MODELLING, SIMULATION AND
OPTIMIZATION OF BIOPROCESSES
BT401
Dr.R.Satish Babu
CONTENTS
• Introduction
• Modelling Principles & Fundamentals of
Modelling
• Modeling approaches
• Neural network modeling
• Simulation using Berkely Madonna Program
• Optimization
What is “Model”
Model
• Three-dimensional representation of a person
or thing or of a proposed structure, typically
on a smaller scale than the original
• synonyms:replicareplica, copyreplica, copy, re
presentationreplica, copy, representation, mo
ck-upreplica, copy, representation, mock-up, d
ummyreplica, copy, representation, mock-up,
dummy, imitationreplica, copy, representation
, mock-up, dummy, imitation, doublereplica, c
opy, representation, mock-up, dummy, imitati
Model?
• A thing used as an example to follow or
imitate
• synonyms:prototypeprototype, stereotypepro
totype, stereotype, archetype,
• versionversion, style.
What is a Scientific Model?
• A scientific model is a representation of a
particular phenomenon in the world using
something else to represent it, making it
easier to understand
• A scientific model could be a diagram or
picture, a physical model like an aircraft
model, a computer program, or set of complex
mathematics that describes a situation.
Model?
• Graphical / Physical (Visual Models),
mathematical (symbolic)representation or
simplified version of a concept
• Visual models are things like flowcharts,
pictures, and diagrams that help us educate
each other
Use?
• The goal is to make the particular thing you're
modeling easier to understand.
• When we do that, we're able to use it to
predict what will happen in the future.
• For example, predicting what will happen as
our climate changes would be easy if we could
make a fully accurate model of the
atmosphere.
• A representation of a system that allows for
investigation of the properties of the system
and, in some cases, prediction of future.
• Scientific models are often mathematical
models, where you use math to describe a
particular phenomenon.
• For example, M-M model
Use of models in Bioprocess?
• Use of Models for Understanding, Design and
Optimization of Bioreactors
Use of models in Bioprocess?
Mechanistic models
Fig.3 Classification of models as mechanistic and nonmechanistic
Different perspectives for cell population kinetic representation (Adapted from
Bailley and Ollis,1986)
Integrative dynamic model
Integrative simultaneous saccharification and fermentation (SSF) model. The
SSF model is a combination of (1) enzyme hydrolysis model describing the
kinetics of enzymatic hydrolysis of lignocellulosic biomass and (2) integrative
dynamic model describing cell growth and fermentation kinetics (adapted from
Unrean et al., submitted)
Why Bioprocess is so complex?
Fig.2 Certain important parameters, phenomena, and interactions which determine
cell population kinetics (Adapted from Bailley and Ollis,1986)
Nonlinear Models
Approaches for model development
Empirical Approach
• Measure productivity for all combinations of
reactor operating conditions, and make
correlations.
• - Advantage: Little thought is necessary
• - Disadvantage: Many experiments are required.
Modelling Approach
• Establish a model and design experiments to
determine the model parameters.
• Compare the model behaviour with the
experimental measurements.
• Use the model for rational design, control and
optimization.
• - Advantage: Fewer experiments are required,
and greater understanding is obtained.
• - Disadvantage: Some strenuous thinking may be
necessary.
Statistical modeling
• In statistical modeling, regression analysis is a
set of statistical processes for estimating the
relationships between a dependent variable
and one or more independent variables.
Objectives/De
pendent
Independent
Enzyme
activity
Product Yield
% degradation
Time
Temp
pH
RPM
D.O
Limiting substrate & product
concentrations
Concentration of inhibitor etc
Statistical models
• Enzyme Activity (Y1) =89.19+4.07A+ 9.37B +
0.55C + 0.82D+ 0.68E+0.034AB-1.12AC
• Yield (Y2)=7.90+0.52A + 0.16B + 0.018C +
0.27D + 0.14E + 0.072AB + 0.041AC + 0.047AD
• Where A,B,C and D are independent variables
Concepts of mass balance models
General Modelling Procedure
the following stages in the modelling procedure
• The first stage involves the proper definition of
the problem and hence the goals and
objectives of the study.
• All the relevant theory must then be assessed
in combination with any practical experience
with the process.
• (ii)The available theory must then be formulated
in mathematical terms.
• Most bioreactor operations involve quite a large
number of variables (cell, substrate and product
concentrations, rates of growth, consumption
and production) and many of these vary as
functions of time (batch, fed-batch operation).
• For these reasons the resulting mathematical
relationships often consist of quite large sets of
differential equations.
• (iii) Having developed a model, the model
equations must then be solved.
• Mathematical models of biological systems are
usually quite complex and highly non-linear.
• Numerical methods of solution must therefore
be employed, with the method preferred in
this text being that of digital simulation.
General Aspects of the Modelling
Approach (Mass & Energy balances)
• An essential stage in the development of any
model, is the formulation of the appropriate
mass and energy balance equations.
• It is required to add appropriate kinetic
equations for rates of cell growth, substrate
consumption and product formation,
equations
• The combination of these relationships
provides a basis for the quantitative
description of the process and comprises the
basic mathematical model.
• The resulting model can range from a very
simple case of relatively few equations to
models of very great complexity.
• Simple models are often very useful, since they
can be used to determine the numerical values
for many important process parameters.
• For example, a model based on a simple Monod
kinetics can be used to determine basic
parameter values such as the specific growth rate
(μ), saturation constant (Ks), biomass yield
coefficient (YX/s) and maintenance coefficient (m).
• A basic use of a process model is to analyze
experimental data and to use this to
characterize the process, by assigning
numerical values to the important process
variables.
• The model can then also be solved with
appropriate numerical data values and the
model predictions compared with actual
practical results.
• This procedure is known as simulation and
may be used to confirm that the model and
the appropriate parameter values are
"correct". Simulations, however, can also be
used in a predictive manner to test probable
behavior under varying conditions.
• This leads on to the use of models for process
optimization and their use in advanced control
strategies.
The application of a combined modelling and simulation
approach leads to the following advantages:
• Modelling improves understanding.
• Forced
to
consider
the
complex
cause-and-effect sequences of the process
• The comparison of a model prediction with
actual behaviour usually leads to an increased
understanding of the process.
• The results of a simulation can also often
suggest reasons as to why certain observed,
and apparently inexplicable, phenomena
occur in practice.
• Models help in experimental design. It is
important that experiments be designed in
such a way that the model can be properly
tested.
• Mathematical models can also be used for the
design of relatively sophisticated control
algorithms.
• Both mathematical and knowledge based
models can be used in designing and
optimizing new processes.
• Models may be used in training and education.
• Many important aspects of bioreactor operation
can be simulated by the use of very simple
models.
• These include such concepts as linear growth,
double substrate limitation, changeover from
batch to fed-batch operation dynamics, fedbatch feeding strategies, aeration dynamics,
measurement probe dynamics, cell retention
systems, microbial interactions, biofilm diffusion
and bioreactor control.
• Models may be used for process optimization.
Optimization usually involves considering the
influence of two or more variables, often one
directly related to the product.
Product Balance V dP1
dt
= rx V
Berkely Madonna Simulation
Program for Batch reactor
•
•
•
•
•
•
•
•
•
•
METHOD RK4
STARTTIME = 0
STOPTIME=10
DT = 0.02
UM = 0.3
KS = 0.1
Y = 0.8
INIT X = 0.01
INIT S = 10
INIT P = 0
•
•
•
•
•
•
•
X' = RX ;
S' = RS ;
P' = RP ;
RX = U*X
RS=-RX/Y
RP=(K1+K2*U)*X
U=UM*S/(KS+S)
Batch Reactor
UM = 0.3
KS = 0.1
X0 = 0.1
S0 = 5
P0 = 0.25
Y1=0.8
Y2=0.7
INIT X = 0.1
INIT S = 5
INIT P = 0.25
X'=RX ;
S'=RS ;
P'=RP ;
RX = U*X
U=UM*S/(KS
CHEMOSTAT
Fed Batch
UM = 0.3
KS = 0.1
X0 = 0.1
S0 = 5
P0 = 0.25
D=0.25
Y1=0.8
Y2=0.7
UM = 0.3
KS = 0.1
Y1 = 0.8
Y2=0.7
X0 = 0.1
S0 = 10
P0 = 0.0
F=25
INIT X = 0.1
INIT S = 5
INIT P = 0.25
INIT V=1
INIT
VX=V*X0
INIT
VS=V*S0
INIT
VP=V*P0
X'=D*(X0-X)
+RX ;
S'=D*(S0-S)
+RS ;
P'=D*(P0-P)
V'=F ;
VX'=RX*V ; Assume:
Sterile feed
VS'=F*S0-RS*V ;
VP'=RP*V;
X = VX/V
S=VS/V
P=VP/V
U=UM*S/(KS+S)
RX=U*X
RS=RX/Y1
RP=Y2*U*X
D=F/V
Infectious disease modelling
SIR Model Framework
• SIR epidemic model
S
I
R
• Large population
• Single initial case
• Rest of the population is fully susceptible
Examples:
–
–
–
–
Influenza pandemics
SARS
Ebola
Covid-19
The equations
Equations:
Initial conditions:
Parameters:
Assumptions:
▪ Homogeneous mixing
▪ Constant recovering rate
SIR output: the epidemic curve
I
R
Susceptible
Removed
Proportion of population
S
Infectious
Time
Full dynamics
Enzyme Kinetics - Inhibition
Types of Inhibition
•
•
•
•
Competitive Inhibition
Noncompetitive Inhibition
Uncompetitive Inhibition
Irreversible Inhibition
Competitive Inhibition
In competitive inhibition,
the inhibitor competes
with the substrate for the
same binding site
Competitive Inhibition
- Reaction Mechanism
In competitive inhibition, the
inhibitor binds only to the
free enzyme, not to the ES
complex
General Michaelis-Menten Equation
This form of the Michaelis-Menten equation can
be used to understand how each type of
inhibitor affects the reaction rate curve
In competitive inhibition, only the apparent Km
is affected (Km,app> Km),
The Vmax remains unchanged by the presence of
the inhibitor.
Competitive inhibitors alter the
apparent Km, not the Vmax
Vmax,app = Vmax
Km,app > Km
The Lineweaver-Burk plot is
diagnostic for competitive inhibition
Relating the Michaelis-Menten equation, the v vs. [S]
plot, and the physical picture of competitive inhibition
Inhibitor
competes with
substrate,
decreasing its
apparent affinity:
Km,app > Km
Formation
FormationofofEI
EI
complex
complex shifts
shiftsreaction
reaction
to
>>KKm
to the
the left:
left:KKm,app
m,app
m
Km,app > Km
Vmax,app = Vmax
Example - Competitive Inhibition
Sulfanilamide is a competitive
inhibitor of p-aminobenzoic
acid. Sulfanilamides (also
known as sulfa drugs,
discovered in the 1930s)
were the first effective
systemic antibacterial
agents.
Because we do not make folic
acid, sulfanilamides do not
affect human cells.
Practical case: Methanol poisoning
A wealthy visitor is taken to
the emergency room, where
he is diagnosed with
methanol poisoning. You
are contacted by a 3rd year
NIT student and asked what
to do? How would you
suggest treating this patient?
Methanol (CH3OH) is metabolized to
formaldehyde and formic acid by alcohol
dehydrogenase. You advisethe third year
student to get the patient very drunk.
Since ethanol (CH3CH2OH) competes with
methanol for the same binding site on
alcohol dehydrogenase, it slows the
metabolism of methanol, allowing the toxic
metabolites to be disposed of before they
build up to dangerous levels. By the way,
the patient was very grateful and decided
to leave all their worldly possessions to the
hospital. Unfortunately, after being
released from the hospital, he went to the
casinos and lost everything he had.
Noncompetitive Inhibition
the inhibitor
does not
interfere with
substrate
binding (and
vice versa)
Noncompetitive Inhibition Reaction Mechanism
In noncompetitive
inhibition, the
inhibitor binds
enzyme
irregardless of
whether the
substrate is bound
Noncompetitive inhibitors decrease the
Vmax,app, but don’t affect the Km
Vmax,app < Vmax
Km,app = Km
Why does Km,app = Km for
noncompetitive inhibition?
The inhibitor binds
equally well to free
enzyme and the ES
complex, so it doesn’t
alter apparent affinity
of the enzyme for the
substrate
The Lineweaver-Burk plot is diagnostic
for noncompetitive inhibition
Relating the Michaelis-Menten equation, the v vs. [S] plot,
and the physical picture of noncompetitive inhibition
Inhibitor doesn’t interfere
with substrate binding,
Km,app = Km
Even at high
substrate levels,
Formation inhibitor
of EI still binds,
[E]t < reaction
[ES]
complex shifts
Vmax,app < Vmax
to the left: Km,app > Km
Vmax,app
Km,app
> K< mVmax
Vmax,app
==V
K
Kmax
m,app
m
Noncompetitive inhibitors
decrease the apparent Vmax, but
do not alter the Km of the
reaction
Example of noncompetitive inhibition:
fructose 1,6-bisphosphatase inhibition by AMP
Fructose 1,6-bisphosphatase is a key regulatory
enzyme in the gluconeogenesis pathway. High
amounts of AMP signal that ATP levels are low and
gluconeogenesis should be shut down while
glycolysis is turned on.
High AMP levels inhibit fructose 1,6-bisphosphatase
(shutting down gluconeogenesis) and activate
phosphofructokinase (turning on glycolysis).
Regulation of fructose 1,6-bisphosphatase and
phosphofructokinase by AMP prevents a futile cycle
in which glucose is simultaneously synthesized and
broken down.
Uncompetitive Inhibition
In uncompetitive
inhibition, the
inhibitor binds
only to the ES
complex
Uncompetitive Inhibition Reaction Mechanism
In uncompetitive
inhibition, the
inhibitor binds only
to the ES complex,
it does not bind to
the free enzyme
Uncompetitive inhibitors decrease
both the Vmax,app and the Km,app
Vmax,app < Vmax
Km,app < Km
Notice that at low substrate
concentrations,
uncompetitive inhibitors
have little effect on the
reaction rate because the
lower Km,app of the enzyme
offsets the decreased Vmax,app
Uncompetitive inhibitors decrease both the
Vmax,app and the Km,app of the enzyme
Notice that
uncompetitive inhibitors
don’t bind to the free
enzyme, so there is no
EI complex in the
reaction mechanism
The Lineweaver-Burk plot is
diagnostic for uncompetitive inhibition
Relating the Michaelis-Menten equation, the v vs. [S]
plot, and the physical picture of uncompetitive inhibition
Inhibitor
increases
the amount of
enzyme bound
to substrate
Km,app < Km
Even at high
substrate
Formation of
EI levels,
inhibitor
binds,
complex shifts
reaction
[E]t < [ES]
to the left: KVm,app >< V
Km
max,app
max
Vmax,app < Vmax
Km,app< Km
Uncompetitive inhibitors
decrease the apparent Km of the
enzyme and decrease the Vmax of
the reaction