on flip-flop membrane systems with proteins andrei paun 1,2, alfonso rodriguez-paton 2 1. computer...
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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
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Summary Motivation of research The new model Previous results More previous results Description of proof technique Improvements of previous results New results Final Remarks
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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
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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
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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
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The Structure of a Cell
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Membrane’s Structure
Transversal view
Pictu
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tmlBuilding block
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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
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Active transport
Done through protein channels
Pic
ture
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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
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Rules: modify object but no move
a[ip|a->[ip’|b
b
p P’
1cp:
a
a[ip|->b[ip’|
b
p P’
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Rules: move object but no modification
a[ip|a->a[ip’|
a
p P’
a
a[ip|->[ip’|a
a
p P’
2cp:
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Rules: modify and move
b
a[ip|a->b[ip’|p P’
a
a[ip|->[ip’|b
b
p P’
3cp:
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Rules: exchange two objects, no modification
4cp: a
b[ip|a->b[ip’|a
b
p P’
b a
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Rules: exchange two objects & modification
5cp:
b
a
b[ip|a->c[ip’|d
d
p P’
c
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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
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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
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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
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FACS
Fluorescence Activated Cell Sorter
cells “undisturbed”
a “feedback” mechanism is possible
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Motivation (cont.)
FACS
What it does? How to change for our purposes? Speed issues?
Muliple lasers/detectors
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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)
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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]
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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]
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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
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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)
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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
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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
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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
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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?
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Thank you !!!