Systems Biology Flashcards
How does the wiring diagram of Simple Regulation look like?
How can Simple Regulation be described?
y’ = β - α * y
with:
- β: Production rate
- α: Removal rate
What is the steady-state of simple regulation?
y_st = β / α
with:
- β: Production rate
- α: Removal rate
What is the response time of simple regulation?
t_H = ln(2) / α
with:
- α: Removal rate
How do growth and removal rate affect the steady-state and the response time of simple regulation?
- Higher β –> higher steady-state, does not affect response time
- Higher α –> lower steady-state and lower response time
How do ON and OFF switch of simple regulation look like?
How does the wiring diagram of Negative Auto Regulation (NAR) look like?
How can NAR be described?
y’ = β * 1 / (1 + (y/k)^n) - αy
with:
- β: Production rate
- α: Removal rate
- k: Half-saturation constant
- n: Hill coefficient
What is the steady-state of NAR?
y_st = K
with:
- k: Half-saturation constant
What is the response time of NAR?
t_H = k/2β
with:
- β: Production rate
- k: Half-saturation constant
How does the wiring diagram of Positive Auto Regulation (PAR) look like?
How can PAR be described?
y’ = β * (y/k)^n / (1 + (y/k)^n) - αy
with:
- β: Production rate
- α: Removal rate
- k: Half-saturation constant
- n: Hill coefficient
What is the steady-state of NAR?
If n >= 2:
- It has two steady-states, a low and a high one –> ON and OFF state
- The steady state is history dependant: a third unstable fixpoint is the threshold where system switches from ON to OFF state
–> Bistability
If n = 1:
- Only one steady state
–> Monostability
What is a feed forward loop?
- 3 genes that regulate each other
- 13 possible motives
- Two different types:
- Coherent: Signals reaching product either both activate or repress
- Incoherent: Signals raching product contradict each other
- Arrows reaching product can be connected through different logic gates, eg. AND, OR
How does the wiring diagram of C1-FFL look like?
How can C1-FFL with an AND Gate be described?
y’ = Sx * β - αy
z’ = Sx * β * (y/k)^n / (1 + (y/k)^n) - αz
with:
- β: Production rate
- α: Removal rate
- k: Half-saturation constant
- n: Hill coefficient
- Sx: Input of x (Either 1 or 0)
What is the steady-state of C1-FFL?
Depends on k: bigger k –> lower steady-state of Z
On what does the response time of C1-FFL depend?
Has a delay if we increase k
With AND gate:
- Has delay on ON SWITCH but no delay on OFF switch
With OR gate:
- Has no delay on ON SWITCH but delay on OFF switch
How does the wiring diagram of I1-FFL look like?
How does the wiring diagram of a toggle switch look like?
How can a toggle switch generally be described?
x’ = f(x,y), y’ = g(x,y)
With f and g Hill functions with n >= 2 plus degradation
What is special about toggle switches and oscillators?
They have a 2D phase plane
They have bifurcation
How many fixpoints does a toggle switch have?
3 FP, otherwise it is not a toggle switch but mono stable
2 of them have to be stable with either x or y low/high but not both, otherwise it would be a double-positive feedback circuit for example
–> n has to be bigger or equal to 2 so that both Nullclines have sigmodial shape and will therefore intersect in at least 3 points
How does the wiring diagram of an oscillator look like?
What is needed in order to have oscillation?
- Feedback
- Delay
- Ultrasensitivity
+ it depends on parameters –> bifurcation
Without feedback:
- Attractive FP –> phase plane arrows point towards FP
- no sustained oscillation
- with noise it can oscillate
How can oscillation be described?
What are the time domains of oscillation and how are they affected by the dillution μ?
- x high and y increases
- x low and y decreases
- Higher μ: increases duration of 1. time domain and decreases 2.
- lower μ: decreases duration of 1. time domain and increases 2.
–> higher μ in general decreases the time period of oscillation
What is the response time of degradation of y in an oscillating system?
t_H = ln(2) / μ
What is a Hill equation?
What do the parameters signify?
- A Model to describe cooperative promotor binding
- Assumes n molecules of Sx can bind X
- Has sigmodial shape
Hill function = Sx^n/(Sx^n + K_d^n)
with:
- n: Hill coefficient (number of molecules that bind to promotor)
- K_d: half-saturation constant (concentration at wich the promotor is bound by Y 50% of the time)
The higher n, the steeper the increase
What is the steady-state?
Concencentration of Y, when Y does not change anymore (y for whitch y’ = 0)
What is the response time?
Time to reach half of a new steady-state
What is a Nullcline?
Points on a phase plane, where at least one variable does not change
What does bifurcation mean?
Qualitative change upon small parameter change
What is a fixpoint? When is it stable?
- Intercept of Nullclines –> points where all variables do not change anymore
- Sometimes the same as steady-state
- Stable if arrows on phase plane point towards it
What does bi-stability mean?
If a system has two stable fixpoints
Only if Hill coefficient n >=2
What does bi-stability mean?
If a system has two stable fixpoints
Only if Hill coefficient n >=2
What are the bifurcation points of oscillation?
What accelerates response time?
- Fast degradation (high cost)
- NAR (only works for TFs)
- I-FFL (all targets)
What slows response time down?
- Slow degradation (limit: one cell cycle)
- PAR
- C-FFL (either for ON or OFF switch only)
How can exponential growth be described?
N(t) = N_0 * 2^(t/t_D)
with:
- t_D: doubling time
How can the growth rate of gene expression be described?
R –> P
R(t) = R_0 * e^(α * γ * t)
P(t) = P_0 * e^(α * γ * t)
μ := α * γ
with:
- γ: rate of protein synthesis by 1 ribosome
- α: fraction of ribosomes making ribosomes
- μ: exponential rate of increase
How does the timing of reproduction and the rate of reproduction affect the rate of population growth?
Earls reproduction –> Faster growth
E.g. mutations that promote early reproduction will generally be selected by evolution, even if they have a negative effect on reproduction later in life
