Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -1-
Dynamic Flux Balance Analysis&
Dynamic Regulatory Flux Balance Analysis
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -2-
LEARNING OBJECTIVES
• Explain dynamic flux balance analysis.
• Describe the strengths and limitations of dynamic flux balance analysis.
• Explain dynamic regulatory flux balance analysis.
• Explain Boolean transcriptional regulation.
• Describe the difference between the regular constraint-based FBA models and the regulatory FBA model.
• Describe the strengths and limitations of regulatory dynamic flux balance analysis.
Each student should be able to:
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -3-
Lesson Outline
• Dynamic Flux Balance Analysis (dynamicFBA)Basic OperationMinimal Media ExamplesLimiting Media Examples
• Regulatory Flux Balance Analysis (dynamicRFBA)
Regulated E.coli Core ModelRegulatory GenesCatabolite Repression ExamplesGrowth on Non-glucose Carbon Sources
• Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -4-
Dynamic Flux Balance Analysis• FBA can be used to examine dynamic processes such as microbial
growth in batch cultures by combining FBA with an iterative approach based on a quasi-steady-state assumption (static optimization–based dynamic FBA).
• At each time step, FBA is used to predict growth, nutrient uptake and by-product secretion rates.
• These rates are then used to calculate biomass and nutrient concentrations in the culture at the end of the time step.
• The concentrations can, in turn, be used to calculate maximum uptake rates of nutrients for the next time step.
• Using this iterative procedure, dynamic FBA has allowed the simulation of batch experiments.
• This function will perform dynamic FBA to predict the outcomes of growth in batch culture conditions.
Becker, S. A., A. M. Feist, et al. (2007). "Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox." Nature protocols 2(3): 727-738.
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -5-
Dynamic Flux Balance Analysis• The substrate concentration (Sc ) (mmol/L) is determined from the substrate concentration predicted for the previous step
(Sco ) or from the initial substrate concentration if it is the first time step:
Sc= Sco
• The substrate concentration is scaled to define the amount of substrate available per unit of biomass per unit of time (mmol
gDW-1h-1):
where X is the current cell density and Xo is the cell density from the previous step.
• FBA is then used to calculate the substrate uptake ( Su ) and the growth rate (µ).
• Concentrations for the next time step are calculated from the standard differential equations:
• The output of dynamic FBA is two graphs: one showing the flux through the objective reaction over time, and one showing the flux through the exchange reactions for the selected metabolites over time.
cSSubstrate available
X t
to
dXX X X e
dt
(1 )tc uu c co o
dS SS X S S X e
dt
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -6-
Dynamic Flux Balance Analysis
• The dynamic flux balance analysis function is called as:
dynamicFBA(model, substrateRxns, initConcentrations, initBiomass, tStep, nSteps,plotRxns)
• The list of exchange reactions corresponding to the substrates that are initially in the media (e.g., glucose, ammonia, phosphate) is described in substrateRxns.
• The initConcentrations variable sets the initial concentrations of substrates in the substrateRxns vector.
• The initBiomass variable is needed to specify the initial amount of biomass in the simulation.
• The tStep variable sets the time step size interval (h) and the nSteps variable designates the maximum number of time steps for the analysis.
• The plotRxns variable is optional and contains the names of the exchange reactions for the metabolites whose time-dependent concentrations should be plotted graphically.
Varma, A. and B. O. Palsson (1994). "Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110." Applied and Environmental Microbiology 60(10): 3724-3731.
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -7-
Lesson Outline
• Dynamic Flux Balance Analysis (dynamicFBA)Basic OperationMinimal Media ExamplesLimiting Media Examples
• Regulatory Flux Balance Analysis (dynamicRFBA)
Regulated E.coli Core ModelRegulatory GenesCatabolite Repression ExamplesGrowth on Non-glucose Carbon Sources
• Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -8-
Aerobic, Glucose Substrate DynamicFBA Growth
% DynamicGrowth_Aerobic_JO1366.m
clear;
model=readCbModel('ecoli_iJO1366');
model = changeRxnBounds(model, {'EX_glc(e)','EX_o2(e)'},[-10 -30], 'l');
model = changeObjective(model,'Ec_biomass_iJO1366_core_53p95M');
% Set-up variables for dynamicFBA
substrateRxns = {'EX_glc(e)'};
initConcentrations = [10];
initBiomass = .01;
timeStep = .25; nSteps = 100;
plotRxns = {'EX_ac(e)','EX_acald(e)','EX_etoh(e)','EX_for(e)','EX_glc(e)','EX_lac-L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec] = ...
dynamicFBA(model,substrateRxns,initConcentrations, initBiomass, timeStep, nSteps, plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -9-
Low Aerobic, Glucose Substrate DynamicFBA Growth
% DynamicGrowth_Aerobic_JO1366.m
clear;
model=readCbModel('ecoli_iJO1366');
model = changeRxnBounds(model, {'EX_glc(e)','EX_o2(e)'},[-10 -5], 'l');
model = changeObjective(model,'Ec_biomass_iJO1366_core_53p95M');
% Set-up variables for dynamicFBA
substrateRxns = {'EX_glc(e)'};
initConcentrations = [10];
initBiomass = .01;
timeStep = .25; nSteps = 100;
plotRxns = {'EX_ac(e)','EX_acald(e)','EX_etoh(e)','EX_for(e)','EX_glc(e)','EX_lac-L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec] = ...
dynamicFBA(model,substrateRxns,initConcentrations, initBiomass, timeStep, nSteps, plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -10-
Substrate Maximum Growth Rate
Substrate Aerobic (hr-1) Anaerobic (hr-1)acetate 0.3893 0
acetaldehyde 0.6073 0
2-oxoglutarate 1.0982 0
ethanol 0.6996 0
D-fructose 1.7906 0.5163
fumarate 0.7865 0
D-glucose 1.7906 0.5163
L-glutamine 1.1636 0
L-glutamate 1.2425 0
D-lactate 0.7403 0
L-malate 0.7865 0
pyruvate 0.6221 0.0655
succinate 0.8401 0("What is flux balance analysis? - Supplementary
tutorial“)
The core E. coli model contains exchange reactions for 13 different organic compounds, each of which can be used as the sole carbon source under aerobic or anaerobic conditions.
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -11-
Anaerobic, Glucose Substrate DynamicFBA Growth
% DynamicGrowth_Aerobic_JO1366.m
clear;
model=readCbModel('ecoli_iJO1366');
model = changeRxnBounds(model, {'EX_glc(e)','EX_o2(e)'},[-10 0], 'l');
model = changeObjective(model,'Ec_biomass_iJO1366_core_53p95M');
% Set-up variables for dynamicFBA
substrateRxns = {'EX_glc(e)'};
initConcentrations = [10];
initBiomass = .01;
timeStep = .25; nSteps = 100;
plotRxns = {'EX_ac(e)','EX_acald(e)','EX_etoh(e)','EX_for(e)','EX_glc(e)','EX_lac-L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec] = ...
dynamicFBA(model,substrateRxns,initConcentrations, initBiomass, timeStep, nSteps, plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -12-
DynamicFBA: Ethanol Production with Glucose Substrate
% DynamicEthanolProduction_JO1366.m
clear;
model=readCbModel('ecoli_iJO1366');
model = changeRxnBounds(model, {'EX_glc(e)','EX_o2(e)'},[-10 -0], 'l');
model = changeObjective(model,'Ec_biomass_iJO1366_core_53p95M');
% Knockouts
model = changeRxnBounds(model, {'PFL','PPC','PPKr'},[-0 -0 -0], 'b');
% Set-up variables for dynamicFBA
substrateRxns = {'EX_glc(e)'};
initConcentrations = [20];
initBiomass = .01;
timeStep = .25; nSteps = 125;
plotRxns = {'EX_ac(e)','EX_acald(e)','EX_etoh(e)','EX_for(e)','EX_glc(e)','EX_lac-L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec] = ...
dynamicFBA(model,substrateRxns,initConcentrations, initBiomass, timeStep, nSteps, plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -13-
Lesson Outline
• Dynamic Flux Balance Analysis (dynamicFBA)Basic OperationMinimal Media ExamplesLimiting Media Examples
• Regulatory Flux Balance Analysis (dynamicRFBA)
Regulated E.coli Core ModelRegulatory GenesCatabolite Repression ExamplesGrowth on Non-glucose Carbon Sources
• Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -14-
% Dynamic_Growth_K12media.m
clear;
% Read model
model = readCbModel('ecoli_iJO1366');
model = changeObjective(model,'Ec_biomass_iJO1366_core_53p95M');
%Setting carbon source and oxygen
model = changeRxnBounds(model,'EX_glc(e)',-10,'l');
model = changeRxnBounds(model,'EX_o2(e)',-30,'l');
% Set uptake values for amino acids & Minerals;
...
% Set-up variables for dynamicFBA: % NOTE- substrate rxns and plot rxns need to be in the order that they appear in the model
initBiomass = .01;
timeStep = 0.5; nSteps = 100;
substrateRxns = {'EX_ala-L(e)','EX_arg-L(e)','EX_asn-L(e)','EX_asp-L(e)','EX_cl(e)','EX_cu2(e)','EX_cys-L(e)','EX_fe3(e)','EX_glc(e)','EX_gln-L(e)',
'EX_glu-L(e)','EX_gly(e)','EX_his-L(e)','EX_ile-L(e)','EX_k(e)','EX_leu-L(e)','EX_lys-L(e)','EX_met-L(e)','EX_mg2(e)','EX_mn2(e)','EX_mobd(e)','EX_na1(e)','EX_nh4(e)',
'EX_phe-L(e)','EX_pi(e)','EX_pro-L(e)','EX_ser-L(e)','EX_so4(e)','EX_thm(e)','EX_thr-L(e)','EX_tyr-L(e)','EX_val-L(e)','EX_zn2(e)'};
initConcentrations = [2.525535975,0.832376579,1.211020285,1.202103681,1.750214773,0.008010093,0.165070981,0.087865335,138.7655417,2.360749966,2.344865085, 1.798321567,
0.386722527,1.105435694,49.74894838,1.600975833,1.504890895,0.301588365,2.028562155,0.101058487,0.019031286,1.295164976,75.71742258, 0.726436225,70.08147994,
0.998870842,1.237034922,2.11641021,0.009421519,1.133310947,0.496716154,1.408450704,0.017388304];
plotRxns = {'EX_ac(e)','EX_acald(e)','EX_ala-L(e)','EX_arg-L(e)','EX_asn-L(e)','EX_asp-L(e)','EX_cl(e)','EX_cu2(e)','EX_cys-L(e)','EX_etoh(e)','EX_fe3(e)','EX_for(e)',
'EX_glc(e)','EX_gln-L(e)','EX_glu-L(e)','EX_gly(e)','EX_his-L(e)','EX_ile-L(e)','EX_k(e)','EX_lac-L(e)','EX_leu-L(e)','EX_lys-L(e)','EX_met-L(e)','EX_mg2(e)',
'EX_mn2(e)','EX_mobd(e)','EX_na1(e)','EX_nh4(e)','EX_phe-L(e)','EX_pi(e)','EX_pro-L(e)','EX_ser-L(e)','EX_so4(e)','EX_succ(e)','EX_thm(e)','EX_thr-L(e)',
'EX_tyr-L(e)','EX_val-L(e)','EX_zn2(e)'};
dynamicFBA(model,substrateRxns,initConcentrations, initBiomass, timeStep, nSteps, plotRxns);
%labeling
subplot(1,2,1); title('Growth rate'); xlabel('Time steps'); ylabel('g biomass/gDW*h');
subplot(1,2,2); title('Substrate Concentrations'); xlabel('Time steps'); ylabel('Concentrations (mmol/L)');
DynamicFBA: Growth on Glucose with limiting K12 Media
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -15-
Glucose
Phosphate
Ammonium
Potassium
Dynamic_Growth_K12media.m
Low Oxygen: EX_o2(e) = -30
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -16-
MatlabProperty
Editor
Under View Menu
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -17-
Glucose
Phosphate
Ammonium
Potassium
Dynamic_Growth_K12media.m Formate
Acetate
Low Oxygen: EX_o2(e) = -5
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -18-
Aerobic Biliverdin Production% DynamicBiliverdinProduction_JO1366.m
clear;
model=readCbModel('ecoli_iJO1366');
% Add heme oxygenase enzyme
...
model = changeRxnBounds(model, {'EX_glc(e)','EX_o2(e)'},[-10 -20], 'l');
model = changeRxnBounds(model,'EX_biliverdin(e)',1.2,'l');
model = changeRxnBounds(model,'HEMEOX',1.2,'b');
model = changeObjective(model,'Ec_biomass_iJO1366_core_53p95M');
% Set-up for one variables for dynamicFBA
substrateRxns = {'EX_glc(e)'};
initConcentrations = 20;
initBiomass = .01;
timeStep = .25; nSteps = 250;
plotRxns = {'EX_ac(e)','EX_biliverdin(e)','EX_etoh(e)','EX_for(e)','EX_glc(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec] = ...
dynamicFBA(model,substrateRxns,initConcentrations, initBiomass, timeStep, nSteps, plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -19-
Low-Aerobic Biliverdin Production% DynamicBiliverdinProduction_JO1366.m
clear;
model=readCbModel('ecoli_iJO1366');
% Add heme oxygenase enzyme
...
model = changeRxnBounds(model, {'EX_glc(e)','EX_o2(e)'},[-10 -10], 'l');
model = changeRxnBounds(model,'EX_biliverdin(e)',1.2,'l');
model = changeRxnBounds(model,'HEMEOX',1.2,'b');
model = changeObjective(model,'Ec_biomass_iJO1366_core_53p95M');
% Set-up for one variables for dynamicFBA
substrateRxns = {'EX_glc(e)'};
initConcentrations = 20;
initBiomass = .01;
timeStep = .25; nSteps = 250;
plotRxns = {'EX_ac(e)','EX_biliverdin(e)','EX_etoh(e)','EX_for(e)','EX_glc(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec] = ...
dynamicFBA(model,substrateRxns,initConcentrations, initBiomass, timeStep, nSteps, plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -20-
Aerobic PHB Production% DynamicPHBProduction_JO1366.m
clear;
model=readCbModel('ecoli_iJO1366');
% Add PHB Reactions
...
% Add demand reaction
model = addDemandReaction(model,'phb[c]');
model = changeRxnBounds(model,'PHBpoly',10,'l');
% Set key parameters
model = changeRxnBounds(model, {'EX_glc(e)','EX_o2(e)'},[-10 -20], 'l');
model = changeObjective(model,'Ec_biomass_iJO1366_core_53p95M');
% Set-up for one variables for dynamicFBA
substrateRxns = {'EX_glc(e)'};
initConcentrations = 20;
initBiomass = .01;
timeStep = .25; nSteps = 400;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_glc(e)','DM_phb[c]'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec] = ...
dynamicFBA(model,substrateRxns,initConcentrations, initBiomass, timeStep, nSteps, plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -21-
Aerobic Spider Silk Production% DynamicSpiderSilkProduction_JO1366.m
clear;
model=readCbModel('ecoli_iJO1366');
%Add FlYS3 reaction, change lower bound
model = addReaction(model,'FlYS3','120 ala-L[c] + 4 asp-L[c] + 522 gly[c]
+ 12 his-L[c] + ile-L[c] + lys-L[c] + 2 met-L[c] + 189 pro-L[c] + 111 ser-L[c]
+ thr-L[c] + 78 tyr-L[c] + 4476.3 atp[c] + 4476.3 h2o[c] -> flys3[c]
+ 4476.3 adp[c] + 4476.3 h[c] + 4476.3 pi[c]');
model = changeRxnBounds(model,'FlYS3',0.00336705,'b');
% Add demand reaction
model = addDemandReaction(model,'flys3[c]'); %'DM_flys3[c]'
% Set key parameters
model = changeRxnBounds(model, {'EX_glc(e)','EX_o2(e)'},[-10 -20], 'l');
model = changeObjective(model,'Ec_biomass_iJO1366_core_53p95M');
% Set-up for one variables for dynamicFBA
substrateRxns = {'EX_glc(e)'};
initConcentrations = 20;
initBiomass = .01;
timeStep = .25; nSteps = 400;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_glc(e)','DM_flys3[c]'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec] = ...
dynamicFBA(model,substrateRxns,initConcentrations, initBiomass, timeStep, nSteps, plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -22-
dynamicFBA Limitations
• The dynamicFBA tool cannot simulate the fed batch mode. There is no way to account for substrates that enter the medium via fed batch mode, so it can only show what becomes of the initial concentrations.
• The dynamicFBA was created to optimize the biomass reaction, so there is currently no way to maximize reactions for protein production, or to maximize both the growth rate and protein production at the same time.
• The predicted growth rate can reach values higher than possible because the calculated growth rate is constantly in the exponential phase.
• These aspects make the dynamicFBA tool more useful for qualitative rather than quantitative study.
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -23-
Dynamic FBA Review Questions
1. Explain the basic operation of dynamic flux balance analysis.
2. What are the key inputs required for dynamicFBA operation?
3. Why aren’t the fermentation products used as carbon sources after all the glucose has
been used in an anaerobic environment?
4. In an environment with a large number of plotted metabolites how can the Matlab Property
Editor be useful?
5. What are the strengths of dynamic FBA?
6. What are the weaknesses of dynamic FBA?
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -24-
Lesson Outline
• Dynamic Flux Balance Analysis (dynamicFBA)Basic OperationMinimal Media ExamplesLimiting Media Examples
• Regulatory Flux Balance Analysis (dynamicRFBA)
Regulated E.coli Core ModelRegulatory GenesCatabolite Repression ExamplesGrowth on Non-glucose Carbon Sources
• Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -25-
Transcriptional Regulatory Networks
• In addition to the metabolic reconstruction, the core E. coli model also contains a Boolean representation of part of the associated transcriptional regulatory network.
• In response to external and internal stimuli, in silica transcription factors can either activate or repress genes associated with metabolic reactions. This regulation improves the predictive fidelity of the metabolic model by imposing additional context dependent constraints on certain reactions.
• The transcriptional regulatory reconstruction consists of a set of Boolean rules that dictate whether a gene is either fully induced or fully repressed.
• If the genes associated with an enzyme or transport protein/complex are repressed, then in silica flux is set to zero for the corresponding reaction. The solution space of the network shrinks when these additional constraints are imposed. Reactions that are not used due to regulatory effects are thus restricted, so when using flux balance analysis, the optimal flux distribution will be consistent with known regulation.
• This optimal flux distribution may be different from the flux distribution of an unregulated model. In this case, the flux distribution of the unregulated model violated at least one regulatory constraint, making it biologically unrealistic.
• The use of computationally implemented Boolean rules in a genome scale model has been shown to lead to more accurate flux balance analysis predictionsReconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -26-
Transcriptional Regulatory Networks
E.coli metabolic core network E.coli core regulatory network
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -27-
Boolean Regulatory Networks
• A gene is considered to be induced when evaluation of the corresponding Boolean rule gives 'true'.
• In contrast, a gene is considered to be repressed, when evaluation of the corresponding Boolean rule gives 'false'.
• Boolean logic is used to evaluate each Boolean rule.
• Complex regulatory conditions will be represented with variables that represent a complex regulatory rule for a transcription factor that cannot be accurately represented with only one variable.
• By using Boolean logic, all rules in a regulatory network can be reduced to either 'true' or 'false', and ultimately this dictates whether each metabolic gene is induced or repressed.
• Not every gene in the metabolic network is controlled by the regulatory network, so the unregulated genes are assumed to always be active, and their fluxes are never constrained to zero.
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -28-
dynamicRFBA - perform dynamic rFBA simulation using the static optimization approach
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ... dynamicRFBA(model,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns,exclUptakeRxns)
model a regulatory COBRA model substrateRxns list of exchange reaction names for substrates initially in the media that may change (i.e. not h2o or co2) initConcentrations initial concentrations of substrates (in the same structure as substrateRxns) initBiomass initial biomass timeStep time step size nSteps maximum number of time steps plotRxns reactions to be plotted exclUptakeRxns list of uptake reactions whose substrate concentrations do not change (opt, default {'EX_co2(e)','EX_o2(e)','EX_h2o(e)','EX_h(e)'}) concentrationMatrix matrix of extracellular metabolite concentrations excRxnNames names of exchange reactions for the EC metabolites timeVec vector of time points biomassVec vector of biomass values drGenes vector of downregulated genes constrainedRxns vector of downregulated reactions states vector of regulatory network states
If no initial concentration is given for a substrate that has an open uptake in the model (i.e. model.lb < 0) the concentration is assumed to be high enough to not be limiting. If the uptake rate for a nutrient is calculated to exceed the maximum uptake rate for that nutrient specified in the model and the max uptake rate specified is > 0, the maximum uptake rate specified in the model is used instead of the calculated uptake rate.
Dynamic Regulatory Flux Balance Analysis
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -29-
Growth with Glucose Substrate in Low Aerobic Environment
% Glucose_Low_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-5, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_glc(e)'};
initConcentrations = [20];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fru(e)','EX_glc(e)',
'EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -30-
What is a Regulated Model?
A regulated model will include the following extra cells• A list of the regulatory genes
b4014, b4015, etc.• A list of the external metabolites that are
regulatory inputs (regulatoryInputs1)• A list of the internal reactions that are
regulatory changes (regulatoryInputs2)• A list of the regulatory rules
true Crp NOT ArcA NOT PdhR OR Fis CRPnoGLM AND (NOT ArcA) AND
DcuRSee core_regulatory_rules.xls
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -31-
bNum Gene Ruleb4401 ArcA NOT o2[e]b3357 Crp CRPnoGLCb4124 DcuR DcuSb4125 DcuS succ[e] OR fum[e] OR mal-L[e]b1187 FadR glc-D[e] OR (NOT ac[e])b3261 Fis Biomass_Ecoli_core_w_GAMb1334 Fnr NOT o2[e]b0080 FruR NOT surplusFDPb2980 GlcC ac[e]b3868 GlnG NOT nh4[e]b4018 IclR FadRb1594 Mlc NOT glc-D[e]b1988 Nac NRI_lowb0113 PdhR NOT surplusPYRb0399 PhoB PhoRb0400 PhoR NOT pi[e]
CRPnoGLC NOT glc-D[e]CRPnoGLM NOT (glc-D[e] OR mal-L[e] OR lac-D[e])NRI_hi NRI_lowNRI_low GlnGsurplusFDP ((NOT FBP) AND (NOT (TKT2 OR TALA OR PGI))) OR fru[e]surplusPYR (NOT (ME2 OR ME1)) AND (NOT (GLCpts OR PYK OR PFK OR LDH_D OR
SUCCt2_2))
Regulatory Genes in the
Regulated Core Model
core_regulatory_rules.xls
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -32-
Regulatory Inputs
Metabolite Inputs
o2[e]
glu-L[e]
glc-D[e]
nh4[e]
succ[e]
fum[e]
mal-L[e]
ac[e]
pi[e]
lac-D[e]
fru[e]
Reaction Inputs
FBP
TKT2
TALA
PGI
ME2
ME1
GLCpts
PYK
PFK
LDH_D
SUCCt2_2
Biomass_Ecoli_core_w_GAMcore_regulatory_rules.xls
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -33-
Regulatory Map of the Regulated
Core Model
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -34-
Lesson Outline
• Dynamic Flux Balance Analysis (dynamicFBA)Basic OperationMinimal Media ExamplesLimiting Media Examples
• Regulatory Flux Balance Analysis (dynamicRFBA)
Regulated E.coli Core ModelRegulatory GenesCatabolite Repression ExamplesGrowth on Non-glucose Carbon Sources
• Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -35-
ArcA
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• Low oxygen availability signals the
activation of the global regulator ArcA.• Represses the transporters for malate,
fumarase, lactate, and succinate.• Downregulates the glycoxylate cycle• Downregulates the energy producing
portion of the TCA cycle• Upregulates the fermentation pathway
for formate• Downregulates oxidative
phosphorylation
NOT o2[e]-> ArcA ArcA
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -36-
CRPnoGLC
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• The activity of the cAMP receptor
protein, Crp is modeled when no glucose
is present in the media using CRPnoGLM.• Upregulates the reductive pathway in
the TCA cycle (fumB) • Upregulates the formate and acetate
fermentation pathways • Upregulates the conversion from
glutamate to glutamine• Downregulates the conversion from
glutamine to glutamate
NOT glc-D[e] -> CRPnoGLC
fumB
CRPnoGLC
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -37-
DcuR & DcuS
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• Activated when malate, fumarate, or
succinate are present in the media.• DcuS and DcuR form a two component
histidine kinase system.• Upregulates the reductive pathway in the
TCA cycle (fumB) • Upregulates the transport pathways for
malate, fumarate, and succinate
(C4-dicarboxylate compounds)
DcuS
DcuR
fumB
succ[e] OR fum[e] OR mal-L[e] -> DcuS
DcuS -> DcuR
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -38-
FadR, IclR & GlcC
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• FadR and IclR are activated when either
glucose is present in the media or acetate
is not.• FadR and IclR form a two component
histidine kinase system.• Down regulates the glycoxylate cycle. • GlcC is activated when acetate is present
in the media• Upregulates the transport pathway for
D-lactate
FadR
glc-D[e] OR ( NOT ac[e] ) -> FadRFadR -> IclR
IclR
GlcC
ac[e] -> GlcC
glcB
aceB
glcA
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -39-
Fis
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• Fis is activated when the cell is in
exponential growth phase.• Down regulates the energy producing
portion of the TCA cycle• Up regulates the ethanol pathway • Up regulates SUCDi• When modeling the balanced steady state
growth typical of the exponential growth
phase, the state of Fis is always set to be
true.
Fis
Biomass Objectiv
e Functio
n
Biomass_Ecoli_core_w_GAM -> Fis
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -40-
FnR
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• FnR is activated in anaerobic conditions• Downregulates the energy producing
portion of the TCA cycle• Upregulates the reductive pathway in
the TCA cycle (fumB) • Upregulates the fermentation pathway
for formate and acetate• Downregulates oxidative
phosphorylation
FnR
fumB
NOT o2[e] -> FnR
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -41-
FruR &surplusFDP
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• When FruR is activated by low fructose
levels (surplusFDP = false)• FruR reverses the flow of carbon to
replenish glycolytic intermediates • Upregulates the glycoxylate cycle• Upregulates the Gluconeogenesis pathway • Downregulates ethanol and acetaldehyde
fermentation pathway• Downregulates the uptake of glucose
fumB
surplusFDP
FruR
The surplusFDP condition is met when fructose, fru [e] is present in the media or the reactions FBP and any of TKT2, TALA , or PGI have zero flux.
((NOT FBP) AND (NOT (TKT2 OR TALA OR PGI))) OR fru[e]
NOT surplusFDP -> FnR
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -42-
GlnG, Nac & NRI
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• GlnG is activated by a low extracellular
ammonium (nh4[e]) concentration and then
activates the low-level (fast) nitrogen
response, NRI_low. • NRI_low activates Nac which down
regulates the production of L-glutamate
from 2-Oxoglutarate.• NRI_low also activates NRI_hi (high-level,
slow response) which down regulates the
production of L-glutamate from L-glutamine
and 2-Oxoglutarate.• The total response is to reduce the
production of L-gluamate.
NOT nh4[e] -> GlnG
NRI_hi
NRI_low
GlnG
Nac
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -43-
Mlc
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• mlc is activated when no glucose is
present in the media.• When no glucose is present in the
media, the transporters for both
glucose and fructose are down
regulated.
glc-D [e] -> mlc
mlc
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -44-
PdhR &surplusPYR
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• The dual transcriptional regulator pdhR
down regulates pyruvate dehydrogenase,
PDH, when the pyruvate concentration in
the cell is low. • High pyruvate concentration is
represented by the variable surplusPYR,
which is true when there is no flux through
MEl or ME2, and no flux through either one
of GLGpts, PYK, PFK, LDH_D, or SUGGt2_2.
surplusPYR
PdhR
The surplusPYR condition is true when there is no flux through MEl or ME2, and no flux through either one of GLGpts, PYK, PFK, LDH_D,or SUGGt2_2.
(NOT (ME2 OR MEl)) AND (NOT (GLCpts OR PYK OR PFK OR LDH_D OR SUCCt2_2))
NOT surplusPYR -> PdhR
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -45-
PhoB & PhoR
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• Phosphorus uptake is regulated by the two-
component system phoR/ phoB. • phoR codes for a sensor kinase that is
phosphorylated when extracellular inorganic
phosphate is not present. • The phosphorylated enzyme is activated, and it
phosphorylates the transcriptional regulator
PhoB. • Phosphorylated PhoB then represses the
phosphate transporter, PIt2r. • The overall effect of phosphorus regulation is to
down regulate the phosphate transport reaction,
Plt2r, when no extracellular inorganic phosphate
is present.
PhoR
NOT pi[e] -> PhoR
PhoB
PhoR -> PhoB
NOT PhoR -> PIt2r
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -46-
CRPnoGLM
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• GLM stands for glucose, lactate or
malate• The activity of the cAMP receptor
protein, Crp is modeled when no
glucose, malate or lactate are
present in the media using
CRPnoGLM.• Upregulates the transport pathways
for fructose, malate, fumarate, and
succinate
CRPnoGLC
NOT ( glc-D[e] OR mal-L[e] OR lac-D[e] ) -> CRPnoGLM
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -47-
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -48-
Lesson Outline
• Dynamic Flux Balance Analysis (dynamicFBA)Basic OperationMinimal Media ExamplesLimiting Media Examples
• Regulatory Flux Balance Analysis (dynamicRFBA)
Regulated E.coli Core ModelRegulatory GenesCatabolite Repression ExamplesGrowth on Non-glucose Carbon Sources
• Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -49-
CataboliteRepression
• In media containing glucose and other
sugar substrates (lactate or malate), E. coli
preferentially catabolizes glucose until it is
depleted, and then switches to the other
substrates.• The activity of the cAMP receptor protein,
Crp is modeled using CRPnoGLM and
CRPnoGLC.• The CRPnoGLM regulatory condition is true
when either glucose (glc-D[e]) , malate
(mal-L[e]) or lactate (lac-D[e]) are not
present.• The CRPnoGLC regulatory condition is true
when glucose (glc-D[e]) is absent.• The transcription factor, mlc, is also
activated when glucose is not present.
No glucose: Fermentation pathways are upregulated
No GLM: glucose and fructose pathways are downregulated
No GLM: Upregulate malate, fumerate, succinate, and fructose transporters
No glucose: Change glutamate pathway
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -50-
Aerobic Glucose & Fructose% GlucoseFructose_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_fru(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_fru(e)','EX_glc(e)'};
initConcentrations = [5 10];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fru(e)','EX_glc(e)','EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -51-
Anoxic Growth“Low Oxygen”
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• Upregulates the fermentation
pathway for formate, acetate, and
ethanol• Upregulates the reductive pathway
in the TCA cycle • Downregulates the transporters for
malate, fumarase, lactate, and
succinate.• Downregulates the glycoxylate cycle• Downregulates the energy
producing portion of the TCA cycle• Downregulates oxidative
phosphorylation
Fnr (fumB)
Fnr
ArcA
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -52-
Low-Aerobic Glucose & Fructose% GlucoseFructose_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_fru(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-5, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_fru(e)','EX_glc(e)'};
initConcentrations = [5 10];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fru(e)','EX_glc(e)','EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -53-
Aerobic Glucose & Fumerate% GlucoseFumerateCatabolite_Repression.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_fum(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_glc(e)','EX_fum(e)'};
initConcentrations = [10 10];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fru(e)','EX_fum(e)','EX_glc(e)','EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -54-
Comparing dynamicFBA and dynamicRFBA
dynamicGlucoseFumerate_Core.m GlucoseFumerateCatabolite_Repression.m
Fumerate is not used until after glucose is goneGlucose and
fumerate start at the same time
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -55-
Low-Aerobic Glucose & Fumerate% GlucoseFumerateCatabolite_Repression.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_fum(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-5, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_glc(e)','EX_fum(e)'};
initConcentrations = [10 10];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fru(e)','EX_fum(e)','EX_glc(e)','EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -56-
Aerobic Glucose, Fructose & Lactate% GlucoseFructoseLactate_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_fru(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-8, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_lac_D(e)',-6, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_fru(e)','EX_glc(e)','EX_lac_D(e)'};
initConcentrations = [10 8 6];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fru(e)','EX_glc(e)','EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -57-
Low-Aerobic Glucose, Fructose & Lactate% GlucoseFructoseLactate_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_fru(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-8, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_lac_D(e)',-6, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-5, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_fru(e)','EX_glc(e)','EX_lac_D(e)'};
initConcentrations = [10 8 6];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fru(e)','EX_glc(e)','EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -58-
Lesson Outline
• Dynamic Flux Balance Analysis (dynamicFBA)Basic OperationMinimal Media ExamplesLimiting Media Examples
• Regulatory Flux Balance Analysis (dynamicRFBA)
Regulated E.coli Core ModelRegulatory GenesCatabolite Repression ExamplesGrowth on Non-glucose Carbon Sources
• Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -59-
Growth on Acetate
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• FadR and IclR are activated when either
glucose is present in the media or
acetate is not.• FadR and IclR form a two component
histidine kinase system.• Down regulates the glycoxylate cycle. • GlcC is activated when acetate is
present in the media• GlcC Upregulates the transport
pathway for D-lactate
FadR
glc-D[e] OR ( NOT ac[e] ) -> FadRFadR -> IclR
IclR
GlcC
ac[e] -> GlcC
glcB
aceB
glcA
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -60-
Aerobic Acetate & Lactate
% AcetateLactate_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-0, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_ac(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_lac_D(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_ac(e)','EX_lac_D(e)'};
initConcentrations = [10 8];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns =
{'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fru(e)','EX_glc(e)','EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -61-
Growth on C4-Dicarboxylate
Compounds
Ana TCA
OxP
PPP
Glyc
Ferm
N
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)
• Activated when malate, fumarate, or
succinate (C4-dicarboxylate compounds)
are present in the media.• DcuS and DcuR form a two component
histidine kinase system.• The presence of malate, fumarate, and
succinate upregulates the reductive
pathway in the TCA cycle (fumB) • Upregulates the transport pathways for
malate, fumarate, and succinate
DcuS
DcuR
fumB
succ[e] OR fum[e] OR mal-L[e] -> DcuS
DcuS -> DcuR
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -62-
Aerobic Fumerate
% Fumerate_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-0, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_fum(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_fum(e)'};
initConcentrations = [10];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fum(e)','EX_fru(e)','EX_glc(e)', ...
'EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -63-
Aerobic Succinate
% Succinate_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-0, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_succ(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_succ(e)'};
initConcentrations = [10];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fum(e)','EX_fru(e)','EX_glc(e)','EX_gln_L(e)', ...
'EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -64-
Aerobic Fumerate & Succinate
% FumerateSuccinate_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-0, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_fum(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_succ(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_fum(e)','EX_succ(e)'};
initConcentrations = [10 8];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fum(e)','EX_fru(e)','EX_glc(e)', ...
'EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -65-
Aerobic Pyruvate
% Pyruvate_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-0, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_pyr(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_pyr(e)'};
initConcentrations = [10];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fum(e)','EX_fru(e)','EX_glc(e)',...
'EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_pyr(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -66-
Anaerobic Pyruvate
% Pyruvate_Anaerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-0, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_pyr(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-5, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_pyr(e)'};
initConcentrations = [10];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fum(e)','EX_fru(e)','EX_glc(e)',...
'EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_pyr(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -67-
dynamicRFBA Limitations
• The dynamicRFBA tool cannot simulate the fed batch mode. There is no way to
account for substrates that enter the medium via fed batch mode, so it can
only show what becomes of the initial concentrations.
• The dynamicRFBA was created to optimize the biomass reaction, so there is
currently no way to maximize reactions for protein production, or to maximize
both the growth rate and protein production at the same time.
• The predicted growth rate can reach values higher than possible because the
calculated growth rate is constantly in the exponential phase.
• The dynamicFBA tool more useful for qualitative rather than quantitative
study.
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -68-
Dynamic Regulatory FBA Review Questions
1. What is a transcriptional regulatory network?
2. What is a boolean regulatory network?
3. What are the key inputs required for dynamic regulatory FBA operation?
4. What is a regulated model? How is it different from a normal FBA model?
5. What is a regulatory rule?
6. What is the difference between a regulatory gene and a gene that is controlled by regulation?
7. What are some of the differences between the output of dynamicFBA and dynamicRFBA?
8. What are the strengths of dynamic regulatory FBA?
9. What are the weaknesses of dynamic regulatory FBA?
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -69-
Lesson Outline
• Dynamic Flux Balance Analysis (dynamicFBA)Basic OperationMinimal Media ExamplesLimiting Media Examples
• Regulatory Flux Balance Analysis (dynamicRFBA)
Regulated E.coli Core ModelRegulatory GenesCatabolite Repression ExamplesGrowth on Non-glucose Carbon Sources
• Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -70-
• imc1010v2 Model• Regulatory genes have been added to the ijo904 model
• Based on dynamicRFBA
• Covert, M. W., E. M. Knight, et al. (2004). "Integrating high-throughput and computational data elucidates bacterial networks." Nature 429(6987): 92-96.
• SR-FBA• This method works by iteratively predicting a regulatory and metabolic steady state for short successive time intervals. For each time
interval, a regulatory state that is consistent with the metabolic steady state of the previous interval (and with the availability of nutrients in the changing growth media) is computed. Then, FBA is used to find a steady-state flux distribution that is consistent with the regulatory state of the current time interval.
• Shlomi, T., Y. Eisenberg, et al. (2007). "A genome-scale computational study of the interplay between transcriptional regulation and metabolism." Molecular Systems Biology 3: 101.
• Feuer• Combination of iAF1260 and iMC1010v2: The computation of a regulatory model combined with metabolic model was outlined by Covert
et al.
• Based on dynamicRFBA
• Feuer, R., K. Gottlieb, et al. (2012). "Model-based analysis of an adaptive evolution experiment with Escherichia coli in a pyruvate limited continuous culture with glycerol." EURASIP J Bioinform Syst Biol 2012(1): 14.
• Tiger• TIGER converts a series of generalized, Boolean or multilevel rules into a set of mixed integer inequalities. The package also includes
implementations of existing algorithms to integrate high-throughput expression data with genome-scale models of metabolism and transcriptional regulation.
• Jensen, P. A., K. A. Lutz, et al. (2011). "TIGER: Toolbox for integrating genome-scale metabolic models, expression data, and transcriptional regulatory networks." BMC systems biology 5: 147.
Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -71-
Lesson Outline
• Dynamic Flux Balance Analysis (dynamicFBA)Basic OperationMinimal Media ExamplesLimiting Media Examples
• Regulatory Flux Balance Analysis (dynamicRFBA)
Regulated E.coli Core ModelRegulatory GenesCatabolite Repression ExamplesGrowth on Non-glucose Carbon Sources
• Other Regulatory-based Model Approaches
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -72-
EXTRA SLIDES
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -73-
Aerobic Malate
% Malate_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-0, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_mal_L(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_mal_L(e)'};
initConcentrations = [10];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fum(e)','EX_fru(e)','EX_glc(e)', ...
'EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
X
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -74-
Aerobic Malate, Fumerate & Succinate
% MalateFumerateSuccinate_Aerobic.m
clear;
load('modelReg');
modelReg = changeRxnBounds(modelReg, 'EX_glc(e)',-0, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_mal_L(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_fum(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_succ(e)',-10, 'l');
modelReg = changeRxnBounds(modelReg, 'EX_o2(e)',-30, 'l');
[FBAsols,DRgenes,constrainedRxns,cycleStart,states]= optimizeRegModel(modelReg);
substrateRxns = {'EX_fum(e)','EX_mal_L(e)','EX_succ(e)'};
initConcentrations = [10 8 6];
initBiomass = .035;
timeStep = .25;
nSteps = 100;
plotRxns = {'EX_ac(e)','EX_etoh(e)','EX_for(e)','EX_fum(e)','EX_fru(e)','EX_glc(e)',...
'EX_gln_L(e)','EX_glu_L(e)','EX_lac_D(e)','EX_mal_L(e)','EX_succ(e)'};
[concentrationMatrix,excRxnNames,timeVec,biomassVec,drGenes,constrainedRxns,states] = ...
dynamicRFBA(modelReg,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns);
X
Lesson: dFBA & dRFBABIE 5500/6500Utah State University
H. Scott Hinton, 2015Constraint-based Metabolic Reconstructions & Analysis -75-
Nac, NRI_low, & NRI_hi
• Regulation of nitrogen metabolism in
the E.coli core model.
• Extracellular ammonium, nh4[e]:
activates the low and high level
nitrogen responses, NRI_low and NRI_
hi, which, along with extracellular
glutamate, glu-L[e], inhibit the
reactions glutamate dehydrogenase,
GLUDy: and glutamate synthase,
GLUSy. • Glutaminase, GLUN, is also activated
by extracellular ammonium. • Extracellular glucose, glc-D[e],
through CRPnoGLC, inhibits glutamine
synthetase, GLNS, and glutaminase,
GLUN.
Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010)