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

On Flip-Flop Membrane Systems with Proteins

Andrei Paun1,2, Alfonso Rodriguez-Paton2

1. Computer Science Louisiana Tech University

2. Universidad Politecnica de Madrid - UPM, Facultad de Informatica

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

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

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

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

The Structure of a Cell

Membrane’s Structure

Transversal view

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Trans-membrane transport

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

Active transport

Done through protein channels

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The new model

Symbol objects, we have also special symbols (proteins) associated with membranes

Normal membrane structure Rules: description in next slides

Rules: modify object but no move

a[ip|a->[ip’|b

b

p P’

1cp:

a

a[ip|->b[ip’|

b

p P’

Rules: move object but no modification

a[ip|a->a[ip’|

a

p P’

a

a[ip|->[ip’|a

a

p P’

2cp:

Rules: modify and move

b

a[ip|a->b[ip’|p P’

a

a[ip|->[ip’|b

b

p P’

3cp:

Rules: exchange two objects, no modification

4cp: a

b[ip|a->b[ip’|a

b

p P’

b a

Rules: exchange two objects & modification

5cp:

b

a

b[ip|a->c[ip’|d

d

p P’

c

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

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

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

FACS

Fluorescence Activated Cell Sorter

cells “undisturbed”

a “feedback” mechanism is possible

Motivation (cont.)

FACS

What it does? How to change for our purposes? Speed issues?

Muliple lasers/detectors

Notation

NOPm(pron, types of rules)

For m membranes For n proteins on membranes in the

system Using only the types of rules

mentioned NTOPm(pron, types of rules) (time)

Previous results in this area

NOP1(pro2, 2cpp)=NRE NOP1(pro*, 3ffp)=NRE NOP1(pro2, 2res,4cpp)=NRE NOP1(pro2, 2res, 1cpp)=NRE NOP1(pro*, 1res, 2ffp)=NRE

In [Paun Popa 2006]

More previous results (ffp) NOP1(pro7, 3ffp)=NRE NOP1(pro7, 2ffp, 4ffp)=NRE NOP1(pro10, 1res,2ffp)=NRE NOP1(pro7, 1ffp,2ffp)=NRE NOP1(pro9, 1ffp,2res)=NRE NOP1(pro9, 2ffp,3res)=NRE NOP1(pro8, 1ffp,3res)=NRE NOP1(pro9, 4ffp,3res)=NRE NOP1(pro8, 2ffp,5res)=NRE

[Krishna 2006]

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

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)

NOP1(pro6, 3ffp)=NRE NOP1(pro6, 2ffp, 4ffp)=NRE NOP1(pro9, 1res,2ffp)=NRE NOP1(pro6, 1ffp,2ffp)=NRE NOP1(pro8, 1ffp,2res)=NRE NOP1(pro8, 2ffp,3res)=NRE NOP1(pro7, 1ffp,3res)=NRE NOP1(pro8, 4ffp,3res)=NRE NOP1(pro7, 2ffp,5res)=NRE

New results OLD: NOP1(pro9, 4ffp,3res)=NRE OLDISH: NOP1(pro8, 4ffp,3res)=NRE

NEW, time: NTOP1(pro7, 4ffp,3res)=NRE NEW: NOP1(pro7, 4ffp,3res)=NRE

New results (2)

Old: NOP1(pro8, 2ffp,5res)=NRE Oldish: NOP1(pro7, 2ffp,5res)=NRE

New, time: NTOP1(pro3, 2ffp,5res)=NRE

New: NOP1(pro4, 2ff,5res)=NRE

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?

Thank you !!!