HiPC 2002 12 19 2002. xS-systems: eXtended S-systems & Algebraic Differential Automata for Modeling Cellular Behavior. ¦ Bud Mishra Professor (Cold Spring Harbor Laboratory) Professor of CS & Mathematics (Courant, NYU) With M. Antoniotti, A. Policriti and N. Ugel. Why Systems Biology?.
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12 19 2002
Professor (Cold Spring Harbor Laboratory)
Professor of CS & Mathematics (Courant, NYU)
With M. Antoniotti, A. Policriti and N. Ugel
The SYSTEMS BIOLOGYSystems Biology
Combining the mathematical rigor of numerology with the predictive power of astrology.
How much of reasoning about biology can be automated?
Single splitting reaction
generating two products X2 and X3, in stoichiometric proportion.
Divergence Branch Point: Degradation processes of X1 into X2 and X3 are independent
Single synthetic reaction
involving two source components X1 and X2, in stoichiometric proportion.
Convergence Branch Point: Degradation processes of X1 and X2 into X3 are independent
The conversion of X1 into X2 is modulated by X3
The conversion of X1 into X2 is modulated by an inhibitor X3
The reaction between X1 and X2 requires coenzyme X3 which is converted to X4
LacI!:tetR; tetR! TetR
TetR!:l cI; l cI !l cI
l cI!:lacI; lacI! LacI
completing the cycle.
x6Cascade Model: Repressilator?
dx2/dt = a2 X6g26X1g21 - b2 X2h22
dx4/dt = a4 X2g42X3g43 - b4 X4h44
dx6/dt = a6 X4g64X5g65 - b6 X6h66
X1, X3, X5 = const
SimPathica:Trace Analysis System
= (instantaneous) rate of change in Xi at time t
= Function of substrate concentrations, enzymes, factors and products:
dXi/dt = f(S1, S2, …, E1, E2, …, F1, F2,…, P1, P2,…)
Vi+(X1, X2, …, Xn, U1, U2, …, Um)
– Vi-(X1, X2, …, Xn, U1, U2, …, Um):
Simple one-to-one construction of the
“trace” automata AS for an S-system S
The effects of the collapsing construction of the
“trace” automata AS for an S-system S
<?xml version="1.0" ?>-<map xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="map.xsd">-<substrate><id>1</id><concentration>5</concentration><name>PRPP</name></substrate>-<substrate><id>2</id><concentration>100</concentration><name>IMP</name></substrate>-<substrate><id>3</id><concentration>2500</concentration><name>Ado</name></substrate>-<substrate><id>4</id><concentration>425</concentration><name>GMP</name></substrate>-
Variation of the initial concentration of PRPP does not change the steady state.(PRPP = 10 * PRPP1) implies steady_state()
This query will be true when evaluated against the modified simulation run (i.e. the one where the initial concentration of PRPP is 10 times the initial concentration in the first run – PRPP1).
Persistent increase in the initial concentration of PRPP does cause unwanted changes in the steady state values of some metabolites.
If the increase in the level of PRPP is in the order of 70% then the system does reach a steady state, and we expect to see increases in the levels of IMP and of the hypoxanthine pool in a “comparable” order of magnitude.Always (PRPP = 1.7*PRPP1) implies steady_state()Queries
Consider the following statement: change the steady state.
(Always (PRPP = 1.7 * PRPP1) implies steady_state() and Eventually
(Always(IMP < 2 * IMP1))and Eventually (Always
(hx_pool < 10*hx_pool1)))
where IMP1 and hx_pool1 are the values observed in the unmodified trace. The above statement turns out to be false over the modified experiment trace..
In fact, the increase in IMP is about 6.5 fold while the hypoxanthine pool increase is about 60 fold.
Since the above queries turn out to be false over the modified trace, we conclude that the model “over-predicts” the increases in some of its products and that it should therefore be amendedQueries
Always(PRPP > 50 * PRPP1implies(steady_state() and Eventually(IMP > IMP1) and Eventually(HX < HX1) and Eventually(Always(IMP = IMP1)) and Eventually(Always(HX = HX1))