Systems Biology Flashcards

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1
Q

How does the wiring diagram of Simple Regulation look like?

A
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2
Q

How can Simple Regulation be described?

A

y’ = β - α * y

with:
- β: Production rate
- α: Removal rate

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3
Q

What is the steady-state of simple regulation?

A

y_st = β / α

with:
- β: Production rate
- α: Removal rate

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4
Q

What is the response time of simple regulation?

A

t_H = ln(2) / α

with:
- α: Removal rate

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5
Q

How do growth and removal rate affect the steady-state and the response time of simple regulation?

A
  • Higher β –> higher steady-state, does not affect response time
  • Higher α –> lower steady-state and lower response time
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6
Q

How do ON and OFF switch of simple regulation look like?

A
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7
Q

How does the wiring diagram of Negative Auto Regulation (NAR) look like?

A
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8
Q

How can NAR be described?

A

y’ = β * 1 / (1 + (y/k)^n) - αy

with:
- β: Production rate
- α: Removal rate
- k: Half-saturation constant
- n: Hill coefficient

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9
Q

What is the steady-state of NAR?

A

y_st = K

with:
- k: Half-saturation constant

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10
Q

What is the response time of NAR?

A

t_H = k/2β

with:
- β: Production rate
- k: Half-saturation constant

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11
Q

How does the wiring diagram of Positive Auto Regulation (PAR) look like?

A
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12
Q

How can PAR be described?

A

y’ = β * (y/k)^n / (1 + (y/k)^n) - αy

with:
- β: Production rate
- α: Removal rate
- k: Half-saturation constant
- n: Hill coefficient

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13
Q

What is the steady-state of NAR?

A

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

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14
Q

What is a feed forward loop?

A
  • 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
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15
Q

How does the wiring diagram of C1-FFL look like?

A
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16
Q

How can C1-FFL with an AND Gate be described?

A

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)

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17
Q

What is the steady-state of C1-FFL?

A

Depends on k: bigger k –> lower steady-state of Z

18
Q

On what does the response time of C1-FFL depend?

A

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

19
Q

How does the wiring diagram of I1-FFL look like?

A
20
Q

How does the wiring diagram of a toggle switch look like?

A
21
Q

How can a toggle switch generally be described?

A

x’ = f(x,y), y’ = g(x,y)

With f and g Hill functions with n >= 2 plus degradation

22
Q

What is special about toggle switches and oscillators?

A

They have a 2D phase plane
They have bifurcation

23
Q

How many fixpoints does a toggle switch have?

A

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

24
Q

How does the wiring diagram of an oscillator look like?

A
25
Q

What is needed in order to have oscillation?

A
  • 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

26
Q

How can oscillation be described?

A
27
Q

What are the time domains of oscillation and how are they affected by the dillution μ?

A
  1. x high and y increases
  2. 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

28
Q

What is the response time of degradation of y in an oscillating system?

A

t_H = ln(2) / μ

29
Q

What is a Hill equation?
What do the parameters signify?

A
  • 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

30
Q

What is the steady-state?

A

Concencentration of Y, when Y does not change anymore (y for whitch y’ = 0)

31
Q

What is the response time?

A

Time to reach half of a new steady-state

32
Q

What is a Nullcline?

A

Points on a phase plane, where at least one variable does not change

33
Q

What does bifurcation mean?

A

Qualitative change upon small parameter change

34
Q

What is a fixpoint? When is it stable?

A
  • 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
35
Q

What does bi-stability mean?

A

If a system has two stable fixpoints
Only if Hill coefficient n >=2

35
Q

What does bi-stability mean?

A

If a system has two stable fixpoints
Only if Hill coefficient n >=2

36
Q

What are the bifurcation points of oscillation?

A
37
Q

What accelerates response time?

A
  • Fast degradation (high cost)
  • NAR (only works for TFs)
  • I-FFL (all targets)
38
Q

What slows response time down?

A
  • Slow degradation (limit: one cell cycle)
  • PAR
  • C-FFL (either for ON or OFF switch only)
39
Q

How can exponential growth be described?

A

N(t) = N_0 * 2^(t/t_D)

with:
- t_D: doubling time

40
Q

How can the growth rate of gene expression be described?
R –> P

A

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

41
Q

How does the timing of reproduction and the rate of reproduction affect the rate of population growth?

A

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