10/11/2023 Jonas Cremer – The interdependence of growth
and cell-size control in bacteria
Talk given at the Population Dynamics Virtual Seminars
Seminars about Quantitative Life-Science and Biophysics
hosted by the group of Prof. Rosalind Allen and organised by Dr. Marco Mauri
School of physics and astronomy -The University of Edinburgh
Friedrich Schiller University Jena
yeah I think it’s working yeah so I will share my screen for a second I hope you can see the screen of the moment so anyway welcome everyone to this population Dynamics virtual seminar this is the one last uh one before last one of the Year actually the next one will be the last of the year today we have Yas scamer from Stanford University and we’ll chat about the interdependence of growth and cell size control in bacteria so uh few words regarding Yas so he’s interested in physiology and growth of procariotas his resarch is focused on Val scales of procaryotic life from coordination of fundamental processes within cells to the collective behavior of cells in specific ecological settings and uh he has also a specific focus on gut bacteria and eoli so I studied physics and biophysics in Germany Munich then he did a post at the University of California San Diego he became assistant professor at the University of Gran and now is assistant professor in biology at uh Stanford University so with vison I will stop sharing my screen uh thank you again yonas for being here because it’s actually quite early by him and you can yeah share your screen and the stage is yours thank you so much Marco for in the introduction and thank you everyone for being here um can you hear me okay or do I need to speak louder fine yeah great okay um so yeah we are in general interested in in in in my microbes and and figuring out how they live and I I I like this short summary of how how we think about microbial life is is really like this triangle of ecology Evolution and cell physiology and since this is a population Dynamic seminar um of course you know we all are interested in ecology and evolution but I want to highlight that in this context is also always important to think about what the cells are doing and how do eles are able to do what they’re doing um so we need to really think about self physiology and this talk today is actually mostly about self physiology and um but but then particularly if we think about microbial populations we for sure have to think about the cell physiology of growth so how is it that bacteria cells can double so efficiently um you know [Music] with with a short amount of time every 50 minutes or so the f is the fastest rate right um and and and so we we try to approach this question or we study this question right now still exclusively I would say with the model organism eoli and and I really like this organism it was isolated actually or used as a model organism starting roughly 100 years ago at least the best studied version the K12 strain um actually here in Palo Alto 100 years ago but since then so many people have studied this organism and we know so much so it’s so great because we can really build on so much knowledge which people have accumulated over the time so that’s that’s our organism we study and the other thing the other disclaimer at least for this talk I exclusively will talk about growth in steady state um that is of course not a ecologically realistic scenario in in in in fact it’s it’s kind of an artificial scenario in ecological settings but it really helps us to to better understand some basics of cell physiology and and so here’s an example how we typically grow cells in a well mixed state and if we do that in a steady growth we get this wonderful perfect exponential growth and we can quantify the growth rate very well and in different carbon sources the growth rate is different so the biomass is increasing exponentially here with a growth rate varying between depending on conditions almost zero to let’s say three and that corresponds to a fastest doubling of roughly 15 minutes so then given this observation um there are immediately some questions right one is what sets this upper limit of growth rate and another important one would be given these changes in growth rates how is the cell actually accomplishing this in the growth in different growth conditions how is the cell physiology varying and um I think to today I I want to focus on on on on on the on these growth laws um these observations that cells actually show some very well defined Trends with growth conditions um one is what is what I would call the ribosomal growth law here is this very striking and old observation that the amount of ribosomes in a cell increases with growth rate and particularly the easiest way to measure that is if we measure the total RNA to total protein content in cells in cell cultures then it increases strongly with growth rate and this is striking because um we do this in in different conditions and we see this change um so why is it that this simple relation exists but but there’s another also strikingly simple growth law already observed in Parts by Shea in 1958 and that is that the cell size of steadily growing cells is increasing with growth rate so um larger growing cells are actually quite bigger than slower growing cells and so let’s let’s talk about this why why these growth laws exist and I will in this talk particularly focus on this size growth law but to start with I I will I will talk quickly about the ribosomal growth law since this is the one I would argue we understand much better at this point and so let’s start here with the ribosomal growth law and let’s just start with the simplest picture possible and that is I think we have to we have to consider composition what is it what is in a Cell what is making up a cell and of course the cell is is a very complex entity with thousands of genes and proteins and different metabolites and and also thousands of MRN species and all that right so it’s a very complex um construct with many many different components but we can zoom out and focus for a while just on the micromolecular composition so if you do that then um then people have studied this now since 100 years almost um then we see that roughly depending on conditions roughly 50 to 60 70% uh of the dry mass is protein roughly 20% is RNA there’s DNA and then there are other components right and and and I want to stress here that these numbers change with conditions right but we can simplify this even further by realizing that RNA here in this context is actually mostly ribosomal RNA so we can we can highlight this like this that actually most of the dry mass is ribosomes other proteins and than other components but the majorities are really ribosomes and other proteins which are made by ribosomes and so already this composition picture really clearly highlights that we have to think about protein synthesis to understand growth at least in these steady state fast growth conditions and so so then let’s talk in this context about protein synthesis um in particular not only growth but protein synthesis what sets the rate of protein synthesis for that we clearly have to think about ribosomes how fast they translate they take TRNA to make um or charge TRNA to make new sequences of amino acids and how many ribosomes are there in a cell and um I like to start to think about this question with a really hypothetical scenario uh which is let’s assume for now we have a bag this we consider the cell as a bag where where there are just some molecules in there and let’s say for in this scenario we have a bag with only ribosomes so in this scenario we have ribosomes making only ribosomes at full speed um so we have a feedback here Loop here ribosomes making ribosomes at full speed and if you do that and if you look at known translation rates how fast ribosomes work and if we if we if we look at how how how many proteins are needed to make a new ribosome then we get an upper limit um of of growth of doubling which is a doubling every six minutes that’s the fastest which is possible and the point here is that that this is already very close to the to the fastest doubling we really see in the lab under perfect conditions okay so that supports this idea that we have to think about protein synthesis um but how can we then understand this better and go a bit beyond this hypothetical scenario because obviously this hypothetical scenario cannot work in real life because ribosomes are not just growing operating at full speed but they but they need things to work they particularly need charg trnas and so what is really needed then for ribosomes to work is also that the metabolism works so that amino acids are synthesized and that energy in form of ATP um or other forms is available and of course this is also a very very very complex um Network supporting this this metabol ISM um but it’s important to realize that most of these metabolic functions are really supported by metabolic proteins and and so let’s think about these metabolic proteins which somehow do the magic trick in taking up nutrients and providing charge TRNA and so if you do that and take take our our feedback loop now and extend it a bit then it looks more like this right so we still have this feedback ribosomes need to make new ribosomes to grow but ribosomes also need to make metabolic proteins which are then providing charged TRNA so that ribosomes can grow and of course that’s not the end of the story because a lot of other proteins are needed for growth and um so we we we end up with this cartoon um where which I really like because it highlights very well that to think about growth we have to think about this question how cells are allocating uh the activity of their ribosomes what’s the fractions of ribosomes making ribosomal proteins what the fraction of ribosomes making metabolic proteins and um what I presented you so far these ideas that’s my version of introducing it but but these ideas are really not new and many people people over the years have studied the the the these allocation models and and they’re actually remarkable successful I would argue in describing certain growth phenotypes and um I want to briefly now to rationalize this ribosoma growth law talk about our most recent work um which which I which which really was driven by Griffin Cherry a a post do in our group um who who did all the all really all the modeling and Analysis work I describe in a moment and so the idea here is that we have this allocation picture we have to think understand better how cells allocate ribosomes in making new ribosomes and other proteins and can we model this more in in a more self-consistent way without for example integrating having as a starting point the r roral growth loss and so we did that by particularly looking at the global regulator ppgpp which is really known to regulate metabolic genes a bunch of different things but particularly in this context also metabolic genes and ribosomal genes and it is also known that PPG synthesis um is driven or depends at least in part on the activity of ribosomes and it controls um as I just said the the synthesis of ribosomes and metabolic proteins right so how can we what’s the simplest way we can we can model now allocation based on this regulator well we know from from these molecular studies that um that ppgpp synthesis really depends on the it but but but then we tried this ANS where we say let’s try how far we can get if we take this ANS that the ppgpp concentration is really dependent on the ratio of uncharged to charged TRNA so if uncharged TRNA concentrations are really high ppgpp is high if charged TRNA concentrations are high compared to uncharged one ppgpp is low okay so how far can we get just with the simple ANW and now formulating an allocation model I won’t go into the mathematical details but but here is a cartoon how this model works so we have at the core ppgpp which as I just said depends on the ratio of charged and uncharged TRNA um but then it really sets the synthesis of making new ribosome and making new metabolic proteins if ppgpp is high Met more metabolic proteins are made if ppgpp is low more ribosomes are made so now the question is what sets the abundance of charged and uncharged TRNA um trnas are made by transcription but the more important thing in this context is really the turn over of charged and uncharged TRNA which really depends on metabolism metabolism leads to the charging of TRNA and translation translation leads to the uncharging of TRNA so we formulated this model and and then see and then tested how valid does in predicting um certain growth Trends particularly the the the ribosomal growth law I already mentioned here it’s it’s it’s plotted in a slightly different way not total Pro total RNA over total protein versus growth rate but um really the fraction of ribosome the fraction of proteins being ribosomal proteins but you see here that the simple an we just did um describes actually then four different growth rates um the variation of ribosomal content B growth rate very well I should I should specify here one last thing how do we in the model measure the uh change the growth rate that is by changing the efficiency with which um which with with which metabolism works with which this charging works okay so so so that is promising but it’s I think the the simple an and the model is remarkable because it can describe more than that it cannot only descri describe the ribosomal growth law but it also can recapture quite well how translation rates change with growth rate so it’s it’s it’s it’s a well-known observation that um at faster growth rates um ribosomes work a bit faster than its slower growth rates and the model can uh describe this trend also very well and last but not least the model can at least roughly describe observed trends in the ppgpp concentration with different growth rates and so what what what are the major takeaways here then so we have a model which can predict these Trends um particularly in the context of this talk we we we this this model rationalizes this this observe growth law the ribosomal growth law but it also Al emphasizes another point and that and that is that this simple regulation is is really quite good in optimizing in optimizing the ribosome content to ensure efficient growth and how how did we probe that we just formulated also another model where we didn’t assume this feedback with ppgpp but where we just asked four different models conditions what is the best amount of ribosomes to optimize growth and this is shown here in in this is shown here in the model predictions as blue lines and you see that these blue lines match very well with the red lines okay so and that is really the the main summary I want to I I I want to make here that we have models including our own model which can recapture ribosomal growth laws and overall um this study the allocation study emphasizes this idea that ribosome content is regulated to support efficient growth okay so so now let’s let’s let’s move on then to think a bit about cell size and before doing that I I want to quickly talk about why we think this simple model could work in the first place and and so um for that let’s remind ourselves of the complexity of the cell we have really thousands of different components and you know even more parameters we would need to really describe every single component instead what these low dimensional allocation models do is they just reduce everything to a few variables and a few parameters and so how the heck is that even working when we have such a complex cell and I would argue that all these models work not despite the cellular complexity but really because of the cellular complexity because in the back besides protein synthesis this Machinery is coordinating a lot of different things to make sure that at the end protein synthesis is a major bottleneck of growth if that wouldn’t happen if the na application wouldn’t be coordinated in the right way if RNA synthesis wouldn’t be coordinated in the right way this model would also fail and last but not least we assumed here constant rates over different growth conditions which for example can only work if if if if if if cells control really the the the the macromolecular density in the cytoplasm and really other conditions so that braides don’t change so much okay so so with that I would argue we understand this ribosomal growth law quite well so let’s switch then to the size growth law to this observation that faster growing cells are much F much larger than slower growing ones and for for that this is also work which was driv by by Griffin and another post um rosali de Silva who contributed with a lot of biochemistry experiments and that is that is our most recent pref we just put this on bio archive roughly 10 days ago and so the first thing I want to say is I want to take back what I just said you before that we can treat cells as bags cells are not really simple bags of course but cells have a more complex speciaal structure of course many different things vary in space but particularly the cell has an envelope with for gram negative bacteria a distinct cytoplasm inner membrane and and and periplasm and so what we just started to do is to analyze very systematically Mass back data to see how many envelope proteins there are how many proteins are in the inner membrane and how many proteins are in the periplasm and so what’s what’s shown here for membrane proteins is the fraction of all proteins the fraction of the total proteum being membrane proteins and it’s a bit hard to see here because we have your data analyzed from different studies but if you consider one study only then these Trends are remark then basically you don’t see much of a change with growth rate this is really different when you look at periplasmic proteins all the proteins the fraction of all the proteins being perlas mic proteins where we see a strong change with growth rate for faster growth less per plasmic proteins are there so that is an interesting observation so it seems like that we also have simple growth relations for these envelope proteins but can we put this into context and what we then started to think about particularly was the role of density right so we personally all know that we care a lot about density and we don’t really feel comfortable if if the density of people around us is too high or too low but but what about the cell and there’s this Wonder wonderful there is this wonderful set of pictures by David Godel trying to give an idea how this might look like in a Cell but we started to quantify now more right and and I want to stress here that many stud Studies have thought about this role of density micromolecular density in the cell and that there are many good arguments that the density of micromolecules the crowding of micromolecules in the cell really matters because it sets the diffusion behavior of of different reagents enzymes components but it also really sets uh the efficiency of biochemical rates so let’s then analyze density but let’s do this independently in the cytoplasm and in the periplasm so in the cytoplasm as a good proxy we can measure we can take measurements from different studies on dry mass density and we see a very well uh conserved quantity dryas density of cells is not changing much with growth condition um and so so that is based on reported study but we can do a similar thing and look at now the density of proteins on the membrane and for that what we did is we took our analysis of massp data with the fraction of membrane proteins with the fraction of proteins being membrane proteins and then we took available data on cell size and on the surface area of cells how that is changing with different growth conditions and if we do that see really a remarkably well conserved quantity the density of proteins on the membrane seems to be quite well conserved um the the to to to quantify this better we we did some inference methods um and and and this is the prediction of that analysis that that we really expect a very well conserved dry mass density but also quite well conserved membrane density and that then as a consequence me also means that the ratio of these densities is is constant so given this observation let’s think about this density um more so or this ratio of density being conserved more so what’s this ratio of cytoplasmic versus membrane densities well we can start with the definitions where the cytoplasmic densities is all the all the things in the in the in the cytoplasm including RNA and cytoplasmic proteins um divided by the volume while the definition of the membrane density is membrane protein density is the mass of proteins divided by the surface area and we we we have two membranes in the coli so we have a factor two here so now we can consider more systematically what proteins are in the cytoplasm um well all the proteins except for membrane proteins and periplasmic proteins if we do that and now introduce again our fractions of proteins so going thinking about fractions of proteins instead of total masses then we end up with a relation which relates the surface area to volume with the micromolecular composition of the cell particularly the surface area to volume ratio depends on the fraction of proteins being membrane proteins divided by a term which really has the RNA to protein ratio in there and the fraction of membrane in periplasmic proteins so this is this is based on this this conserved density ratio a prediction we have how the density how the surface area to volume ratio changes with with the composition of the cell so let’s now test this Theory and for that we analyzed first how these different terms here change with the RNA to protein ratio um of cells um particular the so the fraction of membrane proteins and the fraction of periplasmic proteins and and and this is related to the analysis I showed you before the fraction of membrane is not changing much uh the fracture of periplasmic protein is changing so with that we can plot the prediction how the surface area to volume ratio should change with the RNA to protein ratio of cells and the prediction here is shown as as this green area with different shades um predicting the the the the uncertainty but we see overall a very well very very good agreement um with with with previous measurements and we did something more than and that was really most of the work experimentally we started our own experiments to confirm this further one is we measured the surface area to volume ratio how it’s changing with RNA to protein ratio directly in the same culturing conditions measuring surface area to volume and RNA to protein so that again confirms this trend very well but we also develop biochemical essays to at least estimate the fraction of periplasmic and membrane proteins so these are biochemical essays where we separate these proteins from other proteins in the cells and then quantify the total protein amount we have in these fractions and overall these measurements again confirm very well our massp analysis and our theory in general um so that I think is very promising that that that that you know that this idea of density maintainment is is the cell really cares about that but we can we can now try to try to analyze further how you know we can probe this Theory further right if we change something in a cell is the cell is is the surface area to volume ratio changing as predicted and particularly what we did here is we looked at the RNA to protein ratio and we changed that and that is actually something I already talked about before in the context of the ribosomal growth law right so the RNA to protein ratio in cells is is is in can you still yeah I lost you I I don’t know some how suddenly all your faces disappeared no it’s okay good um I the the the surf the the the the RNA to protein ratio is in large part controlled by the ppgpp in the cell and so what we can do then is we can modify the ppgpp levels in the cells by genetic constructs and particularly what we did here we used constructs which were developed um um recently in a in a really beautiful study from sanatan Lab where they already showed that modification of ppgpp leads to changes in the cell size and particularly um how these constructs work is you have inducers and inducers modify the abundance of of of an enzyme ra a which needs to the leads to the synthesis of PPG gpp and then another enzyme which leads to the degration of ppgpp so with these constructs we can now change ppgpp levels but we can then by measuring also the total RNA to protein ratio in the cell check if our Theory works and so this is what’s shown here so if it change in the same growth conditions here steady growth on glucose the gpp levels we see that the RNA to pro protein ra is is is is varying as expected but we then also really see that the surface to volume ratio is changing and in agreement with our Theory we see that the surface area to volume ratio is really decreasing with the RNA to protein content um so so overall then this suggests that density maintenance is important constrains the surface area to volume ratio but if we have this observation can we even go further and at this point it becomes a bit more spec speculation but I think still a very very um important consideration here to do and that is let’s think about aspect ratio control so in these Rod shap bacterias we have a very well defined aspect ratio um so the aspect ratio is just the ratio of the length and the width and during the cell cycle the aspect ratio is changing all the time um because cells are elongating then dividing elongating again with mostly constant width and steady growth conditions but the aspect ratio doesn’t seem to change much ACR the average aspect ratio doesn’t seem to change much across conditions meaning the average aspect ratio for very slow growth with a very low rna2 protein content is roughly the same as the aspect r as average aspect ratio for very fast drawing cells um so if we take this observation that this quantity is roughly constant um we can we can simply consider what the surface area to volume ratio would be and with a constant aspect ratio it exclusively depends on the width we can again test specifically our Theory shown here in green um how well that predicts changes in cell width with ribosome content um that is shown here and again the the white faced markers are measurements other other points are from the literature but again the trend is very well defined and so we we we can explain cell width changes but since the aspect R we assume the aspect ratio is is constant with also really determines the average cell length and and and so we get a prediction out how cell length is changing with growth rate but if we have a prediction how length in with are both changing with growth rate we have a prediction how volume is changing with growth rate and and and that is this final plot where we see that at least the trend we observed is is very well defined by this by this Simple Theory assuming again density maintenance setting surface area to volume ratio and then and then the additional conservation of the aspect ratio setting then in addition volume um so this brings me on ready to to to the summary um um I want to highlight here that again that I discussed at the beginning of the talk about the ribosomal growth law and how we can rationalize this better based on this idea of allocation modeling and I introduced our own work which more specifically considered how ppgpp levels are changing across conditions and overall these allocation models can rationalize the ribosomal growth L very well so we feel like we are now in a good state to say really in a state where we can say we we understand this ribosomal growth law um but then in addition I talked about cell size and this idea of density maintenance and that density maintenance at least sets the surface area to volume ratio which in Rod shaped cells is mostly controlled by width but if there in addition is is is is an aspect ratio conser if the aspect ratio is also conserved then this density consideration can even rationalize the the cell size growth law um finally um given this summary um Let me let me let me try to put this in into perspective how how I think we we should we should really think about growth rate and that is I think we should really consider growth rate not so much as a starting point when trying to formulate self- physiological models but really as a consequence of some other basic organizations and but we really should prevent having models where growth rates are fundamental variables growth rates should come out and and and and to highlight this um this is this is roughly how how the consensus view currently is about how how growth rate determines sales size and so the idea is the following that in different environments cells change their composition and that affects growth rate that’s in line with the ribosomal growth low I talked about but then volume control at least in the classical picture by hamand and Cooper is then more of a consequence of DNA replication in combination with growth so the timing of DNA replication and growth together right um with again growth rate being a fundamental physiological variable in the thinking about how this works um while our view is more that yes the environment sets the cell composition cells react changing their composition depending on the environment that sets grow grow rates in in line with the ribosomal growth law and ppgpp regulation for example but then it is density maintenance which then leads to the adjustment of cell volume and as a result we have in many observations in many conditions of course a correlation between growth rate and cell size but the growth rate is really not the fundament a fundamental variable um which which which we should think about to rationalize sales size um okay and with that I I I really want to thank uh the great people in in in in my group particularly the work I talked about was really driven by by by by Griffin by rosali Risha Sharma and M Lance contributed for for the Sal size project and um with that thanks so much for your attention and happy to take any questions thank you Yas for when I talk so um I’ll stop recording