SYSTEMS BIOLOGY MIDTERM EXAM
QUESTIONS AND ANSWERS
canonical models - ANSWER-linear, mass-action system (GMA no exponent), Lotka-
Volterra system (GMA with special structure), generalized mass action model
(GMA), s-system
mass action models - ANSWER-proposed by guldberg and waage
biochemical kinetics
used in other contexts (SIR, Lotka-Volterra)
Issue- several implicit assumptions (seldom satisfied in vivo); regulation difficult to
take into account
lotka-volterra models - ANSWER-main application- models of interaction populations
contain two species
can be written as taylor expansion
typical application- ecology, predator-prey systems, competing populations,
metapopulations, microbiomes
issues- problems for metabolic systems (two-substrate rxns, feedback inhibition,
other types of regulation)
power-law models - ANSWER-all processes represented as univariate or
multivariate power functions
format corresponds to linearization in log space
can represent any differentiable processes
eg GMA and s-system (only 1 in and 1 out)
alternative- approximation - ANSWER-generic features for approximating an
arbitrary function F(x)- operating point (OP)
Range of Validity (Brook Taylor)
perfect (approximation at OP), great, good (approximation close to OP), usually not
good (approximation far from OP)
Operating point (OP) - ANSWER-OP=x, location on x-axis where F(x) is
approximated; OP=(x,F(x)), point where approximation is anchored
linearization - ANSWER-given nonlinear function, want to use linear function to
approximate it
select OP, compute tangent
fundamental theorem for nonlinear systems (hartman and grobman) - ANSWER-for
"nice" systems, linearized system has essentially same features as nonlinear system
in vicinity of OP
consequence- allows us to analyzed linearized system (in tangent plane)
power-law approximation - ANSWER-select type of approximation and OP- compute
parameter values
choose different OP, piecewise approximation possible
, analysis of dynamic models-what to analyze - ANSWER-four aspects (2 modeling
phases, 2 classes of features)
static (diagnostic- sensitivities, analysis/model use- steady state); dynamic
(diagnostic- trajectories, analysis/model use- what if, possible, likely, best, worst
scenarios)
analysis of dynamic models- issues - ANSWER-diagnostics and analysis not always
clearly discernible
static and dynamic features may blend into each other
typical dynamic analysis - ANSWER-trajectories
analysis seldom possible with algebra/calculus (explicit solutions of function of time v
ODE cannot be obtained)
use linear ODE systems (Laplace transforms instead)
choice of model type - ANSWER-guided by the following: scope of model (goals,
objectives, possible applications), data availability/need (types, quantity, quality),
other available information (non-quantitative, heuristics, qualitative input from
experts), expected feasibility of model, relevance/degree of interest within scientific
community
components of system/model - ANSWER-variables (dependent, independent, time),
processes (flow of material, flow of information), parameters, constants (pi, e,
Avogadro's number)
dependent variables - ANSWER-quantities of prime interest in model, may change
over time, typically affected by system action
independent variables - ANSWER-quantities in model that are constant/under control
of experiment, not affected by system action
parameters - ANSWER-quantities in model that do not change during experiment,
may change from one experiment to next, are assigned numerical values, connect
model to reality, model structure -> totality of all model can possibly do, parameter
values -> characterize one model implementation (eg dx/dt = aX -bX^2)
SIRS-> a model system - ANSWER-decide on model structure: interested in
numbers, not geographic spread; interested in populations, not individuals,
population large enough to ignore random effects,
Goal -> find ways of manipulating epidemic; optimize
ODE model (generally mass action model) used
markov models (definition) - ANSWER-discrete, stochastic models
markov model - ANSWER-describes system that can assume m different states, at
each (discrete) time point, system is in exactly one of these states, in discrete time
steps- system transitions with some probability into different state/stays where it is
QUESTIONS AND ANSWERS
canonical models - ANSWER-linear, mass-action system (GMA no exponent), Lotka-
Volterra system (GMA with special structure), generalized mass action model
(GMA), s-system
mass action models - ANSWER-proposed by guldberg and waage
biochemical kinetics
used in other contexts (SIR, Lotka-Volterra)
Issue- several implicit assumptions (seldom satisfied in vivo); regulation difficult to
take into account
lotka-volterra models - ANSWER-main application- models of interaction populations
contain two species
can be written as taylor expansion
typical application- ecology, predator-prey systems, competing populations,
metapopulations, microbiomes
issues- problems for metabolic systems (two-substrate rxns, feedback inhibition,
other types of regulation)
power-law models - ANSWER-all processes represented as univariate or
multivariate power functions
format corresponds to linearization in log space
can represent any differentiable processes
eg GMA and s-system (only 1 in and 1 out)
alternative- approximation - ANSWER-generic features for approximating an
arbitrary function F(x)- operating point (OP)
Range of Validity (Brook Taylor)
perfect (approximation at OP), great, good (approximation close to OP), usually not
good (approximation far from OP)
Operating point (OP) - ANSWER-OP=x, location on x-axis where F(x) is
approximated; OP=(x,F(x)), point where approximation is anchored
linearization - ANSWER-given nonlinear function, want to use linear function to
approximate it
select OP, compute tangent
fundamental theorem for nonlinear systems (hartman and grobman) - ANSWER-for
"nice" systems, linearized system has essentially same features as nonlinear system
in vicinity of OP
consequence- allows us to analyzed linearized system (in tangent plane)
power-law approximation - ANSWER-select type of approximation and OP- compute
parameter values
choose different OP, piecewise approximation possible
, analysis of dynamic models-what to analyze - ANSWER-four aspects (2 modeling
phases, 2 classes of features)
static (diagnostic- sensitivities, analysis/model use- steady state); dynamic
(diagnostic- trajectories, analysis/model use- what if, possible, likely, best, worst
scenarios)
analysis of dynamic models- issues - ANSWER-diagnostics and analysis not always
clearly discernible
static and dynamic features may blend into each other
typical dynamic analysis - ANSWER-trajectories
analysis seldom possible with algebra/calculus (explicit solutions of function of time v
ODE cannot be obtained)
use linear ODE systems (Laplace transforms instead)
choice of model type - ANSWER-guided by the following: scope of model (goals,
objectives, possible applications), data availability/need (types, quantity, quality),
other available information (non-quantitative, heuristics, qualitative input from
experts), expected feasibility of model, relevance/degree of interest within scientific
community
components of system/model - ANSWER-variables (dependent, independent, time),
processes (flow of material, flow of information), parameters, constants (pi, e,
Avogadro's number)
dependent variables - ANSWER-quantities of prime interest in model, may change
over time, typically affected by system action
independent variables - ANSWER-quantities in model that are constant/under control
of experiment, not affected by system action
parameters - ANSWER-quantities in model that do not change during experiment,
may change from one experiment to next, are assigned numerical values, connect
model to reality, model structure -> totality of all model can possibly do, parameter
values -> characterize one model implementation (eg dx/dt = aX -bX^2)
SIRS-> a model system - ANSWER-decide on model structure: interested in
numbers, not geographic spread; interested in populations, not individuals,
population large enough to ignore random effects,
Goal -> find ways of manipulating epidemic; optimize
ODE model (generally mass action model) used
markov models (definition) - ANSWER-discrete, stochastic models
markov model - ANSWER-describes system that can assume m different states, at
each (discrete) time point, system is in exactly one of these states, in discrete time
steps- system transitions with some probability into different state/stays where it is
