Hello welcome to our course on Introduction
to Dynamical models in Biology This is week
1 and this is model 1 here we have general
discussion on modelling in biology specifically
in dynamical models in biology As a biology
student you must be aware that once upon a
time biology used to be just like star gazing
You can look at the star you can observe the
motion but you cannot actually change its
position and do experiment on the star Biology
used to be like that once upon a time you
can observe a bird you can observe a flower
you can measure the size of a lizard tail
you can note them down but cannot actually
change manipulate that biological form life
form
But biology has graduated from that observation
based science and now we can actually decide
what type of experiment we will do based on
our hypothesis Based on our requirement we
do (inter) interfere with the system you inject
a drug in an animal and then study how its
blood pressure is changing If required we
genetically modify a bacteria introduce a
new genes in that to see what will be the
effect of that genes on the bacterial metabolism
or bacterial survival You create a whole new
organism a transgenic mouse to do your study
to understand the effect of the gene on the
physiological development of the mouse these
are very common And we have graduated from
the days of measuring tail length and colour
of flower now we have a diverse type of data
We have genomic data sequences of genes AMRE
sequence genomic sequence sequences of micro
aranais You have large amount of proteomic
data which tells about which protein is expressed
in how much amount in different types of cells
in human body
We have data on structure proteins we have
network maps showing interaction between different
molecules So we have huge amount of data now
in our hand and everyday thousands of scientists
are generating different forms of data in
different biological systems These observations
is key in understanding how life works and
that is how we have made progress tremendous
progress rather in understanding living systems
But sometimes these data or observations or
experimental observation rather has some limitations
and that is where the mathematical models
come into play For example suppose you have
treated someone with a drug and you are doing
a dose dependent experiment you are treating
yourselves with different doses of drug You
observe that particular phenomena happen only
when you are using a higher amount of the
drug
So through experiment you have seen the phenomena
you may measure changes in some molecules
as you are treating the (dru) cells with the
drug and you may have seen that also has a
dose dependent behaviour Now the question
comes why do we have a dose dependent behaviour
your experimental observation many a time
may not give you a clear clue Rather you can
make multiple hypothesis create mathematical
models for them and then taste those models
using models and identify which hypothesis
is correct and then go back and design the
experiment to check whether whatever your
mathematical model is telling is correct or
not So in a sense I can have limitations of
my experiment where my experiments cannot
give a clear physical explanation of a phenomena
But take another case in that case you actually
cannot design experiment
For example I am studying suppose the evolution
of the gene P53 which is present in human
So I want to know step by step how the P53
gene has evolved I can know the sequence of
P53 right now in different organisms but the
sequences P53 in those organisms which were
our ancestors and already disappeared from
earth I have no option to know those sequences
So I cannot design experiment to know what
was the sequence of P53 in those organisms
We all know that we draw a phylogenetic tree
to understand the evolution of sequences nucleotides
and amino type sequences In those cases to
understand the ancestor and the evolutionary
process of the gene you cannot actually do
the experiment In some cases you can do experiment
and you are actually doing experiment but
the amount of data generated is huge
For example you are doing genome skill study
you are doing proteome skills study you are
screening drugs using proteomics and genomics
too You are generating a huge amount of data
and to distil out of that data and to understand
that data intuitively is very difficult for
us human being In this case also building
a mathematical model may help you to distil
out the observation and to create new hypothesis
or make new predictions So in a sense as I
have said and written down here is the mathematical
models are nothing but complementation to
your experimental observations They may help
you to give physical explanation to phenomena
a mathematical model may help you to make
predictions and most of the time a mathematical
model helps you to make new hypothesis that
you can go back in your bench and taste by
experiments Now let us look into how a mathematical
model fits into as the whole scientific endeavour
we are in
So in general science has a cycle it starts
with the experiment you design a experiment
in a ideal condition For example you grow
cells in a plate and then you treat them with
a particular drug that is your experiment
from this experiment you major some observable
and then using that observed behaviour you
create a hypothesis Now once you have treated
the hypothesis you go back again to the experiment
design a new experiment to test this hypothesis
This cycle from experiment to hypothesis experiment
to hypothesis keep on happening and eventually
what we get eventually we get is knowledge
about the system So this is a cyclic process
of scientific endeavour mathematical model
fits just there As I said in some cases experimental
observation may not be good enough to understand
a phenomena or they may be so so huge that
you cannot actually intuitively understand
the implication of that and make meaning out
of it or distil out the essence of that observations
So what you have you have done the experiment
based on the observation and physical principals
that involve you understand you created a
mathematical model That mathematical model
helps you to make new hypothesis and from
this hypothesis again you go back to your
experiments So this cycle goes on with experiment
mathematical model hypothesis building and
again experiments and again this way we develop
new knowledge So essentially what I want to
say is that mathematical models are actually
compliment to your experiments and honestly
speaking mathematical models are not new to
you Very frequently structures of protein
are predicted by mathematical modelling what
you call usually homology model per say
You have a sequence of amino acid of a gene
amino acid sequence of gene you want to know
what type of function it may have what type
of molecule is it what type of biological
function it is related to As we know function
of a protein depends on a structure so what
you do you try to understand the structure
of the protein but if you do not know the
real structure of the protein you create a
model of that using some mathematical constant
and you get a 3D model of the protein from
that you try to understand what may be the
function of the protein or you may have (know)
done the experiment to understand the function
you know what is the function of it You go
back to this 3D model and try to explain that
function using the 3D structure and this is
very common in biology
Another type of model is very common in biology
that I mentioned few slides back is Phylogenetic
tree You know the sequence of certain gene
right now you want to know how they have evolved
how they are connected to each other s you
build a mathematical model which you call
Phylogenetic tree to understand the evolution
of this gene these types of models are very
common in Biology There is another type of
model that is focus of course that is dynamical
model
No living system is static anything that is
living as it processes changes with time which
is dynamic Take the example growth of a human
being growth of a bacteria in a fermenter
or growth of solid tumour in a patient or
may be dynamics between a predator and prey
in the jungle all these are dynamical system
things are changing with time take the issue
of pattern formation in Zebra or the pattern
formation during evolution sorry (de de) development
of the embryo that is changing with time You
can have oscillation in your sleep cycle you
can oscillation and secretion of in insulin
in your body that is also a dynamic process
If you disturb that (dy) oscillatory process
your metabolism will get disturbed If you
look at the cellular level the protein production
transcription gene regulation expression and
its regulation all dynamic processes they
are changing with time
Talk about signal transaction calcium signalling
or signalling by the phosphorelay system these
are all dynamic processes So most of the biological
processes from cellular molecular level to
population level are actually dynamical processes
and the focus of our course is to how to model
these dynamical processes So we will focus
on building model for dynamical processes
or systems in biology and the most interesting
thing is that the mathematical formulation
the mathematical techniques that we will use
will be the same whether you are using it
for a molecular level problem or you are dealing
with a population level problem for example
the dynamics between the predator and the
prey in a forest The techniques and the method
that we will use will be same
Before we go further and discuss about it
let us understand one key issue key concept
over here In this course we will build mathematical
model for dynamical processes or dynamical
models or different models for different biological
systems So we will build models and we have
to keep in mind that models are not reality
Let me give you an example I want to understand
flight of a plane I am designing a new plane
or suppose we do not know how plane flies
we want to understand that I can create a
paper plane that paper plane is a model for
a real plane obviously you understand that
this paper plane is not a real plane But using
this paper plane if I fly it I can understand
certain behaviour of flight I can understand
how the shape of the plane effects affects
its flight I can understand the basic phenomena
of floating in air basic phenomena of flying
in air
But obviously using this paper plane you may
not ask complicated question like what will
happen if there is rain how navigation system
will be there all these complicated questions
you may have to answer using this paper plane
So paper plane is a model of a real plane
so it is not exactly same of the real plane
it is just a model it is not a reality And
paper plane can help you to understand only
certain unknown things it cannot tell or answer
you all questions about flight of a plane
real plane so all models are like that all
mathematical models whether for a dynamic
system or not that we will built are actually
a replica not a exact replica or a reduced
replica of a real phenomena that you are dealing
with and it can only answer few certain specific
question that we can ask that we have to keep
in mind when we are building models
Now the next question comes then what is a
mathematical model mathematical models are
actually nothing but a set of mathematical
constant By mathematical constant I mean it
may be a set of equations for example in the
course you will learn how to write ordinary
differential equation set of ordinary differential
equations which will create our model So in
all mathematical model is nothing but a set
of mathematical construct which can equations
relation like that And these equations or
relations of mathematical constructs are based
on certain physical principal that we believe
are playing behind the phenomena that I am
studying and based on my observation which
is coming from the experiments
So based on your observation and the physical
processes the physical laws that we know from
nature we build certain mathematical equations
and relationship that is our mathematical
model So suppose you want to model the dynamics
of P53 in a cell when you apply your ionisation
radiation on the cell there will be DNA damage
and the cell will produce P53 to increase
the amount of active P53 and it has been observed
that the (amou) the concentration of P53 oscillates
with time so I want to understand this behaviour
So I will write down certain equation representing
these oscillations and those equations will
be based on my observation for P53 (o o) oscillation
of P53 and the physical (pheno) processes
that is going behind this oscillation as I
understand As a whole I will write down some
equations or mathematical constant this is
my model now I will ask these questions to
this model that means I will analyse these
models or sometimes I simulate
I will use a computer to simulate the behaviour
of this model using those equations so that
will be simulation So this analysis or stimulation
of the mathematical model will give answer
to my questions So mathematical modelling
for example dynamical modelling in biology
will have two part first part will be to write
a right model write a correct sets of equations
and mathematical construct as we believe will
represent the process and then you analyse
them using the different techniques some will
be using symbolic math using paper and pen
sometimes you will use computer to simulate
and analyse the model and that will give you
answer to your question that will make prediction
what will happen if you do a particular experiment
that will help you to create new hypothesis
which you can go back and check by experiments
So if I jote down mathematical models as I
have said is very common in biology they come
in different forms and you have to remember
that mathematical models are actually complimentary
to experimental observation They comes in
hands in hands and as I have shown from observation
of experiments you create a mathematical model
that helps you to create a hypothesis again
you back to experiment using this cycle we
get knowledge
And mathematic in our course or (math) modelling
we will focus on dynamical systems and rather
we will keep mathematical model to understand
the dynamics of different processes And as
I have said models are nothing but a set of
mathematical relations equations we analyse
them to understand the behaviour of the system
the phenomena We analyse them or simulate
them to understand what will happen if we
do a particular type of experiment that is
prediction Using these model and by analysing
these models we try to make generate some
new hypothesis which we can go back and check
by experiments
This is the theme of the whole course initially
we will try to learn the basics of building
mathematical model how to write down those
equations then we will learn how to analyse
them and then step by step we will try to
build different aspects of mathematical modelling
for dynamical systems in biology Thank you
for listening see you in the next model
