Systems biology course 2018 Uri Alon - Lecture 8 A - Dynamic Compensation

Summary

This lecture covers dynamic compensation in physiological circuits, focusing on robustness in biological systems. It explores how biological circuits maintain stable function despite natural variations, such as organ size control, glucose regulation, and resistance to mutations. The discussion moves from cell-level circuits to organ-level communication, particularly focusing on the glucose-insulin circuit. The lecture emphasizes how organs maintain their size despite continuous cell turnover, and how insulin sensitivity and resistance play a key role in glucose regulation. Real-life examples, such as diabetes and pregnancy-induced insulin resistance, are used to demonstrate these principles.

Takeaways

• 📚 The lecture focuses on dynamic compensation in physiological circuits, emphasizing the robustness of biological systems to natural variations.
• 🔬 Robustness in biological circuits is defined as the insensitivity to naturally occurring variations, which is crucial for precise functioning.
• 🐕 The lecture welcomes all species, highlighting the universal presence of physiological circuits in different organisms.
• 🧬 The discussion transitions from cellular to physiological levels, examining how organs communicate through hormones like insulin to maintain homeostasis.
• 🩸 Glucose homeostasis is critical for health, with the body striving to maintain blood glucose levels within a narrow range for optimal brain function.
• 💉 Insulin, produced by the pancreas, is central to glucose regulation, prompting cells to take up glucose and lower blood sugar levels.
• 🏋️‍♀️ Insulin sensitivity varies and can be influenced by factors like exercise, infection, and obesity, affecting how effectively insulin works.
• 📉 The body can compensate for changes in insulin sensitivity, maintaining glucose dynamics despite significant variations in this parameter.
• 🤰 Insulin resistance is a common issue, especially in Western societies, and can be influenced by factors like obesity, lack of exercise, and aging.
• 📊 The classic glucose tolerance test is used to measure how the body handles glucose, providing insights into insulin sensitivity and glucose regulation.

Q & A

What is the main topic of the lecture?

The main topic of the lecture is dynamic compensation in physiological circuits, focusing on robustness in biological systems and how it applies to the communication between organs in our body.

What is meant by robustness in the context of biological circuits?

Robustness in biological circuits refers to the property where these systems remain functional and maintain their performance despite naturally occurring variations.

What is the concept of 'network motifs' mentioned in the lecture?

Network motifs are recurring circuit elements that carry out different computational functions within biological networks.

How does the concept of exact adaptation apply to bacterial chemotaxis?

Exact adaptation in bacterial chemotaxis refers to the ability of bacteria to maintain a constant tumbling frequency despite changes in their environment, such as the presence or absence of food.

What is the role of insulin in the body as discussed in the lecture?

Insulin is a hormone that stimulates the uptake of glucose from the blood by cells like muscles, fat, and liver, thereby helping to regulate blood sugar levels.

What is insulin sensitivity and why is it significant?

Insulin sensitivity refers to the effectiveness of insulin in promoting glucose uptake by cells. It is significant because it can vary under different physiological conditions and is a key factor in glucose homeostasis.

How does the body maintain a stable organ size despite cells constantly dividing and dying?

The body maintains stable organ size through a balance between cell division and cell death, ensuring that the overall size of organs remains constant throughout adulthood.

What is the glucose tolerance test and why is it important?

The glucose tolerance test is a procedure used to determine how well the body processes glucose. It is important for diagnosing conditions like diabetes and understanding how the body handles glucose after a meal.

What are some factors that can influence insulin resistance?

Factors that can influence insulin resistance include obesity, lack of exercise, aging, infections, and certain hormonal changes such as those that occur during pregnancy.

How does the body compensate for changes in insulin sensitivity?

The body compensates for changes in insulin sensitivity by adjusting the amount of insulin produced and secreted by the pancreas, as well as by tuning the sensitivity of cells to insulin.

What is the minimal model for glucose-insulin dynamics mentioned in the lecture?

The minimal model for glucose-insulin dynamics is a mathematical model that describes how glucose levels in the blood change over time in response to insulin and other factors, such as meal intake.

Outlines

00:00

🧬 Introduction to Dynamic Compensation in Physiological Circuits

The lecture begins with a focus on dynamic compensation within physiological circuits, emphasizing the concept of robustness in biological systems. Robustness is defined as the insensitivity of biological circuits to naturally occurring variations. The lecture builds upon the previously discussed principle of network motifs, which are recurring circuit elements that perform different computational functions. The speaker highlights the challenges that biological circuits face due to the inherent problems in biological materials and aims to explore how these circuits maintain precise operations despite these challenges. The lecture also introduces the idea of moving up a level of organization from individual proteins within cells to entire organs that communicate with each other through hormones and other signaling mechanisms.

05:00

🌡️ Exploring Robustness in Hormonal Communication

This section delves into the robustness of hormonal communication between organs, using the example of glucose and insulin regulation. The speaker discusses the importance of maintaining proper glucose levels in the bloodstream, as both high and low levels can be detrimental to health. The lecture explains how the body uses insulin, produced by the pancreas, to regulate glucose uptake by muscles, fat, and liver. The concept of insulin sensitivity is introduced, which refers to the effectiveness of insulin in promoting glucose uptake by tissues. The speaker also touches on how insulin sensitivity can vary under different physiological conditions, such as exercise, infection, and pregnancy, and how these variations are managed by the body to maintain glucose homeostasis.

10:04

🩺 The Glucose-Insulin Feedback System

The paragraph explains the feedback mechanism between glucose and insulin in the body. When blood glucose levels rise, such as after a meal, the pancreas releases insulin. Insulin then signals cells in muscles, fat, and liver to take up glucose, thereby reducing blood glucose levels. The speaker simplifies the complex physiological process into a mathematical model to illustrate how the body can maintain a stable glucose level despite variations in insulin sensitivity. The model is a differential equation that represents the balance between glucose input from food and glucose removal by tissues, modulated by insulin sensitivity. The lecture aims to demonstrate how such a model can help understand the body's ability to compensate for changes in insulin sensitivity and maintain glucose levels within a healthy range.

15:04

🏋️‍♀️ Impact of Insulin Sensitivity on Glucose Dynamics

This section discusses how insulin sensitivity impacts glucose dynamics in the body. The speaker explores the physiological mechanisms behind insulin resistance, which can occur due to various factors such as obesity, lack of exercise, and aging. The lecture explains that insulin resistance is a significant health issue, particularly in Western societies, and is associated with conditions like type 2 diabetes. The speaker also addresses the question of why the body would evolve a system that includes insulin resistance, suggesting that it serves a purpose in resource allocation during different physiological states, such as during exercise or infection. The lecture emphasizes the importance of understanding not just the 'what' and 'how' but also the 'why' behind biological processes.

20:07

📚 Mathematical Model of Glucose and Insulin Dynamics

The speaker introduces a mathematical model of glucose and insulin dynamics, which is crucial for understanding how the body maintains glucose homeostasis. The model is a differential equation that describes the change in glucose levels over time, influenced by meal intake and glucose removal by tissues. The removal rate is determined by insulin sensitivity (s), the amount of insulin (I), and the effectiveness of insulin in promoting glucose uptake. The speaker highlights that while this model is widely used in clinical settings to interpret glucose tolerance tests, it does not fully explain the body's ability to compensate for changes in insulin sensitivity. The lecture encourages students to think critically about the models and to consider the broader implications of parameter changes in biological systems.

25:09

🔍 Measuring Insulin Sensitivity and Its Clinical Relevance

In this part, the speaker discusses how insulin sensitivity can be measured clinically and its importance in understanding an individual's response to insulin. The measurement involves injecting a unit of insulin and observing the subsequent decrease in blood glucose levels. This method provides a quantitative measure of s, the insulin sensitivity parameter. The speaker emphasizes that understanding insulin sensitivity is crucial for managing conditions like diabetes and for personalizing treatment strategies. The lecture also touches on the dynamic nature of insulin sensitivity, which can change rapidly in response to physiological needs, such as during exercise or infection, and how these changes are clinically relevant.

Keywords

💡Dynamic Compensation

Dynamic compensation refers to the ability of biological systems to adjust and maintain stability in response to changes in their environment or internal conditions. In the context of the video, it is discussed in relation to physiological circuits, which are networks of interactions within an organism that perform specific functions. The lecturer mentions that dynamic compensation is crucial for maintaining precise operations despite variations in biological materials, such as fluctuations in protein concentrations.

💡Physiological Circuits

Physiological circuits are the interconnected systems within an organism that regulate various bodily functions. These circuits can involve networks of cells, tissues, and organs that communicate through hormones and other signaling molecules. The video lecture focuses on how these circuits achieve robustness, which is the ability to maintain function despite natural variations. An example given is the communication between organs through the bloodstream, which is a key aspect of physiological regulation.

💡Robustness

Robustness, in the context of the video, is a property of biological circuits that allows them to remain functional and maintain their performance despite variations in their components or environment. The lecturer discusses how biological systems, such as cells and organs, achieve robustness through various mechanisms, including differential equations and feedback loops. This concept is central to understanding how organisms can maintain stability and function in the face of natural fluctuations.

💡Network Motifs

Network motifs are recurring patterns of connections within biological networks that perform specific computational functions. The video script mentions that the first part of the course covered the principles of network motifs, which are the fundamental building blocks of complex biological systems. These motifs are important for understanding how different components of a biological circuit interact and contribute to the overall function of the system.

💡Bacterial Chemotaxis

Bacterial chemotaxis is the process by which bacteria move towards or away from chemicals in their environment, which is an example of a biological system's response to stimuli. In the video, the lecturer uses bacterial chemotaxis to illustrate the concept of robustness, specifically how bacteria can maintain a consistent tumbling frequency despite changes in their environment. This is an example of how biological systems can adapt and maintain function in varying conditions.

💡Insulin

Insulin is a hormone produced by the pancreas that plays a critical role in regulating glucose levels in the blood. The video discusses insulin as part of the hormone circuit for glucose regulation, highlighting its importance in maintaining homeostasis. Insulin sensitivity, or the effectiveness of insulin in promoting glucose uptake by cells, is a key parameter in this circuit, and variations in this parameter can lead to conditions like diabetes.

💡Glucose Tolerance Test

The glucose tolerance test is a medical procedure used to determine how effectively an individual's body processes glucose. The video script mentions this test as a way to measure the body's response to glucose intake, which is a critical aspect of understanding insulin sensitivity and glucose regulation. The test involves measuring blood glucose levels after a person consumes a glucose-rich drink, providing insights into the dynamics of glucose homeostasis.

💡Insulin Resistance

Insulin resistance is a condition in which the cells of the body do not respond properly to the hormone insulin, leading to higher than normal blood glucose levels. The video discusses insulin resistance in the context of various physiological states, such as obesity and infection, where the body's tissues become less sensitive to insulin. This resistance can lead to health complications, including type 2 diabetes, and is an important aspect of the glucose-insulin regulatory circuit.

💡Hormones

Hormones are signaling molecules produced by glands in the endocrine system that regulate various physiological processes in the body. In the video, hormones are discussed as key players in the communication between organs, allowing them to coordinate their functions and maintain homeostasis. The example of insulin, which regulates glucose levels, is used to illustrate how hormones can act as messengers in physiological circuits.

💡Cytokines

Cytokines are a broad category of small proteins that are important in cell signaling, particularly in the immune system. The video mentions cytokines in the context of infection, where they can influence insulin sensitivity. During an infection, cytokines can be produced that signal to the body's cells to reduce their sensitivity to insulin, thereby allocating more glucose to the immune system to fight off the infection. This is an example of how the body's response to external threats can impact physiological circuits.

Highlights

Introduction to dynamic compensation in physiological circuits and the concept of robustness in biological systems.

Review of network motifs as recurring circuit elements carrying out different computational functions.

Discussion on how biological circuits maintain precise function despite naturally occurring variations.

Explanation of robust input-output relationships in phosphorylation circuits.

Introduction to bacterial chemotaxis as an example of robustness in biological systems.

Concept of exact adaptation and integral feedback in maintaining steady state in biological circuits.

Shift in focus from cellular to physiological level, examining organs and their communication through hormones.

Importance of maintaining organ size despite constant cell turnover.

Challenges in inter-organ communication due to variations in parameters and the need for robustness.

Addressing the issue of mutations in cells and their impact on robustness.

Overview of the hormone circuit for glucose and insulin as a well-characterized example.

Role of insulin in glucose uptake by muscles, fat, and liver, and its regulation by insulin sensitivity.

Function of the pancreas and beta cells in insulin production in response to blood glucose levels.

Variability in insulin sensitivity and its impact on glucose dynamics.

Physiological mechanisms behind changes in insulin sensitivity, such as during infection or exercise.

Discussion on insulin resistance, its causes, and its implications in society and health.

Exploration of how the body compensates for changes in insulin sensitivity to maintain glucose homeostasis.

Introduction to the minimal model for glucose and insulin dynamics and its limitations.

Invitation for feedback on the course material for the development of a textbook.

Transcripts

everyone welcome to our lecture on

dynamic compensation in physiological

circuits we're gonna turn off the music

and but as always let's invite you to

take a nice deep sigh of relief I love

the way the class is getting better and

better at letting out a you know I want

a ridiculous sound because that's when

you're really relaxed and it's review

and of course you know we finished the

the first part which was about principle

of network motifs the recurring circuit

elements that carry of different

computational functions and now we're in

the second part of the course about

robustness robustness is a property of

biological circuits where they're a

central feature is insensitive to

naturally occurring variations so we're

learning more and more about the

problems in biological material the

problems which circuits have to overcome

in order to work precisely and so far

we've been a nice deep sigh of relief

welcome there's even a dog it's great

great another sigh of relief for the dog

what's his name - Lee classic yeah yeah

all species are welcome another

really because all species actually have

all these physiological circuits we'll

talk about today about the hormones

stuff super and actually dogs played a

big role you know and so we talked about

so we said that robustness of what of a

feature with respect to a variation that

occurs naturally so we talked about for

example how to have a robust

input-output relationships in a circuit

a circuit phosphorylation circuit it's

saying by having these by functional

components and then if you vary the

concentration of the proteins you don't

get input output to change and we talked

about bacterial chemotaxis have material

sense and food and they change your

tumbling frequency the tumbling

frequency and has some level and then

when if they sense food it goes back to

the same level so this is the property

of exact adapt ation and how we can

build circuits that have exact

temptations basically differential

equations where they where the output

appears the only way to get a zero is

for the output to be at its steady state

level that's we call that integral

feedback they'll play a role today too

so I'll review it if you don't worry and

we talked about full change detection

which is the ability of systems to

respond to fold change there's a

relative changes is to normalize out if

you give them an input a constant and

multiplies that input we talked about

these forms of robustness and we all so

far we talked in this course about

basically about cells like bacteria and

about the cell we started the cell is

the level of organization that we worked

on how to cell sensor the environment

how it computes how it responds and

today what I want to show you is that

you can take very similar equations and

ways of thinking and go up a level of

organization so now instead of proteins

inside cells that make a circuit we're

going to talk about cells that

communicate with each other making each

other / etc

and the context we'll talk about is

organs in our body so we're going to

move to the physiological level our

body's made of organs brain liver

pancreas muscles etc and these organs

talk to each other a lot of times

through the bloodstream by secreted

hormones for example send messages to

each other in order to keep us in a good

balanced situation all the thousands of

important parameters in the body like

blood sugar calcium are kept there good

level so that our brains can work our

body can work and this is done by

circuits of communication between organs

and between the cells and the organs

right so we're talking this level and

I'd like to demonstrate how our way of

thinking applies to the physiological

level too but in the physiological level

this level of organs there are new

problems to overcome we don't need to

worry now about fluctuations of proteins

inside the cell we have more dangerous

problems to think about we should for

example and the organs in our body the

cells turn over all the time they divide

and die and the cells basically replace

themselves every let's say few weeks and

still the body organs keep their proper

size it's not the deliver expands or

shrinks right it stains basically the

same size throughout adulthood

how do organs keep their size even

though they're made of exponentially

dividing cells so we'll talk about this

problem of so organ size control

big big issue and this check how come

our bodies right when I say the word

body a million cells in my body divided

and another million died and if that's

just a little bit different I'll soon

explode if it's more diversion or

degenerate if it's more death right how

does that work it's critical question

right also when you have this

communication between organs the liver

doesn't know the parameters of the brain

and the muscle sitter those parameters

can change so how can you communicate

despite variation in the parameters you

can say in the listening ability of

distant tissues distant organs and

finally our our bodies that says cells

are constantly turning over it's

inevitable that you'll get a mutation a

dangerous mutation that can let's say

make the cell now sense to sensitive or

insensitive to a signal so how do you

deal with that problem now robustness to

see resistance to mutations that are

guaranteed to to arise because there's

so many divisions you know when you

reach old age and more and more

mutations so we're going to deal with

these three naturally occurring

variations and see how how it basically

a really elegant circuit in our body it

can it's once deal with all three so

they say three problems solved in one

any questions so far about the

motivation for this lecture

I'm positive there is a question who's

going to ask the question you okay so

that's the mystic a nice deep sigh of

relief

things are so crystal clear and so we

looked at the cell circuits organs and

I'm going to talk here just to

demonstrate this about the probably the

best characterized hormone circuits

communication between tissues and that

is the famous a hormone circuit for

glucose and insulin yeah

just wondering how many of you have

heard of insulin so majority so I want

to describe the circuit a and and see

how how it deals with these problems

we can have the privilege of dealing

with problems that can be solved in

principle and not think about the news

at least for the next hour and a half

you know okay let's take a nice deep

sigh of relief yeah and so when you look

at one of the important parameters

that's in the body is blood sugar

glucose glucose is the sugar not only

bacteria love it ourselves love it it's

the main fuel of the brain and it's it's

very important to have a good level of

glucose because if it drops you can

faint this beer doesn't enough energy

you can die because the brain makes

alternative energy sources which are

acidic and you can you can basically die

from too low glucose too high glucose

it's a big problem it causes the

symptoms of diabetes it starts getting

attached to different proteins in the

body and messing up our blood vessels

and you have these symptoms I think

you're all aware of so you need to keep

glucose in a good level and indeed if

you do a blood test you'll see that you

supposed to have five milli molar

glucose and plus minus 10% is the normal

range so different people here in the

room at different times have a set point

well five millimolar then when you're

fasting at night because deliver deliver

makes glucose for you when you're not

eating and then when you eat a meal the

sugars are absorbed and glucose Rises

right and causes the glucose called G of

T to rise but then it goes back to five

millimolar

so in the classic glucose tolerance test

for instance there's a lot of people in

pregnancy a good you get 75 milligrams

of glucose to drink that's disgusting

and then you measure glucose in the

blood this is the meal input okay and

goes up and then it goes down so it goes

back to five millimolar maybe goes up to

six seven something like that within

about an hour now different people not

only have the same five millimolar

different people have the same dynamics

in this glucose tolerance that's

different I mean people who are healthy

people so different people of the

ZeniMax if you get this that's if you

get eleven millimolar after two hours

that's that's that's a criterion for

diabetes so these dynamics are very well

controlled they explain myself so far so

we want to understand this this five

millimolar setpoint and in the entire G

of T dynamics after given very little

very controlled stimulus now when the

body really you eat you have all x

sugars fats amino acids they all play

into this I'm going to ignore everything

but glucose input and ignore a lot of

other details in order to just get to

the essence so we're so we said five

molar glucose the glucose tolerance test

you know what what makes this go back is

glucose is removed and so what makes us

go back is basically the body all those

organs I feel like must

in fact they take up glucose from the

blood removed and this removal by

muscles for example muscle fat liver and

removal is stimulated by a hormone

called insulin so different cells in our

body

send the muscles have receptors for

insulin and when they sense insulin they

make and put into the membrane pumps

that transport glucose from the blood

and therefore remove glucose from the

blood they explain myself then they make

pumps the take glucose from the blood

and glucose levels go down know what who

makes insulin so we have a little organ

in our body called the pancreas I love

love and on this Oregon it does a lot of

things are tiny little islands of South

of a thousand cells each a million

little islands like that made of special

cells called betta cells make insulin

produce insulin that's their main job

their insulin factories yeah and and

when glucose is in the insulin a in a

rate that depends and increases with

glucose in the blood so the more glucose

the more insulin the more insulin the

last glucose so here is the better cells

they have some function he sends how

much glucose new reason they produce

insulin and insulin increases the

removal rate of glucose

there's an important parameter here

called insulin sensitivity which is the

effect of one unit of insulin on glucose

removal so this has to do with what I

said how distant tissues can hear you so

different distant tissues a given unit

of insulin can be more or less powerful

in removing glucose and soon read write

the equations and yeah yeah typically

normally different tissues have

coordinated needed sensitivity yes and

if they don't that's a problem that

effect that's it that's a disease state

you can say and this instant sensitivity

is is used by the body it's not just

varying for no reason it's used by a

body because the body wants to allocate

glucose properly so if you're exercising

for example for a long time the body is

going to make the cells in your whole

body more sensitive to insulin so that

means that they're giving them out of

insulin the body takes more glucose your

muscles take more glucose because you're

exercising it so exercise make this

insulin sensitivity go up but things

like a infection now you have a pathogen

and basically your immune system which

is in the blood primarily needs a lot of

glucose so what it does is mix the

muscle and all the other tissues take up

less so you have more glucose in the

blood that the immune system can use it

I know also the bacteria can use it but

it's more important the immune system

can use this so s goes down so this is

called insulin resistance and maybe

you've heard of insulin resistance it's

a big problem in our society in Western

world because insulin resistance also

happens with obesity

it happens with lack of exercise

it happens with does anybody know

insulin resistance with age what else

insulin resistance how many of you heard

of insulin resistance this issue okay

and and so this parameter changes it's

changes that's a fact and it's different

physiological situations change it it

varies between people that say by a

factor of ten but but I still want to

say most people with obesity let's say

I'd say 80% of people with publicity

which I should say which all have all

people to visit of insulin resistance

but they still have normal glucose five

millimolar normal dynamics so despite

let's say a tenfold variation in how

much they're distant issues here insulin

so there's s is a tenth of that of a

lean person let's say detain the five

millimolar and the dynamics in the

glucose are on distance are fine yeah

what is the physiological mechanism for

instance sensitivity and so an infection

I think it's in kind of immune cytokines

that are sensed by the body which is a

sign of affection and they make the

signaling system that sends insulin less

active so there's like you can think of

the receptor in the cells and all the

signaling mechanism can be tuned by

other physiological systems also in

pregnancy agency where pregnancy the

fetus secretes hormones into mom that

makes the mother insulin resistance why

does that make sense it means that after

a meal mom takes less glucose into her

system and more goes to the fetus so

it's a and in pathological situations

you can get pregnancy induced diabetes

which is why a lot of people will

impress me take this glucose tolerance

test to make sure that things are fine

or not they explain myself what can I am

saying that a the a pregnancy induces

insulin resistance and now depends on

the person lifestyle resist a genetics

it said or whether we get diabetes and

we'll talk about how you get diabetes in

this lecture you'll end this lecture I

hope your understanding is there at

least one way of thinking about and a I

think that off

does anybody know here does it after

pregnancy does it can you still stay

yeah it can stay yeah it's also high

risk for type 2 diabetes later right

yeah your name is then in your where do

you work yeah

rotation thank you in your last name one

benefit okay so I just wanted to give

credit there's a lot of knowledge here

yeah yeah so can you reduce resistant so

the princess you know what in diabetes

prescription is changing diet and

exercising right so exercise definitely

improves it's a great great thing to do

yeah and fasting and I'm not

yeah fasting yeah the diet rates in

general diet dietary changes will affect

insulin resistance and it will affect

also in the circuit because of this

input yeah so the timescale of the

resistance I think that tensile

resistance resistance can change quite

dynamically so it's because the body

needs to it's basically the resource

allocation which part of the body now

needs more or less glucose and it's

fizzy but it's good resistance it's good

it has an involved purpose to allocate

resources so it's a dynamic thing shall

we continue

yeah why or how okay so let's talk about

this we have what how and why so thanks

for asking it's really important because

of course it's not obvious when I say

what I say

things like what are we working on

insulin resistance and then how what is

the mechanism of this resistance so I

can say let's say and in the case of

infection it's the site of certain

cytokine that binds receptors in the

cell the changes gene expression to

affect the insulin binding pathway to

make it let's say more have a higher

amplification that's a how then the Y is

usually an evolutionary question so

exercising means your muscle needs more

energy so if you make us bigger a given

unit of insulin will make put more more

glucose into your muscle into your liver

into your and all the our organs of

concern so that's the the why so there's

usually what how and why in this course

we talk about

all three hey hopefully right so this

why why a could be a robustness

principle how is it achieved so thanks

it's really I love this I love this

point about how what and how what and

why in biology and so we talked about

insulin muscle liver fat insulin

sensitivity obesity insulin resistance

and now we can ask how do we understand

how is it that people can have 10 fold

lower s but identical dynamics in

basically a differential equation in a

feedback circuit how can you change the

parameter by 10 an important parameter

and still have dynamics that are

identical there's hardly any equations

it to do that it's very unusual okay and

just to demonstrate that I'm gonna write

down the standard model for glucose

insulin which is used it's important

actually was developed in 1979 and and

it's used to interpret these glucose

tolerance tests the clinically relevant

model that's actually in the example of

mathematical model that had big impact

on medicine hey but I'll show you it

doesn't address this particular question

it doesn't explain sensitivity to what's

the point what's the point of changing

of the physiological changes in s what I

said that most obese people people with

obesity you should say and remember

they're people because there's a

question of time skills so when you

write after you change the parameter you

get an effect on resource allocation but

I'll show you the compensation if you if

the parameter change is different for a

long time weeks the system can

compensate for it

understand why that is so this this is

the situation so there's a fast time

skill where you change resources

exorcising infection days let's say and

then the slow time skill where you want

you don't want to be away from your set

point for for very long so that's that's

what happens yeah so thanks these

questions really help because you know

this is a new chapter in the book I'm

writing up these new chapters and

putting it you know for you on the

website and also the movies are there

and I hope you can how many people have

seen the movie movie of the course so

far ok so I want to know and also I'm

going to ask you guys to comment on the

PDFs of the book chapters because your

input could help me write this text of

second edition of the textbook and prove

it for other people to benefit so if you

get the PDF and you write comments on it

and you said to me I'll be very grateful

ok I'm going to stop with the question

now okay I'm gonna write the minimal

model I can't can't wait to write the

minimal model so I'm gonna just do it

and and how would I do it I'm gonna just

do it right so again what we're doing

this in our course is translating

biology into math so the point will be

the dis minimal model explains a lot of

things but not this ability to

compensate for the parameter so what I'm

going to write I'm gonna write how

glucose changes with time so glucose

changes with time is M this is the meal

input fine and now it's removed so

removable remember it's always glucose

times the removal rate like in so far we

talked about removal by cell growth and

dilution here it's removal by other

different tissues taking up glucose and

and and the removal rate is this s times

I because and the more insulin there is

the more removal and s is this parameter

insulin sensitivity how much a unit of

AI affects the removal so this is

insulin sensitivity and I of course is

insulin any questions about this

equation yeah

that's right thank you so this number s

depends on the number of receptors and

on many many molecular details

downstream of the receptors all the

phosphorylations everything that allows

you to tune the gain of this of this

amplifier a little bit like we talked

about these input-output relationships

now you amplify them or should I explain

myself yes that's all rolled up here so

we're talk about a level of organization

out of organs we have parameters that

including them let details on the lower

level of organization all the proteins

in the phosphorylation that's what

happens when you do multi each scale

like if I talked about glucose it's made

of carbon atoms that have electrons and

protons but I don't care about that they

can roll them up into chemical

properties of glucose they do care about

yeah yeah how you measure yes thank you

yes of course you can measure clinically

by the following you inject a unit of

insulin and you measure blood glucose

and you see how this unit insulin causes

a reduction in glucose you don't take a

meal you increase insulin yeah it's

increased insulin and see how glucose

goes down that's how you can give a

number a number for s for a given person

okay this is urgent