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OMICS in de Biomedische Wetenschappen 2 > HC 10 - Systems Modelling > Flashcards

HC 10 - Systems Modelling Flashcards

hoorcollege 10

1
Q

Moleculaire interacties (celfunctie) en regulatie hangt af van … interactions van duizenden macromoleculen

A

transient

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2
Q

For complete picture, what is needed to judge importance of a situation?

A

Quantitative information
-Concentrations
-Affinities
-Kinetic behavior

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3
Q

For molecular interactions, what do we need to describe?

A

-Molecule interaction
-Catalyse reactions
-Change of molecules in time
-Gene Y promotes gene Z for example

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4
Q

Types of interaction

A

-Inhibition of geneX to geneZ > transcription repressor X inhibits expression if Z
-Promotion via activator X

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5
Q

Gene transcription regulation

A

-RNAp(olymerase) binding site within promotor
-TFs with X binding sites within the promotor
> binding to DNA
> expression gene Y
> increased transcription

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6
Q

The time for transcription and translation is

A

somewhat equal

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7
Q

Gene transcription regulation: activator characteristics

A

Activator increases rate of mRNA transcriptions when bound to promotor, it typically transits rapidly between active and inactive forms (e.g. phosphorylation state)

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8
Q

Repressor mechanism of action

A

Blocks RNAp for binding by binding the promotor

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9
Q

Interaction model between protein (TF) A and promotor p-x

A

A + p-x <=> A:p-x
kon and koff are the rate constants

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10
Q

Rate of complex formation and dissociation for promotor and protein

A

complex formation: d[A:px]/dt = kon[A][px]
complex dissociation: d[px]/dt = koff[A:px]

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11
Q

what is kon

A

Number of productive collisions per unit time per protein at a given concentration of px

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12
Q

[kon] and [koff]

A

[kon] = M^-1s^-1
[koff] = s^-1
these are different because the units on both sides of the equations must be equal.

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13
Q

At steady-state, the promotor model looks like

A

Rate of formation = rate of dissociation
kon[A][px] = koff[A:px]
[A:px] = (kon/koff) [A][px]
=K[A][px]

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14
Q

What does K mean in the promotor model? And K_D

A

K = kon/koff: association constant in M^-1
K_D = 1/D: dissociation constant in M

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15
Q

When there is a strong interaction between A and px, K becomes larger/smaller

A

larger

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16
Q

In general we know the amount of total px: pxT. Substitute to a equation of [A:px] at steady state

A

[px] = [pxT] - [A:px]
[A:px]steadystate = K[A][px]
[A:px] = (K[A]/(1+K[A]))*[pxT]

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17
Q

The production rate of protein X is determined by … in the promotor model

A

the occupancy of the promotor

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18
Q

bound fraction of promotor

A

[A:px]/[pxT] = K[A]/(1+K[A])

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19
Q

Transcription rate

A

beta * K[A]/(1+K[A])
beta: represents binding of RNAp and the steps to mRNA > transcription rate when activator is bound

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20
Q

Protein production rate

A

beta * m * K[A]/(1+K[A])
m: rate of protein made per mRNA

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21
Q

Protein degradation

A

-Degradation leads to exponential decline in protein levels
-Mean life time tau
-takes active degradation and dilution due to cell growth into account

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22
Q

Protein degradation rate

A

= [X] / tauX
concentration / life time (halfwaardetijd)

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23
Q

A low tau means a … degradation rate

A

high

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24
Q

d[X]/dt formula

A

= protein production rate - protein degradation rate
= beta m (K[A]/(1+K[A])) - ([X]/tauX)

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25
Q

[Xst] formula (at steadystate)

A

[Xst] =beta m (K[A]/(1+K[A])) tauX
> fill in zero for d[X]/dt

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26
Q

The faster X is degraded (smaller tau), the … time is needed to reach steady-state

A

less

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27
Q

Faster response means …

A

higher metabolic cost
> proteins are produced and degraded at higher rates

28
Q

Solution of differential equation

A

X = [Xst] (1-e^-t/tauX)
by integrating

29
Q

When using a repressor model, we are interested in the unbound fraction. The formula is:

A

px = pxT-[R:px] and [R:px] = K[R][px] give
[R:px] / pxT = K[R]/1+K[R]
unbound factor = 1 - bound factor
= 1 - K[R]/(1+K[R])
= 1/(1+K[R])

30
Q

At 0.5 bound factor …

A

1/K_A and 1/K_R

31
Q

Protein production rate, d[X]/dt and [Xst] based on repressor model

A

ppr = beta * m * 1/(1+K[R])
d[X]/dt = beta * m * 1/(1+K[R]) - [X]/tauX
[Xst] = beta * m * 1/(1+K[R]) * tauX

32
Q

Are the beta, m, and tauX functions different for the activator and repressor models?

A

No

33
Q

Solutions of
dx/dt = -x
dy/dt = -2y

A

x(t) = e^-t
y(t) = e^-2t
because the x’(t) is -1 * e^-t which is -x

34
Q

What is the steady state of
dx/dt = -x
dy/dt = -2y

A

0 = -x
x= 0
0 = -2y
y = 0
steady-state at (0,0)

35
Q

Initial condition

A

Initial values for x and y (starting point of model)

36
Q

write as a vector
dx/dt = -x
dy/dt = -2y

A

(-x)
(-2y)
vector format
(dx/dt)
(dy/dt)
> direction from starting point (change)

37
Q

Why use vectors in model?

A

Solutions of differential equations are shown in a field over time with multiple paths dependent on initial values

38
Q

to fill in the vector (-x | -2y), you need

A

the starting point (x,y)

39
Q

In the direction field, what is shown

A

Directions of x and y based on different starting positions and their differential equations
> moving to steady-state(s)

40
Q

What is a trajectory

A

A path of x and y in the direction field from a given starting point, by following the direction vectors
> shows the change of x and y over time

41
Q

What to do with negative time in a time plot (plot x and y as two lines over time > solution of differential equation)?

A

Neglect it, does not exist in biology

42
Q

From the directory field, you can … the solutions of the trajectory differential equations

A

sketch, by following the line over time and checking the development of the x and y values

43
Q

What is a nullcline

A

The lines/conditions in which x or y do not change
> the steady-state is the condition in which both x an y do not change
>dx/dt or dy/dt = 0

44
Q

How to calculate nullclines

A

dx/dt = 0 for x nullcline(s)
dy/dt = 0 for y nullcline(s)

45
Q

How to calculate steady-state

A

Calculate nullclines and fill in the x and y values for the dx or dy/dt =0 in the other formula and match the x and y values for steady-state(s)

46
Q

Where is the steady-state found in the directional field?

A

Crossing point of nullclines

47
Q

At a x-nullcline, x cannot change. How does the trajectory change in x while crossing the x-nullcline

A

From this point, it changes in y and from that point it can change in x again

48
Q

A swirl in the trajectory means

A

oscillations

49
Q

How to draw direction field

A

Take some random starting points and fill in differential equations to calculate some vectors

50
Q

If y approaches a steady-state, but X reaches till infinity and won’t, than there is …

A

no absolute steady-state, this is realistic in a cellular system

51
Q

Instable steady-state

A

There is just one steady-state but the starting point has to be that value, or it will never reach it and trajectories will reach a stable steady-state or reach till infinity
> dx/dt = x + 2y and dy/dt = -y
>y-null: y=0
>x-null: y=-0.5x
> steady-state instable at (0,0)

52
Q

Positive feedback: promotors can have multiple adjacent binding sites for the same TF. Regulators can interact: more expression than normal > give the formulas for bound fraction for activator or repressor

A

bound fraction
= (K_a[A])^h / 1+(K_a_[A])^h
or
=(K_r[R])^h / 1+(K_r_[R])^h

53
Q

What is the Hill coefficient h

A

degree of cooperativity

54
Q

Increasing h means

A

dependence of binding on protein concentration becomes steeper

55
Q

Hill functions are

A

Sigmoid functions

56
Q

Positive feedback can give a system …

A

switch-like response and bistability

57
Q

bistable system provides system with a ..

A

memory > present state depends on its history: hysteresis

58
Q

Bistability steady-states

A

-One instable steady-state
-Two stable steady-states

59
Q

Protein X inhibits Gene Y and Protein Y inhibits gene X. Give the differential equations

A

dX/dt = Beta_X * m_X * (1/1+(K_Y_(Y)^h_Y) - [X] / tauX
dY/dt = Beta_Y * m_Y * (1/1+(K_X_(X)^h_X) - [Y] / tauY
> because: X is the repressor of Y

60
Q

x-nullcline for positive feedback through inhibition of X and Y

A

Fill in 0
X = tau_X * beta_X * m_X * (1/1+(K_Y_(Y)^h_Y)
> y-nullcline
tau_Y * beta_Y * m_Y * (1/1+(K_X_(X)^h_X)

61
Q

When is a steady-state instable when looking at the direction field

A

If the trajectories are not attracted by this steady-state

62
Q

Region of attraction: If the region of attraction around one steady-state is large, then …

A

If the region of attraction around one steady-state is large then most cells in the population will assume this particular state

63
Q

The state is likely to be … by … cells

A

inherited by daughter cells (same steady-state)
> minor perturbation due to asymmetric distribution of molecules in cell division, but rarely sufficient to switch from one steady-state to another

64
Q

Positive feedback coupled to cooperativity will oftern be associated with systems requiring …

A

stable cell memory

65
Q

[Xst] is the … and [Yst] is the

A

nullclines

66
Q

Nullcline analysis

A

Use nullclines to calculate steady-states

OMICS in de Biomedische Wetenschappen 2 (14 decks)

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