This document discusses stochastic modeling and its applications in bioinformatics. It defines stochastic models and processes, and explains how they differ from deterministic models in accounting for uncertainty. Some examples of stochastic modeling approaches described include stochastic process algebra using tools like π-calculus and Petri nets, Markov models including Markov chains and hidden Markov models, and BioAmbients for modeling biological systems with mobile boundaries. The document argues that stochastic methods are better suited than deterministic ones for describing complex and dynamically evolving biological systems.

1. APPLICATIONS OF
STOCHASTIC MODELLING IN
BIOINFORMATICS
Information Science & Informatics
Informatics and Neuroinformatics
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STOCHASTIC MODEL
 Stochastic model is any mathematical model of a system
that is governed by the laws of probability and contains
elements uncertainty.
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Stochastic vs Conventional Printing
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STOCHASTIC PROCESS
 The basic steps for creating stochastic models are:
 The sample definition
 The probability assignment to the sample data
 The identification of the facts of interest
 The calculation of the desired probability
 A stochastic process is a family of random variables X (t)
where t is a parameter running through an appropriate
set of indicators T. Usually the index t corresponds to
units of time, and the whole set can be something like
T = {0, 1, 2 ,. . .}
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ApplicationsofStochasticModellinginBioinformatics

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STOCHASTIC VS DETERMINISTIC MODELS
 In deterministic models, the output of the model is fully
determined by the values ​​of parameters and initial
conditions. A process is deterministic if the future is
determined by its present and its past state.
 A stochastic model is a random process which evolves in
time. Even if we have full knowledge of the current state
of system we can not be sure of the effect in future
periods. A stochastic process is a collection of random
variables.
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STOCHASTIC VS DETERMINISTIC MODELS IN BIOLOGY
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STOCHASTIC PROCESS ALGEBRA
 Combinability is expressly provided by combinators and
they are supported by the semantics of the language.
 This structure offers benefits when modelling a system
composed of interacting elements (these elements, and
their interaction can be modelled separately).
 Models have a clear structure and is easy to understand.
 Can be build consistently, either by processing or by
improvement.
 It is possible to maintaining a library of the model
components, supporting reuse.
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STOCHASTIC PROCESS ALGEBRA EXAMPLE
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ApplicationsofStochasticModellinginBioinformatics
Image from Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes
Lucia Cloth, Henrik C. Bohnenkamp, Boudewijn R. Haverkort 2001

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STOCHASTIC PROCESS ALGEBRA BETA-BINDERS
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ApplicationsofStochasticModellinginBioinformatics
 The Beta-binders is a process algebra based on π-
calculus (π-calculus allows channel names to
communicate together with the channels itself). A name
can be a channel of communication and thus can
describe parallel computing with networks that can be
changed during the course of the calculations
 Designed for the modelling and simulation of biological
processes.
 A biological process is modelled by a bio-process, which
is a π-calculus process in a box with expressed
interaction capabilities as Beta-binders.

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STOCHASTIC PROCESS ALGEBRA PETRI NETS
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ApplicationsofStochasticModellinginBioinformatics
 A Petri Net is a collection of directed arcs connecting
places and transitions. The places may have tokens. Any
distribution of tokens over the places will represent a
configuration of the net called a marking.

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BIOAMBIENTS
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ApplicationsofStochasticModellinginBioinformatics
 The fundamental element in Ambient calculus is the
ambient (environment). The ambient is a certain place
where calculations can take place. The concept of
bounds is considered key to the description of mobility
as a boundary defines a limited computational agent
that can be moved as a whole.
 Examples of BioAmbient modeling
 Blood transfusion
 Bacteriophage viruses

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MARKOV MODEL
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ApplicationsofStochasticModellinginBioinformatics
 In probability theory, a Markov model is a stochastic model
used for modeling systems that can change at random and
where it is considered that future situation depends only
on the current situation and not related to events that
occurred before it.
 This assumption allows reasoning and calculation with
models that would otherwise be intractable.

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MARKOV MODEL
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 The simplest Markov model is the Markov chain. It
Models the state of a system with a random variable
that changes over time.
 In this context, the status Markov suggests that
distribution for this variable depends only on the
distribution of the previous situation.
 A Hidden Markov model is a Markov chain, for which the
state is only partially observable. There are Observations
on the state of the system, but is typically insufficient to
accurately determine the situation.

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MARKOV MODEL - EXAMPLE
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 Observe what happens the next day of a day with headache in order to predict how you will feel
tomorrow. After many observations we can construct a model that estimates the probabilities of
transitioning between our two states (1,2)
a11 = P[W(n+1) = H | W(n) = H] = 0.5
a12 = P[W(n+1) = H | W(n) = NH] = 0.5
a21 = P[W(n+1) = NH | W(n) = NH] = 0.99
a22 = P[W(n+1) = NH | W(n) = H] = 0.01
“a” indicates a probability of state transition. “a11” is the probability of transitioning from state 1 to state 1. Because
this model has the Markov property, only today’s status (Headache or No Headache) matters in trying to predict
tomorrow’s status.
Headache No headache
0.5
0.01
0.5
0.99

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CONCLUSIONS
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 This main motivation for applying stochastic methods of Computer
Science in the description of biological systems is that is easier to
do so when complexity of biological systems is increased compared
to deterministic methods.
 Finally, All biological systems evolve dynamically according to
stochastic forces either can not predict or understand. Thus the
stochastic modeling will continue to gain ground.
ApplicationsofStochasticModellinginBioinformatics

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CONCLUSIONS
15Thank you!
ApplicationsofStochasticModellinginBioinformatics
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