10 | Stochastic Reaction Kinetics Flashcards
In which situation(s) is a stochastic description of a reaction system useful?
a. short simulation times
b. low numbers of molecules
c. low numbers of reactions
(ungraded quiz)
b. low numbers of molecules
In which type of reaction kinetic models are reaction counters used?
a. Stochastic, but not deterministic models
b. Stochastic and deterministic models
c. Deterministic, but not stochastic models
(ungraded quiz)
b. Stochastic and deterministic models
What is the reaction propensity aμ(X(t))?
a. Probability that reaction Rμ occurs at time t
b. Probability that reaction Rμ occurs in the next infinitesimal time interval [t,t+Δt], normalized by the length of that interval.
c. Probability that reaction Rμ occurs after time t
d. Probability that reaction Rμ occurs in the next infinitesimal time interval [t,t+Δt]
(ungraded quiz)
b. Probability that reaction Rμ occurs in the next infinitesimal time interval [t,t+Δt], normalized by the length of that interval.
What are the deterministic analogues of the following concepts from stochastic reaction kinetics?
Stochastic reaction constant
Reaction propensity
(ungraded quiz)
Stochastic reaction constant –> Reaction rate constant
Reaction propensity –> Reaction rate
The reaction propensity corresponding to the dimerization reaction A + A ⟶cμ A:A
is…
a. cμXAXA
b. cμ(XA−1)
c. cμXA(XA−1) ) / 2
d. cμXA
e. cμ
(ungraded quiz)
c. cμXA(XA−1) ) / 2
What is the chemical master equation?
a. An ODE system describing X(t)
b. The deterministic analogue of the stochastic reaction model
c. An ODE system describing the probability distribution of X(t)
(ungraded quiz)
c. An ODE system describing the probability distribution of X(t)
What are the limitations of the chemical master equation (CME)?
a. The lack of accuracy of solving it numerically
b. The computational cost of solving it numerically
c. Its solution cannot be interpreted well
(ungraded quiz)
b. The computational cost of solving it numerically
What is the CME corresponding to the reaction system
A ⟶c1 B, B⟶c2A, with A(0)=1, B(0)=0 and X=(XA,XB)?
a.The ODE system
ddtp(1,0)=−c1p(0,1)+c2p(1,0)
ddtp(0,1)=+c1p(0,1)−c2p(1,0)
b. None of the other answers is correct
c. The ODE system
ddtp(1,0)=−c1p(1,0)+c2p(0,1)
ddtp(0,1)=+c1p(0,1)−c2p(1,0)
d. The ODE system
ddtp(1,0)=−c1p(1,0)+c2p(0,1)
ddtp(0,1)=+c1p(1,0)−c2p(0,1)
e. The ODE system
ddtp(1,0)=−c1p(0,1)+c2p(0,1)
ddtp(0,1)=+c1p(1,0)−c2p(1,0)
(ungraded quiz)
d. The ODE system
ddtp(1,0)=−c1p(1,0)+c2p(0,1)
ddtp(0,1)=+c1p(1,0)−c2p(0,1)
What is the main idea of the stochastic simulation algorithm?
a. Compute individual trajectories based on the CME
b. Use a stochastic rather than a deterministic description of the reaction system
c. Treat occurrence of reactions apart from the type of occurred reaction
Treat occurrence of reactions apart from the type of occurred reaction
How are stochastic trajectories linked to the CME?
a. The distribution of the state from a large number of stochastic trajectories is described approximately by the CME
b. The two descriptions cannot be linked
c. The distribution of the types of reactions from a large number of stochastic trajectories is described approximately by the CME
d. The distribution of the total reaction counter from a large number of stochastic trajectories is described approximately by the CME
(ungraded quiz)
a. The distribution of the state from a large number of stochastic trajectories is described approximately by the CME
Consider a stochastic reaction system with three reactions, with current reaction propensities a1 = 1/min, a2 = 3/min and a3 = 4/min.
What is the probability that the next occurring reaction will be R2?
(ungraded quiz)
3/(1+3+4) = 3/8 = 0.375
Consider the stochastic model for the reaction network R1 : ∗ → A (c1), R2 : A → ∗ (c2), with c1 = 1/s and c2 = 2/s. Assume that initially, the number of A molecules A(0) = 2. What is the probability that the first reaction occuring will be a degradation reaction (i.e., R2)?
◦ 1/5
◦ 1/3
◦ 1/2
◦ 2/3
◦ 4/5
(2023_1, 2020_2)
2/(1+2) = 2/3
A → *
B → *
A(0) = 1, B(0) = 1
write possible states of the system.
How do the states relate to the CME?
(2023_1)
Possible states: (1,1), (0,1), (1,0), (0,0)
- States directly correspond to possible configurations in CME.
- CME describes and tracks prob. of system being in each states at any given time.
- As reactions progress, system will transition between states,
A → *
B → *
A(0) = 1, B(0) = 1
Possible states: (1,1), (0,1), (1,0), (0,0)
Write down the CME of the system.
(2023_1)
dp11/dt = -c1p11 -c2p11
dp01/dt = c1p11 - c2p01
dp10/dt = c2p11 - c1p10
dp00/dt = c2p01 + c1p10
A → *
B → *
A(0) = 1, B(0) = 1
Possible states: (1,1), (0,1), (1,0), (0,0)
dp11/dt = -c1p11 -c2p11
dp01/dt = c1p11 - c2p01
dp10/dt = c2p11 - c1p10
dp00/dt = c2p01 + c1p10
Does a deterministic model approximate the system well?
(2023_1)
Deterministic can model fairly as these are only 1st-order reactions (2 or more does not work well for small number of molecules), but its better to use when there is a large number of molecules, not for small number of molecules.
