Diapositiva 1

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AGENTS BASED MODELLING AND SIMULATION OF
CELLULAR PROCESSES
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Cellular systems and subsystems can be simulated
at three different scales
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Nanoscale (10-10 10-9)
At the level of atoms and molecules (nanoscale)
we typically use molecular dynamics (MD) or
Brownian dynamics to model the behavior of 100s
to 1000s of discrete atoms over relatively short
periods of time (10-10 to 10-9 s) and space (10-9
m). MD is Fully deterministic Used to simulate
state or conformational changes, predict binding
affinities, investigate single molecule
trajectories and model stochastic or diffusive
interactions between small numbers (lt5) of
macromolecules it is still impossible to model
large numbers of molecules (gt106) or
macromolecules (gt102) over extended periods of
times and space (milliseconds to millimetres).
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Macroscale (10-3)
On the other side of the spectrum there are the
continuum approaches Molecules essentially lose
their discreteness and become infinitely small
and infinitely numerous To model at the
macroscale or continuum level, we must turn to
ordinary (ODEs) or partial differential
equations (PDEs) to describe our systems of
interest. Time dependent ODEs are routinely
used to describe individual enzyme reactions,
diffusion events and other rate-dependent
processes Most of the nowadays systems biology
is based on Differential Equations
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Not all systems are amenable to descriptions by
differential equations. For instance, state
changes, discontinuities, irregular geometries or
discreteness (low copy numbers) are not easily
described by differential equations.
Furthermore, due to their continuum nature, the
solutions to differential equations always
generate smooth curves or surfaces that fail to
capture the true granularity or stochasticity of
living systems. An additional challenge to
using differential equations is that they require
a strong foundation in mathematics, a detailed
knowledge of many (sometimes unknowable) rate
constants or initial conditions, and a powerful
solver to generate solutions.
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Mesoscale (10-8 10-7)
Macromolecules can still be treated as discrete
objects occupying a defined space or volume.
Mesoscale models display the stochasticity or
granularity found in real biological systems.
Because Brownian motion dominates over all
other forces at this scale, it turns out that
significant dynamic simplifications are possible
with mesoscale modeling. These simplifications
potentially allow very long time scales and large
numbers of entities or reactions to be modeled
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Dynamic Cellular Automata (agent based
modeling)
Simulated Brownian motion on a 2D grid Simple
pairwise interaction rules . DCA can be used to
easily and accurately model a variety of spatial
and temporal phenomena including macromolecular
diffusion, viscous drag, enzyme rate processes,
the Krebs cycle, and complex genetic circuits.
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Cellular Automata
Cellular automata (CA) are mutli-object computer
simulation tools that consist of large numbers of
simple identical components with local
interactions layered over a lattice or grid. The
states or values of the components evolve
synchronously in discrete time steps according to
identical rules. The value of a particular site
is determined by the previous values or states of
a neighbourhood of sites around it. Originally
conceived by von Neumann in the late 1940s
cellular automata have been used to model a wide
range of physical processes including heat flow,
spin networks and reaction-diffusion processes
Cellular automata also have a long history in
biological modeling. Indeed, one of the first
computer applications in biology was a CA
simulation called Conways Game of Life Gardner,
1970. This simple model simulated the birth,
death and interaction between cells randomly
scattered over a square lattice or grid. The fate
of every cell was determined according to three
pair-wise interaction rules. These interaction
rules were typically "if-then-else" statements
describing what a cell could do depending on the
number of adjacent neighbors. Nowadays, perhaps
the most widespread and familiar use of CA can be
found in popular computer games such as SimCity,
SimEarth and The Sims
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• Macromolecules at the mesoscale appear as
  discrete, but largely unstructured tubes, cubes
  or spheres.
• The objects (proteins, DNA) can still interact
  with each other, but their interactions are no
  longer constrained or described by shape
  complementarity or lock-and-key fitting as they
  would be if we were modeling at the nanoscale.
• Instead the interactions can be described by
  simple, logical operations or statements such as
  
• If A is adjacent to B, then A binds B.
• While C is bound to D, produce F.
• If A is adjacent to M, then M is converted to P
• DCA differs from conventional CA in that the DCA
  model attempts to simulate real motions via
  Brownian dynamics.

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SimCell
A very general structure that would allow the
accurate simulation of most cellular pheonomena
(transport, enzyme kinetics, metabolism,
reaction-diffusion, signaling, genetic circuits
and transcription/translation) 4 kinds of
component molecules 1) small molecules
(metabolites, ligands), 2) membrane proteins
(which can only exist in membranes), 3) soluble
protein/RNA molecules and, 4) DNA molecules
(which are non-mobile). Because cells are
composed of subcellular organelles and because
some simulations require compartmentalization of
reactants, products or metabolites, we also
introduced a fifth type of molecule or
super-molecule 5) the membrane (non-mobile
entities that describe boxes or borders that may
be permeable or impermeable to certain molecules )
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3 major types of pairwise interactions 1) bind
and stick (BS) , 2) touch and go (TG) , 3)
directional transport (TR) . Molecules that bind
and stick have association and dissociation
constants or on/off probabilities and rates. Many
protein receptors, DNA binding proteins,
catabolic repressors and gene activators will
bind and stick to a target molecule. Under the
SimCell rules, molecules that bind and stick with
each other must necessarily transform themselves
into a new entity (a third molecule) or, in the
case of DNA binding, lead to changes in the
creation or transcription rate of a third
molecule. Non-interacting molecules will
typically touch and go (bump), always leaving
each other in tact. However, some touch and go
operations do lead to a molecular transformation,
particularly when we consider enzymes such as
metabolic enzymes, nucleases or proteases. While
enzymatic catalysis technically involves some
binding, given the time step used in our
mesoscale simulations (1 ms), catalysis is, for
all intents and purposes, instantaneous. In these
enzymatic touch and go operations, two objects
will meet leaving one object in tact and one
transformed. Finally, in transport operations
an object (usually a small molecule) is taken and
almost instantaneously (lt 1 microsecond) moved
across a barrier (usually a membrane)
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In SimCell the motion for all objects (except
membranes and DNA molecules) is performed in a
step-wise fashion over the space defined by a
regular 2-dimensional grid. Within the grid
each object or molecule occupies a square,
typically measuring 3 nm on a side. The choice of
3 nm as the standard grid increment is based on a
number of criteria. The diameter for an average
protein is approximately 3 nm, The average width
of a cellular membrane is approximately 3 nm,
The average width of a supercoiled DNA molecule
is about 3 nm The average velocity of a
macromolecule in a cell is approximately 3 nm per
millisecond This macromolecular diffusion rate
also helps to define a time step that is
appropriate for these mesoscale simulations
namely a millisecond.
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Macromolecules such as proteins or RNA molecules
are allowed to occupy only a single square at a
time, whereas up to 100 small molecules (which
typically measure 0.3 nm across) are permitted to
occupy a single square. This multiple occupancy
rule for small molecules avoids the need to
reduce the grid size and time steps by a factor
of 10. This simplification also makes the
simulations run much faster. Small molecules
are known to diffuse at approximately 50 nm/ms,
or approximately 10 times faster than
macromolecules. To accommodate their faster
diffusion rate, SimCell performs 10 small
molecule movements/interaction checks for each
macromolecular movement step.
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Validations
-Enzyme kinetics -Macromolecular diffusion
-Metabolic simulation -The repressilator gene
circuit
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Formal computational modelling approach to model
a crucial biological systemthe intracellular
NF-kB signalling pathway. The pathway is vital
to immune response regulation, and is fundamental
to basic survival in a range of species.
Alterations in pathway regulation underlie many
diseases, including atherosclerosis and
arthritis. Modelling of individual molecules,
receptors and genes provides a more comprehensive
outline of regulatory network mechanisms than
previously possible with equation-based
approaches.
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Activation of the NF-kB pathway is controlled by
inhibitors of NF-kB (IkB) proteins, which
sequester the majority of NF-kB in the cytoplasm
as complexes by masking their nuclear
localisation signals. During activation, IkB is
phosphorylated by IkB kinases (IKK), causing its
destruction. The newly freed NF-kB is
consequently transported into the nucleus,
inducing inflammatory genes, including those
encoding IkB, thus regulating the pathway through
negative feedback
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Due to the complexity of signalling pathways,
large numbers of linked ODEs are often necessary
for a reaction kinetics model. (ODEs) to
describe each chemical concentration with time.
This implicitly assumes homogeneity, treating the
cell as a well-mixed bag of chemicals. Such
models can be narrowly limited in the range in
which they function properly, which is at odds
with the robustness of nature. The many
interdependent differential equations can be very
sensitive to their initial conditions and
constants, with small changes in these sometimes
causing huge behavioural changes in the system.
Solutions may be liable to describe unrealistic
or impossible behaviour, such as negative
concentrations, unless the initial conditions and
constants are correct to a high degree of
precision. While differential equation models
may produce useful results under certain
conditions, they provide a rather incomplete view
of what is actually happening in
the Cell Spatial effects on pathways are also
often crucial, but again difficult to incorporate
into such a model, though partial differential
equations (PDEs) could theoretically be used.
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Many aspects of life involve the interaction of
multiple components and subunits and the
corresponding emergence of both form and
function. Agent-based (sometimes called
individual based) approaches whereby the
components are represented as autonomous software
artefacts that exist within a software
environment provide a mechanism for
understanding their behaviour through simulation
of the actual behaviour of the equivalent
biological system.
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Communicating X-machine
Various computational models exist to represent
agents, though the Communicating X-machine is
perhaps the most powerful and intuitive (Elefthera
kis et al., 2001 Balanescu et al.,
1999). Agent-based modelling has recently been
applied to a variety of biological systems,
including insect communities and epithelial
tissue (Jackson et al., 2004a, 2004b Walker et
al., 2004 Holcombe et al., 2003).
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An agent-based chemical model does not have the
same restrictions as a differential equation
model Any number (low or high, within
computational limitations) and distribution of
molecules can be modelled, spatial concerns can
easily be accounted for, as can time delays. An
agent-based model also provides a clearer picture
of what is actually occurring in the cell. More
details must be defined. The movement of agents
must be explicitly stated. Agents must at least
move around enough to regularly collide. It is
vital that the agent-based model is able to deal
with individual interactions of molecule agents
with the same accuracy as reaction kinetics.
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Developing software for agent-based systems can
make use of many modern software engineering
techniques, including decomposition, or dividing
a problem into small, manageable parts,
abstraction, or choosing which details of a
problem to model and which to suppress, and
organization, or identifying and managing the
relationships among the various system
components. The agent-based model is a
bottom-up paradigm wherein the lowest level
entities, called agents, interact with each other
autonomously. An agent is an encapsulated
computer system that is situated in some
environment and that is capable of flexible,
autonomous action in that environment in order to
meet its design objectives
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The agents are situated in space and time and
have some properties and certain sets of local
interaction rules. Though intelligent, they
cannot by themselves deduce the global behavior
resulting from their dynamic interactions. The
system evolves from the micro level to the macro
level. Thus agent-based modeling uses a bottom-up
design strategy rather than a top-down strategy.
Agents are commonly assumed to have
well-defined bounds and interfaces, as well as
spatial and temporal properties, including such
dynamic properties as movement, velocity,
acceleration, and collision. They exist in an
environment which they sense and can communicate
with through their interfaces. They are assumed
to respond in a timely manner to changes in their
environment. They are autonomous, encapsulating
a state and changing state based on their current
state and information they receive.
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ODE method does not account for spatial aspects.
Dimerization of monomer proteins, dissociation of
dimers, Repressor binding to Operator regions,
and RNA Polymerase binding to Promoter regions
are all processes in which the spatial aspects
play a crucial role. Agent-based models account
for these spatial and temporal aspects and hence
can be closer to actual biological
processes. The greater the number of details
that go into describing the behavior of the
system, the greater is the computational power
that is required to simulate the behaviors of all
constituent agents. This is a limitation in
modeling large systems using ABM. A reasonable
approach is to provide several levels of
abstraction and granularity, which can be chosen
depending on the level of detail needed and the
computational resources available. Here we are
modeling reactions at the molecular level, for a
relatively small number of molecules, so we have
chosen a very fine-grained level of modeling.
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Agents simulators
There are a few popular packages for simulation
of decentralized systems which provide 2D
visualization. MASON Repast Swarm StarLogo
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BREVE
BREVE is a 3D simulation engine developed to
provide quick and easy simulations of
decentralized systems. It is an open-source
package available for Mac OS, Linux, and Windows
platforms. It allows users to define and
visualize decentralized agent behaviors in
continuous time and continuous 3D space. The
package comes with its own interpreted
object-oriented scripting language called steve,
an OpenGL display engine, and collision
detection. BREVE also has a library of built-in
classes and provides graphical 3D visualization
and collisions between 3D bodies. These
features remove a significant amount of
programming overhead.
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LAMBDA PHAGE E. coli
Escherichia coli (E. coli) is an intestinal
bacterium and is a commonly studied prototype for
bacteria. When a passively infected E. coli
bacterium is exposed to a dose of ultraviolet
light, it stops reproducing and starts to produce
a crop of viruses called phage lambda into the
culture medium. This process of rapid
reproduction of the phage lambda viruses is
called lysis. The newly-formed lambda phages
multiply by infecting fresh bacteria. Some of the
infected bacteria lyse further, causing more
phages to be produced, whereas some bacteria may
carry the phage in a passive form, causing the
bacteria to grow and divide normally. This
process of passive reproduction of the phage
lambda is called lysogeny
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