Transcript Regulation of Gene Expression in Flux Balance Models of Metabolism

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 ai or bi 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
Limitations
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.
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)
vrxn(t) = 0 , when E is not present
at timepoint t (t1<=t<=t2)
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
The experimental time is divided into small time steps, Δt.
Beginning at t0 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.
t0 t1 t2 t3 t 4 t5
A simplified core carbon metabolic network
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
o2
o
Re 2
R5b and Rres
R5a
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
R7
R2a
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.
2001 Nov 7;213(1):73-88.
• Flux balance analysis of biological systems: applications and challenges,
karthik Raman and Nagasuma Chandra, Brief Bioinform (2009) 10 (4):
435-449. doi: 10.1093/bib/bbp011
• http://cmt.hkbu.edu.hk/colloquium/Flux%20Balance%20Analysis.ppt
• Advances in flux balance analysis. K. Kauffman, P. Prakash, and J. Edwards.
Current Opinion in Biotechnology 2003, 14:4910496
• Analysis of optimality in natural and perturbed metabolic networks. D.
Segre et al. PNAS 2002, 99:1511-15117