Gene modelling

Question 1

state of a system

Answer 1

snapshot of the system at a given time that

contains enough information to predict the behavior of the system for all future times.

Question 2

differential equation models

Answer 2

list of concentrations of each chemical type

Question 3

boolean models

Answer 3

a list, for each gene involved, of whether the gene is expressed or not expressed

Question 4

stochastic model configuration

Answer 4

list of the actual number of molecules of each type

- state is configuration or current probability distribution

Question 5

molecular dynamics model

Answer 5

list of positions and momenta of each molecule

Question 6

Each model does ______

Answer 6

• defines what it means by the state of the system
• model predicts which state or states can occur next (given current state)
• some states are equilibrium states in the sense that once in that state, the system stays in that state

Question 7

kinetics

Answer 7

changes of state

Question 8

equilibria

Answer 8

which states are equilibrium states

Question 9

A state is said to be at equilibrium when

Answer 9

its state ceases to change

- forward reaction = back reaction

Question 10

differential equation for [X*DNA]

Answer 10

d[XDNA]/dt = k1[X][DNA] - k-1[XDNA] = 0(at equilibrium)

Question 11

Keq

Answer 11

k1/k-1 = [X*DNA]/[X][DNA]

Question 12

What happens when applying the equilibrium condition to the differential equation of the change in [X*DNA]

Answer 12

the differential equation is reduced to an algebraic equation
(d[XDNA]/dt = k1[X][DNA] - k-1[XDNA] –> k1/k-1 = [X*DNA]/[X][DNA]

Question 13

stochastic equation typically uses the _______ of molecules rather than the _______ of molecules

Answer 13

number

concentration

Question 14

Real physical systems tend towards equilibrium unless

Answer 14

energy is added

Question 15

equilibrium

Answer 15

the state of the system as time->∞

Question 16

To simplify models

Answer 16

fast reactions assumed to be at equilibrium

Question 17

If a and b are in equilibirum and b and c are in equilibrium, then __________-

Answer 17

a and c are in equilibrium

Question 18

From an energy difference

Answer 18

one can predict the final state of the system,

cannot predict the time course of the state from initial to final

Question 19

Gibbs free energy

G =

Answer 19

(total internal energy) - (absolute temperature) * entropy + pressure * volume = ∑(chemical potential) * (partical number)

Question 20

for reactants and products with the free energy difference ∆G
Keq =

Answer 20

e^(-∆G/RT)

Question 21

Paritition functions
[DNA]3/[DNA]total = 
Z = 
K3 = 
[DNA]total

Answer 21

k3[P][Q]/Z
1 + K + K + K 1 2 3 [P] [Q] [P][Q].
[DNA]3/[P][Q][DNA]0
[DNA]0 + k1[P][DNA]0 + K2[Q][DNA]0 + K3[P][Q][DNA]0 = [DNA]0Z

Question 22

Questions to consider when evaluating models

Answer 22

State of the model
How does the state change over time
What are the equilibrium states

Others
What assumptions(biological and computational)
For what time scale is model valid
# molecules present
Time complexity
Amount of data available
What can it expect to predict

Question 23

If the # of molecules is small (_______) ______ must be used

Once very large, use _______

Answer 23

tens or low hundreds
stochastic models
differential equations

Question 24

Boolean network models

Answer 24

• each gene fully expressed or not expressed at all
• state space in finite
• obtain a first representation of a complex system
• all genes change state at same time

Question 25

kinetic logic models

Answer 25

state of each gene as a discrete value - deal with rates at which systems change from one state to another - genes change state at independent rates

Question 26

continuous logical models

Answer 26

transition | from one state to another is governed by linear differential equations with constant coefficients

Question 27

Differential equation models

Answer 27

provide a general framework in which to consider gene | regulation processes

Question 28

One way to transform a system of chemical reactions and physical constraints into a system of non-ordinary differential equations

Answer 28

reaction/enzyme kinetics: considering the transition rates between all microscopic states

Question 29

differential equations assume

Answer 29

changes of state are continuous and deterministic

Question 30

Langevin approach

Answer 30

adding a noise term to a differential equation (useful for non-deterministic problems)

Question 31

Fokker-plank method

Answer 31

- start from a probabilistic framework - write equations that describe a change in probabilistic framework as a function of time - assume continuity: probability distribution is a continuous function of concentration

Question 32

Fully stochastic models consider

Answer 32

the individual molecules involved in gene regulation

Question 33

Langevin and Fokker-Plank models are approximations of

Answer 33

a fully stochastic model

Question 34

Truth tables

Answer 34

specify what the next state is for each current state | with n genes, there are 2^n states, exactly one next state

Question 35

Ways to represent boolean models

Answer 35

Truth tables | finite-state machines

Question 36

differential equations approach to modelling gene regulations

Answer 36

state is a list of concentrations of each chemical species | - concentrations continuous

Question 37

Use a stochastic model when

Answer 37

assume solution is well mixed(a given molecule is equally likely to be anywhere in the solution) - rate of molecular collisions is much greater than the rate of molecular reactions

Question 38

Assumptions for differential equations framework

Answer 38

- # of molecules is sufficiently high that discrete changes of a single molecule can be approximated as continuous changes in concentration - Fluctuations about the mean are small compared to the mean itself

Question 39

To go from differential equations to boolean models

Answer 39

one assumes that the function ƒ in the differential equation (d/dt)v = ƒ(v) has saturating nonlinearities (when v is very small or very large, ƒ(v) tends towards a limit) - one assumes that the nonsaturated region between two extremes is transient and can be ignored