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Computational Biology Lund University
Computational models of stem cell fates
Carsten Peterson
Summer workshop“Mathematical medicine and biology”Nottingham, July 7-11, 2008Part 1
Computational Biology & Biological PhysicsLund University, Sweden
http://home.thep.lu.se/~carsten
Part 1:
Stem cell systems
Computational challenges
Modeling transcriptional dynamics
Part 2:
The embryonic stem cell switch
Hematopoietic switches
Bistability, irreversibility, priming
Computational Biology Lund University
Computational models of stem cell fates
Carsten Peterson
Summer workshop“Mathematical medicine and biology”Nottingham, July 7-11, 2008
Part 1:
Stem cell systems
Computational challenges
Modeling transcriptional dynamics
Computational Biology & Biological PhysicsLund University, Sweden
http://home.thep.lu.se/~carsten
Part 2:
The embryonic stem cell switch
Hematopoietic switches
Bistability, irreversibility, priming
Computational Biology Lund University
Computational models of stem cell fates
Part 1:
Stem cell systems
Computational challenges
Modeling transcriptional dynamics
Part 2:
The embryonic stem cell switch
Hematopoietic switches
Bistability, irreversibility, priming
Important issues not covered:
- Interactions between cells
- Signaling pathways
- Cell population models
Computational Biology Lund University
Stem cells – development and maintenance
Mature stem cells – organ specific
Embryonic stem cell
.......brainblood skinintestinalliver
Development
Maintenance
Self-renewal Differentiation
Computational Biology Lund University
Stem cells – development and maintenance
Mature stem cells – organ specific
Embryonic stem cell
.......brainblood skinintestinalliver
Development
Maintenance
Self-renewal Differentiation
Computational Biology Lund University
The cancer stem cell connection
100 cancer stemcells 100.000 cancer cells
Computational Biology Lund University
Stem cell fates
Self-renewal, pluripotency
Differentiation
Apoptosis
What is the program determining this fate
External signals triggers the transcriptional machinery
Provides switch behaviour
- Genetic network architecture
- Dynamics
Computational Biology Lund University
Transcriptional regulation
Example:
Transcription factors (TF) A and B causes gene g1 to transcribe
With proper interactions e.g. AND logics is obtained
For mammals in general more than 2 TFs
Model small modules of genes:
Verify functionality
Infer additional components/interactions
RNAp
OBpromoterOA
g1
AND
BA
Computational Biology Lund University
Modeling transcriptional regulation
• Boolean models
High level description; crude approach; does not relate to underlying physics/chemistry
• Michaelis-Menten
Useful phenomenological parametrizations
• Shea-Ackers thermodynamical formalism
Transparent with regard to different interaction components; gateway to stochastic methods
• Stochastic methods
Both Michaelis-Menten and Shea-Ackers assume a “large” number of molecules – one works with concentrations. When this is not the case, one has to treat each molecule stochastically (e.g. Gillespie algorithm).
Computationally tedious.
Computational Biology Lund University
The Shea-Ackers statistical mechanics approach
Method originally developed for the lysis/lysogeny switch in Lambda phage
Two time scales:
- Slow:
Transcription/Translation/Degradation
- Fast:
Binding/unbinding of TFs to gene – thermal equilibrium makes sense
Possible cases: TF, TF+RNAP, RNAP - probability associated with each
Enumerate all cases, compute probability of bound RNAP
Transcription rate is proportional to promoter occupancy
Gene
TFs RNAP
PromoterOperons
Computational Biology Lund University
Example: Two transcription factors A and B
Enumerate all possibilities - binding/unbinding of A,B and RNAP The “partition function” Z contain 23 = 8 terms
The Shea-Ackers approach
i,j,k = [1, 0] (binding/unbinding)
[A] and [B]: TF concentrations[R]: RNAP concentration
T: temperature
Free energies (parameters)
Low free energy – strong binding and vice versa
Computational Biology Lund University
The Shea-Ackers approach
One can write down a “truth table”
A B R weights
1 1 1
1 0 1
0 1 1 . . .
Example: Two transcription factors A and B
Enumerate all possibilities - binding/unbinding of A,B and RNAP The “partition function” Z contain 23 = 8 terms
Computational Biology Lund University
The Shea-Ackers approach
bound
The transcription rate is proprtional to
not bound
Example: Two transcription factors A and B
Enumerate all possibilities - binding/unbinding of A,B and RNAP The “partition function” Z contain 23 = 8 terms
Computational Biology Lund University
Relation to equilibrium calculations
Equilibrium calculations, commonly used in enzymatic reactions, yields the same transcription rates as the Shea-Ackers approach (as it should)
We illustrate this with a single autoregulatory gene X that binds to itself
The transition rate is given by
There are four possible states subject to the normalization
Computational Biology Lund University
Reaction scheme defining the network
At thermodynamic equilibrium one has
In this lingo the fractional probability of the gene being bound by RNAP is
Relation to equilibrium calculations
Computational Biology Lund University
Relation to equilibrium calculations
• The statistical mechanics (Shea-Ackers) approach is more intuitive
• However: The equilibrium approach allows us to define a reaction scheme in terms of measured kinetic constants
Platform for stochastic simulations (Gillespie)
Equilibrium approach
Shea-Ackers
Computational Biology Lund University
The Michaelis-Menten approach
Yet another way of doing it (deterministically)
In general: An enzyme E binds to a substrate S and turns it into a product P
Rate equations for the concentrations:
1 2
Computational Biology Lund University
The Michaelis-Menten approach
Yet another way of doing it (deterministically)
In general: An enzyme E binds to a substrate S and turns it into a product P
Rate equations for the concentrations:
1 2
Fast - equilibrium
Approximate to zeroe
Solving the fixed point equation
Computational Biology Lund University
The Michaelis-Menten approach
Assume a constant amount of enzyme
One gets
For the production of P as function of S one has
Computational Biology Lund University
The Michaelis-Menten and Hill equations
With P being the transcribed gene, TF the substrate and DNA the enzyme one has
Similarly for repression, one has
Problem: slow response with [TF]
Improvement: Hill exponents n
Can be deduced from a model where the TFs have multiple binding sites
Computational Biology Lund University
What about noise? - The Langevin equation
Biochemical reactions take place in noisy environments
Yet, we propose deterministic ordinary differential equations (ODEs)
Large number of molecules needed for justification. How large? Problem dependent (10-100)
Biochemical reactions take place in noisy environments
Langevin stochastic differential equation for genes X
If the noise is white (uncorrelated), we have
Mean
Variance
Computational Biology Lund University
The Langevin equation
Computational Biology Lund University
The Langevin equation
LangevinGillespie
From D. Gonze
Computational Biology Lund University
Putting things together – bistability etc.
This is where the fun starts .....
So far transcription of single genes
With a set of interacting genes (subnetwork) probe the dynamics e.g. stationary solutions
Computational Biology Lund University
Bistability
Hill-type equations plus degradation terms
In Gardner et. al. (2000) a genetic switch was constructed with two genes repressing each other by manipulation of DNA in E.Coli
Allows for direct comparisons with models
Compute the nullclines
Computational Biology Lund University
Bistability
Compute the nullclines
More later ... stem cell switches
Bistability – either or needs to be larger than 1
Computational Biology Lund University
Model summary
Reaction kinetics
Michaelis-Menten (Hill function)
Shea-Ackers
Boolean
Stochastic simulations (e.g. Gillespie)
Computational Biology Lund University
Model summary
Reaction kinetics
Michaelis-Menten (Hill function)
Shea-Ackers
Boolean
Stochastic simulations (e.g. Gillespie)
Deterministic
Stochastic
Computational Biology Lund University
Model summary
Reaction kinetics
Michaelis-Menten (Hill function)
Shea-Ackers
Boolean
Stochastic simulations (e.g. Gillespie)
Langevin Langevin
Deterministic
Stochastic
Computational Biology Lund University
Stem cell fates
Self-renewal, pluripotency
Differentiation
Apoptosis
What is the program determining this fate
External signals triggers the transcriptional machinery
Provides switch behaviour
- Genetic network architecture
- Dynamics
Computational Biology Lund University
Sneak preview (part 2)
The embryonic stem cell switch
Indentify motifs, bistability, missing components etc.
Computational Biology Lund University
Sneak preview (part 2)
The erythroid - myeloid switch
Indentify motifs, bistability, missing components etc.
Computational Biology Lund University
References (minimal/incomplete)
V. Chickarmane, C. Troein, U. Nuber, H.M. Sauro and C. Peterson (2006) PLoS Computational Biology 2, e123 (2006)
N.E. Buchler, C. Gerland and T. Hwa PNAS 100, 5136-5141 (2003)
L. Bintu, N.E. Buchler, H.G. Garcia, C. Gerland and T. Hwa Curr Opin Gen Dev 15, 125-135 (2005)
V. Chickarmane, S.R. Paladagdu, F. Bergmann and H.R. Sauro Bioinformatics 18, 3688-3690 (2005)
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