# Presentation: 122345

## 

June 25, 2004

Richard L. Schiek & Elebeoba E. May
Department of Computation Sciences

**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.

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

## Outline

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

## 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)**

## 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**

## Biological Circuits

**Simplified Genetic Switch**

## Biological Circuits

**Simplified Genetic Switch**

- RNA

- Protein

- N. On

## Biological Circuits

- RNA

- Protein

- N. On

- N. Off

**Simplified Genetic Switch**

## Biological Circuits

- RNA

- Protein

- Environmental Factor

**Simplified Genetic Switch**

- N. On

- N. Off

## Biological Circuits

- Pro

- Opr

- Gene 1

- Pro

- Opr

- Gene 2

- DNA

- RNA

- Environmental
-  Factor

- N. On

- N. Off

- Protein

**Time**

**Concentration**

**Gene 1**

**Gene 2**

## 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.**

**Uses network information because hierarchy is useful.**

**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.**

## Implementation and Modeling Approach

| Charge | Mass |
| --- | --- |
| Current | Rate of mass change |
| Voltage | Concentration |
| Kirchoff’s Voltage Law | Stoichiometry |
| Kirchoff’s Current Law | Conservation of Mass |

- Electrical Domain

- Biochemical Domain

**Cellular machinery can be modeled by charge sources/sinks and behavioral devices.**

## Implementation and Modeling Approach

| Charge | Mass |
| --- | --- |
| Current | Rate of mass change |
| Voltage | Concentration |
| Kirchoff’s Voltage Law | Stoichiometry |
| Kirchoff’s Current Law | Conservation of Mass |

- Electrical Domain

- Biochemical Domain

**Cellular machinery can be modeled by charge sources/sinks and behavioral devices.**

**2 H****2**** + O****2**** ******** 2 H****2****O**
**2 H****2****O ******** 2 H****2**** + O****2**

## Implementation and Modeling Approach

- Pro

- Opr

- Gene 1

- Pro

- Opr

- Gene 2

- DNA

- RNA

- Environmental
-  Factor

- On

- Off

**Biological circuits are typically modeled as RC-circuits where voltage on a given circuit line is proportional to a chemical concentration.**

- Protein

## 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, ...)**

## 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**

## Metabolic and Genetic Coupling

## Bacterial Systems

**To simulate entire cell systems an automated method was created to convert public databases into circuits.**

## Bacterial Systems

**E. coli K-12 data.**
**Approximately 8350 circuit unknowns.**
**Serial and Parallel simulations.**
**Model verification underway.**

## 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.**

## Tissue Differentiation Systems

**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.**

**Solve PDE problem**
**(Xyce or custom code)**

**Solve circuits problem**
**(Xyce)**

## 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)**

## 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.**

## Cellular Differentiation in Drosophila sp.

**Cells develop into two types**
**  ****wg expressing and**
**  ****hh expressing**

## Cellular Differentiation in Drosophila sp.

- en

- EN

- cid

- CID

- wg

- ptc

- WG

- PTC

- PH

- CN

- hh

- HH

- +

- Cell
- Boundary

**von Dassow *****et. al.*****, *****Nature***** v. 406, July 2000.**

**Promotes Reaction**

**Inhibits Reaction**

**  ****wg expressing**

## Cellular Differentiation in Drosophila sp.

- en

- EN

- cid

- CID

- wg

- ptc

- WG

- PTC

- PH

- CN

- hh

- HH

- +

- Cell
- Boundary

**von Dassow *****et. al.*****, *****Nature***** v. 406, July 2000.**

**Promotes Reaction**

**Inhibits Reaction**

**hh expressing**

## Cellular Differentiation in Drosophila sp.

**Simulated a culture of 676 cells (26 x 26 grid) **
**Applied a WG concentration gradient of 50%**
**Two dimensional, full diffusion model joins cells**

**High WG**

**Low WG**

**X**

**Y**

## Cellular Differentiation in Drosophila sp.

**Two layers of hh expressing cells surround a layer of wg expressing cells leading to tissue differentiation.**

## 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.**