Enseignement 2023-2024 : Régulation du volume des cellules
Séminaire du 19 février 2024 : Using Mathematical Models and Model-Guided Data Analysis to Understand Cellular Decisions to Grow and Progress the Cell Cycle
Intervenant : Marco Cosentino-Lagomarsino, Professeur, IFOM, Milan, Italie
This seminar investigates the mechanisms guiding cell growth and cell cycle progression decisions, using insights from single-cell dynamics. By utilizing advanced modeling and data-analysis techniques, I will address the stochasticity, homeostatic controls, and decisional logic of these fundamental biological processes, using data from E. coli to mammalian cells, which are reshaping our current knowledge.
Retrouvez les enregistrements audios et vidéos du cycle :
https://www.college-de-france.fr/fr/agenda/seminaire/regulation-du-volume-des-cellules
Chaire Matière molle et biophysique
Professeur : Jean-François Joanny
Retrouvez tous ses enseignements :
https://www.college-de-france.fr/chaire/jean-francois-joanny-matiere-molle-et-biophysique-chaire-statutaire
Le Collège de France est une institution de recherche fondamentale dans tous les domaines de la connaissance et un lieu de diffusion du « savoir en train de se faire » ouvert à tous.
Les cours, séminaires, colloques sont enregistrés puis mis à disposition du public sur le site internet du Collège de France.
Découvrez toutes les ressources du Collège de France :
https://www.college-de-france.fr
Suivez-nous sur :
Facebook : https://www.facebook.com/College.de.France
Instagram : https://www.instagram.com/collegedefrance
X (ex-Twitter) : https://twitter.com/cdf1530
LinkedIn : https://fr.linkedin.com/company/collègedefrance
Mar Mar so I will switch to English because I my friend is really not good enough um so first of all I want to thank John franois for this invitation it’s very nice to be here and and also I really like the lecture and I I did change my topic uh so
Originally wanted to talk about cell cycle control the way I see this course is a some kind of a an encounter between um models of cell cycle progression or um biosynthesis and we saw this morning and uh these uh let’s say PLM biophysical models of osmosis and all uh
Together um and originally I wanted to talk about this but I will talk about this instead um which is very related to what we just saw in Jean fris talk and um I will uh deliberately uh not talk about the intersection with the biophysical aspects but for most of the talk I will
Assume that we have a cell with constant density basically and um what I wanted to do is uh uh give a very broad introduction to this uh literature and we’re going to see basically the same uh uh equations and the same kind of data that we just saw
Uh just from a different point of view and then in the second part of the talk um I I wanted to talk about a little bit more about some work we did um in this area um with two examples uh one is uh as you will see really really related to
This kinetic model uh that Jean franois just presented and the other one uh is about um how you connect sensing of nutrients with allocation of uh ribosomes so you have to know you know the flux of amino acids for example that we just saw uh and then decide how much
Ribosomes um in um you want to allocate to make ribosomes which will make your um ribosomal sector which will Define your growth rate and we tried to build a coherent model of that uh so this is just a group it’s a theory group um Everybody in the group has a experi of
Statistical physics we do a lot of data driven work and a lot of the time we try to build the model from data um although it’s not always a good idea sometimes it’s better to take a step back and um try to um Start From First principles
Which is what I will try to do here I will show you data uh let’s say after I will show you uh the modeling Frameworks uh just as uh the same approach that Jean Fran so this was a kind of a very Broad and philosophical introduction uh because if you talk
About these three areas um it’s like um undebatable that you’re talking about physics when you are in this area but when you are in the theory of cell cycle progression or biosynthesis in which sense are you talking about uh physics so okay um I will not do this
Interactively but I will just uh show you that um I think uh physics is two things one thing it’s a corpus a body of literature a body of knowledge and in this example uh this body of knowledge is embodied by a t-shirt where you have
I think uh I don’t know 200 200 at least 200 years you have electromagnetism here you have DX equation and you have an interaction with some scar field so this is like at least 150 years so uh physics but it’s also and I think it’s first and foremost an approach so
Uh it’s how you approach a system when you try to um build a model with very few parameters when you try to do dimensional analysis um and this is what we’re going to uh do here so um we’re um not really going to uh do let’s say
Physics in the strict sense but we’re going to do models of biosynthesis as a physicist would do it uh so what is a law because we’re going to see something that is called growth laws it’s something that it’s really inside the framework uh that uh J something went wrong with my yeah okay
Um because so it’s really related to the framework that John Fran presented but it’s it wasn’t like he didn’t touch this topic which is I think how the framework got famous U about this growth laws and uh um so a law I think there’s a um there
Can be a debate about what is a law um and there can there is also like a debate on whether biology has laws so um here’s like a sort of uh General definition of law that is kind of I don’t know out there to debate to discuss but at least it should occur
With without our intervention and uh it should explain some of the experiments we do uh and it it has to be falsifiable okay and then in physics we like stuff like this we like this one we like it so much that we like ends up on
Our tombstones and uh uh but in biology this is not really the case it’s not I mean I think it’s arguable that in biology there are laws and biologists think a lot um in terms of uh um let’s say statement statements that fit all three definitions above but they’re not
Expressed by a mathematical formula but we like to express our laws by mathematical formulas and um I will show you and argue that um even in biology the biology of growth there are these law we we just saw SS and uh some of these and um and um I will show you basically
Um a general framework that tries to describe them so and and the other let’s say big topic is that we need to introduce um is whether this um growth physiology is universal and um I think Jean franois assumed this which is I like it I like it a lot but uh usually
If you have a biologist in the audience uh um it’s it’s not so automatic um because biology if you know it or if you have been in touch with the biologist is really about a lot of details um for example when I was presenting previously I presented this work this literature to
To an audience of biologist they they um I I got a lot of uh objections like uh uh for example Je fris had a law for like a a mathematical equation uh for the translation of Messengers okay and then they’re going to tell you okay but uh which organism
Are you thinking about if it’s this is bacteria then the MERS are in the cytoplasm uh if not um if it’s like East then the everybody knows that the nuclear pores are the limiting factor for the export of messenger RNA so um your biosynthesis rate is going to be um
A function of the number of nuclear pores um so there’s a lot of these details that make these um laws maybe not always applicable and we we always have to be very very cautious but at the same time I think Jean franois is really really right that there are general
Principles um because the architecture is the same because there are ribosomes are ribosomes everywhere and I will try to walk walk you through three or four of these principles that uh um basically are from the literature I didn’t invent anything it’s the same literature that John Francois is following I guess one
Name that needs to be mentioned is is the name of Terence H if you haven’t seen his work he’s a statistical physicist uh he’s the one that around 2008 2010 um put together this framework um putting together also data from older literature with where these laws started
Emerging and uh uh but it was I think the first one to uh put it together in a coherent way so what are the three or four general principles that I think uh are important for this kind of theories of biosynthesis one for sure is autocatalysis so prod production
Something that is producing itself and and the something that is producing itself is the reason why you have um exponential growth or exponential biosynthesis typically what is producing itself it’s not the only thing that’s producing itself you have different autocatalytic Cycles but the typical thing that’s producing itself is the
Ribosome so ribosomes are making ribosomes uh and ribosomes make protein Mass which is as Jean franois said uh probably multiple times um um let’s say it’s a proxy we consider it a proxy of the protein um of the total cellular Mass so I can write simple mean field
Like equations that we just saw for total protein total protein is proportional to ribosomes times an effective um um translation rate let’s call it and uh um to ribosomes are are made by the ribos the fraction of ribosomes that are making ribosomes so there’s a there’s a difference between ribosomal fraction in
Your um proteum so the fraction of your proteum that is ribosomes and ribosomal allocation so the fraction of ribosomes in your proteum KY in this equation that are making ribosomes and Johan Fran said okay these are the same at s State and we’re going to see in in a
Second uh so I don’t know how to do this ah yes okay I just said this because you have autocatalysis you have exponential growth which is in especially in the bacterial literature is called balanced growth because it’s a steady state for allocation and um proteon fractions so everything um is producing itself
Exponentially but these KS and Fs that we saw and these fractions of um let’s say biosynthetic ribosomes for example that are um producing everything are constant in these exponentially growing uh study States so the second thing that we also saw that is a general principle that we
Should have in this framework and it’s gener every every cell that does biosynthesis has a flux of nutrients which through a complex uh Network comprising catabolism and also metabolism becomes amino acids gives me a flux of amino acids uh which is used uh to make proteins so uh most of my let’s say
Let’s assume that this this is a proxy of my biomass and there’s also turnover so basically this can go back here uh but uh degradation times especially for microbes and today we’re going to think mostly about East which is a microb and um eoli which is a
Microb it’s bacterium um that are fast growing if you give them enough enough nutrients um they grow fast enough that these degradation terms are small so in in this framework um I’m going to neglect it for the moment and uh sometimes it’s probably going to pop up but let’s assume for today that
We are going fast enough that we can neglect degradation and recycling it’s a very interesting topic then if and which becomes relevant especially if you grow slow so um if I neglect this flux then I only have two fluxes and then I’m going to assume that these are given by rates
Times a number of effective enzymes so this flux is going to be given by a rate per enzyme times the number of enzymes and this flux is going to be given by um a rate per ribosomes times the number of ribosomes and I sort of have to balance them to get a steady
State we actually uh um we actually no we didn’t see it it’s a bit more tricky if you keep into account volume dilution uh but let’s assume that at um this is not relevant I think the the relevant thing is that you you have to take account for Mass conservation and this
Is a general principle and this we already touched uh so you have allocation of resources which is going to get reflected by the um cellular composition so you these are this is interesting because both allocation of resources and the cellular composition are measurable experimentally um so um cellular
Composition in terms of proteum is easily measurable experimentally by mass spectrometry you can do proteomics and get the amount of every protein uh and then you divide them by sectors and get this P chart and you can also think about measuring allocation which is a bit trickier you would have to um there
Are techniques that basically tell you where ribos which um transcripts are being transcribed by ribosomes so in principle you can test you can test this um and the third aspect is homeostasis and here we’re going to talk um about homeostasis of um let’s say um proteum fraction of
Cellular composition so the fraction of for example uh these fire is the fraction of your proteum which is ribosome um of course these fractions are going to be in tradeoff so if you make more enzymes okay uh you’re going to increase this flux but you’re also going to
Decrease um the ribosomes that you’re making so you need an optimal um to optimize if you want a tradeoff between how much ribosomes you have which guarantee you this uh um um um this flux so um the rate of biosynthesis and how much amino acids are preparing for your
Ribosomes to make your proteins which is this other flux and assuming that this other other part is constant there will be something else that is constant these two uh fractions of the pi um will be in tradeoff so how do you get I’m just going to this is a standard material
Which by the way most of it we just saw so how do you get this homeostasis it’s it’s very simple you get it directly from the equations that we just um saw so um um from the first equation uh we can write it it’s very um from the first
Equation you get a a a relationship that is always valid um I can divide by [Applause] P and this is Lambda and this is f the fraction of proteon which is ribosome and then I’m going to get a relationship which relates the fraction of proteon which is ribosomes with the
Growth rate and they have to be in a linear relationship so this is a testable uh uh statement okay if I take the other equation it’s a bit uh um it’s a bit uh different uh but it’s quite so sorry but I can do the same okay let’s let’s do it
So I I can divide by P and then I can apply chain rule so I’m going to get two terms and here I’m going to get um the derivative of r/ P so from these two terms I easily got this equation which is nice because it tells me about the
Transient um it tells me it’s a um it’s kind of a logistic equation I can put this is like Sigma f * KR minus F so in order to get a steady state this equation tells me that KR has to be equal to F so the allocation of
Ribosomes um determines the steady state for the proteon fraction of ribosomes and um um and then it it tells me the kinetic so if I do a nutrient shift for example if I change some of these parameters I can use this is an instantaneous equation I can use uh this equation to
Describe the kinetics okay but I have a missing ingredient and this is actually what we will try to F later on uh like how do I uh how do I decide the allocation of my ribosomes so the way um Terry W did it in this paper that was
Published now a few years ago where they had a lot of data they described these nutrient shifts they put this phenomenological assumption that my allocation is just a function of my elongation rate and uh they could do it because they went uh around with bacteria with E coli and they measured
For every nutrient condition elongation rate and ribosomal fraction F and they said okay KY is equal to are at every steady state I can show you the plot um because I don’t have it I have it somewhere but so they add the sigma and which is K at steady
State and then it was like I don’t know something like this and then they said Okay I I have these points I’m going to assume that this relation K of Sigma is always the steady state relation so my model is closed and I can make predictions and they made predictions
And they um they tested these predictions okay so uh these predictions uh predict some laws we said that the first law was that there has to be a linear relationship between ribosome fraction uh which is like this axis and growth rate which should not depend on
How you grow your bacteria this is all teras data from eoli from now 14 years ago and U It also says that the slope of this relationship uh should depend on the translation rate so they did it with translation rate mutants where they measured the translation rates and they
Found that this was verified which is striking I think if you are a biologist I think if you are a physicist but uh if I think if you hang out with the biologist for sufficiently long I think this is almost a miracle um but anyway
It works very well um and then they said okay um now we’re going to put antibiotics and we are going to um decrease the translation we’re going to sto ribosomes with these uh antibiotics and then we see what happens and what happens is exactly what predicts what is predicted by this model
That you get um an increased ribosomal fraction okay um it’s kind of tricky but this is not the same situation as changing the translation rate in fact if you measure um there’s a whole hidden topic that I’m not going to enter which is which fraction of your ribosomes are
Really active are really actively translated if you stall ribosomes with an antibiotic um you are decreasing the number of actively translating ribosomes but you’re as they measured you’re actually increasing the translation rate of the ones that are translating which is not what happens here here all ribosomes are translating just with
Different translation rate because they they have mutations in ribosomal proteins that affect the translation rate but anyway quantitative l the last quantitative law that I want to show you because it will be relevant for us now I don’t know I have until uh 515 so and that clock is right let me see
Yeah that is right okay and um is this one still from the same paper by terwa which uh um is uh is also quite interesting because what they did is they had several ways to express proteins that are completely useless for eoli uh again everything was done in
Eoli uh and these are the different ways um and then they measured growth rate as a function of the fraction of unnecessary protein uh that they were expressing and then they say they they found that the growth rate is just a linear function of the fraction of unnecessary protein so you could have
Actually very principle very complex phys physiology in response to the expression of unnecessary proteins um but you don’t this very simple pie chart model that we just discussed is predictive how is it predictive uh because unneeded proteins are going to be a sector Fu that’s going to be in competition with the um
Catabolic and ribosomal sector so if you increase FIU F has to go down and F is Lambda so your growth rate has to go down accordingly if ribosomes are the only limiting factor for for growth which is this expression is expressed by this expression so um this is uh okay it
May seem trivial but think about um uh for example one of the ways that eoli is used I think the most uh which is you have um you use it to make stuff that you need um so you need uh whatever an antibody a protein uh you
Put it in E coli and you make it express it and you want to have as much as possible of your protein from your bioreactor so your first idea is that okay let’s crank up the expression of my protein as much as possible so I I’m
Going to get I’m going to get Fu as much as possible but f um um is going to affect my growth rate is Fu is 30% my growth rate is going to be zero so um I’m going to get zero of my my protein so I have to try to optimize and
My yield is something like um the concentration of the protein that I get Fu times let’s say the exponential Factor if I wait for a constant time and my Biore reactor is giving me an exponential growth um which is something um e to the Lambda T so um so it’s e to
The sigma time P RT that the waiting time so this is fu time e to the sigma you know the maximum allocation that I can get from um for for uh uh all the sectors that are not [Applause] Q times te waiting time tww so you see here that you get an
Optimum which you can compute and actually if you think about it more carefully there are some other factors that you have to um take into account if you want to optimize and um and biologists and biotechnologists in this case are very very aware that there is an Optimum it’s just that um they’re
Trying to get it empirically or they they just are happy when they get something um but these kind of Frameworks and you know more complex than this uh can give you like like an a priori theoretical ground uh to get this Optima can I yeah sure I’m just
Wondering if simple model would actually tell you that a finite fraction of zero r that sounds strange you you can stall growth with it’s actually what they measure right no I know it’s what they measure but what does it mean I mean why is this finite fraction
Because I guess when you you add um because um this uh plot I didn’t it’s actually a very good question I didn’t I didn’t go through it um if you look at this plot um you you can interpret it um so the cell is trying to increase its ribosomes um
Um when when you try when you stole them um so it’s trying to compensate for the inhibitory uh let’s say signal that you’re giving it to growth and uh it gets to some Maximum fraction between 0.6 and 0.8 so this is interpreted as the maximum um fraction that ribosomes can
Occupy if you look at ribosomal proteins so not the whole ribosomal sector in eoli this is like 25% % which means that at 25 um let’s say uh um if your useless protein is going to occupy this most of this 25% then you cannot grow because you
Also need everything else so this 5q is the everything else that you need other than ribosomes which is not 100% okay so we are trying as a program uh to to reproduce this uh grow laws Beyond bacteria uh because uh it might be surprising but not many people did these
Measurements Beyond bacteria with East people did and we actually have one member of the lab who’s a theorist with support of an experimental group in our Institute is taking this data so this is actually the same data that we just saw but then for East and it’s um as you can see
It’s more or less the same I’m going I’m not going to say it’s the same because it’s very preliminary data uh but for sure you get an increase of RNA over protein which is the classic proxy for a ribosomal sector um if you inhibit translation and you get the same linear
Trend with nutrient quality uh and we are also trying to do this through a collaboration um in mamalian cells and we do have some preliminary results that are um promising but I’m not going to talk about that today and I’m also not going to talk about because I thought you
Already saw it in the previous seminar uh about what you get if you combine um this framework with PLM um because I think you’re going to get it for free uh from Jean franois course and uh and Matia seminar uh but let’s say the the only message that
Probably you got already last week uh that I wanted to give you is that if you use this framework so the way you saw it in the previous lecture uh you can uh predict one of the important trends that you saw last week which is that the volume growth rate is a linear
Positive linear function of the um dryas density macromolecular dryas density um which means that you have ostasis because because if your density is too large um you will dilute if you if you’re too dilute uh uh you will slow down this uh this growth rate but this ends the introduction and
I what I wanted to talk to you today is something simpler uh in the framework of these pure biosynthesis models basically that work under the assumption that um cell density is constant and I’m going to show you as I said two things and the first one is try
To challenge this rosent view that I just showed you work so well and uh how do we challenge it uh we start with a simple flux argument which is the same I think ex almost I don’t know because I didn’t read the Wang and Lee paper but
Uh it looks like it’s almost the same as the one that wangan Lee proposed for um transcription but we propose it for for translation again we’re going to think we’re going to assume I mean we did everything with degradation but for Simplicity now we’re going to assume
That there is no degradation and we’re just going to look at one transcript and the um ribosomes that are elongating we are going to say that there is an influx initiation rate if you want um that depends on the concentration of free ribosomes so it’s kind of a diffusion limited
Initiation uh and this is a rate per concentration um and then we’re going to get um ribosomes elongating uh so there is um current that is speed times density uh so uh speed is elongation rate per amino acid and density is the the number of bound ribosomes divided by
The number of amino acids in a protein but I I clamp it into this parameter Epsilon which is related to the sigma that we had before um which is the elongation rate divided by the so it’s the protein production basically it’s the time inverse time it
Takes you to make a protein instead of one amino acid so the density speed time density is actually Epsilon times the number of bound ribosomes so at steady state same assumption that we did before uh I get a relationship for one transcript between the bound ribosomes and the free ribosomes uh with this
Ratio Alpha 0 over Epsilon uh which is a proportionality constant um so if I have if I want to multiply um by the number of transcripts I get the total translation current so I use this so the total transition current is the number of transcripts time this
Which is the number of transcripts time this thanks to this stady state relationship and now I can use that the total ribosomes which is the ones that I used here are just the sum of the bound and Unbound ribosomes uh so if I use this I go back to this equation and I
Get M * Alpha 0 * RF I substitute this and I get an answer to a question that was formulated to Jean franois it’s a different answer so somebody asked I think he’s he’s not here anymore but somebody asked okay why don’t I get the number of transcripts in this equation
So you do get the number of transcripts just in this if you do this assumption it cancels out but if you do this kinetic argument it doesn’t so instead of this simple relationship we propose that Lambda is Epsilon which is Sigma is the same here f r
Times um the M Caris meant and like function of the concentration of ribosomes which has this thresold this is um we say the rate and rate divided by concentration so so here this is like a characteristic concentration of uh uh Messengers um above and below which you have different
Regimes okay so um yeah this is what we propos in this uh work which is unpublished and we do basically we do the model where we do this argument both for transcription and translation and then we take a terwa kind of framework which is the same that we saw previously
With these assumptions and uh we explore the consequences so the first consequence is that the limitation phase diagram which is the same that was discussed by Jean Francois uh becomes a bit different because you have these intermediate regimes of complex which we call uh complex formation limiting in
Lack of let’s say it’s a CO limitations so where both concentration of Messengers and ribosomal fraction play a role for into the expression for GR trate um so in between uh let’s say in the previous diagram you had translation limiting and then you have uh saturation uh so transcription is
Limiting but if you explore this uh uh concent this axis which is the concentration of Messengers you can have other this other this other regime um and then we went to the data and um we tried to um argue with this data we show I think we show that uh you
Need this model to understand some of the data and um for sure the data don’t work with this translation limited model or the transcription limited model and let’s say ours is a proposition how they could work so one is that um um there is and again yeah I’m not cting in here
But I’m going to site it in a second there is another paper from terwa which is another science paper that just got published where they say guys there is also a gr law for Messengers if you look at uh the amount of Messengers concentration of messenger RNA total
Concentration of messenger name per cell in eoli um it’s a linear function of growth rate okay and um this model doesn’t explain it and the other results that we wanted to try to understand are results from narai group in East where they show that actually the cost of the expression
Of the unneeded protein is not just a function of the fraction of proteum occupied by this protein but it changes if you change the copy number of the gene expressing this protein or the the gradation rate of the messenger uh making this protein we had this like T
And they have plots like this basically uh where they can have basically at fixed this is a um a proxy of the um fraction of the proteum flues the protein is gfp so it’s green fluorescent protein uh and they can measure it so for the same level of green fluorescent
Protein um depending on the messenger degradation rate um they they get very different um growth rates okay so uh this cannot be explained uh okay this is just uh let’s say this would be the prediction for um let’s go through these plots this is the plot that we saw for
Eoli for f uh which is transl I mean it’s really the Assumption of a translation limited growth transcription limited growth you wouldn’t have this you would have a constant uh and vice versa you would have this um if you get transcription limited growth um and um you wouldn’t have it if you have
Transition limited growth um and uh once again this is the prediction for the cost of un needed protein expression if translation is limiting um and um this would wouldn’t be reproducible if transition is limiting so I’m I don’t think the details are uh really important there
Are some details but I I I don’t think it’s a good idea to enter these details now so you just have to know that you can reproduce this data uh with this model and then we can discuss the details and you can also um reproduce the results of Nama barai um under
Changing messenger stability Um using this model uh based on this kinetic argum argument so this ends basically the first example that I wanted to give you and now I turn to the second example which is again something that we have out uh on bio archive which is about the other question so um these
Guys assumed here that allocation is a function of translation rate and they said okay cool I have a now I have a kinetic theory of growth rate changes in variable environments and then they applied it to experiments where you shift the nutrients you change the nutrients and you look at uh grow
Rate Rosal location Etc uh but we think that um let’s say uh let’s go through it I think if I can change ah yeah before we go H okay so I’m I’m going to tell you what we think before we go through it because there’s a there there are details um we think
That it’s a shk cut so if you want this is um an adiabatic assumption so you’re assuming that the system behaves at steady state even in transits what it really does it will have time scales for sensing a nutrients probably quick but also time scales for expressing ribosomes according to the nutrients
Ribosomes are expressed by transcription and also uh by translation because you have to transcribe ribosomal rnas and ribosomal proteins and then you have to translate ribosomal proteins so it will take a while usually to transcribe and translate protein it takes you time that is of the order of one cell cycle to get
To steady state so it will there will be a response time okay um but then there are details because if you want to describe the sensing and the allocation you need to provide these details to your model so if you ask Bianca because that’s actually how it happened I asked Bianca
How do bacteria respond to nutrient changes and Bianca is any other biologist she told me by ppgpp so ppgpp in um bacteria is the central regulation of ribosomal allocation what is ppgpp it’s a small molecule that’s made of GTP so the guanine the base that gets into
DNA um um three phosphates plus one ex phosphate and for some reason it’s used as a signal of how how fast you have to grow to the point that bacteria actually um compete ecologically by telling other people other bacteria not to grow by ppgpp they have toxins that are uh
Producers of of ppgpp that as I will tell you in a second will decrease the ribosomal um allocation of these bacteria so it’s a sensor and it’s a Defector ppgpp why is it’s a sensor um the standard theory is that um it sits on ribosomes um there s sorry there’s a
Protein called Rel that sits on ribosomes that is able to sense when uncharged um um trnas um are basically bound on the ribosome and produces ppgpp from G TP so if there’s a lot of uncharged trnas um your ppgpp goes up tell which is the signal that tells the cell to um
Slow down ribosomal location to decrease ribosomal location how because ppgpp can bind to through a protein to RNA polymerase um repressing the transcription of ribosomal rnas okay uh why only ribosomal RNA because there’s a specific region so it’s sequence specific sequence that you find only in ribosomal rnas that’s
Sensitive to this um transcriptional repression signal so um if I’m starving I will have less charged trnas because I will have less amino acids charging my trnas uh which will through relay increase my ppgpp levels which which will repress my Rosal allocation so a lot of steps which is probably unlikely
That are just made by um this kind of um phenomenological um steady state assumption that uh that’s the standard more or less the standard so we we built uh these details into this model um same framework that we saw before actually the translation limiting framework work for Simplicity
Uh where we add the sensor and the actuator system um this is just the cartoon um and we said we had to provide um an equation for amino acids which we’re going to see in a second is exactly the same that we saw before on
The board um and we had to provide an assumption an assumption for ribosome allocation and we say that the fraction of ribosome making ribosomes is just a fraction of transcripts that are ribosomes over transcripts that are all transcripts okay so this is an assumption and we don’t know if this is
The case but um because um it’s it’s a bit tricky because actually it’s ribosomal rnas that are um regulated and we assume that we here we’re assuming that it’s ribosomal proteins but ribosomal proteins are also under the regulation of ppgpp through the same transcriptional system these are the
Equations uh which are uh we we had to add to the framework one equation for ppgpp production uh which sets these fraction of RNA polymerases that are making ribosomes okay which is another allocation function which is different from the KY that we saw before the k for
Us um is due um to transcripts so Omega R is the fraction of RNA polymerases that are making ribosomes uh which enters some these are transcript production rate equations exactly like the ones that Jean Francois was writing we’re just saying that Omega R is a
Function of G is going to tell us the rate of transcription of ribosomal transcripts then we um if this goes to steady state with the time scale uh or any time let’s say uh the fraction of ribosomes that are making ribosomes we assume are the ratio of ribosomal transcripts to Total
Transcripts we also have to provide an equation for um the steady state of amino acids because then we have to provide an assumption um for uh how elongation rate T charging is related to pbpp so this enters this equation what I want to try to the details are not important but
Amino what I want to convey is that amino acid levels are going to affect TRNA charging which is going to affect ppgpp which is going to affect um RNA polymerase on ribosome which is going to affect ribosome allocation which is in turn uh sorry yes which is in turn
Affecting translation which is affecting um amino acid flues so there can there is a full feedback loop which which was not present in the other theories so if we go to steady state I will cut the long story short but I have time we can fit standard
Data uh and again uh theory is good for fast growth because at slow growth um there are things that happen that I didn’t tell you about at slow growth I told you that something is happening which is that degradation becomes relevant but there’s something else is happening that is not really well
Characterized even in eoli which is that ribosomes somehow get inactive so and this is why there is an offset in this law uh this prediction is that there is no offset this offset tells me that at zero growth there are a fraction of ribosomes but those ribosomes are inactive now
Some of these ribosomes are actually compensating uh the turn over due to degradation and initially I thought these were all the ribosomes I mean uh there are ribosomes because there is degradation and there is turnover so there’s maintenance ribosomes that are actually doing turnover but if you try to explain it you only
Get explain one/ third of this offset um so what Terry was says is that there are proteins and and again this must be specific of eoli but the offset somehow is not specific of eoli um there are proteins that sequester ribosomes and make them inactive at slow growth and why what’s the interpretation
Because if you’re growing slowly you might be growing faster later on in your life so you have to be ready but all this is like kind of a shady area that is not really I think totally understood so we’re going to stay in fast growth
And where are and our data um let say our Theory fits very well the data at fast growth where you don’t have all these mess um we uh we also fit uh um let’s say reproduce um um steady state data that uh are more um sorry um that are
More um mechanistic if you want uh like the relationship between ppgpp levels and growth rate and ppgpp levels and fire okay and now we are also uh looking into perturbations where you increase relay expression with some other collaborators and uh um now you have some nutrient flux some nutrient quality but you force
The cells to have the wrong signal for ribosomal location and then we’re looking whether this model can predict the steady state and also the shift but as usual in biology it’s more complicated than you would think um and then we also have predictions um for things that people didn’t really measure
As a as you know across growth rates for example the amino acid pool but the problem is that you don’t have one amino acid like in our Theory you have um 21 amino acids and probably so we would have to generalize the theory to more than one amino acid and try to
Understand the limitation regimes of um the amino acid levels in order to actually test um this Theory and it’s a mess because you have requirements of amino acids that are different for every amino acid because they depend on the proteum composition which changes with the growth rate and um and then you have
Amino acids that are not used uh I think at some point Jean Fran is going to touch this issue you have amino acids that are not used to make proteins Roman makes a big deal about this and he’s right I think because glutamine and glutamate are you is used for many like
To make other amino acids for example but uh if you look also the um at the con intracellular concentrations of these amino acids they cannot be explained just by um protein making but then we we did the theory to describe um out of equilibrium situations and that’s why we wanted to
Build this whole feedback because we noticed that it was not done by theories that were available in the literature and uh um because you have this mixed feedback loop you get oscillatory response everywhere you actually even get a h bif forcation if you go and and physical growth rates
That are unachievable but it’s fun to know um and this is very general and it’s due to this basically uh architecture that I just uh discussed we think is built into this system so we think this system must do oscillation because it has to unless it has ways
That we don’t really understand or have characterized well yet to avoid these oscillations so it’s a sensor um and there is an actuator with a time delay so if you be Fe it back it has to give you oscillations and then we went to data uh and these are data that were
Actually produced within our collaboration uh in fancy microfluidic devices where we think which are actually our original motivation we started to do this Theory because we wanted to understand this data uh but we don’t have a lot of this data so we need to produce more of this data we also
Went to ter wasas data and we think that they fit something that does not oscillate on some data that might actually have at least an overshoot and uh these are data from the 80s maybe we shouldn’t even show them or trust them but or maybe they’re good
It’s just there aren’t a lot of data about this but we’re pretty sure that if you you do the theory seriously that’s what you get and this is uh my uh let’s say the end of my story I have four minutes so basically what I wanted to
Try to convince you is that despite of the like uh dominant specificity in biology and in particular in the biology of cell growth there are general principles like flux balance Mass conservation autocatalysis that allow us to build these Frameworks then of course if you have an experiment you have to
Understand what’s going on there’s going to be a lot of things that are specific that are relevant that you have to understand but this doesn’t mean that there is a general uh setting that there isn’t sorry U then we have these two specific stories where we I think that this kind of colimitation
Regime is what a consistent argument uh uh on the um messenger flux would give you we actually generalized it now allowing for traffic on the on the messengers and on the genes with with the these uh 1D traffic models from statistical physics um and you get a face diagram that is even
Richer um and then we have this theory that tries to put all the steps together about about sensing and allocation and what we get is that you must have oscillations and then I already told you that these things are relevant people are going in now this field you know
Almost as like between 50 and 20 years without the physics let’s say I would say this field was there for a long time and now one of the direction that it’s going is try to figure out also the soft matter and uh um electrolyte physics parts and the others
Are um ecology and cell cycle progression you’re going to get some of that so I’m done I think almost on time uh yeah and these yeah these are the people that basically worked on our project are ludoo from the first project and I don’t know what I’m
Doing maybe I should do it here Ludo for the first project who just left our lab and Rosana is another PhD student who’s still working on this and then I want to mention some collaborators I already mentioned maer on but on the this things I didn’t show
You a lot of data I didn’t do data first as times I like to do but uh we do interact on data uh with with Bianca and with Petro in uh in Cambridge and more recently with Greg and Milan um in Del on this ppgpp perturbations okay thank [Applause] You