An Application Of Cybernetic Principles To The Modeling And Optimization Of Bioreactors
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- @PhdThesis{Mandli:thesis,
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author = "Aravinda Reddy Mandli",
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title = "An Application Of Cybernetic Principles To The
Modeling And Optimization Of Bioreactors",
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school = "Chemical Engineering, Division of Mechanical Sciences,
Indian Institute of Science",
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year = "2017",
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address = "Bangalore, India",
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keywords = "genetic algorithms, genetic programming, biochemical
engineering, bioreactors, fed-batch bioreactors,
cybernetic models, cybernetics, cybernetic modeling,
microbial products, bioreactor operation, microbial
growth, bioreactor optimisation, cybernetic variables,
bioreactor trajectory",
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bibsource = "OAI-PMH server at etd.ncsi.iisc.ernet.in",
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contributor = "Jayant M Modak",
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language = "en_US",
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oai = "oai:etd.ncsi.iisc.ernet.in:2005/2640",
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URL = "https://etd.iisc.ac.in/handle/2005/2640",
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broken = "http://hdl.handle.net/2005/2640",
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URL = "http://etd.ncsi.iisc.ernet.in/abstracts/3444/G26691-Abs.pdf",
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broken = "http://etd.ncsi.iisc.ernet.in/bitstream/2005/2640/1/G26691.pdf",
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abstract = "The word cybernetics has its roots in the Greek word
kybernetes or steers-man and was coined by Norbert
Wiener in 1948 to describe the science of control and
communication, in the animal and the machine. The
discipline focuses on the way various complex systems
(animals/machines) steer towards/maintain their goals
using information, models and control actions in the
face of various disturbances. For a given
animal/machine, cybernetics considers all the possible
behaviours that the animal/machine can exhibit and then
enquires about the constraints that result in a
particular behaviour. The thesis focuses on the
application of principles of cybernetics to the
modelling and optimisation of bioreactors and lies at
the interface of systems engineering and biology.
Specifically, it lies at the interface of control
theory and the growth behaviour exhibited by
microorganisms. The hypothesis of the present work is
that the principles and tools of control theory can
give novel insights into the growth behaviour of
microorganisms and that the growth behaviour exhibited
by microorganisms can in turn provide insights for the
development of principles and tools of control theory.
Mathematical models for the growth of microorganisms
such as stoichiometric, optimal and cybernetic assume
that microorganisms have evolved to become optimal with
respect to certain cellular goals or objectives.
Typical cellular goals used in the literature are the
maximization of instantaneous/short term objectives
such biomass yield, instantaneous growth rate,
instantaneous ATP production rate etc. Since
microorganisms live in a dynamic world, it is expected
that the microorganisms have evolved towards maximising
long term goals. In the literature, it is often assumed
that the maximization of a short term cellular goal
results in the maximization of the long term cellular
goal. However, in the systems engineering literature,
it has long been recognised that the maximization of a
short term goal does not necessarily result in the
maximization of the long term goal. For example,
maximization of product production in a fed-batch
bioreactor involves two separate phases: a first phase
in which the growth of microorganisms is maximised and
a second phase in which the production of product is
maximised. An analogous situation arises when the
bacterium E. coli passes through the digestive tract of
mammals wherein it first encounters the sugar lactose
in the proximal portions and the sugar maltose in the
distal portions. Mitchell et al. (2009) have
experimentally shown that when E. coli encounters the
sugar lactose, it expresses the genes of maltose
operons anticipatorily which reduces its growth rate on
lactose. This regulatory strategy of E. coli has been
termed asymmetric anticipatory regulation (AAR) and is
shown to be beneficial for long term cellular fitness
by Mitchell et al. (2009). The cybernetic modelling
framework for the growth of microorganisms, developed
by Ramakrishna and co-workers, is extended in the
present thesis for modelling the AAR strategy of E.
coli. The developed model accurately captures the
experimental observations of the AAR phenomenon,
reveals the inherent advantages of the cybernetic
modelling framework over other frameworks in explaining
the AAR phenomenon, while at the same time suggesting a
scope for the generalisation of the cybernetic
framework. As cybernetics is interested in all the
possible behaviours that a machine (which is, in the
present case, microorganism) can exhibit, a rigorous
analysis of the optimal dynamic growth behaviour of
microorganisms under various constraints is carried out
next using the methods of optimal control theory. An
optimal control problem is formulated using a
generalised version of the unstructured Monod model
with the objective of maximization of cellular
concentration at a fixed final time. Optimal control
analysis of the above problem reveals that the long
term objective of maximization of cellular
concentration at a final time is equivalent to
maximization of instantaneous growth rate for the
growth of microorganisms under various constraints in a
two substrate batch environment. In addition,
reformulation of the above optimal control problem
together with its necessary conditions of optimality
reveals the existence of generalised governing dynamic
equations of the structured cybernetic modelling
framework. The dynamic behaviour of the generalised
equations of the cybernetic modelling framework is
analysed further to gain insights into the growth of
microorganisms. For growth of microorganisms on a
single growth limiting carbon substrate, the analysis
reveals that the cybernetic model exhibits linear
growth behaviour, similar to that of the unstructured
Contois model at high cellular concentrations, under
appropriate constraints. During the growth of
microorganisms on multiple substitutable substrates,
the analysis reveals the existence of simple
correlations that quantitatively predict the mixed
substrate maximum specific growth rate from single
substrate maximum specific growth rates during
simultaneous consumption of the substrates in several
cases. Further analysis of the cybernetic model of the
growth of S. cerevisiae on the mixture of glucose and
galactose reveals that S. cerevisiae exhibits
sub-optimal dynamic growth with a long diauxic lag
phase and suggests the possibility for S. cerevisiae to
grow optimally with a significantly reduced diauxic lag
period. Since cybernetics is interested in
understanding the constraints under which a particular
machine (microorganism) exhibits a particular
behaviour, a methodology is then developed for
inferring the internal constraints experienced by the
microorganisms from experimental data. The methodology
is used for inferring the internal constraints
experienced by E. coli during its growth on the mixture
of glycerol and lactose. An interesting question in the
study of the growth behaviour of microorganisms
concerns the objective that the microorganisms
optimise. Several studies aim to determine these
cellular objectives experimentally. A similar question
that is relevant to the optimisation of fed-batch
bioreactors is \what are the objectives that are to be
optimised by the feed flow rate in various time
intervals for the optimisation of a final objective?{"}
It was mentioned previously that the maximization of
product production in a fed-batch bioreactor involves
maximization of growth of microorganisms first and the
maximization of product production later. However, such
guidelines can only be stated for relatively simple
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Aravinda Reddy Mandli
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