Casey Henderson and Necmettin Yildirim NCF LOGO Introduction

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion Computer Algebra Approach to Sensitivity Analysis: Application to TRP Modeling Use ordinary differential equations to model mass action kinetics Sensitivity Analysis Use partial differential equations to model concentration sensitivities with respect to parameters Computer Algebra Use CAS to solve the large system of Approach equations simultaneously Tryptophan Application Implementation of the method for E. coli 05 March 2021

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion Variable Concentrations Constant Parameters Modeling Basics

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion Parameter Changes Effect System Dynamics

Casey Henderson and Necmettin Yildirim NCF LOGO How do we get Sensitivity equations? Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion Normalized Unitless Sensitivity Score

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion A Simple Example Recall, and, Then,

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion Computer Algebra Software Sensitivity Analysis requires a PDE for each variable with respect to each parameter. For m variables and n parameters, this is n(m+1) equations. Maple can do symbolic calculus to find the required PDE’s, building the sensitivity matrix. Matlab can take this matrix, along with the modeling ODE’s, and solve the resulting system numerically.

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion What is an Operon? A operon is a genetic regulatory network. It is defined by a set of common genes with one operator. The operator is a binding site for a regulatory protein.

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion What is the TRP Operon? The tryptophan operon in E. Coli is a repressive operon, that shuts down tryptophan production when tryptophan is present in the environment. The presence of tryptophan enables a repressor to bind to the operator, disabling the operon.

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion The TRP Operon

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion The TRP Operon

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion CAS Implementation 4 concentrations: Of, Mf, E, T x 24 parameters = 96 sensitivities Maple will find these sensitivities quickly with matrix algebra. 4 concentrations + 96 sensitivities = 100 differential equations Matlab will solve this system simultaneously and print sensitivity scores.

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion TRP Sensitivities Revealed

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion TRP Sensitivities Revealed

Casey Henderson and Necmettin Yildirim NCF LOGO TRP Sensitivities Revealed [T]/k-t Repressor Dissassociation Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion Transcription Termination [T]/b

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion Correlation to Experimental Results b =. 85 b =. 9996

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Future Work Improve the Model The operon is more complex than the model presented here. For example, there is a time delay in transcription. Parameter Estimation Parameter values directly effect the numeric solution. Better estimations will give more accurate results. Conclusion Collaborative Work A database of results to check against.

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion References Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data Moises Santillan and Michael C. Mackey (2001) Modeling operon dynamics: the tryptophan and lactose operons as paradigms Michael C. Mackey, Moises Santillan, Necmettin Yildirim (2004)

Casey Henderson and Necmettin Yildirim NCF LOGO Introduction Math Modeling Sensitivity Analysis Computer Algebra Operon Application to TRP Conclusion Questions? Thank You!