1 / 12

Rules with Constraints

Rules with Constraints. Mathias John , Cédric Lhoussaine, Joachim Niehren, Cristian Versari ESOP 2011. Stochastic Modeling. chemical reactions:. initial solution:. k 1. 2*. Mon. 1*. Dim. Mon. Mon. Dim. k 2. 2*. 4*. 0*. Mon. Mon. Mon. 0*. 1*. 2*. Dim. Dim. Dim. ctmc:.

giolla
Download Presentation

Rules with Constraints

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Rules withConstraints Mathias John, Cédric Lhoussaine, Joachim Niehren, Cristian Versari ESOP 2011

  2. Stochastic Modeling • chemical reactions: • initial solution: k1 2* Mon 1* Dim Mon Mon Dim k2 2* 4* 0* Mon Mon Mon 0* 1* 2* Dim Dim Dim • ctmc: r1 r2 r3 r4

  3. Combinatorial Explosion of Reaction Sets • [Goldstein04], [Hlavacek06] • example: monomer with single modification side for phosphorylation and methylation • sides act mostly independently • All these reactions do the very same thing k k Dim_P_P Mon_P Dim_P Mon k k Dim_P Dim Dim_M_P Dim_M [Hlavacek06] Rules for Modeling Signal-Transduction Systems, Science Signaling. [Goldstein04] MathematicandComputational Models of Immune-Receptor Signalling, Nature Reviews, Immunolgy.

  4. View on Chemical Species • example: monomer with single modification side for phosphorylation and methylation M N P F F F binding site to other monomer Mon Mon Mon Mon modification site Mon_P Mon_M Mon = = = F – free, N - not modified, P – phosphorylated, M - methylated

  5. View on Chemical Solutions bond denoted by shared identifier b bond b b N N N N = = Dim Mon Mon Mon Mon = Dim_M_P … M P b b Mon Mon

  6. Reaction with Structured Species • accessing structures with variables --> decrease reaction number x – variable, i.e. for all values k N P x x Mon_P Mon Mon Mon k Dim_P Dim k k Dim_P_P Dim_P k Dim_M_P Dim_M

  7. Rules with constraints

  8. Examples for Using Constraints • occasional dependence of binding sites • increased compactness • in combination with rate expressions x2 x1 b b x2 k F x1 F Mon Mon Mon Mon x N N x F F F F x1 != M & x2 != M Mon Mon Mon Mon k x in {M,P} if x=M then kM else kP x in {M,P}

  9. Space kd neighbors(p1, p2) x1 x2 x1 x2 x x F F F F F F Mon Mon Mon Mon Mon Mon p2 p1 p1 p1 p2 p2 p1 p2 p1 p2 f(kd,p1, p2)

  10. Expressing the Pi-Calculus • all pi-calculus models can now be formulated in rules • idea: • given a set of process definitions (pi-calculus) • turn interaction capabilities into rules z x y x A C A B A(x) = x!().0 + x!(y).0 B(y) = y?().B’() C(z) = z?().C’() k k B’ C’ x = y x = z k = rate constant of x

  11. Semantics: Enumerating Reactions rule set current state (solution) k 2* 2* P M N N P N N N F x F F x F F x Mon Mon Mon Mon Mon Mon Mon Mon one match: replace variables by values (F->x) k replace variables also in constraints & rate expressions then solve / evaluate bond creation: introduce names not present in solution

  12. The Price: Analysis Complexity • size of CTMC -> simulation only • complexity of single simulation step mn, where n maixmal number of reactants • our idea: use constraint solvers • good news: element constraints • first prototype implementation: promising results

More Related