Computational Biology

1
Computational Biology
Information encoded in biological systems

• One-dimensional digital (quaternary) code of DNA.

• Three-dimensional structure of proteins.

• Multi-dimensional intra-cellular biochemical
  networks.

• Vast complexity of multi-cellular biological
  organisms.

2
Example of a Biological Circuit
Lambda Phage model of Arkin et al., 1998
3
Intracellular Biochemical Networks
Formulation varies from qualitative and imprecise

4
Intracellular Biochemical Networks
... to quantitative and highly precise
5
Biochemical Reactions
Lingua Franca of computational biology.
Reaction
1 molecule of type A combines with 2
molecules of type B to produce 2 molecules of
type C.
Reaction is annotated with a rate constant and
physical constraints (localization, gradients,
etc.)
6
Biochemical Reactions
Lingua Franca of computational biology.
Reaction
Species

• Elementary molecules (e.g., hydrogen,
  phosphorous, ...)

• Complex molecules (e.g., proteins,
  enzymes, RNA ...)

Reaction

• Conglomeration of steps (e.g., transcription
  of gene product)

7
Biochemical Reactions
Lingua Franca of computational biology.
Coupled Set Reactions
Goal given initial conditions, analyze
(predict) the evolution of such a system.
8
Biochemical Reactions
Convential Approach numerical calculations based
on coupled ordinary differential equations.

• Computationally challenging (sometimes
  intractable).

• Assumes that molecular quantities are
  continuous values that vary deterministically
  over time.

9
Biochemical Reactions
Convential Approach numerical calculations based
on coupled ordinary differential equations.

• In intracellular networks, the number of
  molecules of each complex type is generally
  small (10s, 100s, at most 1000s).

• Individual reactions matter.

10
Gillespies Framework
Track precise (integer) quantities of molecular
species.
States
Reactions
A
B
C
S1
4
7
5
S2
2
6
8
S3
22
0
997
A reaction transforms one state into another
11
StochasticSimulation
S1 5, 5, 5 0
Ri
Choose the next reaction according to
where
12
StochasticSimulation
S1 5, 5, 5 0
Ri
Choose the time of the next reaction according to
13
StochasticSimulation
S1 5, 5, 5 0
See D. Gillespie, Exact Stochastic Simulation
of Coupled Chemical Reactions,J. Phys. Chem.
1977
14
StochasticSimulation
S1 5, 5, 5 0
Choose R3 and t 3 seconds.
R1
R2
R3
S2 4, 7, 4
3
Choose R1 and t 1 seconds.
S3 2, 6, 7 4
Choose R3 and t 2 seconds.
S4 1, 8, 6 6
Choose R2 and t 1 seconds.
15
StochasticSimulation
S1 5, 5, 5 0
Choose R3 and t 3 seconds.
S2 4, 7, 4
3
7
Choose R1 and t 1 seconds.
S3 2, 6, 7 4
Choose R3 and t 2 seconds.
S4 1, 8, 6 6
Choose R2 and t 1 seconds.