Genome projects identify the components of gene networks in biological organisms, gene after gene, yet the static pictures of networks these experiments give us cannot adequately explain biomolecular phenomena or enable rational engineering of dynamic gene expression regulation. Rational design principles can only come in terms of molecular components, the kinetics and the thermodynamics of their interaction. Experimentally, the designs can only be realized by mutating regulatory DNA sequences, mutating regulatory protein sequences and connecting the genes through specific regulatory relationships (e.g. gene A activating gene B). Hence, design principles must be attainable experimentally through molecular biology techniques.
Because of the large number of participating species and the complexity of their interactions, quantitative modeling can allow investigating dynamic gene expression in a way fit for analysis and design. Dynamic models of all the biomolecular interactions involved in transcription, translation, regulation and induction enable rational engineering of regulatable gene transcription systems. Based on such models, designs are detailed at the molecular level and are attainable with genetic engineering techniques.
We represent all gene expression molecular level events with reactions. For any two molecular species A and B (proteins, DNA promoter, operator sites, RNA binding sites, signaling molecules, etc.) interacting in solution to form a complex A*B (e.g. a repressor protein and the corresponding DNA operator site) we write

[A]aq + [B]aq   =     [A*B]aq

with k1 and k-1 the association and dissociation kinetic constants, respectively. Our models incorporate all individual molecular species and interactions known to be involved in gene expression.
If we considered the cell as a well-stirred reactor we could calculate the behavior of the network using a set of ordinary differential equations, which determine concentration changes as prescribed by kinetic laws. However, the underlying assumption of such continuous-deterministic models, that the number of molecules approaches the thermodynamic limit (i.e. that the volume of the system is infinite), can be invalid for biological systems, since for some components (DNA for example) there are only a few copies available. Hence, accurate modeling of biomolecular events requires a discrete-stochastic algorithm, in order to capture discrete biomolecular interaction events that occur with certain probability in time.  We have developed a computationally efficient version of such an algorithm, the stochastic simulation algorithm (SSA), initially described by Gillespie [1]. SSA is a Markov process describing the transition from one discrete state of the system to another. Although accurate in capturing the dynamic of biomolecular interaction systems, SSA becomes computationally intractable, if the time scales of involved interaction events are disparate, because it simulates every single biomolecular interaction event, spending inordinate amounts on fast reactions for very few simulated occurrences of slow reactions. There have been numerous attempts to improve the efficiency of the SSA [2]. In one such attempt, where the reactions can be considered fast, the representation of each fast reaction is changed to a continuous Markov process, deriving a chemical Langevin equation (CLE) [3]. One would then need to either use discrete-stochastic or continuous-stochastic equations, again not simulating biomolecular interactions with disparate time scales.
We were recently successful in developing a hybrid algorithm that integrates accurately the SSA and CLE schemes [4]. What we have produced is a truly multiple-scale algorithm for simulating arbitrarily complex reaction networks. In comparisons, our hybrid stochastic-discrete, stochastic-continuous, deterministic-continuous algorithm outperforms all other existing algorithms in terms of computational performance and accuracy.  We have recently extended the algorithmic capabilities with a probabilistic steady state approximation, an adaptive time step integration method for stochastic differential equations and a dynamic decision method for separating the time scales of reactions in reaction networks [5-7].
With a user friendly graphics user interface, we have made our algorithms publicly available with Open Software licenses. The name of the suite of codes is Hy3S (Hybrid Stochastic Simulations for Supercomputers) and they are available at SourceForge.net [7].
We have also developed a simulated annealing optimization algorithm for designing novel gene regulatory networks in silico. We have designed bistabled switched, oscillators, AND and NOR gates [8-11].
In this talk we will describe the mathematics behind the multi-scale methods, the designs of novel gene networks and the connections we are establishing with experimental genetic engineering methods for improving the theory and guiding the experiments.

1. Gillespie DT: Exact stochastic simulation of coupled chemical reactions. J Phys Chem 1977, 81:2340 - 2361.
2. Gibson MA, Bruck J: Efficient exact stochastic simulation of chemical systems with many species and many channels. Journal of Physical Chemistry A 2000, 104:1876.
3. Gillespie DT: The chemical Langevin equation. Journal of Chemical Physics 2000, 113:297.H. Salis, Y. Kaznessis, “Accurate Hybrid Stochastic Simulation of a System of Coupled Chemical or Biochemical Reactions”, J. Chem. Phys. Vol. 122, p. 054103 1-13, 2005.
4. H. Salis, Y. Kaznessis, “Stochastic Simulations of Gene Regulatory Modules”, Computers in Chemical Engineering, Vol. 29, p. 577-588, 2005.
5. H. Salis, Y. Kaznessis “An equation-free probabilistic steady state approximation: Dynamic application to the stochastic simulation of biochemical reaction networks”, Journal of Chemical Physics, Vol. 123(21), p. 214106, 2005.
6. Y. Kaznessis, “Multi-Scale Models for Gene Network Engineering”, Chemical Engineering Science, Vol. 61(3), p. 940-953, 2006.
7. H. Salis, V. Sotiropoulos, Y. Kaznessis “Multiscale Hy3S: Hybrid Stochastic Simulations for Supercomputers”, BMC Bioinformatics, (highly accessed), Vol. 7:93, 2006.
8. J. Tomshine, Y. Kaznessis, "Optimization of a stochastically-simulated gene network model via simulated annealing," Biophysical Journal, 2006, in press, available online
9. L. Tuttle, H. Salis, J. Tomshine, Y. Kaznessis, “Model-Driven Design Principles of Gene Networks: the Oscillator”, Biophysical Journal, Vol. 89(6), p. 3873-83, 2005.
10. V. Sotiropoulos, Y. Kaznessis, "Computer-aided design of synthetic tetracycline-inducible regulatory networks" submitted.
11. H. Salis, Y. Kaznessis, "Using scaffold proteins to design gene-activating binary and ternary biological AND gates" submitted.

Extended Abstract Status: Not Uploaded