Pathway Analysis using Cybernetic Modeling Approach

1
Pathway Analysis using Cybernetic Modeling
Approach

• Dae Ryook Yang
• Process System Engineering Laboratory
• Department of Chemical Biological Engineering.
• Korea University

2
Contents

• Introduction
• Metabolism
• Metabolic Engineering
• Cybernetic Modeling
• Case Study
• Cephalosporin C Fermentation Process
• Simultaneous Saccharification and Fermentation

3

• Introduction
• Systems Approach
• Metabolic Engineering
• Cybernetic Modeling

4
Systems (Systemic) Approach

• Systems approaches are to study dynamic processes
  within and between cells.
• Nature, 402 (1999) c47
• The best test of our understanding of cells
  will be to make quantitative predictions about
  their behavior and test them. This will require
  detailed simulations of the biochemical processes
  taking place within cells.
• We need to develop simplifying, higher-level
  models and find general principles that will
  allow us to grasp and manipulate the functions of
  biochemical networks.

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Observation vs. Analysis Systems Approach
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What is Metabolism?

• The sum of all the chemical transformations
  taking place in a cell or organism, occurs
  through a series of enzyme-catalyzed reactions
  that constitute metabolic pathways.

Principles of biochemistry.3rd
7
What is Metabolic Engineering? (1)

• Metabolic engineering is about the analysis and
  modification of metabolic pathways.
• Metabolic networks consist of reactions
  transforming molecules of one type into molecules
  of another type.
• In modeling terms, the concentration of the
  molecules and their rates of change are of
  special interest.

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What is Metabolic Engineering? (2)

• The field of metabolic engineering
• Methods to model complex metabolic pathways
• Techniques to manipulate these pathways for a
  desired metabolic outcome.
• Goals of Metabolic Engineering
• To better understand and model cellular
  metabolism in a quantitative manner.
• To generate new and/or improved metabolic
  outcomes using biochemical and genetic
  engineering techniques.

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Objectives of Metabolic Engineering

• Metabolic Engineering
• Heterologous protein production
• Extension of substrate range
• Pathway leading to new products
• Pathways for degradation of xenobiotics
• Engineering cellular physiology for process
  improvement
• Elimination or reduction of by-product formation
• Improvement of yield or productivity

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Sample Metabolic Pathway

• DAHP production from glucose
• Condensation of PEP and E4P By E. coli.
• DAHP 3-deoxy-D-arabino-heptulosonate 7-phosphate
• PEP phospoenolpyruvate
• E4P erythrose-4-P
• PTS phospotransferase system
• Deletion of both pykA and pykF resulted in a
  three-fold increase in DAHP yield.
• Deletion of tktA resulted in a four-fold increase
  in DAHP yield.
• PTS mutant with deletion of both pykA and pykF
  resulted in a ten-fold increase in DAHP yield

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Metabolic Pathway of Glycolysis (1)

• Reaction network of Glycolysis in Saccharomyces
  cerevisiae

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Metabolic Pathway of Glycolysis (2)
Time courses of concentrations for the running
model presented.
13
Cycle of metabolic engineering
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Metabolic modeling tools and techniques
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Cybernetic Framework

• Kompala et al. (1986) and etc.
• Predicting complex nutrient uptake and growth
  profile
• Purely first principle perspective
• Varner and Ramkrishna (1999)
• Grey box approach
• A degree of biological insight topological
  pathway structure

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What is Cybernetic Modeling? (1)

• Cybernetic modeling is based on the hypothesis
  that microorganisms optimize utilization of
  available substrates to maximize their growth
  rate all times.
• The cybernetic perspective of microbial growth by
  Ramkrishna (1982) was reported that the metabolic
  regulation of biochemical process could be
  controlled by enzyme synthesis (u) and enzyme
  activity (v).

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What is Cybernetic modeling? (2)

• The cybernetic model developed by Kompala (1986)
  described the dynamic associated with diauxic
  growth, or the sequential utilization of
  substrates with the preferential utilization of
  the substrate supporting the higher growth rate.

Four elementary pathways derived by Straight and
Ramkrishna. Journal of Biotechnology, 71 (1999)
67
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What is Cybernetic modeling? (3)

• It replaces the detailed modeling of regulatory
  processes with cybernetic variables ui and vi
  presenting the optimal strategies for enzyme
  synthesis and activity, respectively.

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What is Cybernetic modeling? (4)

• Various Enzyme Inhibition Kinetics

(a) Competitive inhibition
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Diauxie Growth Model

• Bacterial cells
• Growth on multiple substrates
• Sequential utilization in batch reactor

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Monod Model Vs. Cybernetic Model

• Monod model cannot describe the diauxic growth
  efficiently.
• Multiple Monod models or its variation have
  limited extrapolation capability.

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Postulations of Cybernetic Model

• A Metabolic Network has physiological objectives
• The expression and activity of the enzymes that
  catalyze network functionality are regulated by
  the cybernetic control variable which steer
  network operation toward the physiological
  objectives in an optimal manner
• The control of a biological process can be
  decomposed into a hierarchy of elementary
  components
• Each elementary component steers toward its
  physiological objectives in an optimal manner
• The cells utilize the limited pool of resources
  in an optimal manner

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Characteristic of the Cybernetic Model

• Captures cellular regulatory mechanisms
• Sufficiently accurate description of average
  cell in a batch, fed-batch or continuous culture
• Diauxic growth
• Mammalian cultures
• Storage synthesis
• Model parameters have physical meaning

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MODEL FORMULATION

• Elementary pathway
• Substitutable competition
• Convergent
• Linear
• Complementary competition
• Divergent
• Cyclic

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Elementary convergent pathway

• Metabolite degradation rate
• Enzyme induction
• Intermediate consumption
• Notations
• Rk specific material flux (constant), pj
  metabolite level
• ej enzyme level, max. specific
  enzyme level
• Kj saturation constant, rate
  constants

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• Objective of elementary convergent pathway
• Maximize the production of the intermediate pn1
  subject to the constraint on resource available
  for enzyme expression
• The optimality condition
• The resource allocation for enzyme production
  should be

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• The activity of the key enzyme should be
• (cybernetic proportional law)
• Modification of the rate of reaction and enzyme
  synthesis
• Synthesis of pn1 via ej
• Enzyme expression rate
• Complete mass balance

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Elementary complementary pathway

• Metabolite degradation rate
• Enzyme induction
• Intermediate consumption

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• Objective of elementary divergent pathway
• Maximize the mathematical product of the branch
  point metabolites subject to the constraint on
  resource available for the expression of branch
  point key enzyme
• The optimality condition
• The resource allocation for enzyme production
  should be

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• The activity of the key enzyme should be
• (cybernetic proportional law)
• Modification of the rate of reaction and enzyme
  synthesis
• Synthesis of p1j via e0j
• Enzyme expression rate
• Complete mass balance

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Elementary linear pathway

• Objective of elementary linear pathway
• Maximize the production of the intermediate pn
  subject to the constraint on resource available
  for enzyme expression
• The optimality condition
• The resource allocation for enzyme production
  should be

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Elementary cyclic pathway

• Objective of elementary divergent pathway
• Maximize the mathematical product of the branch
  point metabolites subject to the constraint on
  resource available for the expression of branch
  point key enzyme
• The optimality condition
• The resource allocation for enzyme production
  should be

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Overlapping pathway

• Let an arbitrary metabolic pathway be composed of
  n key enzymes.
• Suppose jth key enzyme can be written with
  respect to q elementary pathways.
• The cybernetic variable that controls the
  expression of ej is given by

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Genetic Alteration

• If there are deletions of existing pathway
  enzymes, then set the corresponding cybernetic
  variables to zero
• If there are genetic alteration of the gene which
  encodes for a key enzyme, use fractional
  cybernetic variable for activity

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Example I

• Hybrid overlapping network can be decomposed into
  two elementary pathway

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• Overall cybernetic variables

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• Complete model

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• Steady-state behavior of continuous culture
• If , then e0 is seen as attractive
  resource investment and e1a levels are driven to
  zero. There is no bifurcation
• If , then the bifurcation occurs.
  Depending on the operating condition, one is that
  e0 level can be driven to zero because e1a
  represents better resource investment, the other
  is that p2 can be produced via both routes.

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Example II

• Decomposition
• Cybernetic variables
• Yi yield coefficient for i-th reaction

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• Complete Model (continuous)

Intermediate level, mass per unit cell mass
Dilution of intracellular intermediate pools due
to growth
Depletion due to biomass formation
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Conclusions

• Cybernetic modeling framework which can describe
  complex behavior of microbial growth are
  presented.
• Useful tool for abstraction of metabolic pathways
• Cybernetic model can be used for batch, fed-batch
  and continuous cultures.
• The expression and activity of the key enzymes
  are rationally modulated as a result of network
  control action in the face of generic alteration.

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• Case Study
• 1. Cephalosporin C Fermentation Process
• 2. Simultaneous Saccharification and Fermentation

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Case1. CPC Production Process

• Production of antibiotic by the fungus
  Cephalosporium acremonium
• Diauxic growth on multiple substrates in a batch
  reactor
• Growth phase vs. production phase
• Morphological differentiation
• Repression of differentiation and production by
  the preferred substrate

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Typical Morphological Changesof Cephalosporium
Acremonium
2 days
6 days
4 days
Xs Swollen hyphal fragments
Xa Arthrospores
Xh filamentous Hyphae
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Schematic of Metabolic Pathway
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Two Cybernetic Variables

• Cybernetic variable controlling enzyme synthesis
• Cybernetic variable controlling enzyme activity
• Actual rate of enzyme synthesis
• Actual rate of biomass production (growth)

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Rate Equations in the Process

• Growth rates of the cells
• Synthesis rates of the key enzymes
• Differentiation rates of the cells

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Governing Equations

• Material balance on the biomasses

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Governing Equations (contd.)

• Material balance on the substrate utilization
• Material balance on the CPC production

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Experimental Data (I) Matsumura et al. (1978)
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Simulation Results (I)
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Experimental Data (II) Chu Constantinides (1988)
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Simulation Results (II)
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Experimental Data (III) Araujo et al. (1996)
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Simulation Results (III)
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Experimental Data (IV) Cruz et al. (1999)
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Simulation Results (IV)
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Conclusions of Case1

• A mathematical model of the cybernetic viewpoints
  was developed to describe the production process
  of cephalosporin C (CPC).
• The proposed model was tested on the experimental
  data on the literature.
• The model can adequately describe the
  morphological differentiation of cells, the
  sequential utilization of carbon sources and the
  production of cephalosporin C.
• A modeling of the self-inhibitory effect of CPC
  on its production mechanism was well described
  the production phase of CPC.

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Case 2. Simultaneous Saccharification and
Fermentation

• consists of the enzymatic saccharification of
  cellulose and fermentation of sugars to ethanol
  by yeast performed in the same vessel and time.
• reduces the product inhibition on cellulase and
  ß-glucosidase activities by sugars.
• offers a high ethanol production compared with
  separate saccharification and fermentation.

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Schematic of SSF Pathway (1)

• Comparison of Previous Researches

• ? The cellulose content of the treated oak wood
  chips was about 54.5 on a dry weight basis. 3
• ? ? noncompetitive inhibition of cellulase by
  cellobiose (B), glucose (G), and ethanol (E). 1
• the action of ß-glucosidase is inhibited
  by its substrate, cellobiose, and also
  competitively inhibited by its product, glucose.
  1
• The model equations include
  noncompetitive inhibition of cellulase by
  cellobiose, glucose, and ethanol and of
  ß-glucosidase by ethanol, competitive inhibition
  of ß-glucosidase by glucose, as well as substrate
  inhibition by cellobiose. 2
• noncompetitive inhibition of cellulase by
  cellulose and glucose, noncompetitive inhibition
  of ß-glucosidase by glucose, substrate inhibition
  by cellobiose, and enzyme deactivation. 3

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Schematic of SSF Pathway (2)

• ? A Monod kinetic expression that includes
  substrate and product inhibition is used to
  account for the dependence of microbial growth on
  glucose concentration. 1
• ? The ethanol formation rate consists of a
  growth-associated and a nongrowth-associate term,
  and also depends directly on the concentration of
  glucose (G). 1
• ? Cellulase and ß-glucosidase also adsorb,
  although irreversibly, to lignin. 1
• A linear dependency of reduction in the
  maximum specific growth rate in the presence of
  inhibitory compounds and the maximum specific
  rate in the presence of inhibitory compounds
  relative to the SEW concentration (W) was
  assumed. 3

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Governing Equations

• Model Equations

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• Methods
• Simulation processes were saccharification,
  fermentation, and SSF.
• The experimental data of saccharification,
  fermentation, and SSF and associated methods have
  been reported previously.
• Simulation equations for saccharification,
  fermentation, and SSF were solved via non-stiff
  differential equations, medium order method
  (fourth-order Runge-Kutta algorithm) and the
  multidimensional unconstrained nonlinear
  minimization (Nelder-Mead) in MATLAB.

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Simulation Results (I)

• Saccharification with 80g/l a-cellulose,
  ball-milled SEW and untreated SEW
• Sum of Square-Error 20.610, 16.180, 6.542 vs.
  5.731, 4.712, 2.986

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Simulation Results (II)

• Fermentation with 80g/l ball-milled SEW
• Sum of Square-Error 8.660, 22.716, 4.110 vs.
  1.406, 1.190, 1.833

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Simulation Results (III)

• SSF with 80g/l, 100g/l and 120g/l ball-milled SEW
• Sum of Square-Error 3.586, 6.672, 3.143 vs.
  2.260, 1.905, 1.340

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Simulation Results (IV)

• SSF with 80g/l, 100g/l and 120g/l ball-milled SEW

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Conclusions of Case2

• The proposed model with cybernetic variables for
  SSF was established by taking into account
  glucose and cellobiose fermenting yeast,
  Brettanomyces custersii and effects of SEW,
  cellulose, cellobiose, glucose and ethanol as
  inhibitory compounds.
• The model was capable of representing ethanol
  production more accurately, compared with
  previous models.

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Thank you!Are there any questions?
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Metabolism

• The metabolism
• is the chemical engine that drives the living
  process.
• The organisms
• process and convert thousands of organic compound
  into the various biomolecules necessary to
  support their existence by utilizing enzymatic
  reactions and transport processes.
• direct the distribution and processing of
  metabolites throughout its extensive map of
  pathways in switchboard-like fashion.

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• The microorganisms
• try to survive despite the changes in
  environmental conditions
• The cellular engineers
• attempt to manipulate and exploit these pathways
  to direct the microorganisms to produce favorable
  materials for human.
• utilize the technique to delete, create, and
  modify the pathways of the microorganisms.
• need to understand how the cell meets its
  metabolic objectives through the analysis of its
  metabolic pathways.

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Metabolic Engineering

• Definition
• The directed improvement of product formation or
  cellular properties through the modification of
  specific biochemical reactions or the
  introduction of new ones with the use of
  recombinant DNA technology
• Via amplifying, inhibiting, deleting,
  transferring, and deregulating the corresponding
  genes and enzymes.
• The essence of metabolic engineering
• The combination of analytical methods to quantify
  fluxes and their control with molecular
  biological techniques to implement suggested
  genetic modifications

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Mathematical Models of Metabolic pathway

• Stoichiometric models and flux analysis
• Descriptive snapshot of physiology
• Flux balancing analysis stoichiometric model
• NMR and GC/MS technique with isotope labeling
• Valid only in steady state situations
• Dynamic mathematical model
• Kinetic modeling including metabolic regulation
  and control
• Metabolic Control Analysis (MCA) can describe the
  degree of control exercised on each pathway flux

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• Metabolic Pathway Analysis
• Identification of the metabolic network structure
  (or pathway topology)
• From the biochemistry literature
• Enzyme analysis and isotope labeling pattern
• Quantification of the fluxes through the braches
  of the metabolic network
• Metabolite balancing
• Identification of the control structures within
  the metabolic network
• Rapid quenching of the cellular metabolism
• Metabolic Control Analysis

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• Metabolic Control Analysis (MCA)
• Kascer and Burns (1973)
• Not a modeling framework
• Systematic computation of network sensitivities
  to single perturbations in the environmental or
  network parameters
• Flux control coeff. a measure of how a change in
  the concentration of enzyme affects the
  steady-state flux through an enzyme (degree of
  control exerted by an enzyme on this steady-state
  flux)
• Concentration control coeff. a measure of the
  degree of control exerted by an enzyme on
  steady-state concentration of a metabolite
• Elasticity coeff. a measure of how a reaction
  rate will respond to variations in the metabolite
  concentration
• The sensitivity coefficients depend on the
  conditions of the data used for analysis
• In general, valid only locally

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Introduction to Cybernetic Modeling

• Modeling Approach
• White box model
• based on first principle
• Neglect unnecessary physical detail
• Deep fundamental understanding is required
• Metabolic intermediates and pathways are crucial
• Black box model
• Force mathematical model to obey experimental
  observations
• Locally accurate but not globally
• Grey box model

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Metabolic networks

• Through millions of years of evolutionary
  pressure, metabolic network have evolved the
  ability to respond to changes in environment of
  the microorganism ensuring survival.
• The developed flexibility and adaptive potential
  hamper human attempts to redirect the metabolic
  flux.
• More emphasis is given to the entire system of
  reactions rather than isolated individual
  reaction
• The key distinction between conventional chemical
  kinetics and metabolic network is the influence
  of regulation and control.

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Continuous Culture

• Simultaneous and preferential utilization
• Multiple physiological states observed

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Dynamic Mass Balance

• For Substrates

Dilution rate, D
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• For biomass constituents