How do cells know how big they are?

My main research question is how cells trigger mitosis ¹. A key problem here is how a cell knows when to start the cell division process. At least two critical processes need to be monitored: the genome has to be fully duplicated and the cell has to add enough mass to maintain a reasonable size of the two resulting daughter cells. If either of these processes are incomplete at the point of division the daughter cells will loose critical genetic information, or will drastically change its size. We understand the monitoring system for genome duplication relatively well; its the replication checkpoint guarded by the ATR kinase ². The link between size and cell division control is fascinating, but lacks detailed mechanistic understanding ³. It raises a deceptively simple question: how does a cell know how big it is? The question is simple. The answer, it turns out, is not, and requires mathematical thinking. I have to admit, Im terrible at maths but I’d like to dig into this. This blog is me working through the theory out loud and building a simulation here that delivers a practical understanding.

Exponential growth

Single cells growing in steady conditions follow exponential trajectories ⁴. This means, the more mass you have the more new mass you generate. The reason is that the machinery that makes new mass is itself part of the mass it makes. In cells that machinery is the ribosome, and a constant proportion of the new protein that ribosomes produce is ribosomal protein. So the more ribosomes a cell has, the faster it builds new ones. Cells hold that proportion roughly constant as long as conditions stay constant, although fine tuned control of ribosome production may well be an important element in controlling size.

The basic equation that captures the increase of cell mass over time is thus:

V(t) = V₀ e^rt

With V(t) being the Volume at time interval t, V₀ the initial birth volume, and r the growth rate.

Exponential growth causes a problem, because bigger cells grow more, which quickly causes run away conditions. Cell biologists have convereged on three main models how, in principle, cells could control their size: the timer, sizer and adder ⁵⁶⁷ I'll go through these below and map the predictions they make and then test this using a simulation.

The timer model

A simple way to solve the cell growth and division problem is a timer. A new born cell has a given fixed time interval before it divides again regardless of how big it is at the time of birth. This was actually the dominant model in the early days of the cell cycle field powered by observations of cell division cycles in embryos that appear to progress in a clock like manner ⁸.

But lets think this through, what would actually happen when cells dont divide exactly equally but with some stochastic variation. This is where exponential growth causes a probelm. If we assume that the bigger a cell is, the more it will grow. This means that the bigger cell will grow more in the next division, giving rise again to a larger and smaller cell because of the slighty unequal nature of division. If this repeats again and again the exponential growth properties will cause the size distribution across the population to gradually spread, with the tails growing heavier with each generation. Some cells will become enormously big, just like wealth accumulates in a few back accounts in a capitalist economy.

In essence, the timer model makes several testable predictions:

• Cells that are bigger at birth add more volume in the next cell division. Because a timer cell simply doubles, the amount it adds equals its own birth volume, so the slope of V_added vs V_birth should be close to 1.
• Looking instead at how birth size is passed on: a timer cell doubles in volume, then splits into two, so each daughter is born at the same size her mother was born at. On this second plot, mother and daughter birth volumes line up as V_birth(daughter) = V_birth(mother), again a slope of 1. This means there is no size correction happening at all: whatever size a mother happens to be born at, she passes it straight on to her daughters, undiluted.
• The time from one division to the next should be independent of the volume at birth.
• Due to small variations in size distribution of new born cells we would expect a large variety of size to emerge over time that would eventually produce giant cells.

Single cell measurements in bacteria, yeast and mammalian cells dont support this model, and this agrees with common sense. You wouldn't design a size control system independently of size simply based on a stop watch. That would not work out very well!

The sizer model

The next option is probably the most obvious one: cells have a way of measuring their mass or volume and divide once a fixed threshold is reached. This would introduce homeostasis. A cell that is born bigger due to stochastic noise, will simply grow less before the next division and the daughters will immediately return back to the average volume. If I would design a growth control mechanism from scratch, this is the model I would choose. It results in low variation and an intrinsic and rapid correction mechanism. To keep our economy metaphor alive, this would compare to an adaptive taxation mechanism that prevents wealth from spinning out of control.

Compared to the timer model the sizer model results in significantly different outcomes for our set of predictions:

• Cells that are bigger at birth add less volume in the next division cycle. So the slope of V_added vs V_birth is negative
• Because birth volume is corrected in each cycle, there should be no correlation between V_birth mother and V_birth daughter. Regardless how big, or small the mother is due to noise variations, the daughter volume will be corrected by the sizer,
• The bigger the mother, the shorter the time to the next division, resulting in a negative slope of the relationship. This is a key sizer signature. The correction mechanism is built around this adaptation of division time to size.
• Stochastic variation is corrected in each cycle, so the population settles into a narrow, stable distribution

Even though a sizer seems like the sensible design choice to reach size homeostasis, single cell volume measurements across species from bacteria to mammalian cells do not agree with the above predictions. One exception to this rule is S.pombe which appears to be the closest thing to a sizer to maintain size homeostasis ⁹.

The adder model

So cells aren't timers, and, against our engineering intuition they aren't sizers either. Evolution mostly settled on a third, less obvious strategy, the adder. This model simply implies that each cell adds a fixed volume regardless of its birth size. This also leads to a correction mechanism, but one that happens slower than with a sizer. Lets say a cell is born big with a size V_mean + V_extra. At the next division the cell adds the fixed V_mean, so it is 2xV_mean + V_extra before division, so the daughter cells have a volume V_mean + V_extra/2. Assuming the mean volume is now maintained each division will reduce V_extra further to V_extra/4, V_extra/8 and so on, leading to a gradual disappearance of the accidental size increase. Compared to the sizer, where correction is instance, the adder takes its time but achieves the same end result. It behaves markedly different in our prediction list:

• The size of the mother cell at birth does not correlate with the added size. This is the signature result for the adder: Added volume is constant and does not correlate with volume at birth.
• A daughter's birth size is still positively correlated with her mother's. So, like the timer and unlike the flat sizer, the cloud tilts upward but with a shallower slope of ½, instead of 1. The reason is that the adder tops every cell up by the same fixed volume, regardless of birth size. A large mother isn't rewarded with a proportionally larger division volume (as she would be under the timer's doubling), she just gets + V_c like everyone else.
• The time to the next division will decrease with size of the mother at birth. This is because of exponential growth, a bigger cell will take less time to add the fixed amount of adder volume.
• Because it takes longer to correct stochastic variation the distribution of size in the adder population should be narrower than the timer cells but broader than the sizer population.

Building the simulation

To test these predictions I built a simple cell growth and division simulation. It starts with a single cell that grows exponentially. Division time is dictated by the three different models, a fixed time interval for the timer, a size threshold for the sizer, and the time when a fixed added volume is reached for the adder. Stochastic noise is introduced to blur the division time and introduce size variation, and also in the division process resulting in slightly unequal volumes for the daughter cell. The simulation runs until a n_max number of cells is generated (3000 by default). For each generation it records the division time, volume at birth and volume at division for each cell.

By selecting a model you can run the simulation yourself and check the results below. The two noise parameters can be changed to increase or decrease overall variation in the population. The plots show our four predictions: A) birth volume of the mother vs added volume B) birth volume mother vs birth volume daughter C) birth volume mother vs time to the next division D) distribution of birth volume of the final population.

Figure 1 — The three size-control models, simulated. Toggle models and drag the two noise sources; every panel re-runs live in your browser. (A) Added volume ΔV against birth volume V_b — the slope is α: timer ≈ +1, adder ≈ 0, sizer ≈ −1. (B) The return map — each daughter's birth size against her mother's, with the dashed y = x line. Its slope is (1+α)/2: timer 1 (rides the diagonal, no correction), adder ½, sizer 0 (flat, full correction). (C) Time to division against birth size — flat for the timer (fixed cycle), sloping down for sizer and adder (bigger cells reach threshold sooner). (D) The steady-state birth-size distribution — broadest for the timer, and, as discussed, similar for sizer and adder at the default noise.

As you can see, the behaviour of each model are all as predicted, with the exception of the size distribution. I would have expected that the sizer distribution in D should be the narrowest width but it actually doesnt show much difference to the adder. The answer to this is a bit tricky but it reveals a tug of war between how strongly the model corrects and how much noise is injected. The adder noise only affects the added volume which is only roughly half the volume before division, while the sizer noise takes the full division volume, so twice as much. Thus, with the default noise settings, the two models achieve approximately the same distribution. This is a good warning shot that just looking at size distribution is not sufficient to distinguish between sizer and adder; we need additional informstion from the correlation plots.

The alpha-model

Sizer, timer and adder are discrete hypotheses that deliver precise, testable predictions. Unfortunately nature rarely follows this clean separation, and delivers more murky "in-between" results. Measurements in bacteria, budding yeast and mammalian cells ^5101112 reveal that most organisms follow the adder model, but with minor deviations either towards a sizer or a timer. How can al state of affairs? A simple assumption isthat the mother's birth size feeds back onto how much volume the daughter adds — contributing either correction (sizer-ward) or amplification (timer-ward) . A simple model captures this gradual spectrum from pure sipure timer.

V_d = (1 + α) · V_birth + V_c

Here V_d is the volume at which the cell divides, and α is the measured slope of the added-volume-vs-birth-size plot (panel A), read straight off experimental data. It tilts the adder. At α = 0 a cell adds the same volume regardless of size (pure adder); make α negative and larger cells add less, a correction that pulls sizes together (sizer-ward); make it positive and larger cells add more, weakening the correction and pushing towards runaway (timer-ward). A single dial therefore slides continuously from sizer (−1) through adder (0) to timer (+1).

One subtlety is worth spelling out, because the equation is easy to misread. V_c is not an independent constant here. In the simulation it is set to (1 − α)·V₀, where V₀ is the characteristic birth size. This guarantees that whatever α you dial in, the population still settles at the same average size V₀, so the slider changes how cells control their size, not what size they end up at. Without it, the sizer and timer clouds would drift to entirely different sizes and the comparison would be muddied by a moving size axis rather than the control behaviour we want to see. The three named models fall straight out of this: α = 0 gives V_c = V₀ (an adder topping up by one V₀); α = −1 gives V_c = 2·V₀ (a sizer dividing at a fixed absolute size); α = +1 gives V_c = 0 (a timer that simply doubles).

Applied to measurements across organisms, the "near-adder" label describes most size-control systems from prokaryotes to mammalian cells. Most cell types cluster around α ≈ 0, drifting only slightly negative (budding yeast) or positive (some bacteria), but never near the α = 1 cliff where homeostasis fails. Interestingly, fission yeast has a measured α of about −0.8, making it the closest thing we have to a pure sizer.

I have adapted the simulation to this model, with an α that can be changed dynamically from −1 to +1, shifting the population from sizer to timer. Changing α in the interactive graph below re-runs the simulation and redraws the plots, which should help make concrete how the size-control behaviour changes as the single dial turns.

Figure 2 — One dial from sizer to timer. α interpolates continuously between the models: −1 a pure sizer, 0 a pure adder, +1 a pure timer. Drag it and the same four panels morph together; the readout tracks the two diagnostic slopes (α in panel A, (1+α)/2 in panel B). Notice the cloud stays centred on the same average size as α changes — V_c is pinned to (1−α)·V₀ precisely so the dial changes how cells control size, not the size they settle at.

Conclusion

Thats it for the maths! Building the simulation and working through the predictions was fun and has helped me solidify my understanding of the models and their implications. But what I'm really interested in, is how this system actually works. How does a cell actually know how much mass it has generated and then trigger division? The α dial in the model is only a description, not a mechanism. Fitting α ≈ 0 to a dataset tells you that a cell behaves like a near-adder, but it says nothing about which molecule is doing the counting, or how. How does this actually work? What's the mechanism? That will need its own article, but I'll sketch some ideas here to finish this blog.

While the adder behaviour seems to be evolutionarily conserved, there is no unified mechanism behind it. In fact even different species of bacteria use completely different molecular machinery to control the timing of division. What's striking is that despite this variability at the molecular level, the basic logic appears to be conserved. An inhibitor holds a brake on the division machinery, and the brake is released once the cell is ready. Why evolution reaches for a brake to be released rather than an activator to be switched on is, I think, no accident. Two mutually inhibiting components make a bistable switch, so the cell can sit poised and then commit to division sharply and irreversibly rather than drifting across the threshold. In eukaryotic cells we have several such brake systems, and the most direct are the Wee1/Myt1 inhibitors of Cdk1, the master trigger of mitotic entry.

Wee1 is in fact the main target of size control in fission yeast ¹³, the one organism that behaves like a sizer (α ≈ −0.8) rather than an adder. So our best mechanistic handle on cell-size control comes from the species that solves the problem differently from the norm. The eucaryotic near-adders - budding yeast, our own cells -don't seem to read their size through the same Wee1 brake ¹⁴, but I dont think we can as yet rule out a link between Cdk1 regulation and cell size control. In the end, the ultimate point that determines the size of the next generation is the switch into mitosis, so it would be strange is this switch is uncoupled from size control! Additionally, we do not know how added mass is measured in the first place, and how that measurement is fed to the brake. This remains a genuine mystery. It's one of the fundamental unsolved problems in biology.

Ultimately this question is not just about single cells. Organ and organism size is set by the balance of two things: Firstly, how many cells there are, and secondly, how big each one is. Both questions are downstream of the cell size control and division regulation we have been circling here all along. When cell growth and proliferation is coupled correctly, tissues grow to the correct size; uncoupling will cause overgrowth, or cancer. So asking how a cell knows how big it is turns out to be a small corner of a much bigger question: how living things build themselves to the right scale at all.

Acknowledgements

This blog was inspired by reading Mike Lynch's excellent Evolutionary Cell Biology specifically chapter 9; I struggled to follow the logic of the equations, and building a simulation helped me understand the models better.

The simulation is written in Rust, compiled to WebAssembly with wasm-pack, and called straight from the page. Each time you move a slider, the Rust code re-runs and hands the numbers to a small React component that redraws the plots. The runs are seeded, so the same settings always give the same figure.

I used Claude Code with Opus 4.8 extensively for this project, but mainly as a teacher and reviewer rather than as an agent, so most of the text and simulation code is written by hand, the result of planning and discussing with the LLM rather than an agentic loop on autopilot.

References