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HiPC 2002 12 19 2002. xSsystems: eXtended Ssystems & 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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HiPC 2002
12 19 2002
xSsystems:eXtended Ssystems & 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
The SYSTEMS BIOLOGY
Combining the mathematical rigor of numerology with the predictive power of astrology.
Cyberia
Numerlogy
Astrology
Numeristan
HOTzone
Astrostan
Infostan
Interpretive Biology
Computational Biology
Integrative Biology
Bioinformatics
BioSpice
Computational/Systems Biology
How much of reasoning about biology can be automated?
X2
Reversible Reaction
X1
X2
Single splitting reaction
generating two products X2 and X3, in stoichiometric proportion.
X1
X3
X2
Divergence Branch Point: Degradation processes of X1 into X2 and X3 are independent
X1
X3
X1
Single synthetic reaction
involving two source components X1 and X2, in stoichiometric proportion.
X3
X1
Convergence Branch Point: Degradation processes of X1 and X2 into X3 are independent
X2
X3
X2
X3
X4
X2
X1
X3
The conversion of X1 into X2 is modulated by X3
X2
X1
X3
The conversion of X1 into X2 is modulated by an inhibitor X3

X2
X1
The reaction between X1 and X2 requires coenzyme X3 which is converted to X4
Glycogen
P_i
Glucose
Glucose1P
Phosphorylase a
Phosphoglucomutase
Glucokinase
Glucose6P
Phosphoglucose isomerase
Fructose6P
Phosphofructokinase
LacI!:tetR; tetR! TetR
TetR!:l cI; l cI !l cI
l cI!:lacI; lacI! LacI
completing the cycle.

x1
x2

x3
x4

x5
x6
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
Canonical Forms
= (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,…)
dXi/dt =
Vi+(X1, X2, …, Xn, U1, U2, …, Um)
– Vi(X1, X2, …, Xn, U1, U2, …, Um):
Canonical Forms
Simple onetoone construction of the
“trace” automata AS for an Ssystem S
The effects of the collapsing construction of the
“trace” automata AS for an Ssystem S
Purine Metabolism
<?xml version="1.0" ?><map xmlns:xsi="http://www.w3.org/2001/XMLSchemainstance" 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>
<synthesis><reactant1>1</reactant1><reactant2>8</reactant2><product>2</product><power_function1>1.1</power_function1><rate1>12.570</rate1><power_function2>0.48</power_function2><rate2>12.570</rate2><modulation><enzyme>2</enzyme><power_function_enzyme>0.89</power_function_enzyme></modulation></synthesis><output><reactant>11</reactant><power_function>2.21</power_function><rate>0.00008744</rate></output></map>
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.
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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()
TRUE
TRUE
Consider the following statement:
Eventually
(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 “overpredicts” the increases in some of its products and that it should therefore be amended
False
Always(PRPP > 50 * PRPP1implies(steady_state() and Eventually(IMP > IMP1) and Eventually(HX < HX1) and Eventually(Always(IMP = IMP1)) and Eventually(Always(HX = HX1))
TRUE
The End
Websites
http://cs.nyu.edu/faculty/mishra/ http://bioinformatics.cat.nyu.edu/