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Course outline. Membrane transport. Cell membranes. www.cellsalive.com/. Cell membranes. Cell membranes. At very high magnification & in color. Membrane structure. http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/C/CellMembranes.html. Cell membranes. - PowerPoint PPT Presentation

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Page 1: Course outline
Page 2: Course outline

1 Introduction

2 Theoretical background Biochemistry/molecular biology

3 Theoretical background computer science

4 History of the field

5 Splicing systems

6 P systems

7 Hairpins

8 Detection techniques

9 Micro technology introduction

10 Microchips and fluidics

11 Self assembly

12 Regulatory networks

13 Molecular motors

14 DNA nanowires

15 Protein computers

16 DNA computing - summery

17 Presentation of essay and discussion

Course outline

Page 3: Course outline

Membrane transport

Page 4: Course outline

www.cellsalive.com/

Cell membranes

Page 5: Course outline

Cell membranes

Page 6: Course outline

At very high magnification & in color

Cell membranes

Page 7: Course outline

http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/C/CellMembranes.html

Membrane structure

Page 8: Course outline

Every cell is encircled by a membrane and

most cells contain an extensive

intracellular membrane system. Membranes

fence off the cell's interior from its

surroundings. Membranes let in water,

certain ions and substrates and they excrete

waste substances. They act to protect the

cell.

Without a membrane the cell contents would

diffuse into the surroundings, information

containing molecules would be lost and many

metabolic pathways would cease to work. The

cell would die!

Cell membranes

Page 9: Course outline

Surround all cells Fluid-like composition, like soap bubbles Composed of:

Lipids in a bilayer Proteins embedded in lipid layer (called

trans-membrane proteins) And, Proteins floating within the lipid sea

(called integral proteins) And Proteins associated outside the lipid

bi-layer (peripheral).

Cell membranes

Page 10: Course outline

Transporters are of two general classes:

carriers and channels.

These are exemplified by two ionophores

(ion carriers produced by microorganisms): valinomycin (a carrier) gramicidin (a channel).

Membrane transport

Page 11: Course outline

Valinomycin is a carrier for K+.

It is a circular molecule, made up of 3 repeats

of the sequence shown above.

Valinomycin

N CH C OHC

CH

CH3H3C

O

C N

CH

CH3H3C

OHC

CH

CH3H3C

C O CH

CH3

C

O

H

O

H

3

L-valine D-hydroxy- D-valine L-lactic isovaleric acid acid

Page 12: Course outline

Valinomycin is highly selective for K+ relative to Na+.

The smaller Na+ ion cannot simultaneously interact with all

6 oxygen atoms within valinomycin.

Thus it is energetically less favorable for Na+ to shed its

water of hydration to form a complex with this ionophore.

Valinomycin reversibly binds

a single K+ ion.

The ring closely surrounds

the K+ ion, which interacts

with 6 oxygen atoms of

valinomycin.

Valinomycin

Valinomycin

OO O

O O

Hydrophobic

O

K+

Page 13: Course outline

Whereas the interior of the valinomycin-K+ complex is

polar, the surface of the complex is hydrophobic.

Valinomycin enters the lipid core of the bilayer and

solubilizes K+ within this hydrophobic milieu.

Valinomycin

Valinomycin

OO O

O O

Hydrophobic

O

K+

Crystal structure (at Virtual Museum of Minerals & Molecules).

Page 14: Course outline

Valinomycin is a passive carrier for K+. It can bind or

release K+ when it encounters the membrane surface.

Valinomycin can catalyze net K+ transport because it can

translocated either in the complexed or uncomplexed state.

The direction of net flux depends on the electrochemical K+

gradient.

Valinomycin

Val Val

Val-K+ Val-K+

K+

membrane

K+

Page 15: Course outline

Proteins that act as carriers are too large to

move across the membrane.

They are transmembrane proteins, with fixed

topology.

Example: GLUT1 glucose carrier, found in plasma

membranes of various cells, including

erythrocytes.

GLUT1 is a large integral protein, predicted via

hydropathy plots to include 12 transmembrane α-

helices.

Proteins as carrier

Page 16: Course outline

Carrier proteins cycle between conformations in which a

solute binding site is accessible on one side of the

membrane or the other.

There may be an intermediate conformation in which a

bound substrate is inaccessible to either aqueous phase.

With carrier proteins, there is never an open channel all

the way through the membrane.

Proteins as carrier

conformation

change

conformation

change

Carrier mediated solute transport

Page 17: Course outline

Carriers exhibit Michaelis-Menten kinetics.

The transport rate mediated by carriers is

faster than in the absence of a catalyst, but

slower than with channels.

A carrier transports only one or few solute

molecules per conformational cycle.

Kinetics of transport carriers

Page 18: Course outline

Uniport (facilitated diffusion)

carriers mediate transport of a single solute.

Examples include GLUT1 and valinomycin. These carriers

can undergo the conformational change associated with

solute transfer either empty or with bound substrate.

Thus they can mediate net solute transport.

Classes of carrier proteins

Uniport Symport Antiport

A A B A

B

Page 19: Course outline

Symport (cotransport)

carriers bind 2 dissimilar solutes (substrates) & transport

them together across a membrane.

Transport of the 2 solutes is obligatorily coupled. A

gradient of one substrate, usually an ion, may drive uphill

(against the gradient) transport of a co-substrate.

An example is the plasma membrane glucose-Na+ symport.

Classes of carrier proteins

Uniport Symport Antiport

A A B A

B

Page 20: Course outline

Usually antiporters exhibit "ping pong" kinetics. One

substrate is transported across a membrane and then another

is carried back.

Example: ADP/ATP exchanger (adenine nucleotide translocase)

which catalyzes 1:1 exchange of ADP for ATP across the inner

mitochondrial membrane.

Antiport (exchange diffusion)

carriers exchange one solute for another across a membrane.

Classes of carrier proteins

Uniport Symport Antiport

A A B A

B

Page 21: Course outline

Active transport enzymes couple net solute movement across a

membrane to ATP hydrolysis.

An active transport pump may be a uniporter, or it may be an

antiporter that catalyzes ATP-dependent transport of 2 solutes

in opposite directions.

ATP-dependent ion pumps are grouped into classes, based on

transport mechanism, genetic & structural homology.

Active transport

S1

S2

ATP

ADP + Pi

Side 1 Side 2

Active

Transport

Page 22: Course outline

P-class ion pumps are a gene family exhibiting

sequence homology. They include:

Na+,K+-ATPase, in plasma membranes of most

animal cells, is an antiport pump.

It catalyzes ATP-dependent transport of Na+ out

of a cell in exchange for K+ entering.

(H+, K+)-ATPase, involved in acid secretion in

the stomach, is an antiport pump.

It catalyzes transport of H+ out of the gastric

parietal cell (toward the stomach lumen) in

exchange for K+ entering the cell.

Ion pumps

Page 23: Course outline

P-class pumps (cont): Ca++-ATPases, in endoplasmic reticulum (ER) &

plasma membranes catalyze transport of Ca++

away from the cytosol, either into the ER

lumen or out of the cell.

There is some evidence that H+ may be

transported in the opposite direction.

Ca++-ATPase pumps keep cytosolic Ca++ low,

allowing Ca++ to serve as a signal.

Ion pumps

Page 24: Course outline

The reaction mechanism

for a P-class ion pump

involves transient co-

valent modification of

the enzyme.

At one stage of the reaction cycle, Pi is transferred

from ATP to the carboxyl of a Glu or Asp residue,

forming a “high energy” anhydride linkage (~P).

At a later stage in the reaction cycle, the phosphate

is released by hydrolysis.

Ion pumps

P -Class Pumps

ATP

C

O

O P O -

O -

O

C

O

O H

ADP

Enzym e-

Enzym e-

Pi

H2O

Page 25: Course outline

In this diagram of the SERCA reaction cycle,

conformational changes altering accessibility of Ca++-

binding sites to the cytosol or ER lumen are depicted as

positional changes. Keep in mind that SERCA is a large

protein that maintains its transmembrane orientation.

The ER Ca++ pump is

called SERCA:

Sarco(Endo)plasmic

Reticulum Ca++-ATPase.

Ca++ pump

E

E-Ca++2

2Ca++

ER cytosol membrane lumen

2Ca++

E~P-Ca++2 E~P-Ca++

2

ADP

Pi

ATP

Page 26: Course outline

Reaction cycle

1 2 Ca++ bind tightly

from the cytosolic

side, stabilizing the

conformation that

allows ATP to react

with an active site

aspartate residue.

2 Phosphorylation of the active site aspartate induces a

conformational change that shifts accessibility of the 2 Ca+

+ binding sites from one side of the membrane to the other,

& lowers the affinity of the binding sites for Ca++.

Ca++ pump

E

E-Ca++2

2Ca++

ER cytosol membrane lumen

2Ca++

E~P-Ca++2 E~P-Ca++

2

ADP

Pi

ATP

Page 27: Course outline

3 Ca++ dissociates into the ER lumen.

4 Ca++ dissociation promotes hydrolysis of Pi from the enzyme Asp

and the conformational change (recovery) that causes the Ca++

binding sites to be accessible again from the cytosol.

Ca++ pump

E

E-Ca++2

2Ca++

ER cytosol membrane lumen

2Ca++

E~P-Ca++2 E~P-Ca++

2

ADP

Pi

ATP

Page 28: Course outline

2 Ca++

Asp351

Muscle SERCA PDB 1EUL

membrane

domain

cytosolic

domain The structure of muscle

SERCA, determined by X-

ray crystallography,

shows 2Ca++ ions bound

between transmembrane

α-

helices.

These intramembrane Ca++ binding sites are presumed to

participate in Ca++ transfer across the membrane.

SERCA structure

Page 29: Course outline

2 Ca++

Asp351

Muscle SERCA PDB 1EUL

membrane

domain

cytosolic

domain

The active site Asp351,

which is transiently

phosphorylated during

catalysis, is in a

cytosolic domain, far

from the Ca++ binding

sites.

The sequence adjacent

to Asp351 (DKTGTLT)

is in all P-class

pumps.

Ca++ has been found to induce large structural changes in

cytosolic and transmembrane domains of SERCA, consistent

with the proposed conformational coupling between active

site and membrane domains.

SERCA structure

Page 30: Course outline

Observed changes in rotation and tilt of transmembrane a-

helices may be involved in altering access of Ca++ binding

sites to one side of the membrane or the other, and altering

the affinity of binding sites for Ca++, at different stages

of the SERCA reaction cycle.

Only 2 transmembrane a-helices are represented above.

Animation of mechanism by MacLennan lab.

Ca++ transport

Ca++

enzyme phosphorylation

phosphate

hydrolysis

SERCA Conformational Cycle

Page 31: Course outline

This transport across a cell layer depends on localization

of specific plasma membrane transporters at either the

apical end of each epithelial cell (facing the intestinal

lumen) or the basal end (facing a blood capillary).

In the example shown,

3 carrier proteins

accomplish absorption

of glucose & Na+ in

the small intestine.

Trans-epithelial transportglucose Na+

glucose Na+

ATP ADP + P i

K+ GLUT2 Na+ pump

glucose- Na+ symport

intestinal epithelial cell

apical end

basal end

Page 32: Course outline

The Na+ gradient drives uphill transport of glucose into the

cell at the apical end, via glucose-Na+ symport. [Glucose]

within the cell is thus higher than outside.

Glucose flows passively out of the cell at the basal end,

down its gradient, via GLUT2 (uniport related to GLUT1).

The Na+ pump, at

the basal end of

the cell, keeps

[Na+] lower in the

cell than in

fluid bathing the

apical surface.

Trans-epithelial transportglucose Na+

glucose Na+

ATP ADP + P i

K+ GLUT2 Na+ pump

glucose- Na+ symport

intestinal epithelial cell

apical end

basal end

Page 33: Course outline

Channels cycle between open & closed conformations. When

open, a channel provides a continuous pathway through the

bilayer.

Whereas carriers transport only one or a few ions or

molecules per conformational cycle, many ions flow through a

channel, each time it opens.

Transport rates are higher for channels than for carriers.

Ion channels

closed

conformationchange

open

Page 34: Course outline

Gating (opening & closing) of a gramicidin channel is thought

to involve reversible dimerization.

An open channel forms when two gramicidin molecules join end

to end to span the membrane.

This model is consistent with the finding that at high

[gramicidin] overall transport rate depends on [gramicidin]2.

Gating

open closed

Proposed mechanism of

gramicidin gating

Page 35: Course outline

Membrane computing

Page 36: Course outline

Since the origins, Computer Scientist

have looked to relationships among

machines and living organisms

McCulloch and Pitts, Neural Networks,

1943

Von Neumann, Cellular Automata, 1966

Lindenmayer, L systems, 1968

Holland, Genetic Programming, 1975

A look at history

Page 37: Course outline

L-systems are a mathematical formalism proposed by

the biologist Aristid Lindenmayer in 1968 as a

foundation for an axiomatic theory of biological

development.

More recently, L-systems have found several

applications in computer graphics. Two principal

areas include generation of fractals and realistic

modelling of plants

L-systems

Page 38: Course outline

“....Theoretical arguments suggest that more efficient

and adaptable modes of computing are possible, while

emerging biotechnologies point out to possibilities for

implementation. Their common ground is molecular

computing... It is likely that molecular computing will

prove more valuable outside the context of conventional

Von Neumann computers. Critically important computing

needs such as adaptive patterns and process control may

be refractory to simple decreases in size and increases

in speed. Instead of suppressing the unique properties

of carbon polymers, we should consider how to harness

them to fill these needs....”

Michael Conrad, On Design Principles for a Molecular

Computer, 1985

Molecular computing

Page 39: Course outline

....Inheritance is a discourse, a set

of instructions passed from generation

to generation. It has a vocabulary -

the genes themselves- a grammar, the

way in which the information is

arranged, and a literature, the

thousands of instructions needed to

make a human being...”

Steve Jones, The Language of The

Genes, 1993

Another quote

Page 40: Course outline

DNA may be viewed as a double sequence of four

symbols: A, T, C, G

DNA is naturally processed by duplication,

recombination, etc.

Biologist and Genetists have developed so far a

variety of techniques to manipulate DNA

sequences (Biotechnologies)

Information stored in DNA sequences is

translated into proteins by DNA Transcription

Proteins control and regulate the activity of

the genes (Gene Expression)

How cells process information

Page 41: Course outline

Gh. Păun, Computing with Membranes, 1998

Membrane Computing looks at the whole

cell structure and functioning as a

computing device

Membranes play a fundamental role in the

cell as filters and separators

Modeling the living cell is beyond the

purpose of Membrane Computing

Membrane computing

Page 42: Course outline

references

Page 43: Course outline

Păun, Gh., Membrane Computing. An Introduction,

Springer-Verlag, Berlin, 2002.

Păun, Gh., Rozenberg, G., Salomaa, A., Zandron, C.

(eds.), Membrane Computing, LNCS, 2597, Springer-Verlag,

2003.

Cavaliere, M., Martin-Vide, C., Paun, Gh. (eds.),

Brainstorming Week on Membrane Computing, Technical

Report of the Research Group on Mathematical

Linguistics, N. 26/03, Universitat Rovira I Virgili,

Tarragona, Spain, 2003.

The P systems Web Pages, http://psystems.disco.unimib.it

Alberts, B., et al., Molecular Biology of the Cell,

Garland Science, New York, 2002.

references

Page 44: Course outline

A membrane structure formed by several membranes

embedded in a unique main membrane

Multi-sets of objects placed inside the regions

delimited by the membranes (one per each region)

The objects are represented as symbols of a given

alphabet (each symbol denotes a different object)

Sets of evolution rules associated with the

regions (one per each region), which allow the

system to produce new objects starting form the existing

ones to move objects from one region to another

A membrane system (or P-system)

Page 45: Course outline

A membrane system (or P-system)

Page 46: Course outline

A membrane system (or P-system)

Each region contains a multi-set of objects and a

set of rules. The objects are represented by symbols

from a given alphabet. Typically, a evolution rule

from region r is of the form ca→cbindoutdhere and it

says that a copy of object a in the presence of a

copy of the catalyst c is replaced by a copy of the

object b and 2 copies of the object d.

b has to immediately enter the inner membrane of

region r labeled j, a copy of d is sent out through

the membrane of region r and a copy of d remains in

r.

Page 47: Course outline

We start with an initial configuration: an initial membrane

structure and some initial multi-sets of objects placed

inside the regions of the system.

We apply the rules in a non-deterministic maximal parallel

manner: in each step, in each region, each object that can

be evolved according to some rule must do it

A computation is said successful if it halts, that is, it

reaches a configuration where no rules can be applied.

The result of a successful computation may be the multi-sets

formed either by the objects contained in a specific output

membrane or by the objects sent out of the systems during

the computation

A non-halting computation yields no result

A computation in a P-system

Page 48: Course outline

An example

Page 49: Course outline

An example

Page 50: Course outline

R1: aa → (a,here)(a,in),ab → (b,here)(a,in)

R2: a → (a,out)(b,out)(b,in),a → (c,in)

R3: b → (a,here)(a,out)(b,in),cb → (a,here)

R4: Ø

An other example

Page 51: Course outline

Membrane dissolution: a special operator which can be

used for dissolving a membrane

Example: r: abb → (a,here)(b,in)(a,out)δ

if the rule r is used inside a membrane, such a membrane

is dissolved after the application of the rule r

Membrane thickness: two operators δ, τ for varying the

permeability of the membranes

Priority: a partial order among the rules, which define a

priority relationship

In each step, if a rule with high priority is applied

then no rule with a lower priority can be applied in the

same step

More ingredients

Page 52: Course outline

Cooperation restricted to some special objects called

catalysts

ca → cv

with v = (a1,t1)(a2,t2) … (an,tn), tj ε {in ,here, out}

A catalyst cannot be modified by any rule and cannot

be moved from one region to another

Bi-stable catalysts: catalysts with two states

ca → cv ca → cv

Using catalysts

Page 53: Course outline

P-systems with catalysts are computationally universal

Main result

Page 54: Course outline

Using catalysts and bi-stable catalysts

Bi-stable catalysts

Page 55: Course outline

P-systems are bio-inspired distributed

and parallel computing devices

They operates on multi-sets of objects

The objects are located inside specic

regions delimited by the Membranes

The objects evolve according to local

rules associated with the Regions

The rules can modify the objects or move

them through the membranes

Summary 1

Page 56: Course outline

The objects are strings over a given alphabet

The regions have associated languages instead of multi-

sets of objects. The rules encode string-operations rewriting: X → (y, tar), with tar ε {here, in, out} replicated rewriting: X → (y1, tar1)||…||(yn, tarn), with

tar1,…, tarn ε {here, in, out}

splicing ...

More ingredients: membrane dissolution, membrane

thickness, priority, distributing the rules according to

an underlying state machine (Eilenberg P-sytems)

P-systems with string objects

Page 57: Course outline

Communication of objects through membranes is

one of the most important ingredients of every

P-system

Purely communicative systems: the objects are

not changed during a computation, but they just

change their place inside the system

The systems is embedded in an infinite

environment, which contains an arbitrary number

of copies of each object

The environment provides the objects the system

needs to perform its internal computations

Communicative P-systems

Page 58: Course outline

Computing by communication

Page 59: Course outline

Membrane transport of small molecules

Page 60: Course outline

(Păun, A., Păun, Gh.) Rules encode symport/antiport mechanism and they

are associated with the membranes

Generalization: (x,in), (x,out), (x,in; y,out),

for x, y multi-sets of arbitrary size

P-systems with symport/antiport

Page 61: Course outline

P-systems with symport/antiport are computationally

universal (Păun, A., Frisco, P., Păun, Gh., 2003)

(1,2) + 1Mem = T.M.

(2,0) + 4Mem = T.M.

(3,0) + 2Mem = T.M.

(3,0) + 1Mem = T.M.

(n,m) denotes the size of the rules: for each (x,in),

(x,out), |x| ≤ n, and for each (x,in; y,out), max{|x|,|

y|} ≤ m

The power of communication

Page 62: Course outline

P-systems with boundary rules Communication rules: xx’ [i y’y → xy’ [i x’y

Evolution rules: [i y → [i y’ Evolution-

Communication P-systems

Communication rules: (x,in), (y,out), (x,in;

y,out)

Evolution rules: y → y’ where x, x’, y, y’

represent multi-sets of arbitrary size

EC P-systems

Page 63: Course outline

EC P systems are computationally universal

The power of EC P-systems

Page 64: Course outline

The environment is reduced to some specific

input objects

If the system halts in a final configuration,

we say the system recognizes such an input

P-automata

Page 65: Course outline

A model of communication inspired by a membrane

transport mechanism for small molecules called

symport/antiport

Purely communicative P-systems based on

symport/antiport are computationally universal (if

provided with an infinite environment)

EC P-systems, a model that combines communication

controlled by symport/antiport and evolution rules

for modifying the content of the Membranes

P-automata, Communicating P-systems as recognizing

devices

Summary 2

Page 66: Course outline

Rules are able to perform operation for modifying the

membrane structure:

membrane creation: [i a ]i→ [j b ]j

membrane division: [i a ]i → [k b ]k[j c ]j

membrane duplication: [i a ]i → [k b [j c ]j ]k

membrane dissolution: [i a ]i → a where a, b are objects

and i, j, k are labels of possible membranes

Communication and Evolution rules assume the form

[i a → v ]i, [i a ]i → [i b ]i, [i a ]i → [i b ]i

where a, b are objects and i, j, k are labels of

possible membranes

P-systems with active membranes

Page 67: Course outline

The Hamiltonian Path Problem (HPP) can be

solved in quadratic time and the SAT problem

can be solved in linear time by P-systems

with active membranes, by using membrane

division and dissolution

HPP can be solved in linear time by using

membrane creation

The idea is of generating in an efficient

manner all paths from a specified initial

node, then checking whether or not this at

least one of these paths is Hamiltonian.

Trading time for space

Page 68: Course outline

Manipulating membrane structures to generate

some kind of structured information

Generating in parallel all the sentential

forms of a given grammar

Generating representation for strings in a

language

Generating picture languages

Alternative approach

Page 69: Course outline

G = {S → AC, S → AB, C → SB, A → a, B → b}

with L(G) = {anbn}

All the strings of length n are produced

exactly in 2n-1 steps. Such strings are present

in the membrane structure at depth 2n-1

Generating the sentential forms

Page 70: Course outline

G = {S → AC, S → AB, C → SB, A → a, B → b}

It is possible to provide characterizations

of recursively enumerable languages

Representing strings in a language

Page 71: Course outline

A picture is represented by means of a network of membranes

Generating picture languages

Page 72: Course outline

Whatever you want Energy-Controlled P-systems P-systems with promoters/inhibitors P-systems with carriers P-systems with gemmation of mobile membranes Tissue P-systems Probabilistic P-systems P-systems with elementary graph productions Parallel Rewriting P-systems ... ...

What else

Page 73: Course outline

Membrane Computing provides computational models that

abstract from the living cells structure and functioning

Such models have been proved to be computationally powerful

(equiv. to T.M.) and efficient (solving NP-Complete

problems)

Membrane Computing defines an abstract framework for

reasoning about distribute architectures communication parallel information processing

Such features are relevant both for Computer Science

(Distributed Computing Models, Multi-Agent Systems) and

Biology (Modeling and Simulation of Biological Systems)

Conclusion

Page 74: Course outline

Membranes systems have been developed so far as a

purely generative devices in the context of Formal

Languages Theory

They lack a well-defined semantics for reasoning about real systems

Non-Determinism and Maximal Parallelism are not always desirable features

Conclusion