Transcript Document

Summary of the paper:
Metabolic Flux Balance Analysis and
the in Silico Analysis of Escherichia
coli K-12 Gene Deletions
by Jeremy S. Edwards1,2 and Bernhard O. Palsson1
1Departament of Bioengineering, University of California
2Harvard Medical School Department of Genetics
Catalina Alupoaei
OBJECTIVE
• To analyze the integrated function of the metabolic pathways
with the goal of the development of dynamic models for the
complete simulations of cellular metabolism
• To computationally examine the condition dependent optimal
metabolic pathway utilization using E. coli in silico
• To show that the flux balance analysis can be used to analyze
and interpret the metabolic behavior of wild-type and mutant
E.coli strains.
INTRODUCTION
•The integrated function of biological systems involves many
complex interactions among the components within the cell
•The properties of complex biological process cannot be analyzed
or predicted on a description of the individual components, and
integrated systems based approaches must be applied
•The engineering approach to analyses and design of complex
systems is to have a mathematical or computer model
FLUX BALANCE ANALYSIS (FBA) MODEL
• All biological processes are subject to physico-chemical
constrains (mass balance, osmotic pressure, etc)
•Flux balance analysis analyze the metabolic capabilities of a
cellular system based on the metabolic (reaction) network and
mass balance constraints
•The mass balance constrains can be assigned on a genome
scale for a number of organisms
•The mass balance constraints in a metabolic network can be
represented mathematically by a matrix equation:
S v  0
S = m x n stoichiometric matrix
m = number of metabolites
n = number of reactions in the network
v = vector of all fluxes in the metabolic network (internal, transport, growth)
ADDITIONAL CONSTRAINTS
Used to enforce the reversibility of each metabolic reaction and the
maximal flux in the transport reactions.
 On the magnitude of individual metabolic fluxes:
i  i  i
 The transport flux for some metabolites was unrestrained
 i   ;
 i  ;
 The transport flux for some metabolites was constrained:
0 i i
max
The transport flux was constrained to zero - no metabolite
FEASIBLE SET – OBJECTIVE FUNCTION
• The intersection of the nullspace and the region defined by the
linear inequalities define a region in flux space – feasible set
• The feasible set define the capabilities of the metabolic network
subject to the imposed cellular constraints
•The feasible point can be further reduced by imposing additional
constraints (kinetic or gene regulatory constraints)
• A particular metabolic flux distribution within the feasible set
was found using the linear programming (LP) – identified a
solution that minimize a metabolic objective function, Z:
Minimize  Z ,
Z   ci vi
c = the unit vector in the direction of the growth flux
GROWTH FLUX
• Was defined in terms of the biosynthetic requirements:
v growth
 d m  X m     Biomass
All _ m
dm = biomass composition of metabolite Xm
The growth flux was modeled as a single reaction that converts
all the biosynthetic precursors into biomass.
FLUX BALANCE ANALYSIS - EXAMPLE
A flux balance was written for each metabolite (Xi) within the
metabolic network to yield the dynamic mass balance equation for
each metabolite in the network
The rate of accumulation of Xi was equated to its net rate of
production yielding the dynamic mass balance for Xi:
dX
dt
i
 V syn  V deg  V use  V trans
Vsyn, Vdeg, Vtrans, Vuse = metabolic fluxes
Vsyn, Vdeg = refer to the synthesis and degradation reactions of
metabolite Xi
Vtrans = correspond to exchange fluxes that bring metabolism into or
out of the system boundary
Vuse = refers to the growth and maintenance requirements
FLUX BALANCE ANALYSIS EXAMPLE CONTINUE
or
dX
i
dt
 V syn  V deg  V use  b i
Xi = external metabolite
bi = the net transport of Xi into the defined metabolic system
For the E. coli metabolic network all the transient material balances
were represented by a single matrix equation,
dX
 S v  b
dt
X = m dimensional vector defining the quantity of metabolites in a cell
v = vector of n metabolic fluxes
S = m x n stoichiometric matrix
b = vector of metabolic exchange fluxes
FLUX BALANCE ANALYSIS - EXAMPLE CONTINUE
The time constants characterizing metabolic transients are very rapid
compared to the time constants of cell growth and process dynamics,
therefore, the transient mass balances were simplified to only
consider the steady state behavior.
S v  I b  0
I = identity matrix
U = matrix
br = vector
S  v  U  br  0
S
reactions
S use
 v reactions
U  v use

 b r

0


S  S reactions S use U
'

 v reactions
'
v   v use

 b r
S v  0
'
'
Sreaction = metabolic reactions within the system boundary
Suse = biomasses and maintenance requirement fluxes
U = allow certain metabolites to be transported into and out of the system




PHENOTYPE PHASE PLANE (PhPP) ANALYSIS
• Is a two-dimensional projection of the feasible set
• Two parameters that describes the growth conditions were
defined as the two axes of the two dimensional space
• The optimal flux distribution was calculated by solving the
LP problem while adjusting the exchange flux constraints
• A finite number of qualitatively different patterns of
metabolic pathway utilizations were identified and the
regions were demarcated by lines
• Line of optimality - one demarcation line – represents the
optimal relation between exchange fluxes defined on the
axes of the PhPP
ALTERATION of the GENOTYPE
• FBA and E. coli in silico were used to examine the systemic
effects of in silico gene deletions
• To simulate a gene deletion, all metabolic reactions catalyzed by
a given gene product were simultaneously constrained to zero
• The optimal metabolic flux distribution for the generation of
biomass was calculated for each in silico deletion strain
• The in silico gene deletion analysis was performed with the
transport flux constraints defined by the wild-type PhPP
RESULTS
Gene deletions:
• The growth characteristics of all in silico gene deletions strains
were examined at each point from the PhPP
• The gene were categorized as: essential, critical or non-essential
• The effects of the in silico gene deletions were phase-dependent,
optimal growth phenotypes for each growth condition were identified
• The optimal utilization of the metabolic pathways was dependent on
the specific transport flux constraints
• Metabolic phenotypes based on the optimal biomass yield and
biosynthetic production capabilities were computationally analyzed
DISCUSSION
• The study presented is an example of the rapidly growing field
of in silico biology
• An in silico representation of E. coli was utilized to study the
condition dependent phenotype of E. coli and the central
metabolism gene deletion strains
• It was shown that a computational analysis on the metabolic
behavior can provide valuable insight into cellular metabolism
• FBA can be defined as a metabolic constraining approach
• Metabolic functions based on most reliable information were
constrained
• The E. coli FBA results, with maximal growth rate as the
objective function are consistent with experimental data
CONCLUSIONS
• The in silico representation of E. coli was utilized to study the
condition dependent phenotype of E. coli and the central
metabolism gene deletion strains
• It was shown that a computational analysis on the metabolic
behavior can provide valuable insight into cellular metabolism
• The in silico study builds on the ability to define metabolic
genotypes in bacteria and mathematical methods to analyze the
possible and optimal phenotypes that they can express
• This approach enables the analysis or study of mutant strains
and their metabolic pathways