0:09

Hello.

Welcome to Dynamical Modeling Methods for Systems Biology.

My name is Eric Sobie.

I'm an associate professor at Icahn School of

Medicine at Mount Sinai in the Pharmacology Department,

and I'm going to be the instructor for

your course, Dynamical Modeling Methods for Systems Biology.

0:26

Thank you for, for signing up and I look

forward to working with you as, we, we teach

about different methods that are used in systems biology

to analy, to analyze and implement dynamical mathematical models.

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In this first video, topics that we're

going to cover are illustrated on this outline.

0:50

We're going to talk, we're going to discuss the overall course goals.

We're going to discuss the specific biological topics and

mathematical topics that are going to be covered in the course.

And then we're going to review the overall structure of the course

and how we're going to perform grading and assessment in this course.

1:21

Second we want to teach methods for

mathematical analysis of biological systems and simulation output.

In other words you implement a model, then you

get some output from the model, so what sorts of

approaches do you use to analyze that output, and

gain more insight into the biological system, through that analysis?

And then, third, we want to demonstrate how

dynamical mathematical models can provide novel insight,

the type that you cannot begin to get if you, you're only doing experiments.

So the combination of experiments with dynamical

mathematical models is going to provide novel insight

2:05

So, what do we mean when we talk about dynamical mathematical models?

Well, I think it's helpful to divide different computational

approaches, different types of mathematical models into two categories.

And I like to differentiate between statistical, or what I call

top-down models, versus dynamical, or what I also call bottom-up models.

So what do I mean by that?

2:28

Well, the approach you take in a top down model, can be summarized as follows.

You begin with the dataset and often a very large dataset very large scale

dataset, the kind that you might get

in a genomics experiment or audiomics experiment.

Then you use statistical methods to find patterns in that, in that data set.

And then once you've used statistical methods to

find patterns in that data set you can

generate predictions, and the predictions are based on

the structure that you've uncovered within the data.

And so some of the keywords that you

can associate with this, top down approach are things

like network analysis gene set enrichment analysis, clustering

algorithms, principal component analysis, or, or partially squares regression.

3:16

Now I should note that these top down approaches to doing mathematical

modeling, these statistical models are not the focus of this course here.

These top down approaches were taught in a Coursera

course that was offered by my coleague from Mount Sinai,

Dr. Avi Ma'ayan and Dr. Ma'ayan is planning to offer

this course through Coursera again in the next few months.

So if your primary interest is in these types of models, learning clustering or

learning principal components I would encourage you

to take a look at Dr. Ma'ayan's course.

Our focus here is going to be on a different category of model.

What I, what I like to call dynamical models, or what I also call bottom models.

So the approach here is sort of the opposite

of what we saw with the top down model.

With the bottom up model, you begin with a hypothesis of biological mechanism.

Once you have this hypothesis you write down some equations, to

describe how the components in your

biological system interact with one another.

Then you run simulations to generate the, to

generate predictions for what would happen under different conditions.

4:16

And some of the keywords that are associated with bottom up models, are

things like ordinary differential equations, tools

of dynamical systems to interpret the output.

Methods for parameter estimation, partial

differential equations and stochastic models.

Now in this course, we're not going to be able to cover

everything, so we're going to focus on the first two keywords in here.

Models consisting of systems of ordinary differential equations and tools of

dynamical systems in order to interpret the, the results of these simulations.

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And this dichotomy of statistical models versus dynamical models has

been discussed in the literature in, in, in several review articles.

Including one of ours.

This is an article that my colleagues and I published.

It describes a course, that we developed at Mount Sinai School of Medicine.

And this, this Coursera course is devolved in many ways

from this course that, that we teach at, at Mount Sinai.

So if you're interested in, in learning more about

this, this, dichotomy of, of statistical versus dynamical models.

I would encourage you to, to check out this article.

And there's other articles in the, in the same category and it, you

know, in the same class that also

discuss distinctions between different categories of models.

5:35

I think it's worthwhile to review the general structure

that you frequently see with a dynamical modeling study.

They actually give you some sense of what are the steps are, that are involved.

And what kind of insight do we get from this type of study.

5:50

So usually in a dynamical, mathematical modeling study

you begin with some idea of the mechanism.

What happens biologically.

So I've just illustrated this, with a simple example here.

Where you have some biological species B

can get converted into some other species C.

And this protein, the species A might regulate conversion of B to C.

For instance, A could be an enzyme that catalyzes conversion of, of B into C.

6:18

Once you know something about the mechanism

or you hypothesize something about the mechanism.

You write down some equations describing how the

different components in the system interact with one another.

And this is an example where we have two

equations and these are in the category of ordinary

differential equations; that describe how a particular system, how

the components of a particular system evolve with time.

6:41

Once you've written down the equations then

you write a program to simulate those equations.

These are the first two lines of a, of a program the does such a simulation.

The programming environment we're going to use to, to write these programs

to simulate our ordinary differential equations base models is called mat lab.

And so we're going to have several lectures to introduce you to the MATLAB.

Programming environment before we show you examples

of dynamical,mathematical models that are implemented using MadLab.

7:08

Once you have your program, you run simulations

with your with your program that simulates the equations.

So this is solving the temporal evolution of one species and another species.

And you can see that the black one is oscillating with respect

to time, and the red one is oscillating with respect to time.

Although the actual shape of the oscillation is different between the

one that's represented in black and the one that's represented in red.

So then, after you've run these simulations,

how do you make sense of them?

Well then you often use tools of the

field of dynamical systems to analyze your output.

And one of the things that you might

do frequently, is you might vary some parameter

and then you might look to see how your output changes as you vary this parameter.

And this is a case where you, un, under low values of the parameter.

You can get, high values of output, alternating with low values of output.

That would be analagous to these oscillations we're seeing over here.

But then with higher values of the parameter

you only get a middle value of the output.

So in his case the oscillations have, have ceased.

So, by running these types of simulations where

you vary a parameter and you analyze the

output you can gain insight into how the

behavior of the system changes under different conditions.

So this is the general structure of a

dynamical modeling study, from mechanism to equations, to

a program that simulates the equations, to simulation

results, and then to analysis of the output.

8:33

Now, let's discuss some of the logistics of this course.

The format that we're going to, that we're going to take is as follows.

It's going to be a seven week total course, consisting

of approximately 25 lectures; each lecture being approximately 20 minutes.

9:00

At the end of each lecture we're going to

provide you with one or more self assessment questions.

This is a way for you to think about what you've what you've learned in the lecture,

try to answer the question to assess for yourself;

how well you've understood the material in the lecture

9:16

And then the over all assessment is going to be based on five homework assignments.

They're going to be given after each lecture block so

the 25 lectures are going to be divided into five blocks.

Each of these five blocks is going to be associated with a homework assignment.

And then passing the course is going

to depend on completing these five homework assignments.

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The skills that we wish to teach you in this course are, are the following.

9:56

Next we want to teach you how to develop

models consisting of systems of ordinary differential equations.

And throughout this course we're going to, abbreviate

ordinary differential equations, with ODEs, like that.

10:26

And one of the arguments that we're going to make, as we go through

this course, is that models can be

used for understanding several different biological processes.

And some of the biological processes that we're

going to discuss in this course are the following.

10:49

We're going to talk about regulation of the cell cycle.

This is a case where mathematical models have

been extremely successful and extremely important in understanding.

Weather or not cells want to divide or weather they want to stop dividing.

11:02

And we're also going to talk about

mathematical models of electrical signaling in neurons.

That's another classic case where mathematical models have been really

critical for getting a quantitative understanding of how the biology works.

11:15

And the overall goal is provide you with the

tools necessary to apply these types of models to

your own questions of interest, so some of you

might be interested in some of these specific biological questions.

But many of you are you know, might have some

interest in some other biological

mechanism, or some other biological pathway.

But the hope is that if we teach you the tools, you can use the same tools

to whatever system it is that you're the

most interested, that you have the most interest in.

11:45

How are we going to perform assessment, self-assessment in this class?

Self-assessment is going to be performed by providing you with

one to two questions at the end of each lecture.

And we're going to, I'm going to introduce the question.

Give you some time to think about it.

And then after you think about it and answer

it for yourself, I'm going to go through the explanation.

So this will be a way for you to, think about what you've

heard in each lecture and try to apply the concepts that you've heard.

And then you can see for yourself how

well you understood the material that was covered.

12:18

Overall assessment in this course is going

to be performed through the homework assignments.

The homework assignments are going to require

you to perform simulations with dynamical models.

Because this is a course on teaching you methods, on teaching

teaching you the sorts of approaches that are used in systems biology.

The way that you're going to really learn

these approaches is by doing the simulations yourself.

12:41

So the homework assignments are going to

ask you to perform simulations with dynamical models.

And the general format we're going to use is not

to make you write the the entire model from scratch.

We're going to provide you with some MATLAB code that does one

thing, that might run a simulation of, of a particular biological system.

And then we're going to ask you to adapt it,

to modify it in order to do something else.

And then we're going to provide you with assessment questions that

are designed to, to verify first of all that you've implemented

the model correctly, and also that you can get some biological

interpretation from the results that

you've obtained with that mathematical model.

So we want to test both your your programming skills to implement

it correctly and that you can

get biological interpretation from your results.

13:46

Second, quantitative skills.

Can you get a can you get

a reasonable quantitative interpretation of your simulation results?

And third, can you use this mo, the model, can you use the, the simulation results?

To obtain new biological insight, into the particular

problem and into the particular system that you're looking