Regulation of Gene Expression in Flux Balance Models of Metabolism

Outline Flux Balance Analysis (FBA) Introduction of the new rFBA model Examples of rFBA model

FBA Step I: system definition Step II: obtaining reaction stoichiometries Step III: set constrains and objective function Step IV: optimization

Step I – System definition Reactions and metabolites Transport mechanisms and system boundary

Step II - Mass balance Stoichiometric matrix S Flux matrix v Dx/dt = S · v = 0 in steady state

Step III – Defining measurable fluxes & constraints Experimental data on flux levels, as obtained by isotope labeling or other methods, can also be used to set a i or b i to 0 or to another finite value to constrain the direction or magnitude of a flux.

Step IV – Optimization Define of objective function Z E.g., biomass production in defined proportion

FBA models to date have not accounted for the constraints associated with regulation of gene expression nor activity of the expressed gene product. It has been demonstrated that control of biosynthetic fluxes depends on multiple enzymes. The engineering of cell regulation is an efficient use of an organism's metabolism to produce a desired product. None of the existing models (boolean logic, mixed integer linear optimization, fractal kinetic theory, etc) has been able to be adopted on a scale large enough to represent the entire metabolism of an organism, and thus the systemic regulatory or metabolic properties of an entire organism have yet to be analyzed. Limitations

rFBA model Adding transcriptional regulatory constrains to FBA solution space is restricted to a smaller space

Cells are subject to both invariant and adjustable constraints. Invariant constrains: Physico-chemical constrains in origin and include stoichiometric, capacity and thermodynamic constraints. They can be used to bracket the range of possible behaviors. Adjustable constraints: Biological in origin, and they can be used to further limit allowable behavior. These constraints will change in a condition-dependent manner. The transcriptional regulatory structure can be described using Boolean logic equations, which assigns expression of a transcription unit to 1 if the transcription unit is transcribed, and 0 if it is not. Similarly, the presence of an enzyme or regulatory protein, or the presence of certain conditions inside or outside of the cell, may be expressed as 1 if the enzyme, protein, or a certain condition is present and 0 if it is not.

Boolean logic equation “AND” “OR” “NOT” Trans= IF (G) AND NOT (B) rxn= IF (A) AND (E) v rxn (t) = 0, when E is not present at timepoint t (t 1 <=t<=t 2 ) A simple regulatory circuit. Gene G is transcribed by a process trans to produce an enzyme E. This enzyme then catalyses a reaction rxn which converts substrate A into product B. Product B then represses transcription of G, leading to depletion of E.

Time course of growth t0t0 t1t1 t2t2 t5t5 t4t4 t3t3 The experimental time is divided into small time steps, Δt. Beginning at t 0 where the initial conditions of the experiment are specified, the metabolic model is used to predict the optimal flux. From the transport fluxes, the extracellular concentrations are calculated in a time-dependent fashion. These concentrations are then used as the initial conditions for the next time step.

A simplified core carbon metabolic network

Example 1- diauxie in two carbon sources C1 RpC1 TC2, O2 R5b

A simplified core carbon metabolic network

Example 1- diauxie in two carbon sources

Example 2 – Aerobic/Anaerobic diauxie Remove o 2 Re o 2 R5a R5b and Rres

Example of rFBA

Example 2 – Aerobic/Anaerobic diauxie

Example 3 – Growth on carbon and Amino acid with carbon in excess H R8a, O2 R5b

Example of rFBA

Example 3 – Growth on carbon and Amino acid with carbon in excess

Example 4 – Growth on carbon and Amino acid with amino acid in excess C2 used up Rpb R2a R7

Example 4 – Growth on carbon and Amino acid with amino acid in excess

Reference Markus W Covert, Christophe H. Schilling and Bernhard PalssonRegulation of Gene Expression in Flux Balance Models of Metabolism, J Theor Biol Nov 7;213(1): Flux balance analysis of biological systems: applications and challenges, karthik Raman and Nagasuma Chandra, Brief Bioinform (2009) 10 (4): doi: /bib/bbp Advances in flux balance analysis. K. Kauffman, P. Prakash, and J. Edwards. Current Opinion in Biotechnology 2003, 14: Analysis of optimality in natural and perturbed metabolic networks. D. Segre et al. PNAS 2002, 99: