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On Flip-Flop Membrane Systems with Proteins Andrei Paun 1,2, Alfonso Rodriguez-Paton 2 1. Computer Science Louisiana Tech University 2. Universidad Politecnica.

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Presentation on theme: "On Flip-Flop Membrane Systems with Proteins Andrei Paun 1,2, Alfonso Rodriguez-Paton 2 1. Computer Science Louisiana Tech University 2. Universidad Politecnica."— Presentation transcript:

1 On Flip-Flop Membrane Systems with Proteins Andrei Paun 1,2, Alfonso Rodriguez-Paton 2 1. Computer Science Louisiana Tech University 2. Universidad Politecnica de Madrid - UPM, Facultad de Informatica

2 Summary Motivation of research The new model Previous results More previous results Description of proof technique Improvements of previous results New results Final Remarks

3 Motivation of research Extension to Symport/Antiport systems SA systems are widely studied but contain some non-natural features Max. parallelism forces us to forbid rules (a,in) for skin membrane and a in E

4 Motivation (contd.) to capture also the catalytic/enzymatic properties of trans-membrane or the peripheral proteins Current estimates put the number of these proteins at about 50% of the total proteins of a cell

5 Motivation (contd.) The reactions involving the membrane proteins cannot happen in a massively parallel manner The number of the proteins impose the upper bound for the number of reactions applied simultaneously

6 The Structure of a Cell

7 Membrane’s Structure Transversal view Picture from Building block

8 Trans-membrane transport trans-membrane transfer of molecules can take place in three main ways: active transport passive transport vesicle-mediated transport

9 Active transport Done through protein channels Picture from

10 The new model Symbol objects, we have also special symbols (proteins) associated with membranes Normal membrane structure Rules: description in next slides

11 Rules: modify object but no move a [ i p|a->[ i p’|b b pP’ 1cp: a a[ i p|->b[ i p’| b pP’

12 Rules: move object but no modification a [ i p|a->a[ i p’| a pP’ a a[ i p|->[ i p’|a a pP’ 2cp:

13 Rules: modify and move b a [ i p|a->b[ i p’| pP’ a a[ i p|->[ i p’|b b pP’ 3cp:

14 Rules: exchange two objects, no modification 4cp: a b[ i p|a->b[ i p’|a b pP’ b a

15 Rules: exchange two objects & modification 5cp: b a b[ i p|a->c[ i p’|d d pP’ c

16 One more RULES slide If the protein does not change, we call that rule res (from restricted) If the protein changes only between two states (p and p) for all rules using those two “states” of the protein all those rules are called “flip-flop” ff Pure rules are those that change the protein at each application

17 Particularities of model Each rule application involves one protein Each protein cannot be used more than once each step Thus we have a limitation on paralelism TIME USED AS OUPUT FRAMEWORK

18 Timed systems: motivation Closer to “nature” and biomolecular tools and techniques Time as support for computation Why time? Cell compute=cell accumulate the result Cell unhappy Cell adapts and behaves unpredictably

19 FACS Fluorescence Activated Cell Sorter cells “undisturbed” a “feedback” mechanism is possible

20 Motivation (cont.) FACS What it does? How to change for our purposes? Speed issues? Muliple lasers/detectors

21 Notation NOP m (pro n, types of rules) For m membranes For n proteins on membranes in the system Using only the types of rules mentioned NTOP m (pro n, types of rules) (time)

22 Previous results in this area NOP 1 (pro 2, 2cpp)=NRE NOP 1 (pro *, 3ffp)=NRE NOP 1 (pro 2, 2res,4cpp)=NRE NOP 1 (pro 2, 2res, 1cpp)=NRE NOP 1 (pro *, 1res, 2ffp)=NRE In [Paun Popa 2006]

23 More previous results (ffp) NOP 1 (pro 7, 3ffp)=NRE NOP 1 (pro 7, 2ffp, 4ffp)=NRE NOP 1 (pro 10, 1res,2ffp)=NRE NOP 1 (pro 7, 1ffp,2ffp)=NRE NOP 1 (pro 9, 1ffp,2res)=NRE NOP 1 (pro 9, 2ffp,3res)=NRE NOP 1 (pro 8, 1ffp,3res)=NRE NOP 1 (pro 9, 4ffp,3res)=NRE NOP 1 (pro 8, 2ffp,5res)=NRE [Krishna 2006]

24 Description of proof technique In [Paun Popa 2006] we used the proteins to control the simulation of each type of rule ans usually as a Program Counter in the register machine In [Krishna 2006] the novel idea was to simulate with each protein a specific rule type associated with a specific register: all Sub(r1,XXX,YYY) use same protein

25 Improvements of previous results Since a reg. machine is universal with 3 registers, out of which the output one can be non-decreasing we can improve all the previous results (table 2) by one protein (the protein used for simulating the SUB instructions associated with the output register)

26 NOP 1 (pro 6, 3ffp)=NRE NOP 1 (pro 6, 2ffp, 4ffp)=NRE NOP 1 (pro 9, 1res,2ffp)=NRE NOP 1 (pro 6, 1ffp,2ffp)=NRE NOP 1 (pro 8, 1ffp,2res)=NRE NOP 1 (pro 8, 2ffp,3res)=NRE NOP 1 (pro 7, 1ffp,3res)=NRE NOP 1 (pro 8, 4ffp,3res)=NRE NOP 1 (pro 7, 2ffp,5res)=NRE

27 New results OLD: NOP 1 (pro 9, 4ffp,3res)=NRE OLDISH: NOP 1 (pro 8, 4ffp,3res)=NRE NEW, time: NTOP 1 (pro 7, 4ffp,3res)=NRE NEW: NOP 1 (pro 7, 4ffp,3res)=NRE

28 New results (2) Old: NOP 1 (pro 8, 2ffp,5res)=NRE Oldish: NOP 1 (pro 7, 2ffp,5res)=NRE New, time: NTOP 1 (pro 3, 2ffp,5res)=NRE New: NOP 1 (pro 4, 2ff,5res)=NRE

29 6. Final remarks Systems based on time seem to be more flexible => stronger results We are able to improve several other previous results (future paper) improvement of current results other (better) models Have also symport, not only uniport?

30 Thank you !!!


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