatory network
binary discretizations,
96
discrete dynamical system,
179
neuronal network model,
180
regulatory interactions,
75–
76
Genetic algorithms
in heuristic approach,
167
Graded lexicographic ordering (grlex),
83
Graded reverse lexicographic ordering (grevlex),
83
Graphs
biochemical reaction systems by,
257–
258
Gröbner(Groebner) bases
polynomial equations, ,
26
Gröbner Fan Method, post processing,
93
H
Heuristic approach
in agent based model (ABM),
163
Hidden Markov Models (HMMs)
Baum-Welch algorithm,
296
comma separated value (CSV) parameters,
288–
289
maximum likelyhood estimates,
295–
296
process, description,
274
Hodgkin-Huxley model
membrane potential evolution,
183
Housekeeping genes,
I
Immunocompetent cells,
143
Inducible proteins,
Introns, genomic sequence,
268
L
Lac operon
E. coli (Escherichia coli)and, –
mathematical model 38–39
positive feedback mechanism,
40
regulatory components,
39
Lactose, maintenance concentration,
38
Lexicographic ordering (lex),
83
Life cycles
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,
Boolean network models,
38–
39
deterministic,
differential equation model,
38–
39
discrete-time,
Minimal Sets Algorithm (MSA),
91
space-continuous,
space-discrete,
static,
stochastic,
time-continuous,
time-discrete,
Matrix algebra
Perron-Frobenius Theorem,
228
Maximum-likelihood (ML) method,
308–
309
Metabolic engineering,
241
Metabolic pathways
biochemical production methods,
241
for E.coli257–258
stoichiometry matrix,
242
Metabolism
Michaelis-Menten Equation
enzyme-substrate complex,
42
single enzyme single substrate reaction,
42
in gene regulatory network,
77–
78
Monomial ordering
graded lexicographic (grlex),
83
graded reverse lexicographic (grevlex),
83
mRNA
model parameters,
production levels,
Multiple alignment, phylogenetic tree reconstruction,
307
Multi-molecule binding
Multivariate polynomial,
84
Mycobacterium tuberculosis,
241
N
Neighbor-joining (NJ algorithm),
309,
337,
340
cherry-picking order,
333
Netlogo
uphill and downhill movement,
173
Network connectivity
complete loop-free digraphs,
193
Network dynamics
Network topology
Neuronal system
synchronous activities,
209
Neurons
sequential activation,
182
Nodes. see Boolean model, network dynamics
Numerical simulation, Yildirim-Mackey,
allolactose dynamics,
54–
55
lactose concentration,
52,
54–
55
Steady state analysis,
52,
54–
55
time-series simulations,
55–
56
O
ODE model
biophysical mechanisms of AL and OB,
206
Olfaction
intrinsic properties,
182
network architecture,
182
spatiotemporal firing patterns,
182
Operator
lacgenes, –
lacrepressor, –
transition function,
14–
15
Optimal control
in agent agent-based (ABM),
153
Optimization problems
P
Parsimony methods, phylogenetic tree reconstruction,
307–
309
Perron-Frobenius Theorem,
228–
231
Phylogenetic tree
biological perspectives,
307
continuous-time Markov chains,
308–
309
distance-based methods,
308–
309
Phylogenetic tree reconstruction
continuous-time Markov process,
309
distance-based approach,
320,
334
as multi-layered process,
307
Polynomial dynamical system (PDSs)
in gene regulatory network,
78
reverse engineering,
85,
93
Population growth
Perron-Frobenius Theorem,
228
stage, determinations,
215
stage-structured model,
214
Posterior decoding
forward-backward algorithm,
289
Projection matrices
Perron-Frobenius Theorem,
228–
231
stable distribution, individual stages,
226
R
Random connectivities, network
Central Limit Theorem,
202
Erdös-Rényi digraphs,
202
power law distributions,
202
Regulated genes,
Reverse engineering
in gene regulatory network,
76–
77
PDSs construction,
85,
93
RNA polymerase
gene transcription,
in E. coli,
lac operon mechanism,
S
Saccharomyces cerevisiae (yeast),
241
Sliding window algorithm
CIG identification, different interpretations,
271–
273,
301
quantitative characteristics,
270–
271
Stoichiometry matrix,
242
biochemical reaction network,
242
State space graph,
22,
79
Sugar transport proteins, ,
Synapses
>neuron communication,
180–
181
T
simulation experiments,
132–
133
variables and scales,
130
Training algorithm
Baum-Welch algorithm,
295
Training sequence
Baum-Welch algorithm,
295
Transcription control
E.coli in,
gene expression,
variables and parameters,
U
Uphill movement
in agent based models,
173
V
Viterbi algorithm
computational complexity,
286
Viterbi decoding
posterior probabilities,
293
W
Wiring diagram
Discrete Visualizer of Dynamics (DVD),
17–
18
variables and parameters, ,
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
Yildirim-Mackey 3-variable model,
51
allolactose dynamics,
62–
63
DVD software application,
62
translation and transcription,
61
variables, comparative order,
60–
61
Yildirim-Mackey 5-variable model,
52
Boolean variants of, concentration level,
65–
66
degradation constants,
65
Yildirim-Mackey, numerical simulation
allolactose dynamics,
54–
55
lactose concentration,
52,
54–
55
Steady state analysis,
52,
54–
55
time-series simulations,
55–
56
Z
Zero player game,
109 see also Game of life