1introduction 2theoretical background biochemistry/molecular biology 3theoretical background...
TRANSCRIPT
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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
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Membrane transport
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www.cellsalive.com/
Cell membranes
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Cell membranes
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At very high magnification & in color
Cell membranes
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http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/C/CellMembranes.html
Membrane structure
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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
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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
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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
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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
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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+
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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).
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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+
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Membrane computing
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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
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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
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“....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
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....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
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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
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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
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references
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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
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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)
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A membrane system (or P-system)
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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.
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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
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An example
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An example
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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
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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
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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
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P-systems with catalysts are computationally universal
Main result
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Using catalysts and bi-stable catalysts
Bi-stable catalysts
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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
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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
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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
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Computing by communication
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Membrane transport of small molecules
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(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
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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
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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
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EC P systems are computationally universal
The power of EC P-systems
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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
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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
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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
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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
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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
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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
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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
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A picture is represented by means of a network of membranes
Generating picture languages
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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
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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
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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