[MUSIC]. In this lecture I'm going to talk to you
about integrated reasoning, where one can merge bottom up and top down lines of
thinking and identify emergent properties.
And the property that I'm going to talk about the most and which I actually know
the best about is Bistability. Okay, let's start off with what is an
emergent property? This is sort of a key question in systems
biology because. [UNKNOWN] The word systems says we want
to understand what happens at a systems level.
And emergent properties are properties that a system possesses as a whole, but
cannot be attributed to any individual component of the system.
Emergent properties of cell biological systems include bistability,
ultrasensitivity robustness and probably many others that are waiting to be
discovered. So what is bistability?
Bistability is the ability of a system to exist in two stable states.
That is, a system can switch between one state and another.
Often switching a stimulus-driven, and hence enables change in the state of the
cell, so the cell can receive a stimulus chan, turn on.
a set of networks that enable it to become bistable, and switch to another
state and respond differently. So, you might ask why is this integrated
reasoning. The reason this is integrated reasoning
is because we use the ability of ODE based, in this case ODE based modeling to
understand bistability as a property of the positive feedback loop.
And this, and as I told you positive feedback loops are a regulatory motifs
with, sub-graphs. Within a large network.
And this allows us to enumerate the capability of a network identified by
topological analysis. And so you will combine both, dynamical,
reasoning from dynamical modelling. And reasoning from network modeling.
And hence, I'd like to call this sort of integrated.
Okay let's think about an example of a dynamical analysis of a bistable system.
I'm going to use the example from my paper that [UNKNOWN] worked on back in
1999, because this is sort of any easy one and, uses very classical cell
signaling pathways. And I can put it in the context of known
biological functions now. So, you've seen this diagram of this
positive feedback loop here now many times, so you should feel comfortable
with it. You can get a signal from EGF4 that
activates either phosphate-base c or the RAS pathway that turns on protein kinase
c. Up here on MAP Kinase and together with
PLA2 they form a positive feedback loop that allows a signal to propagate leading
to MAP Kinase. all of the reactions in this network have
been well-studied and these reactions are all sort of given here, and these schemes
are taken from that paper. So to set up a, ODE model what one needs
to do is to identify the reactions involved in the model, and these are
shown below here [SOUND]. You have to parameterize the reaction,
that is find the reaction rates and concentrations.
As I told you these are classical signalling pathways and most of these
proteins. Well, actually I think all of the
proteins in this pathway have been purified.
And so, and there has been a study with respect to their biochemical property so
we had been able to at some work, both find and or estimate the parameter.
Once we get a model with these parameters, what one needs to do is to
constrain the model in a modular fashion, and I'll talk about this in the next
slide in a minute. And also ensure that the simulations
obeys basic thermodynamic principles, that is, mass conservation.
Remember that in this system, except for MKP none of the other components are
either synthesized or degraded. So do, mass conservation one needs to
make sure. That the amount of mass that you start
with at the beginning of the simulation, is the same at which you end the
simulation. So, you can't, so the level, the total
concentration of EGF1/g, the beginning and the end and total concentration of
RAS or MAP Kinase the beginning and the end has to be same.
The fractions of the uh, [INAUDIBLE] part which had activated, may be different and
they vary with respect to time. But if you take the inactive and active
together, they ought to be sort of constant throughout simulations.
This is what one means by mass conservation.
Additionally, because these are all coupled reversible reactions the system
has to obey the thermodynamic principle of microscopic reversability.
Which means that all of the forward reactions thus, product of all of the
forward reactions has to equal the product of all of the reverse reactions.
with these two constrains the mo, modelling should proceed say in a pretty
straightforward manner. Okay, constraining models.
This is sort of, actually, a big deal in building realistic models.
Always remember the famous spherical car with a tail and nine par, eight or ten
parameters. And so, one wants to really constrain
these models so that they are as realistic, plausibly realistic from an
experimental perspective. And since kinetic parameters are drawn
from many sources for instance, the different proteins in this network might
have been purified from many different hm, laboratories.
have been purified in laboratories and could be from different cells and tissues
it's hm, and all these kind of variabilities and they may now have been
assayed in exactly the same conditions. So, it's good practice to constrain the
model by running test simulations to see the model behavior is similar to what
have been observed in experiments. Two, two examples are shown here below.
I already think, I think I discussed the hm, the time course example.
The previous lecture in considering limitations of models, and here is a dose
response example of, of [UNKNOWN] gamma being activated by EGFR.
or EGF in the in high and low calcium, and you can see in both cases, there is
reasonably good agreement between the output of the simulations and the
experimental data. My recommendation generally is not to
tweak or change the parameters so the simulations exactly fit the model.
So, for instance here you see that the time course is a little bit offset, this
is because maybe the rates that we are using in the model are not exactly what
is observed in these cell types. But we sort of let them be.
we know the differences and keep track of them, but we run the model with the most
reasonably selected parameters. The appropriate place to change
parameters is during the systematic parameter variation.
This is a meaningful exercise because it can tell us the best set of parameters
for an observed experimental profile. And by doing this sort of parameter
variations, one can identify parameters that may best suit a specific
experimental system. Then of course one has to go back into
the experimental system and test or verify the parameters that we identified
through the simulations are indeed what we what you can measure.
So, these kind of parameter variations systematic parameter variations, are um,
[UNKNOWN] can generate hypothesis to do more accurate experiments.
So, using all these constraints, one can sort of run simulations to determine
unde, the conditions under which one can get transient and sustained responses.
When we first did these experiment simulations, we were not sure what we
were going to find. And so we ran the simulations under the
variety of conditions to ask the question whether a brief, small or short duration
signals could produce long duration output.
So, here is the result of the simulations.
And [INAUDIBLE] ran these in under multiple conditions, he, what he found
was that simula, a stimulus of a sufficient amplitude, 5 nano molar.
And sufficient duration 100 minutes, moves the system from a basil to a fully
activated state. Other stimuli that are less intense, or,
or smaller in aptitude or smaller in duration might produce transient
activity. But the eventually call the sys, cause
the system to come back to baseline when the stimulus is removed.
So, now one can ask the question, how does this happen?