Using Circuit Modeling to Simulate Large Scale, Multi-Cellular, Biological Pathways

1. Using Circuit Modeling to Simulate Large Scale, Multi-Cellular, Biological Pathways June 25, 2004 Richard L. Schiek & Elebeoba E. May Department of Computation Sciences Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy under contract DE-AC04-94AL85000.

2. Outline • Biological Circuits - What are they? • Implementation and Modeling Approach • Metabolic and Genetic Coupling • Bacterial Systems • Tissue Differentiation Systems • Future Directions

3. Biological Circuits At the biochemical level cells are characterized by: • Many different chemical species(DNA, RNA, enzymes, proteins, …) • Many different reaction mechanisms(kinetic, enzymatic, promoters, repressors, …) Glucose metabolism in Escherichia coli: • 436 chemical species • 720 reactions J. Edwards & B. Palsson, Proc. Nat. Acad. Sci., 97 (2000)

4. Biological Circuits • Mechanism graphs were built to better understand the complexity. • Network or circuit analysis approach is logical. E. Coli Metabolism Map,Systems Biology Research Group, UCSD, http://gcrg.ucsd.edu

5. Gene DNA Opr Gene Pro Opr Pro Biological Circuits Simplified Genetic Switch

6. Gene DNA Opr Gene Pro Opr Pro Biological Circuits Simplified Genetic Switch RNA N. On Protein

7. Gene DNA Opr Gene Pro Opr Pro Biological Circuits Simplified Genetic Switch RNA N. Off Protein N. On

8. Gene DNA Opr Gene Pro Opr Pro Biological Circuits Simplified Genetic Switch RNA N. Off Protein N. On Environmental Factor

9. Biological Circuits DNA Gene 2 RNA Opr Gene 1 Pro N. Off Opr Protein Pro N. On Environmental Factor Gene 1 Concentration Gene 2 Time

10. Implementation and Modeling Approach Two basic approaches: Assume system is well mixed. Describe reactions with differential equations. Integrate species concentrations forward in time. Assume nodes are well mixed. Describe reactions with differential equations. Propagate concentrations only along wires to the nodes. Integrate species concentrations and fluxes forward in time. Neglects network information. McAdams, H. & Shapiro, L., Science, 269 (1995) McAdams, H. & Arkin, Annu. Rev. Biophysics (1998) von Dassow et. al., Nature, 406 (2000) A. Arkin, IEEE Bioinformatics Conf. August (2003) BioSpice Community. Uses network information because hierarchy is useful.

11. Implementation and Modeling Approach Electrical Domain Biochemical Domain Cellular machinery can be modeled by charge sources/sinks and behavioral devices.

12. Implementation and Modeling Approach Electrical Domain Biochemical Domain 2 H2 + O2 2 H2O 2 H2O  2 H2 + O2 Cellular machinery can be modeled by charge sources/sinks and behavioral devices.

13. NO Switch D / R R / P P / Pc NC Switch D / R R / P Implementation and Modeling Approach Biological circuits are typically modeled as RC-circuits where voltage on a given circuit line is proportional to a chemical concentration. DNA Gene 2 RNA Opr Gene 1 Pro Opr Protein Off Pro Environmental Factor On

14. Implementation and Modeling Approach Goal: Large scale biological circuit simulation Approach: Use existing biological databases to develop whole cell circuits(metabolic, genetic, signal transduction …) Couple cells in a comment environment to study multi-cell effects(culture growth, tissue development, synergistic functionality, …)

15. Pyrophosphate PRPP Serine Glutamate glyceraldehyde3-phosphate CO2 Pyruvate N-(5’-phos) Anthranilate Rxn Rxn Rxn CPAD5P Rxn Rxn IGP Anthranilate Chorismate Glutamine Tryptophan Trp EDCBA haloRep Trp EDCBA Operon Delay apoRep mRNA +- +- Metabolic and Genetic Coupling Metabolic pathways translate directly into reaction networks. Genetic control of the metabolic pathways is modeled as a binary network, or truth table. Hybrid modeling of both the metabolic network and its associated genetic control is new and this is one of the first efforts in this field. Metabolic Genetic

16. Pyrophosphate PRPP Serine Glutamate glyceraldehyde3-phosphate CO2 Pyruvate N-(5’-phos) Anthranilate Rxn Rxn Rxn CPAD5P Rxn Rxn IGP Anthranilate Chorismate Glutamine Tryptophan Trp EDCBA haloRep Trp EDCBA Operon Delay apoRep mRNA +- +- Metabolic and Genetic Coupling

17. Escherichia coli K-12 Metabolic Data (Palsson, UCSD) Path2cir Xyce Circuit File(netlist format) Escherichia coli K-12 Genetic Data (EcoCyc) Gene2cir Bacterial Systems To simulate entire cell systems an automated method was created to convert public databases into circuits.

18. Bacterial Systems • E. coli K-12 data. • Approximately 8350 circuit unknowns. • Serial and Parallel simulations. • Model verification underway.

19. Within a cell, a circuit based reaction pathway exists Inputs and outputs to pathway are connected to the diffusion limited environment. Cell to Cell interactions are limited by diffusion. Tissue Differentiation Systems • To simulate and understand how groups of cells interact, one should simulate many cell connected by a diffusive environment. • Implemented a Diffusion PDE device in Xyce and with Trilinos/Entero to couple many cells in one common environment. • Target application is cellular differentiation.

20. Tissue Differentiation Systems Within a cell, a circuit based reaction pathway exists Solve PDE problem (Xyce or custom code) Solve circuits problem (Xyce) Inputs and outputs to pathway are connected to the diffusion limited environment. Cell to Cell interactions are limited by diffusion.

21. Tissue Differentiation Systems Cellular differentiation occurs when neighboring cells influence future development. If this cell secretes a hormone, then… these cells may develop into a different type of tissue (e.g. an artery wall or nerve cell)

22. Cellular Differentiation in Drosophila sp. In a growing Drosophila larva, a series of bands develop which later develop into different tissue types. Similar processes occur in humans as cells turn into skin, nerve, muscle tissue.

23. EN en wg WG + PTC ptc CID PH cid CN HH hh von Dassow et. al., Nature v. 406, July 2000. Cell Boundary Promotes Reaction Inhibits Reaction Cellular Differentiation in Drosophila sp. • Cells develop into two types • wg expressing and • hh expressing

24. Cellular Differentiation in Drosophila sp. EN en wg expressing wg WG + PTC ptc CID PH cid CN HH hh von Dassow et. al., Nature v. 406, July 2000. Cell Boundary Promotes Reaction Inhibits Reaction

25. Cellular Differentiation in Drosophila sp. EN en hh expressing wg WG + PTC ptc CID PH cid CN HH hh von Dassow et. al., Nature v. 406, July 2000. Cell Boundary Promotes Reaction Inhibits Reaction

26. Cellular Differentiation in Drosophila sp. High WG • Simulated a culture of 676 cells (26 x 26 grid) • Applied a WG concentration gradient of 50% • Two dimensional, full diffusion model joins cells Y Low WG X

27. Cellular Differentiation in Drosophila sp. Two layers of hh expressing cells surround a layer of wg expressing cells leading to tissue differentiation.

28. Future Directions Unlike electrical circuits, biological circuits: • Physical parameters are difficult to measure. • Circuit connections may not be well understood. • System architecture is not obvious. Need to focus on: • Parameter studies and parameter sensitivity analysis. • Network stability studies. • Fundamental block studies.