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?. - PowerPoint PPT Presentation
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Why Systems Biology?• It is not uncommon to assume certain biological problems to
have achieved a cognitive finality without rigorous justification. • Rigorous mathematical models with automated tools for
reasoning, simulation, and computation can be of enormous help to uncover – cognitive flaws,– qualitative simplification or– overly generalized assumptions.
• Some ideal candidates for such study would include: – prion hypothesis– cell cycle machinery – muscle contractility– processes involved in cancer (cell cycle regulation, angiogenesis,
DNA repair, apoptosis, cellular senescence, tissue space modeling enzymes, etc.)
• The first repressor protein, LacI from E. coli inhibits the transcription of the second repressor gene, tetR from the tetracycline-resistance transposon Tn10.
• Protein product in turn TetR from tetR inhibits the expression of a third gene, cI from phage.
• Finally, CI inhibits lacI expression,completing the cycle.
• S-System Automata Definition:– Combine snapshots of the IDs (“instantaneous descriptions”) of the
system to create a possible world model– Transitions are inferred from “traces” of the system variables:
• Definition:Given an S-systems S, the S-system automaton AS associated to S is 4-tuple AS = (S, , S0, F), where S µ D1 £ £ D is a set of states, µ S £ S is the binary transition relation, and S0, F ½ S are initial and final states respectively.
• Definition: A trace of an S-system automaton AS is a sequence s0, s1, …, sn,…, such that s0 2 S0, (si, si+1), 8 i = 0.
• In addition to these processes, there appear to be two “salvage” pathways that serve to maintain IMP level and thus of adenosine and guanosine levels as well.
• In these pathways, adenine phosphoribosyltransferase (APRT) and hypoxanthine-guanine phosphoribosyltransferase (HGPRT) combine with PRPP to form ribonucleotides.
• 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.
(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 amended
• This change to the model allows us to reformulate our query as shown below:Always(PRPP > 50 * PRPP1implies(steady_state() and Eventually(IMP > IMP1) and Eventually(HX < HX1) and Eventually(Always(IMP = IMP1)) and Eventually(Always(HX = HX1))
• An (instantaneous) increase in the level of PRPP will not make the system stray from the predicted steady state, even if temporary variations of IMP and HX are allowed. TRUE
Related Publications• “Simulating Large Biochemical and Biological Processes and
Reasoning about their Behavior." (with M. Antoniotti, F. Park, A. Policriti and N. Ugel), ICSB, Sweden, 2003.
• "Foundations of a Query and Simulation System for the Modeling of Biochemical and Biological Processes." (with M. Antoniotti, F. Park, A. Policriti and N. Ugel), The Pacific Symposium on Biocomputing (PSB 2003), Hawaii, January 3-7, 2003.
• "Model Building and Model Checking for Biochemical Processes," (with M. Antoniotti, A. Policriti and N. Ugel), Cell Biochemistry and Biophysics (CBB), Humana Press, 2003, (In press)
• "A Symbolic Approach to Modelling Cellular Behaviour," International Conference On High Performance Computing, HiPC 2002, December 18-21, Bangalore, India, 2002. (In Press)
• "Wild by Nature," (with M. Wigler), Science, 296: 1407-1408, 24 May 2002.