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.
Wide-spread recognition that biology is becoming a computational science.
1D: DNA (i.e., nucleic acids), genomics, bioinformatics. CS people have made tremendous contributions in this area, for instance by applying sophisticated string matching techinques
3D: proteins that DNA codes for (via amino acids). Predicting the 3D shape and configuration of proteins from the 1D list of amino acids that code for them is an interesting (and incredibly challenging problem). Proteomics. Precisce numerical problems in the field of physical chemsitry.
At a higher level, we have the biochemistry within individual cells. There is a whole host of complicated machinery, but much of the interesting behavior stems from the interaction of proteins: protein networks, and genetic regulatory networks.
Finally, vast complexity of organisms and even eco-systems
My entry point into this realm is at the level of intra-cellular chemistry. In collaboration with MSI (post-doc funded through NIH grant, in collaboration with MSI).
Can apply techniques from the field of circuit design: skills at abstracting and scaling computation.
Vast complexity of multi-cellular biological organisms.

2. Example of a Biological Circuit
Describe lamba: lysis vs. lysogeny.
Simple pathway within a very simple organism. Very well studied model.
Information about specific components within models such as lamba varies widely in its precision. <click>
Lambda Phage model of Arkin et al., 1998

3. Intracellular Biochemical Networks
Formulation varies from qualitative and imprecise:
Much of the knowledge in the biology literature is presented in descriptive, narrative form, in terms of causality. (Cartoons)
“e.g., in the presence of an inducer, a complex forms that inhibits binding at an operator side. This in turn leads to transcription....”
Apply techniques from the field of expert systems. (Not my area.)

4. Intracellular Biochemical Networks
... to quantitative and highly precise:
For certain components of certain models, however, there is sufficient information to contemplate quantitative analysis.

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.
The most fundamental concept in this field – in the literature and in practice – is the idea of a reaction. It specifies how something in the system changes:
<click> 1 of A combines with 2 of B to produce 2 of C
Of course, a wealth of information might be annotated: always a rate constant (likelihood of a reaction occurring or the rate at which it occurs). Also localization with a cell, chemical gradients, temperature.
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, ...)
The reactants and products in a reaction may be elementary molecules, or they might be more complex, more interesting molecules (proteins, enzymes, RNA....)
A reaction then could be a simple step, describing an event that can be understood in terms of basic chemistry. Or it could be a conglomeration of steps. That is, it could encapsulate a wealth of information.
Complex molecules (e.g., proteins, enzymes, RNA ...)
Reaction:
Elementary step (e.g., )
Conglomeration of steps (e.g., transcription of gene product)

7. Biochemical Reactions
Lingua Franca of computational biology.
Coupled Set Reactions R1 R2 R3
In an abstract sense, a biological systems can be viewed as a couple set of such reactions. Regardless of the components, the basic problem in computational biology is to characterize the evolution of such a system.
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.
Background: physical chemistry.
Supercomputing power. Result? Numbers that sometimes approximate experimental results, sometimes.
Problem: the model itself contains may unstated assumptions. Many of the parameters are crude guessing. Precise numerical calculations don’t make sense.
Assumptions: continuously-varying concentrations as a function of time.
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. Gillespie’s Framework
Track precise (integer) quantities of molecular species.
“States”
Reactions A B C R1 R2 R3 S1 4 7 5 S2 2 6 8 S3 22
997
Makes sense to characterize such a system in terms of discrete states. Each state consists of integer quantities of the different types of molecules
<click>
Reactions transform the state of the system.
This is a discrete Markov system. All the pertinent information regarding the system is contained with the current state, described by the integer quantities of the different types of molecules. The future evolution of the system depends only on these quantities.
A reaction transforms one state into another:
e.g.,

11. Stochastic SimulationR1 R2 R3 Ri
Choose the next reaction according to:
where

12. Stochastic SimulationR1 R2 R3 Ri
Choose the time of the next reaction according to:

13. Stochastic SimulationR1 R2 R3
See D. Gillespie, “Exact Stochastic Simulation of Coupled Chemical Reactions”, J. Phys. Chem. 1977

14. Stochastic Simulation
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. Stochastic Simulation
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.