0:09

Hello.

Â Welcome to Dynamical Modeling Methods for Systems Biology.

Â My name is Eric Sobie.

Â I'm an associate professor at Icahn School of

Â Medicine at Mount Sinai in the Pharmacology Department,

Â and I'm going to be the instructor for

Â your course, Dynamical Modeling Methods for Systems Biology.

Â 0:26

Thank you for, for signing up and I look

Â forward to working with you as, we, we teach

Â about different methods that are used in systems biology

Â to analy, to analyze and implement dynamical mathematical models.

Â [BLANK_AUDIO]

Â In this first video, topics that we're

Â going to cover are illustrated on this outline.

Â 0:50

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

Â We're going to discuss the specific biological topics and

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

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

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

Â 1:21

Second we want to teach methods for

Â mathematical analysis of biological systems and simulation output.

Â In other words you implement a model, then you

Â get some output from the model, so what sorts of

Â approaches do you use to analyze that output, and

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

Â And then, third, we want to demonstrate how

Â dynamical mathematical models can provide novel insight,

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

Â So the combination of experiments with dynamical

Â mathematical models is going to provide novel insight

Â 2:05

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

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

Â approaches, different types of mathematical models into two categories.

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

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

Â So what do I mean by that?

Â 2:28

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

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

Â dataset, the kind that you might get

Â in a genomics experiment or audiomics experiment.

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

Â And then once you've used statistical methods to

Â find patterns in that data set you can

Â generate predictions, and the predictions are based on

Â the structure that you've uncovered within the data.

Â And so some of the keywords that you

Â can associate with this, top down approach are things

Â like network analysis gene set enrichment analysis, clustering

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

Â 3:16

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

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

Â These top down approaches were taught in a Coursera

Â course that was offered by my coleague from Mount Sinai,

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

Â this course through Coursera again in the next few months.

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

Â learning principal components I would encourage you

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

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

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

Â So the approach here is sort of the opposite

Â of what we saw with the top down model.

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

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

Â describe how the components in your

Â biological system interact with one another.

Â Then you run simulations to generate the, to

Â generate predictions for what would happen under different conditions.

Â 4:16

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

Â things like ordinary differential equations, tools

Â of dynamical systems to interpret the output.

Â Methods for parameter estimation, partial

Â differential equations and stochastic models.

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

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

Â Models consisting of systems of ordinary differential equations and tools of

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

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Â And this dichotomy of statistical models versus dynamical models has

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

Â Including one of ours.

Â This is an article that my colleagues and I published.

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

Â And this, this Coursera course is devolved in many ways

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

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

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

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

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

Â know, in the same class that also

Â discuss distinctions between different categories of models.

Â 5:35

I think it's worthwhile to review the general structure

Â that you frequently see with a dynamical modeling study.

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

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

Â 5:50

So usually in a dynamical, mathematical modeling study

Â you begin with some idea of the mechanism.

Â What happens biologically.

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

Â Where you have some biological species B

Â can get converted into some other species C.

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

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

Â 6:18

Once you know something about the mechanism

Â or you hypothesize something about the mechanism.

Â You write down some equations describing how the

Â different components in the system interact with one another.

Â And this is an example where we have two

Â equations and these are in the category of ordinary

Â differential equations; that describe how a particular system, how

Â the components of a particular system evolve with time.

Â 6:41

Once you've written down the equations then

Â you write a program to simulate those equations.

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

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

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

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

Â Programming environment before we show you examples

Â of dynamical,mathematical models that are implemented using MadLab.

Â 7:08

Once you have your program, you run simulations

Â with your with your program that simulates the equations.

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

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

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

Â Although the actual shape of the oscillation is different between the

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

Â So then, after you've run these simulations,

Â how do you make sense of them?

Â Well then you often use tools of the

Â field of dynamical systems to analyze your output.

Â And one of the things that you might

Â do frequently, is you might vary some parameter

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

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

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

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

Â But then with higher values of the parameter

Â you only get a middle value of the output.

Â So in his case the oscillations have, have ceased.

Â So, by running these types of simulations where

Â you vary a parameter and you analyze the

Â output you can gain insight into how the

Â behavior of the system changes under different conditions.

Â So this is the general structure of a

Â dynamical modeling study, from mechanism to equations, to

Â a program that simulates the equations, to simulation

Â results, and then to analysis of the output.

Â 8:33

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

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

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

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

Â 9:00

At the end of each lecture we're going to

Â provide you with one or more self assessment questions.

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

Â try to answer the question to assess for yourself;

Â how well you've understood the material in the lecture

Â 9:16

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

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

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

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

Â And then passing the course is going

Â to depend on completing these five homework assignments.

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

Â 9:56

Next we want to teach you how to develop

Â models consisting of systems of ordinary differential equations.

Â And throughout this course we're going to, abbreviate

Â ordinary differential equations, with ODEs, like that.

Â 10:26

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

Â this course, is that models can be

Â used for understanding several different biological processes.

Â And some of the biological processes that we're

Â going to discuss in this course are the following.

Â 10:49

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

Â This is a case where mathematical models have

Â been extremely successful and extremely important in understanding.

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

Â 11:02

And we're also going to talk about

Â mathematical models of electrical signaling in neurons.

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

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

Â 11:15

And the overall goal is provide you with the

Â tools necessary to apply these types of models to

Â your own questions of interest, so some of you

Â might be interested in some of these specific biological questions.

Â But many of you are you know, might have some

Â interest in some other biological

Â mechanism, or some other biological pathway.

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

Â to whatever system it is that you're the

Â most interested, that you have the most interest in.

Â 11:45

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

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

Â one to two questions at the end of each lecture.

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

Â Give you some time to think about it.

Â And then after you think about it and answer

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

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

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

Â And then you can see for yourself how

Â well you understood the material that was covered.

Â 12:18

Overall assessment in this course is going

Â to be performed through the homework assignments.

Â The homework assignments are going to require

Â you to perform simulations with dynamical models.

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

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

Â The way that you're going to really learn

Â these approaches is by doing the simulations yourself.

Â 12:41

So the homework assignments are going to

Â ask you to perform simulations with dynamical models.

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

Â to make you write the the entire model from scratch.

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

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

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

Â to modify it in order to do something else.

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

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

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

Â interpretation from the results that

Â you've obtained with that mathematical model.

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

Â it correctly and that you can

Â get biological interpretation from your results.

Â 13:46

Second, quantitative skills.

Â Can you get a can you get

Â a reasonable quantitative interpretation of your simulation results?

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

Â To obtain new biological insight, into the particular

Â problem and into the particular system that you're looking

Â