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Computational Biology: An overview

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Computational Biology: An overview Shrish Tiwari CCMB, Hyderabad Mathematics, Computers & Biology The book of nature is written in the language of mathematics – PowerPoint PPT presentation

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Title: Computational Biology: An overview


1
Computational Biology An overview
  • Shrish Tiwari
  • CCMB, Hyderabad

2
Mathematics, Computers Biology
  • The book of nature is written in the language of
    mathematics
  • - Galileo
  • What about biology?
  • Changing scenario due to the development of
  • Biological sequence data
  • Chaos theory
  • Game theory

3
Computer Applications in Biology
  • Pattern recognition
  • Pattern formation and characterisation
  • Structural modeling of bio-molecules
  • Modeling of macro-systems
  • Image processing
  • Data management and warehousing
  • Statistical analysis
    Next

4
Pattern recognition
  • Predicting protein-coding genes (GenScan)
  • Motif search (MotifScan, promoter search)
  • Finding repeats (TRF, Reputer)
  • Predicting secondary structure (PHDsec,
    nnpredict)
  • Classification of proteins (SCOP)
  • Prediction of active/functional sites in proteins
    (PDBsitescan)
  • Back

5
Patterns in nature
6
Simulated Patterns
Back
7
Structural modeling
  • Protein folding homology modeling, threading, ab
    initio methods
  • Protein interaction networks, biochemical
    pathways
  • Cellular membrane dynamics

  • Back

8
Macro-system modeling
  • Modeling of dynamics of organs like brain and
    heart
  • Modeling of environmental dynamics, interacting
    species
  • Modeling of population growth and expansion

  • Back

9
Image processing
  • Gridding of spots in the image
  • Removing background intensity (usually not
    uniform across the array)
  • Computing the ratio of intensities in case of two
    colour probes
  • Comparison of slides from different arrays
    Back

10
Computational Tools
  • Dynamic programming algorithm
  • Markov Model, Hidden Markov Model, Artificial
    Neural Network, Fourier Transform
  • Molecular dynamics, Monte Carlo, Genetic
    Algorithm simulations
  • Cellular Automata
  • Game theory
  • Statistical tools

11
Dynamic Programming
  • An optimisation tool that works on problems which
    can be broken down to sub-problems
  • Used widely in sequence alignment algorithms in
    bioinformatics
  • Other applications speech, vocabulary, grammar
    recognition
  • Back

12
Pattern recognition tools
  • Markov model state of system at time t depends
    on its state at time t-1, transition
    probabilities between states are defined.
    Example gene finding
  • Artificial neural networks attempt to simulate
    the learning process of real neural network
    system
  • Fourier transform measure correlations between
    states at different time/space points
    Back

13
Optimisation tools
  • Molecular dynamics apply Newtons equation of
    motion to follow the dynamics of a system
  • Monte Carlo simulation randomly hop from one
    state to another until you find the optimal state
    Back
  • Genetic algorithm attempt to simulate
    evolutionary mechanism of mutations and
    recombination to find the optimal solution

14
Cellular Automata
  • Components 1) a lattice, 2) finite number of
    states at each node, 3) rule defining the
    evolution of a state in time
  • Example game of life _ 1) on a 2-d lattice each
    cell represents an individual, 2) states 0 (dead)
    or 1 (live), 3) a cell dies if it has less than 2
    or more than 3 live neighbours, a dead cell
    becomes live if 3 of its neighbours are live

15
Simple life patterns
Still lives
Oscillator
Glider
Back
16
Game theory
  • Game 1) involves 2 or more players, 2) one or
    more outcomes, 3) outcome depends on strategy
    adopted by each player
  • Components 1) 2 or more players, 2) set of all
    possible actions, 3) information available to
    players before deciding on an action, 4) payoff
    consequences, 5) description of players
    preference over payoffs

17
Game theory an example
  • Traffic as a game
  • The commuters are players
  • Traffic rules define the set of possible actions
    (including disobeying traffic rules)
  • Payoff consequences fined if you violate traffic
    rules, you may suffer injury in accidents or die
  • Information available
  • Players preferences safe driving, dangerous
    driving etc.

  • Back

18
Statistical tools
  • Expectation value computation to assess the
    significance of alignment
  • Clustering methods UPGMA, WPGMA, k-means etc.
  • Assessing significance of genotype-phenotype
    association chi-square test, Fishers exact test
    etc.



19
Chaos Theory An Introduction
  • One of the behaviours of a non-linear dynamical
    system
  • Deterministic yet unpredictable!!
  • Sensitive to initial conditions/small
    perturbations
  • First discovered by Lorenz when he was simulating
    the weather dynamics using simplified
    hydro-dynamics model

20
The Lorenz attractor
  • Simplified model of convections in the atmosphere
  • dx / dt a (y - x)
  • dy / dt x (b - z) - y
  • dz / dt xy - c z
  • a 10, b 28, c 8/3

21
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22
The Bernoulli shift
  • Map fx (2x mod 1), 0 x 1.
  • t 0 1 2 3 4 5 6 7
    8
  • x .2 .4 .8 .6 .2 .4 .8 .6
    .2
  • .21 .42 .84 .68 .36 .72 .44 .88 .76
  • Binary representation
  • 0.2 0.001100110011
  • 0.21 0.001101011100

23
Chaotic dynamics An example
  • Simplest system exhibiting chaos, the logistic
    map xn1 rxn(1 xn ), 0 lt xn lt 1
  • This simple equation exhibits a rich dynamical
    behaviour, ranging from stationary state to
    chaotic dynamics, as the parameter r varies from
    0-4
  • This system models the population dynamics of a
    species whose generations do not overlap

24
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27
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28
Logistic map bifurcation diagram
29
First return map
  • Plot of xn1 against xn for discrete systems, and
    xtT against xt for continuous dynamics, where T
    is some fixed interval
  • Return map of a periodic orbit is a finite set of
    points
  • Return map of a stochastic system a scatter of
    infinite number of points
  • Return map of a chaotic system an infinite number
    of points in a structure

30
Return map Logistic map
31
Return map Lorenz attractor
32
Controlling chaos
  • Different kinds of control are possible
  • Suppression of chaos, I.e. bring the system out
    of chaotic behaviour into some regular dynamics
    e.g. adaptive control
  • Remain in the chaotic dynamics, but force the
    system to remain in one of the unstable periodic
    orbits e.g. OGY (Ott, Grebogi Yorke) method
  • Sustain or enhance chaos desirable for example
    in combustion where homogeneous mixing of gas and
    air improves the combustion
  • Synchronisation confidential communication

33
Control of cardiac chaos
  • A. Garfinkel et al. applied the OGY method of
    control to arrest arrhythmia in a rabbits heart
    (Science 257, 1230-35 (1992) )
  • Arrhythmia was induced in the rabbit heart by
    injecting the animal with the drug ouabain
  • The first return map In-1 vs. In, the interbeat
    interval, identified periodic orbits with saddle
    instability
  • When the heart dynamics approached one of these
    points, small electrical pulses were used to
    force the system on the unstable periodic orbit

34
Prey-Predator Model
  • Simplest description of prey-predator
    interactions is given by the Lotka-Volterra
    equations
  • dH/dt rH aHP
  • dP/dt bHP mP
  • H density of prey P denstiy of predators
  • r intrinsic prey growth rate a predation rate
  • b reproduction rate of predator per prey eaten
  • m predator mortality rate

35
Game theory
  • Deals with situations involving
  • 2 or more players
  • Choice of action depends on some strategy
  • One or more outcomes
  • Outcome depends on strategy adopted by all
    players strategic interaction
  • Elements of a game
  • Players
  • Set of all possible actions
  • Information available to players
  • The payoff consequences
  • A description of players preferences over payoffs

36
Prisoners dilemma An example
  • Players 2 prisoners A and B
  • Two possible actions for each prisoner
  • Prisoner A Confess, Dont confess
  • Prisoner B Confess, Dont confess
  • Prisoners choose simultaneously, without knowing
    what the other choses
  • Payoff quantified by years in prison fewer years
    greater payoff
  • Outcomes 1) both dont confess 1 year in prison
    for both, 2) 1 confesses other does not the one
    who confesses is free, other gets 15 years, 3)
    both confess both get 5 years

37
Prey-predator model with predators using hawk and
dove tactics
  • P. Auger et al. recently studied a prey-predator
    model with the predators using a mix of hawk and
    dove strategies (Mathematical Sciences 177178,
    185-200 (2002) )
  • A classical Lotka-Volterra model was used to
    describe the prey-predator interaction
  • Predators use two behavioural tactics when they
    contest a prey with another predator hawk or dove

38
Prey-predator model with predators using hawk and
dove tactics
  • Assumptions
  • Gain depends on the prey density, which modifies
    predator behaviour
  • The prey-predator interaction acts at a slow time
    scale
  • The behavioural change of predator works on fast
    time scale
  • Aim effects of individual predator behaviour on
    the dynamics of the prey-predator system
  • Study carried out for different prey densities

39
Prey-predator model with predators using hawk and
dove tactics
  • Conclusions
  • There is a relationship between behaviour and
    prey density
  • Aggressive (or hawk) behaviour prevails in high
    prey density
  • A mix of hawk and dove strategy observed for low
    prey density
  • A change of view aggressive behaviour is not
    advantageous when prey (resources) are rare and
    collaboration should be favoured

40
This is just the beginning
  • Mathematics and computers are playing an
    increasingly important role in biology
  • We have just begun to scratch the surface of
    biological discoveries
  • The field is vast and largely untapped so we need
    young minds to be fascinated by these problems

41
References
  • A. Garfinkel, M.L. Spano, W.L. Ditto and J.N.
    Weiss Controlling cardiac chaos Science 257,
    1230-1235 (1992).
  • P. Auger, R.B. de la Parra, S. Morand and E.
    Sanchez A prey-predator model with predators
    using a hawk and dove tactics Math. Biosci.
    177178, 185-200 (2002)
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