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

Summary

The transcript discusses the dynamics of insulin and glucose regulation in the body. It explains how insulin is secreted by beta cells in response to glucose levels and how it is degraded, affecting glucose steady-state. The lecturer points out the non-robustness of the system to changes in insulin sensitivity and introduces the concept of compensation through changes in beta cell mass. The talk delves into the feedback loop involving glucose's effect on beta cell proliferation and death rates, which helps maintain a stable glucose level. The summary emphasizes the complexity and robustness of biological systems in maintaining homeostasis.

Takeaways

• 🧬 The discussion revolves around the dynamics of insulin and glucose in the body, focusing on how these levels are regulated and can be affected by various biological factors.
• 📉 The script explains that insulin levels are influenced by the glucose level in the blood, with higher glucose leading to increased insulin secretion by beta cells.
• 💊 The concept of insulin resistance is introduced, where the body's cells become less responsive to insulin, necessitating higher levels of insulin to achieve the same effect.
• 🧠 The speaker mentions the brain as an insulin-independent organ that prioritizes glucose uptake, highlighting the complexity of glucose regulation.
• 🔄 The script delves into the feedback loop involving insulin and glucose, where changes in one can lead to compensatory changes in the other to maintain homeostasis.
• 📊 The mathematical model presented in the script is used to illustrate how changes in parameters like insulin sensitivity (s) can affect glucose steady-state levels.
• 🔗 The importance of the number of beta cells (X) and their insulin production per cell (Q) in regulating glucose levels is emphasized, as these factors can compensate for changes in insulin sensitivity.
• 🔄 The concept of a 'hyperbolic law' in medicine is introduced, which relates insulin sensitivity and insulin steady-state levels, suggesting a constant relationship across different individuals.
• 🌱 The script discusses the proliferation and death rates of beta cells, which are crucial for maintaining a stable number of cells and, by extension, glucose homeostasis.
• ⏱️ The long-term regulation of glucose levels is highlighted, with the body's ability to adjust beta cell mass over weeks to compensate for changes in insulin sensitivity or other parameters.

Q & A

What is the primary function of beta cells in the context of glucose regulation?

Beta cells primarily function to secrete insulin in response to high glucose levels. They sense the glucose levels and secrete more insulin as glucose levels rise, which helps regulate glucose by promoting its uptake into cells.

What is the half-life of insulin as mentioned in the script?

The half-life of insulin is approximately 30 minutes, meaning that half of the insulin in the body is degraded within that time frame.

What is the role of glucagon in glucose regulation?

Glucagon is an enzyme that is released when glucose levels drop below 5 millimolar. It stimulates the liver to produce glucose, thus counteracting the effects of insulin and helping to maintain glucose levels within a certain range.

How does the liver contribute to glucose regulation independently of insulin?

The liver contributes to glucose regulation by producing glucose through a process called gluconeogenesis, especially when insulin is not present or when glucose levels are low, such as during fasting.

What is the significance of the term 'X' in the context of the script?

In the script, 'X' represents the number of beta cells, which are crucial in insulin production. The number of beta cells directly influences the amount of insulin secreted in response to glucose levels.

What is the significance of the term 'Q' in the script?

The term 'Q' in the script refers to the insulin production per beta cell. It is an important parameter in the mathematical model used to understand how changes in insulin production can affect glucose dynamics.

What is the steady-state glucose level that the body aims to maintain?

The body aims to maintain a steady-state glucose level of around 5 millimolar, which is considered the optimal level for normal physiological functioning.

How does insulin resistance affect the steady-state glucose level?

Insulin resistance can lead to a decrease in the effectiveness of insulin in removing glucose from the bloodstream. However, the body can compensate by increasing the number of beta cells or insulin production per cell to maintain the steady-state glucose level at around 5 millimolar.

What is the 'hyperbolic law' mentioned in the script, and how does it relate to insulin sensitivity?

The 'hyperbolic law' is a medical observation that relates insulin sensitivity (SI) and insulin steady-state levels in the blood. It suggests that for healthy individuals, the product of insulin sensitivity and insulin steady-state levels remains constant, forming a hyperbolic relationship. This law helps to explain how different individuals can have varying levels of insulin sensitivity and insulin levels while maintaining glucose homeostasis.

What is the role of neuronal inputs in the anticipation of meals and insulin secretion?

Neuronal inputs can signal to the beta cells in anticipation of a meal, potentially leading to the secretion of insulin before the actual glucose from the meal enters the bloodstream. This anticipatory response can help prepare the body to handle the incoming glucose more effectively.

How does the body compensate for changes in insulin sensitivity over time?

The body compensates for changes in insulin sensitivity by adjusting the number of beta cells (X). If insulin sensitivity decreases (insulin resistance), the body increases the number of beta cells to produce more insulin, which helps to maintain the steady-state glucose level at around 5 millimolar.

Outlines

00:00

🧬 Understanding Insulin and Glucose Dynamics

The paragraph discusses the dynamics of insulin and glucose in the body. It explains that insulin is secreted by beta cells in response to glucose levels, and the rate of insulin secretion is proportional to the glucose level squared. The speaker simplifies the biological complexity by ignoring certain factors like insulin-independent glucose removal in the brain and baseline glucose production by the liver. The focus is on how insulin levels rise in response to glucose and how the body maintains a steady state of glucose, which is crucial for understanding diabetes and other metabolic disorders.

05:03

🔍 Exploring Glucose Steady State and Its Dependencies

This section delves into the concept of glucose steady state, aiming for a 5 millimolar concentration. The speaker uses mathematical equations to illustrate how this steady state is influenced by various parameters, such as insulin sensitivity (s) and insulin production per beta cell (Q). The discussion highlights the non-linear relationship between insulin resistance and glucose levels, indicating that a tenfold decrease in insulin sensitivity doesn't necessarily lead to a doubling of glucose levels, contrary to what a simple model might suggest. The speaker emphasizes the importance of understanding the body's compensatory mechanisms to maintain glucose homeostasis.

10:04

🤔 Addressing the Challenge of Dynamical System Robustness

The speaker addresses the challenge of how the body maintains the same glucose dynamics despite variations in parameters like insulin sensitivity. It is suggested that the body compensates for changes in these parameters by adjusting other factors, such as the number of beta cells. The paragraph introduces the idea of an additional feedback loop that helps maintain the steady state and dynamics of glucose levels. The speaker encourages the audience to discuss these concepts with each other to enhance understanding, indicating the complexity and importance of these biological processes.

15:06

🌱 The Role of Cell Proliferation and Death in Glucose Homeostasis

This paragraph explores the role of cell proliferation and death in maintaining glucose homeostasis. The speaker contrasts the stability of protein circuits with the more dynamic nature of cell circuits, where the rate of cell proliferation depends on the number of existing cells. The discussion introduces the concept of a feedback loop where glucose levels influence the rates of cell proliferation and death in beta cells, which in turn affects insulin production and glucose levels. The speaker highlights the importance of this feedback mechanism in maintaining a stable glucose level of 5 millimolar in the body.

20:09

🔄 Feedback Loops and Glucose Regulation

The speaker elaborates on the feedback loop involving glucose, beta cell proliferation, and death rates. It is explained that at a glucose level of 5 millimolar, the rates of cell proliferation and death are balanced, leading to a stable number of beta cells. This stability is crucial for maintaining a constant glucose level. The paragraph also discusses how changes in glucose levels can lead to adjustments in beta cell numbers over time, which helps to compensate for changes in insulin sensitivity or production. The speaker emphasizes the body's ability to self-regulate and maintain glucose levels within a narrow range, which is vital for health.

25:26

🔄 The Invariance of Glucose Dynamics to Parameter Changes

The final paragraph discusses the remarkable property of the glucose regulation system where changes in certain parameters do not affect the overall dynamics of the system once it reaches a steady state. The speaker illustrates how the system's structure ensures that the dynamics remain invariant to changes in parameters like insulin sensitivity or insulin production per cell. This invariance is attributed to the symmetry in the equations governing the system. The speaker also touches upon the concept of a buffer mechanism in the body that maintains glucose levels constant over time, even in the face of parameter changes, highlighting the body's robustness in glucose regulation.

Keywords

💡Insulin

Insulin is a hormone produced by the pancreas that regulates blood sugar levels by allowing glucose to enter cells. In the video, insulin's role is central to the discussion of glucose homeostasis, with the speaker explaining how insulin levels rise in response to increased glucose and how it is degraded over time, with a half-life of about thirty minutes.

💡Glucose

Glucose is a simple sugar that serves as the body's primary source of energy. The video discusses how glucose levels are regulated in the body, particularly focusing on the dynamics between glucose intake, insulin secretion, and glucose removal rates.

💡Beta Cells

Beta cells are a type of cell found in the pancreas that secrete insulin. The script mentions these cells in the context of their function in sensing glucose levels and secreting insulin accordingly, emphasizing their importance in maintaining blood glucose levels.

💡Glucagon

Glucagon is a hormone that opposes the action of insulin, stimulating the liver to convert stored glycogen into glucose, which is then released into the bloodstream. The video briefly mentions glucagon in the context of the body's response when glucose levels drop.

💡Steady State

In the context of the video, a steady state refers to a stable condition where glucose levels remain constant over time. The speaker discusses how various parameters, such as insulin sensitivity and insulin production, affect the glucose steady state and how the body compensates to maintain it.

💡Glycolysis

Glycolysis is a metabolic process that converts glucose into pyruvate, generating ATP as an energy source. The script refers to glycolysis as the process by which beta cells, like other cells, break down glucose, leading to a change in ATP to ADP ratio and subsequent insulin release.

💡Apoptosis

Apoptosis, also known as programmed cell death, is a process by which cells systematically end their life when they are damaged or no longer needed. The video discusses apoptosis in the context of beta cell death and how it relates to the regulation of beta cell numbers.

💡Proliferation

Proliferation refers to the process by which cells divide and multiply. In the video, the speaker explains how beta cell proliferation is influenced by glucose levels and is part of the body's feedback mechanism to maintain a constant number of beta cells and, consequently, blood glucose levels.

💡Hyperbolic Law

The hyperbolic law mentioned in the video is a medical observation that relates insulin sensitivity (SI) and insulin steady state (I) such that their product remains constant across different individuals. This law helps explain how the body maintains a balance between insulin production and sensitivity.

💡Feedback Loop

A feedback loop is a process in which the output of a system is routed back as input to regulate the system. The video describes how the body uses feedback loops to adjust beta cell numbers and insulin production in response to changes in insulin sensitivity, highlighting the body's ability to compensate for insulin resistance.

Highlights

Exploring how insulin levels are affected by glucose concentration and the body's response to it.

Discussing the role of the liver in glucose production and its significance in maintaining glucose levels.

Introducing the concept of insulin-independent glucose removal, particularly in the brain.

Describing the process of insulin secretion by beta cells in response to glucose levels.

Highlighting the half-life of insulin and its degradation process.

Explaining the role of glucagon as an opposite enzyme to insulin and its function when glucose levels drop.

Discussing the impact of amino acids on glucose dynamics and their role in the body's response to glucose.

Analyzing the steady-state of glucose and the factors that influence it, such as insulin sensitivity and production.

Introducing the concept of insulin resistance and its effect on glucose steady-state.

Discussing the body's compensation mechanisms over weeks to adjust for insulin resistance by increasing beta cell numbers.

Presenting the hyperbolic law in medicine that relates insulin sensitivity to insulin steady-state across different individuals.

Exploring the feedback loop involving glucose that affects the proliferation and death rates of beta cells.

Discussing the stability of organ size and the balance between cell proliferation and death.

Highlighting the unique challenges in cell circuitry compared to protein circuits due to the inherent instability of cell numbers.

Explaining how glucose levels affect the proliferation and death rates of beta cells, creating a built-in feedback mechanism.

Discussing the body's ability to maintain a constant glucose level over time through the dynamic adjustment of beta cell mass.

Introducing the concept of invariant dynamics in the body's glucose regulation system, where changes in certain parameters do not affect the overall system's behavior.

Transcripts

to the system Oh the question was how I

measure s the parameters yeah exactly it

is the same except you instead of

including glucose insert insulin so it's

a different way to perturb the same

equation you explained yeah yeah quick

so when there is if insulin is zero if

it's isn't zero there's I'm neglecting

here some things one is an insulin

independent glucose removal rate that

would happen basically in the brain

especially as an insulin independent

it's like privileged organ and it's the

first organ that gets the glucose and so

and also there's a there's baseline

glucose production by the liver right

when it is so I what just wants it I'm

ignoring a lot of important biology here

in order to get the point it's just it

doesn't matter for what I'm going to say

but I'm also ignoring glucagon which is

the opposite enzyme glucose goes below

five millimolar you get glucagon and it

makes a liver make a insulin there's

then there is a pattern amino acids have

been a lot of things I've been affected

I'm ignoring

oh yeah exactly so when you do me let's

let's analyze it how do insulin levels

go up right so we need to how does this

how does this this is this this is

equation is this one another to do how

insulin levels go up so insulin levels

so these better cells I'm going to call

them X soon you understand what X is the

number of better selves and they secrete

insulin according to some function the

more a glucose the more insulin is

secreted so this is the self sensing

glucose and secreting more and more

insulin and then insulin is of course

degraded and here this is the half life

of insulin it's about half life half

life of about thirty minutes so insulin

itself is a molecule that it gets

degraded so we have a Q is okay thanks

so Q is insulin production per beta cell

this is a number of beta cells and this

is the control function function where

the more glucose you have the more

insulin you make and it's estimated to

go like G squared love test so that's

just of physiological measurements it

more and basically the better cells do

is they take the glucose and they break

it up just like every other cell does

with glycolysis changes their ATP to adp

ratio that causes a calcium ion flux it

causes vesicles of insulin to go the

membrane and release insulin so this is

like a big signal transduction inside

the better cells again I'm just rolling

up in F of G yeah sure so we this is

another parameter we need to worry about

yeah this could be like if you're if

you're better cells are weak in all in

so that's also something to worry about

so that's another robustness and in fact

it's going to be fine

because we'll see it for sure so these

parameters are you need to worry about

them right they need this function

that's usually less variable because

it's more like a coded into the

circuitry thank you kind of circuitry

input/output function that we saw that

can be made robust okay now what was the

point is this if you give em like this

this circuit even if I give em yeah if I

give him like just this circuit will

have in will have good and glucose start

go up because M is increasing then

insulin because G is increasing starts

to go up and then remove of glucose

increases so it goes down and like that

okay so this is the solution a solution

to physically and it's very interesting

now to ask what is the glucose

steady-state so suppose now I even

suppose now I give a constant meal

like for instance I make it take an in

glucose infusion you can do that

sometimes you give a constant meal or

better even when I'm fasting I'm fasting

M it's just the basal production of

glucose by my liver that's what at night

right or in the morning before I eat I

have some M and now what is the glucose

steady state so we want it to be 5

millimolar right let's see the point is

going to be that it's going to depend on

all these parameters like s and Q you

can't go around it with these equations

so it's going to it's going to depend so

my point is going to depend on those

parameters just to solve it so DG DT

equals 0 so s I G

M so G steady state is s I steady state

divided by this M

it's the other way around thank you

now if you can't follow this quick as

quickly as I do it and that's why we

have all the movies and the books just

the important thing is to get the spirit

of it

and on the other hand I am solving it on

the blackboard for you to see to get the

physicality of doing math like that I

think it's so so great and so we have

alpha I study state has two equals Q X F

of G steady state I'm gonna put here G

squared just I'm going to use F equals G

squared and because mmm is not zero in

real life the body deliver makes a

glucose all the time like

gluconeogenesis yeah otherwise we would

be in trouble when we're sleeping yeah

so I think the glucose the way that the

the body works is that the liver is an

amazing organ multitasking organ maybe

we'll talk about it later it can take

you can take amino acids if the muscles

if the muscles break down a little bit

and you takes amino acids and converts

them into glucose all the time so when

you we're starving for a long time

that's our muscles and our fat also fat

secretes all these trades glycerides

that we have in our blood tests there

are too high or too low it depends you

know how old you are eventually and then

that can be converted also into glucose

not mistaken so the liver can do all

that and good let's take a nice big sigh

of relief you know so we're so we're so

g steady-state squared equals alpha i

steady state right by q x-- yeah so

let's plug in i studies a ice taste okay

but now i got lost and all this stuff I

want to calculate yeah let's do it like

this I steady state right is is

0 / SG let's plug that in alpha + 0 / SG

steady-state QX and we move G

steady-state over here so you get a

power 3 and the answer is

the G steady state equals something to

the power one-third that something is

something like alpha M 0 divided by s Q

X what does this mean it means that if I

change s by a factor of 10 like insulin

resistance G steady state changes by 0.1

to the power one-third which is 2 well

1/2 so if I reduce this my factor 10 I

go from 5 millimolar to 10 millimolar

but that's not what's observed so you

can you can be a person with insulin

resistance and have also 5 millimolar

so this model yeah G statistic is not

not robust to changes in s so if you

have insulin resistance that you say you

suddenly have s goes down by a factor of

ten G's steady state will go up by a

factor of two so you have a situation

like this basically and also in the

response time response time to a meal

we'll rise as s goes hello so everything

in this circuit it is very very normal

if you change the parameter in an

equation like a removal rate it'll

change the steady state and the dynamics

if you make this removal rates lower

glucose will go away slower and that's

in contradiction to the observation with

people with different values of s and

basically the same dynamics so we need

to understand this in this compensation

that's why I say it's it's a it's a it's

a non-trivial problem to deal with but

also of course Q this product is

question Q this production per cell also

enters here and the number of better

cells enters here and everything so

everything change the difference they're

not identical they they're both a kind

of glucose goes up and then because of

this term insulin goes up and insulin

eventually is removed but it's not so

important right now okay so we need to

understand how a dynamical system can

have exactly the same steady-state and

dynamics if we change a parameter like

this and how is it work in our body that

you can eventually cancel out and

changes in s on the long time scale so

when the answer is that there is an

additional

feedback loop that's

[Applause]

you know what I think this is a good

time here just like we did previously to

ask you to just to see that you you get

these equations and what's going on here

to turn to the person next to you spend

a couple of minutes explaining to each

other what I just said these equations

the dynamics and the idea of why they're

not robust to s okay just and then I

guarantee it will be good for you to

understand then we'll see if there's any

more questions all right

could be next to you behind you could be

someone behind you or next to you

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totally

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that's probably because there's

additional new neural neuronal inputs to

the Paracels

yeah anticipation it's one of the like

hundred things where you can

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all right I just wanna if I can get your

attention back again and I want you know

the the there was a question about

anticipation so when you know you know

you're gonna eat the comment was your

body already secretes insulin before

glucose comes in right so there could be

neuronal inputs to the better cells are

not taking into account here

maybe they change cue for example and

and many other details I'm not taking

into account you're just yeah so any

questions yes you say maybe those

details and lock chief that is data yeah

so could be yeah yeah so what happens to

the balance of the cells take up too

much insulin in making the muscles and

stuff like that they there's a problem

so weigh the body a lot of times like

muscles their liver makes puts glynne's

glucose into these long polymers called

glycogen and stores it so they're very

we have a lot of glycogen actually in

our body is that's what we can use to

make new glucose also I forgot to say

that and I suppose there's always a

limit some breakdown so I don't know I

don't know oh it's okay so what is this

extra feedback loop that extra feedback

loop has to do with what the observation

is that there's a the body compensates

over weeks for let's say insulin

resistance by increasing the number of

better cells so if you look at obese

people they have many many more better

cells so the way that works is that X X

changes X changes so there's more better

cells makes more insulin to exactly

cancel out the change in the insulin

effective 'ti and there's a really

intriguing finding in medicine called

the hyperbolic law where you take people

you measure their insulin sensitivity

and their insulin steady states so you

look at their blood what source toasted

insulin and then you inject some insulin

and see how effective it is in removing

glucose and different people lie on a

hyperbola where SI x i steady-state

equals constant these are healthy people

obese people are in this region lean

people in this region typically genetics

affects where you are and diabetes type

2 diabetes is here below the paper below

so this is that we want to explain that

observation to wait how about it does

this how it can change insulin secretion

to exactly balance this change in the

parameter yeah and so we need to see how

the body can compensate for increasing X

so we need equations for X the rate of

change of cells and the rate of change

of cells is a fascinating topic because

it adds it adds a really interesting

biology that's new for us in this course

and because cells what the cells do

what can sells do cells just like cells

can divide into two so that's the

process called proliferation that

happens iterate P and cells can also

commit apoptosis or die cells in our

body actually on purpose kill themselves

when they're damaged so the cells of

proliferation and death rate now that

sounds similar to production removal of

proteins that we talked about so far

right so far we talked to the production

and remove of proteins so I just want to

spell out here an important difference

between protein circuits and cell

circuits so where should I write this so

the protein circuits we worked out I add

so far I had production and decay maybe

you remember this this is time you start

somewhere and protein X goes always to

its steady state better over alpha if I

start high if I start low it's just

inherently stable there's no problem you

always go to your steady state because

production balance is removable but in

cells so this is a protein in a Cell

right cells proliferate and die and the

important thing is that the

proliferation rate cells always come

from cells so the proliferation rate

always depends on how many cells there

are unlike proteins which are made do

not Auto catalytic in per se and that

means you can take X out of the

parentheses you have x times something

you have x times you know what's the

problem the problem is that so this is

proteins they're stable

itself if this meal is bigger than 0 you

get explosion if this mew is smaller

than zero that is to say if there's more

proliferation than death you go to

infinity of course it's always limited

by something but if you don't want it

that's like in cancer that happens right

yep unchecked proliferation of cells if

you have more death and proliferation

you get neurodegenerative disease cells

go to 0 basically in order to keep an

organ size to keep organ size constant

justice constant number of cells ya need

a miracle basically you need something

to balance proliferation and death and

so this is a big problem for cells so

see cells live on a knife's edge just

because of their equations so just this

problem organ size control is itself a

big mystery you can say in biology and

there's different solutions right now

normally it's a still not exactly clear

so I'm going to write here x times a

proliferation - death right and here's

the feedback loop that's very well known

and but it hasn't been very recently

appreciated it's such an amazing piece

of a biological feedback is that the

trick is that this tissue better cells

its function is to control glucose and

glucose affects the proliferation and

death rates so glucose so here in front

here glucose averaged over weeks and

here I'm going to call pull out the

death rate and check this out

experimental fact it low glucose the

cells die and high glucose they stop

dying it's a steep curve at 5 millimolar

right so that's what glucose does to

proliferation and this is it's to death

this is proliferation I what no one is

even color proliferation right so you

see that when death equals proliferation

death equals proliferation at this point

you get a set point that's why five

millimolar is built into that circuit so

we're gonna write here mu of G mu of G

8:05 millimolar equals zero so mu is

proliferation - death - plot here mu of

G and it's negative at low numbers and

positive at high numbers and 5mil where

it's a stable situation so if you have

too much glucose check out what happens

more proliferation than death

more proliferation means more better

cells more better cells near is more

insulin more insulin means there's less

glucose so you go back you flow back to

little glucose more death better cells

die these shrink shrink shrink shrink

shrink therefore less insulin therefore

more glucose and therefore you flow back

and it's a stable fixed point it's five

millimolar so it's almost like writing

almost like writing and five millimolar

minus G so the only way this equation

can reach steady state

is only if G equals G zero equals five

millimolar and here's again it's a G

averaged over weeks when so when we add

this equation here it affects everything

here but guarantees that if I change the

parameter s things are gonna respond

right away but then over weeks the only

way the better cells will expensive

suppose I change s better cells will

expand and stop when glucose reaches

five millimolar and so we're going to

tune everything insulin and when change

Q exactly the same thing better cells

start expanding or shrinking until and

when do they stop when five million more

so you get built in over weeks your

basal glucose is going to be locked in

it's like the integral feedback property

basically that we talked about before

and the better cell mass is like a

buffer the buffers a fluctuations in

this parameters yeah

it's gonna stay the same until you

changed into the parameters that you get

insulin resistance or something like

that so it's like it's a way to

compensate in and I just want to say

that and this gives you this gives you

and but there's something even more

amazing that happens here it's not

enough that the steady-state is five

millimolar we wanted the entire the

entire dynamics to be the same so the

amazing thing about these equations is

that they have a structure where if I

change these parameters this parameter

this parameter the entire dynamics and

after the rich system reaches steady

state is just invariant to these

parameters these equations are like a

symmetry that makes an invariant to

change into those parameters and I just

want to draw out the dynamics now so far

we talked about dynamics at the fast

timescale I want to plot out the

dynamics because we added here another

time scale this is time scale of weeks

so here's what happens if insulin

sensitivity drops