welcome to lecture four in this n p t e l online certification course on bioreactors
the ten hour like ten hour course in the last lecture lecture number three we had looked
at how to solve problems in general and we solved a problem related to these sterilization
kinetics what are the things i would like you to note keep in mind and check always
is after you arrive at the final answer please check whether it make some sense for example
if um you had seen or got an answer of about of seven thousand five hundred hours
or something like that then you need to go back and check your calculations its always
good to check your calculations after you finish but always keep the reality of the
number that you get in mind seven thousand five hundred hours seems a little odd for
any situation experience always helps you make better to have a better idea of expected
numbers but even otherwise seven thousand five hundred hours when you are looking at
a bioreactor it seems a little odd at the same time if you had got an answer of about
ten part minus three seconds seems ridiculously shocked so under both these situations i think
it's good to check the approach the math and the over all calculations ok um this is
something similar suppose you are working on let's say pipe sizes and you get an answer
of about fifty meters you know the pipe diameter is fifty meters this taking an odd
example fifty meter diameter is you know something unimaginable the pipe size having
a fifty fifty meter diameter is unimaginable so you should always have this picture
of your answer in mind and check it please do it every time i will again emphasis
this when we do the next practice problem
now let us continue with module two is on biomass cells and bio products biomass
or cells and bio products and these are the two important outcomes of any bio process
they could be cells themselves or they could be molecules made by these cells let us look
at these one by one sometimes the cen cells themselves are the
product might be seem a little odd in the beginning but let us consider this i am sure
you would have heard of artificial organs artificial skin was i think the first popular
organ that was made outside and then put on to burned victims so that they could heal
faster and so on
um now a days we have many different organs produce artificially in appropriate by reactors
they might the bioreactors themselves might look a little different the a cells grow on
a scaffold that resemble the organ and therefore you get the shape and then the functionality
is broughten and so on and so forth so that you have a functional organ which can be transplanted
into probably in the place of an organ there is gone bad definitely have liver kidney
and so on so forth that have made that way we did talk of skin which is popular
you could also grow stem cells which are used for a variety of a purposes using bioreactors
in all the situations the cells themselves are the main product from the bioreactor and
all effort goes to making sure that you have a the required cell concentration the required
they should grow in the required way and so on and so forth and they should
also proper functionally when grown in bioreactors
i think i have a video here as um a suggested video this is from the file that is available
to you websites videos and papers recommended i should also add this disclaimers at I I
t madras and i do not recommend or endorse any of the commercial brands that may be depicted
in some of the sources below the sources were chosen for their pedagogic value this
is number twelve that i just mentioned bioreactor for tissue engineering this is the link you
can click on the link and go and see the video it gives you some idea has to how bioreactors
are used for making organs you may have heard or something called spirulina spirulina is
an algae it is grown and then processed and packaged and that is sold as nutraceuticals
many people consume that these are grown in large bioreactors in fact they grown in ponds
which act as bioreactors for the appropriate production of spirulina and there the spirulina
cells itself themselves become the product effect test
similar is the case with something called single cell protein single cell protein was
a very popular in the nineteen seventies and eighties and so on as fodder for cattle
their nothing but yeast cells and their also grown in bioreactors processed and then
provided as fodder for the cattle these in these two cases spirulina and single
cell protein these cells themselves are the products however as we have already seen in
the introduction there are very many other products I think we saw insulin monoclonal
antibodies ethanol bio oil and so on and so forth that the cells produce these are
these are the molecules that are produced by the cells and they are the products
so there are two major types of products the cells themselves or the molecules that are
made by the cells which are the main products from bioreactors ok in the initial lectures
we saw the need to use rates while considering dynamic systems we said rate is a central
parameter on which we base a decisions um and so on therefore that is considered
as the main parameter we don't consider amounts and so on and so forth which scan
get a little confusing for the kind of decisions that we need to make while dealing with dynamic
systems engineering systems and so on so we will also consider rates every thing will
be geared toward rates the model will models will be geared towards rates mathematical
models will be geared towards the rates all the discussion would be guard towards rates
and so on and so forth
you need to internalizes this this takes a while for internalization especially since
some of these concepts were introduced to you at the school level from the point of
view of a batch system were some um approximations work but not in all cases
and especially not in a continuous case you need to internalize that i will keep repeating
this still it gets a across the rates of cell multiplication on one hand and the rate of
product formation are the important rates for us right and what is cell multiplication
one cell becoming two cells and the bioreactor becoming four cells and so on and so forth
ok
in other words the culture in the bioreactor is growing right therefore in cell multiplication
culture growth are just growth all mean the same thing the um cells you would have probably
learnt in a basic biology course they under go something called a cell cycle and that
is also sometimes seen a some sort of a growth not always but we are not taking about
that we are taking of of the multiplication of cells you need to keep this in mind
it's not the cell volume changing during the cell cycle and so on so forth each each
cells volume is changing during the cell cycle that is not what we consider growth here this
is culture growth or the cells multiplication
if we consider single cell the simplest mathematical representation or a mathematical model is
as follows the rate of cell growth as given by r x is directly proportional to the cell
concentration x first order model or equals a certain mu into x note that mu may or may
not be a constant depending on the situation ok you need to again internalize this mu may
or may not be a constant and also there are organisms called molds for example aspergillus
niger is a common mold that grows on bread they are these stringing stringing organisms
that grow by extension of their strengths or the as they are called you know the extent
their mass increases but the number is still or limited to just that one with the
mass increasing in such a case this may not be valid f x is the number concentration of
the cells you need to keep this in mind
we will use this model as needed in this lecture i am going to present some concepts and
we will use the concepts a little later um so let's just focus on the concepts in
this particular lecture this is not the only model that is available for cell growth
there are many such models and we will see some of them this is ended in an introductory
course so will see only some of them one other model just i think i will just show
you just one other model it's called the logistic equation which is helpful in certain situations
where r x the rate of growth equals k into x into a one minus beta x where k and beta
are the model parameters which change according to the system and this goes with the condition
that x equals the initial cell concentration like zero at time t equals zero this is called
the logistic equation which is valid under certain circumstances and in an advanced
course one can consider structured models which essentially consist of or take
into count compartmentalization in the cell you know they could be actual compartments
such as the nucleus mitochondria so on and so forth or they could be even conceptual
ok
some examples of the compartmental or the structured models are compartmental models
metabolic models cybernetic models and so on so forth be this being an introductory
course let's not get into the details but you would need to probably be exposed them
so that you will able to recognize them when you see them in the future then their
could be some models which take into account the distribution in ages of cells in the culture
the above a models the r x equals mu x or r x equals k x into one minus beta x the
logistic equation they considered all the cells to be at the same age in the bioreactor
that need not be true they could be up variation in the ages of cells and that distribution
the variation is taken into account in the segregated models ok
the substrates you know something called substrates we have already seen what is substrates is
we will seen that in detail now r converted to cells through cell multiplication and bio
products the bio products could be made by the metabolic reactions inside the cells or
the genetic processes inside the cells the genetic processes are transcription translation
you know the gene which is a part of the d n a that gets transcribed translated to probably
a protein the protein could be a product that's what by be mean by the product resulting from
a genetic processes or it could be a metabolite that is made by the metabolic reactions in
the bioreactor so let us look closer at the substrates what are substrates terms substrates
are raw materials that are food for the cells and at typical example is glucose c six h
twelve o six the carbohydrates glucose is nice example of the substrate
why are we looking at glucose because glucose is a starting point of an important metabolic
pathway in the cell called glycolysis and glycolysis has importance from the energy
aspects to they provides energy to the cell it is necessary to provide energy to the cell
and so on um usually glucose which is provided in the extra cell as space gets transported
into the cell through glucose transporters in the membrane then it gets converted to
glucose six phosphate through an enzymatic reaction and to fructose six phosphate through
an other enzymatic reaction and so on so forth until it reaches what is called a pyruvate
which is an important branch point in the metabolic pathway the glycolysis itself is
suppose to be from glucose to pyruvate so since this is an important set of reactions
important metabolic pathway that takes place in the cell glucose is a typical substrate
that is considered
there are many other substrates that can get utilized through other such metabolic pathways
in the cell um let's not get into the details glucose is not the only substrates but it's
a very common substrates in fact many times if there is a mixture of substrates cells
tend to prefer glucose sometimes however from an industry prospector a glucose is expensive
so if you start with an expensive raw material expensive substrate the product is going to
turn out to be more expensive so if you have an alternate of a glucose that is not as expensive
then that's much better for the industry so because it reduces the cost of the bio process
very common alternatives for glucose are starch you know the same starch that you know of
cellulose all the wood around you contains cellulose and ligno cellulosic materials ligno
cellulosic materials are currently regresses heavily for has as a glucose source
cellulose and ligno cellulosic materials are found abundantly in all the plants wood
wooders all that and they are alternative sources of glucose um you know you may have
may or may not have considered this the source for all the photosynthetic the carbon
source for all the photosynthetic organisms happens to be the c o two and the air so all
the wood the carbon and the wood that you find came from c o two and the air although
it is point naught three naught four percent now um and is implicated in global
warming and so on that is the source of carbon for photosynthetic organisms
starch and cellulose happen to be polymers of glucose for example if this is one glucose
molecule here that you see this is oxygen here i have not indicated but this is oxygen
this is carbon one carbon two carbon three carbon four carbon five carbon six c six h
twelve o six so this is the pyranose form as written here and then connected to other
glucose molecules this way this is one form of starch called amylose so if you break down
these bonds from starch then you can get glucose for the cells to consume starch is found in
abundance and therefore it is less expensive then glucose and therefore starch can be a
source of glucose for the cells the cellulose happens to be have a slightly different branching
you know amylose and amylopectin starch and then cellulose is sightly different
bonding and branching and so on so forth so they are all polymers of starch if you find
a way by which you can break down the bonds in between them and release the monomers then
they become available for the cells to consume and produce a product of interest
in general a medium we are talked of media earlier that's the complex subs the substances
in which cells grow it provides the all the nutrients for the cells to grow that is for
the culture to cells to multiply the culture to grow and so on
the medium could either be complex or be defined define this means that you know everything
that is there complex means you may not know all the details of the medium in general
a medium contains a carbon source glucose is a very common carbon source we did talk
of carbon dioxide being the carbon source in the case of plants and another sources
which leads to the formation of eighty p and so on so forth it could be the same as carbon
source or it could be different you known the glucose gets into this pathways glycolysis
and then another pathway called the t c a cycle and the oxidative phosphorylation and
there by produces a t p in this case the glucose itself is the energy source many
time you could have other pathway set produce um energy and the energy source could
be different from the carbon source
glutamine a sometimes energy source for mammalian cells and so on and nitrogen source because
cells require nitrogen carbon nitrogen oxygen hydrogen phosphorous and so on are the
essential elements that are present in living systems in cells the medium contain
salts the medium could contain trace nutrients such as vitamins minerals and so on so this
is what a medium in general contains we looked at a substrate glucose way to get glucose
from other things and so on now we need to look at something called a limiting substrate
now we look at some two or three concepts or three or four concepts we will not use
them now but we will try to understand what they are used them later the limiting substrate
is one such concept the limiting substrate is similar to the concept of limiting reactant
you all know what a limiting reactant is in the case of chemical reactions the limiting
reactant is one the concentration of which limits the extent of reaction or the one that
gets consumed first in a batch in a batch is important their um we will say that the
concentration of which limits the extent of the reaction that is called a limiting reactant
let us see an example to understand this a little better
let us consider the following stoichiometry two a plus three b gives you p in other words
two moles of a needs three moles of b to react completely to give you one moles of p if it
happens that the input stream to the reactor let's say the continuous process there is
an input stream to the reactor this contains ten molar concentration of a and ten molar
concentration of b ok this is molar is nothing but moles per liter this is concentration
of a concentration of b then the reaction is going to be limited by b ok this is because
the ten molar concentration of a would require three by two into ten moles molar concentration
of b to react completely ok there is fifteen mole molar concentration of b to get completely
consumed and since only ten molar concentration of b is present b will limit the reaction
and a will be left over and therefore b which is the limiting reactant
similarly the substrate in the medium that limits growth is called the limiting substrate
ok you could have many different substrate we talked of carbon source and hydrogen
source energy source and all that the one that is going to limit growth is going to
be your limiting substrate if we consider the limiting substrate and let us say if s
is the limiting substrate then the variation of these specific growth rate mu remember
that r x equals mu x we said so let us say this is the same mu here the variation of
specific growth rate with substrate concentration is given in this graph this is rectangular
hyperbola it increases and then it's saturates some where here to a value of mu m maximum
specific growth rate ok there is a way of mathematically representing this this is a
rectangular hyperbola so rectangular hyperbola equation would describe this appropriately
and this is the equation that we are taking about mu equals mu m the maximum value here
times s divided by k s plus s would describe this kind of a behavior this is the well known
monod model which gives the effect of substrate concentration on the growth rate of cells
if it happens to be here if you have enough substrate and you happen to be in this region
then mu becomes a constant equals mu m ok that is a situation when you have mu as a
constant in general r x equals mu x need not be a constant if you have enough substrate
then mu m mu equals mu m which happens to be a constant
let us look at what happens when k s equals s let k s equals s in the monod model we substitute
s for k s let us see what happens then so mu equals mu m s by k s plus s this is the
monod model replace k s by s you have two s s plus s two s in the denominator mu m s
by two s s s gets canceled out you get mu m by two therefore when s equals k s you know
when you have the substrate concentration equal to k s or when k s happens to be the
substrate concentration then you are mu happens to be mu m by two or half maximal
specific growth rate ok so k s is the substrate concentration at which you get half maximal
growth rate ok
there are many other types of effects of substrate and growth rate many other ways of representing
them ok let's look at a few of them here the other models for the effect of substrate
and product also in this case you know product could also effect the specific growth rate
for example i think we did mentioned ethanol beyond a certain percentage some eighteen
percent of so it's starts effecting the growth rate of cells that can also be represented
i will give you some brief representations here there are many models some of them are
mu equals mu m into s power n divided by k s plus s power n this is called the moser
model where you have mu m k s and n as the parameters of the model this is one are the
model when two substrates are limiting simultaneously this can also happen then mu equals mu m into
s one divided by k one plus s one into s two divided by k two plus s two this model is
very popular when two substrates are simultaneously limiting
when the substrates happen to limit growth some substrates do that then you could use
this model which is given by andrews and noack mu equals mu m s by k s plus s into k i the
inhibition constant k i by k i plus s this is the andrews and noack model and i will
probably mentioned one more model which is the jerusalimsky and neronova model which
gives actually the effect of product inhibition on the growth mu equals mu m s by k s plus
s into k p by k p plus p ok so far we looked at models that describe growth ok a specific
growth rate and so on growth rate is a specific growth rate also
now let us look at the product if it happens to be a another molecule apart from the cells
or the product the molecule made by the cells a very simple model a widely used model is
called the luedeking piret model for the product formation rate ok note that again these are
all models for rates the luedeking piret model goes a something like this r p equals alpha
times r x plus beta times x the product formation rate equals something called a growth dependent
parameter times the rate of cell growth plus a growth interdependent parameter times
the cell concentration ok there are growth dependent products and growth independent
products growth dependent products are sometimes called primary metabolites growth independent
products are sometimes are called secondary metabolites um these are a loose associations
but this is what we need to look at r p equals alpha times r x the product
formation rate depends on growth rate and the cell concentration this is in sometimes
beta could be zero sometimes alpha could be zero and so on many other models are available
we will probably not look at other models in this particular course but just remember
that any other models are available
the next concept that we are going to look at useful concept is called the yield coefficient
it's a very simple concept but useful and you could define many yield coefficients for
example y of x slash s yield of cells with respect to substrate that's the way to read
this yield of cells with respect to substrate equals is or is defined as the amount of cells
produced divided by the amount of substrate consumed it's a rate of the amounts or cells
produced by the substrate consumed similarly you could define a yield of product with respect
to substrate which is amount of product formed divided by the amount of substrate consumed
and one more yield of cells with respect to product amount of cells produced divided by
the amount of product formed both both are formed in this case sometimes it forms
sometime consumed you can define what ever yield coefficient that you can
the advantage in doing this is that the yield coefficient can be assume constant for
certain small region of interest you know that is why it becomes very useful and
the constant c is usually a good assumptions if the region happens to be small we will
see how this is done if the the usefulness of this once it is defined is that if you
know one rate you could estimate the other rate from the relevant yield coefficient for
example if the substrate consumption rate is needed and is not known but the growth
rate is known you could estimate the substrate consumption rate from the growth rate if the
yield coefficients is known and can be taken to be a constant for example the substrate
consumption rate r s is one by y x times r x you know this comes directly from the
definition of the yield coefficient itself amount of cells produced by the amount
of substrate consume those are amounts is a yield coefficient therefore if you are look
looking at substrate it will be one by y x s times r x this is the rate of substrate
consumption rate of cell formation so going by our first model this can be written as
r x equals mu x therefore r s equals one by y x s times mu x we will actually use these
to compute some useful parameters in the next module for now just know about this probably
tell you one more thing no ya ya one more concept and i think we will stop the finish
up this module here
this is the concept of maintenance you know the substrate glucose for example goes towards
cell multiplication or culture growth cells multiplying culture growth but the cells are
complex systems they have a lot of reactions happening in them they have a lot of process
happening them there is a lot of genes going to proteins sort of transport happening
in them a t p p made a t p p used all kinds of things are happening and energy is required
for all of them and the substrate needs to provide energy for such processes so such
processes that's metabolism transport genetic transformation genetic processes
and so on so forth are called cell maintenance so the substrate goes for cell maintenance
and ones this is satisfied then it goes for cell multiplication we didn't considered this
explicitly so far we need to consider this because when the substrate level is low it
goes completely towards cell maintenance activities and no growth is apparent no growth is observed
apparent means observed no growth is observed so it's all going to cell maintenance there
will be substrate consumption were it doesnt show up as growth which means everything is
going to maintain the cell maintain the activities of the cell
a way of representing this in terms of rates is the rate of growth equals at apparent specific
growth rate and observed specific growth rate times is cell concentration x and this apparent
specific growth rate can be defined as the difference between the true specific growth
rate which is obtained when all the substrate goals towards cell multiplication alone that's
a that's a concept mu t true specific growth rate and the difference between mu t
and something called an endogenous metabolism constant mu a is apparent or the observed
specific growth rate mu t is the true specific growth rate and k e is the endogenous metabolism
constant so mu a equals mu t minus k e and using the yield coefficient r s the substrate
consumption rate is one by y x s apparent the yield apparent yield times apparent specific
growth rate into cell concentration plus something called m into cell concentration where m is
the specific maintenance rate
i think this is a nice place to close this particular lecture we did see quite a lot
of concepts very briefly i we saw that the cells themselves could be products very
quickly let us go through what all we saw and there could be other products that
are made we are looking at writing down expressions for rates of these rate of growth or cell
multiplication and rate of product formation initially we saw expressions for rate of growth
r x equals mu x mu may or may not be a constant depending on the situation then we said that
they are other models this is the logistic equations and in an advanced course one can
consider structured models segregated models and many other things
the substrates are converted into a cells and products we saw that glucose is a typical
substrate because it participates in one of the important metabolic pathway in the cell
or glycolysis and we saw some alternative of glucose because glucose is expensive from
the context of the industry starch cellulose and ligno cellulosic materials are good alternatives
to glucose starch and cellulose are already heavily used ligno cellulosic materials they
this is lot of research going on in use of ligno cellulosic materials to get glucose
then we saw what a medium contained a carbon source and energy source and nitrogen source
salts and trace nutrients any of them could be a limiting substrate if it is a limiting
substrate which limits growth then the variation of specific growth rate with the variation
in concentration is given by the monod model and there is an interpretation for this k
s which is the substrate concentration at half maximal growth rate
then we said that there are other models for the effect of substrate product concentration
on mu we saw few of them moser model and the model when two substrates are simultaneously
limiting and andrews and noack model which gives you the effect of substrate inhibition
and the model by jerusalimsky and neronova which gives the effect of product inhibition
on growth then we looked at the very popular model called the luedeking piret model for
the product formation rate which goes us r p equals alpha times r x the growth dependent
parameter plus beta times x the growth independent parameter and many other models are available
then we saw what yield coefficients where they can many yield coefficients could be
defined it is essentially amount per amount and then they can be used to convert one rate
into the other that's one of the ways in which we will be using them thus and then we looked
at the concept of maintenance which is the substrate going to maintain the activities
in the cell first such as metabolism transport and other things genetic processes and
then after satisfying this it goes to us multiplication
therefore when the substrate level is very low one may not see growth at all that is
represented by the apparent growth rate and the true growth rate and an endogenous metabolism
constant k e mu t minus k e equals mu a and also the rate of substrate consumption
can be return in terms of the apparent specific growth rate and a maintenance specific maintenance
rate ok i think that is good enough for lecture number four see you again in lecture number
five so