HC 10 - Systems Modelling Flashcards by Tobias H

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

transient

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

Quantitative information
-Concentrations
-Affinities
-Kinetic behavior

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For molecular interactions, what do we need to describe?

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

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Types of interaction

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

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Gene transcription regulation

-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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The time for transcription and translation is

somewhat equal

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Gene transcription regulation: activator characteristics

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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Repressor mechanism of action

Blocks RNAp for binding by binding the promotor

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

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

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Rate of complex formation and dissociation for promotor and protein

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

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what is kon

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

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[kon] and [koff]

[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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At steady-state, the promotor model looks like

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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What does K mean in the promotor model? And K_D

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

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

larger

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

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

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

the occupancy of the promotor

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bound fraction of promotor

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

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Transcription rate

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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Protein production rate

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

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Protein degradation

-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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Protein degradation rate

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

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A low tau means a … degradation rate

high

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d[X]/dt formula

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

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[Xst] formula (at steadystate)

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

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

less

Faster response means ...

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

Solution of differential equation

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

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

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])

At 0.5 bound factor ...

1/K_A and 1/K_R

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

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

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

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

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

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

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

Initial condition

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

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

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

Why use vectors in model?

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

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

the starting point (x,y)

In the direction field, what is shown

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

What is a trajectory

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

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

Neglect it, does not exist in biology

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

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

What is a nullcline

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

How to calculate nullclines

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

How to calculate steady-state

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)

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

Crossing point of nullclines

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

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

A swirl in the trajectory means

oscillations

How to draw direction field

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

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

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

Instable steady-state

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)

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

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

What is the Hill coefficient h

degree of cooperativity

Increasing h means

dependence of binding on protein concentration becomes steeper

Hill functions are

Sigmoid functions

Positive feedback can give a system ...

switch-like response and bistability

bistable system provides system with a ..

memory > present state depends on its history: hysteresis

Bistability steady-states

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

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

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

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

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)

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

If the trajectories are not attracted by this steady-state

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

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

The state is likely to be ... by ... cells

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

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

stable cell memory

[Xst] is the ... and [Yst] is the

nullclines

Nullcline analysis

Use nullclines to calculate steady-states

HC 10 - Systems Modelling Flashcards

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