Computational Biology: An overview

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Computational Biology An overview

• Shrish Tiwari
• CCMB, Hyderabad

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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

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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

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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

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Patterns in nature
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Simulated Patterns
Back
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Structural modeling

• Protein folding homology modeling, threading, ab
  initio methods
• Protein interaction networks, biochemical
  pathways
• Cellular membrane dynamics
• 
  Back

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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

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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

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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

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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

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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

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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

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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

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Simple life patterns
Still lives
Oscillator
Glider
Back
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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

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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

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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.
• 
  
  

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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

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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

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The Bernoulli shift

• Map fx (2x mod 1), 0 x 1.
• t 0 1 2 3 4 5 6 7
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• 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

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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

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Logistic map bifurcation diagram
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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

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Return map Logistic map
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Return map Lorenz attractor
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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

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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

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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

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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

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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

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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

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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

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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

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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

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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)