And part of the problem why this has not been dealt with it is that there is not a

lot of spatial information available on where different models to the components

of the seller localized. As more and more clear spatial

information becomes available, we need to be able to develop networks that can

allow for spatially specified analysis. Let us now consider how, the properties

of dynamical models and what the pluses and minuses are.

Dynamical models provide accurate descriptions of how a system progresses

temporally and spatially. The classic cell cycle model by John

Tyson which you published back in 1991 is a good example of how a model an ODE

based model relatively simple model of a few component cycling through in this

case here, cyclin and cinilic 2 can be used to describe a complex cellular

behavior like proliferation. Similarly PDE or partial differential

equation models can nicely capture the spatial dynamics of signaling molecules,

of signaling actions as in, in this case where the model here which reference for

cyclic AMP production in the dendrites of cultured neurons can capture what is seen

experimentally here. I should just point out that the the loss

of signal is a representative of an increase in Cyclic AMP.

So going from this side to this side, one sees a loss of signal in the in the

dendrite and this appears as a red increase in cyclic AMP in the simulation.

So, for partial differential equation models, and where, for instance, in

virtual cell, can capture the spatial dynamics of signaling.

Dynamical models also provide good descriptions or accurate descriptions of

progression of probabilistic systems. Many important cell biological processes

are inherently stochastic. Some of these processes like like

neurotransmitter release in initiation of gene expression initiation of filapodia

formation entirely different kinds of processes but nevertheless are stochastic

and these stochastic processes arise From stochastic with biochemical reactions,

with the reaction prob, follows some probability function.

as I described previously to you, the Gillespie algorithm provides, an explicit

feasible approach for computing the progress of stochastic reactions.

And, hence, these kinds of models have the ability to stimulate the trajectory

of individual subcellular processes and capture the stochacity of of important

biological or cell biological phenomena. Dynamical models can estimate the ability

of network motifs to process information during signal flow.

In deed, ODE models can be used to get a deep understanding of network behavior

and I come back to the same example I used before to show that having a network

topology by itself does not give us information of what that network motif,

in this case, a positive feedback loop if it's capable of doing from graphateria

analysis or network analysis. However, if the components of this

network small network, a cast has biochemical reactions.

And then, one computes run simulation in an ODE model, to compute the effect of

stimulating with EGFR with EGF or on the levels of MAP kinase or protein kinase C

activity. One can see that one can identify by

stable behaviors. So here are the set of the reactions for

rest of the system. And here is what comes out of the

simulation, where when one looks at MAP kinase activity as a function of putting

kinase activity or vice versa, one can clearly see that the system can exist in

two states. An active and inactive state and this

kind of bistabilities and consequence of the presence of this positive feedback

loop. So dynamical models have a capability to

tell you what a network motif can do. However, dynamical models have

limitations. what kind of limitations do they have?

The model accuracy is dependent on the underlying assumptions and the parameters

that are used. Parameters, kinetic parameters are often

hard to find and larger dynamical models need to be well constrained.

Otherwise, with too many parameters any type of behavior can be simulated.

Remember, some lectures ago, I talked to you about the spherical cow.

And this, this almost sounds like a joke, but in reality, we have too many

parameters that are unconstrained. One can really produce any type of

behavior, and it is not meaningful for our understanding of what a system is

capable of doing. On the right is a plot that shows a match

between an experiment with just black triangles here and simulations which is

the open triangles of EGF or epidermal factor activation of MAP kinase using

these two sets of reactions here. you can see that when, when one compares

the [INAUDIBLE] the simulations to the experiment, that there is a good match in

the amplitude of the, effect. But the time course is sort of for the

simulation is off set. So the match there is not so good.

so this is the way one constrains these reactions, so if you want to build a

larger network, you can say all of the reactions from EGFR to map kinase or EGF

to MAP kinase are constrained using this kind of a time course this kind of a time

course profile. And so, while any one individual

parameter or reaction rate might be not exactly what occurs in real life, as an

aggregate, they [INAUDIBLE] they capitulate, or recapitulate what is seen

experimentally. So in as an aggregate, they must be in

the right range. So one of the reasons why this might be

different between the simulations, the experiment, in terms of time course

effects is that the parameters for this model were measured in, by in vitro

components while the map kinase activity was measured in an intact cell.

Finding kinetic parameters beneath from intact cells is nearly impossible.

There have been, there are, as far as I know there are no real ways of measuring

these in the intact cells. Often finding experimentally measured

kinetic parameters, even in vitro or for purified cell components is quite

impossible. And so many parameters are either

estimated from time course experiments, or guesstimated.

And this lack of data per, data regarding kinetic parameters in the level of

cellular components greatly limits our ability to build this large dynamical

model. So this is sort of a set of data that

needs to be obtained on a genome-wide or proteome-wide basis for us to build

progressively larger dynamical models. The other problem in dynamical models is

that even if you had all the parameters and you could compute such a model, it's

not really easy to understand input, output or relationships between why you

see a certain activity between different between distill components.

So for instance consider this network which is a relatively simple network as

networks go. And in this particular one, one can ask

the question why is the activation of MAP kinase necessary for the activation of

CaMKII too. and just knowing these, that these two

are related or knowing how the activity of sorry the, the activity of CaM, CaMKII

the activity of CaMKII. changes with the respect to MAP kinase,

changes in MAP kinase activity doesn't really, really tell you what the

mechanisms are. You, what you really need to understand

is the topology of the system, the existence of this feedback loop here.

And the connection between protein kinase C and tolciclate 2, and adenylate cyclase

2 and uh, [INAUDIBLE] Cyclic AMP and PP1. So one needs to know network topology to

understand how the input-output relationship between these two entities

are going to work. So, it's like not and relatively

straightforward thing just by knowing dynamical properties of network.

Do you understand how and why connections that operate it and what the

relationships are? So the take home points for this lecture

are as follows. The different modeling approach is each

have their strengths and weaknesses in terms of the knowledge they can provide

from the modeling efforts. Statistical models are very useful in

providing the big picture overview of relationship between distal entities,

examples, genes and disease, or genes and phenotypes and so on.

But they do not tell us anything about the basis for the relationship.

That is, the mechanisms of these relationships, so this is sort of a

limitation of statistical models. Nevertheless, as I told you before, they

are like very good good bookends and provides contours of a functional system,

so statistical models are very, very useful tool in understanding systems.

Network models are essential to understand how the system is organized

and its capability to process information and enable regulation.

So organization leads to information [INAUDIBLE] processing capability and

this capability enables regulations. So network [INAUDIBLE] so this kind of

understanding network apology, and that's why we all spend a lot of time on it is a

critical part of assistance biology. Network models, however, do not help us

predict how the system will change with respect to time, so the predictive

behaviors or the predictive capability from just graph theory analysis is not a

lot. There is some, but it's not, it's, it's

not complete. Dynamical models enable us to understand

and predict how systems behavior change with respect to time and space.

This kind of predictive capability is what we seek in building and analyzing

model. However as systems get larger, such

dynamical models do not help us understand the basis the basis for these

distal input-output or predictive relationships.

And so one really needs a network topology in combination with dynamical

modeling to understand both why something happens and how that if fact is obtained.

So, to really have a predictive understanding of systems, we really need

all three kinds of modeling approaches. And the Strengths and limitations of each

one compensates for the other and as a whole I think when one applies them

carefully to large systems in the future, one is going to have very good

understanding that leads to sort of predictive capabilities that are very

reliable. [SOUND]