Cell length growth in fission yeast: an analysis of its bilinear character and the nature of its rate change transition

Analytical cell size distribution: lineage-population bias and parameter inference

We derive analytical steady-state cell size distributions for size-controlled cells in single-lineage experiments, such as the mother machine, which are fundamentally different from batch cultures where populations of cells grow freely. For exponential single-cell growth, characterizing most bacteria, the lineage-population bias is obtained explicitly. In addition, if volume is evenly split between the daughter cells at division, we show that cells are on average smaller in populations than in lineages. For more general power-law growth rates and deterministic volume partitioning, both symmetric and asymmetric, we derive the exact lineage distribution. This solution is in good agreement with Escherichia coli mother machine data and can be used to infer cell cycle parameters such as the strength of the size control and the asymmetry of the division. When introducing stochastic volume partitioning, we derive the large-size and small-size tails of the lineage distribution and show that the lineage-population bias only depends on the single-cell growth rate. These asymptotic behaviours are extended to the adder model of cell size control. When considering noisy single-cell growth rate, we derive the large-size lineage and population distributions. Finally, we show that introducing noise, either on the volume partitioning or on the single-cell growth rate, can cancel the lineage-population bias.

Scaling of biosynthesis and metabolism with cell size

Cells adopt a size that is optimal for their function, and pushing them beyond this limit can cause cell aging and death by senescence or reduce proliferative potential. However, by increasing their genome copy number (ploidy), cells can increase their size dramatically and homeostatically maintain physiological properties such as biosynthesis rate. Recent studies investigating the relationship between cell size and rates of biosynthesis and metabolism under normal, polyploid, and pathological conditions are revealing new insights into how cells attain the best function or fitness for their size by tuning processes including transcription, translation, and mitochondrial respiration. A new frontier is to connect single-cell scaling relationships with tissue and whole-organism physiology, which promises to reveal molecular and evolutionary principles underlying the astonishing diversity of size observed across the tree of life.

Volume growth in animal cells is cell cycle dependent and shows additive fluctuations

The way proliferating animal cells coordinate the growth of their mass, volume, and other relevant size parameters is a long-standing question in biology. Studies focusing on cell mass have identified patterns of mass growth as a function of time and cell cycle phase, but little is known about volume growth. To address this question, we improved our fluorescence exclusion method of volume measurement (FXm) and obtained 1700 single-cell volume growth trajectories of HeLa cells. We find that, during most of the cell cycle, volume growth is close to exponential and proceeds at a higher rate in S-G2 than in G1. Comparing the data with a mathematical model, we establish that the cell-to-cell variability in volume growth arises from constant-amplitude fluctuations in volume steps rather than fluctuations of the underlying specific growth rate. We hypothesize that such 'additive noise' could emerge from the processes that regulate volume adaptation to biophysical cues, such as tension or osmotic pressure.

Characterizing non-exponential growth and bimodal cell size distributions in fission yeast: An analytical approach

Unlike many single-celled organisms, the growth of fission yeast cells within a cell cycle is not exponential. It is rather characterized by three distinct phases (elongation, septation, and reshaping), each with a different growth rate. Experiments also showed that the distribution of cell size in a lineage can be bimodal, unlike the unimodal distributions measured for the bacterium Escherichia coli. Here we construct a detailed stochastic model of cell size dynamics in fission yeast. The theory leads to analytic expressions for the cell size and the birth size distributions, and explains the origin of bimodality seen in experiments. In particular, our theory shows that the left peak in the bimodal distribution is associated with cells in the elongation phase, while the right peak is due to cells in the septation and reshaping phases. We show that the size control strategy, the variability in the added size during a cell cycle, and the fraction of time spent in each of the three cell growth phases have a strong bearing on the shape of the cell size distribution. Furthermore, we infer all the parameters of our model by matching the theoretical cell size and birth size distributions to those from experimental single-cell time-course data for seven different growth conditions. Our method provides a much more accurate means of determining the size control strategy (timer, adder or sizer) than the standard method based on the slope of the best linear fit between the birth and division sizes. We also show that the variability in added size and the strength of size control in fission yeast depend weakly on the temperature but strongly on the culture medium. More importantly, we find that stronger size homeostasis and larger added size variability are required for fission yeast to adapt to unfavorable environmental conditions.

Advances in microscopy enable us to follow single cells over long timescales from which we can understand how their size varies with time and the nature of innate strategies developed to control cell size. These data show that in many cell types, growth is exponential and the distribution of cell size has one peak, namely there is a single characteristic cell size. However data for fission yeast show remarkable differences: growth is non-exponential and the distribution of cell sizes has two peaks, corresponding to different growth phases. Here we construct a detailed stochastic mathematical model of this organism; by solving the model analytically, we show that it is able to predict the two peaked distributions of cell size seen in data and provide an explanation for each peak in terms of various growth phases of the single-celled organism. Furthermore, by fitting the model to the data, we infer values for the rates of all microscopic processes in our model. This method is shown to provide a much more reliable inference than current methods and shed light on how the strategy used by fission yeast cells to control their size varies with external conditions.

Cell Length Growth in the Fission Yeast Cell Cycle: Is It (Bi)linear or (Bi)exponential?

Fission yeast is commonly used as a model organism in eukaryotic cell growth studies. To describe the cells’ length growth patterns during the mitotic cycle, different models have been proposed previously as linear, exponential, bilinear and biexponential ones. The task of discriminating among these patterns is still challenging. Here, we have analyzed 298 individual cells altogether, namely from three different steady-state cultures (wild-type, wee1-50 mutant and pom1Δ mutant). We have concluded that in 190 cases (63.8%) the bilinear model was more adequate than either the linear or the exponential ones. These 190 cells were further examined by separately analyzing the linear segments of the best fitted bilinear models. Linear and exponential functions have been fitted to these growth segments to determine whether the previously fitted bilinear functions were really correct. The majority of these growth segments were found to be linear; nonetheless, a significant number of exponential ones were also detected. However, exponential ones occurred mainly in cases of rather short segments (<40 min), where there were not enough data for an accurate model fitting. By contrast, in long enough growth segments (≥40 min), linear patterns highly dominated over exponential ones, verifying that overall growth is probably bilinear.

An image analysis method to survey the dynamics of polar protein abundance in the regulation of tip growth

Tip growth is critical for the lifestyle of many walled cells. In yeast and fungi, this process is typically associated with the polarized deposition of conserved tip factors, including landmarks, Rho GTPases, cytoskeleton regulators, and membrane and cell wall remodelers. Because tip growth speeds may vary extensively between life cycles or species, we asked whether the local amount of specific polar elements could determine or limit tip growth speeds. Using the model fission yeast, we developed a quantitative image analysis pipeline to dynamically correlate single tip elongation speeds and polar protein abundance in large data sets. We found that polarity landmarks are typically diluted by growth. In contrast, tip growth speed is positively correlated with the local amount of factors related to actin, secretion or cell wall remodeling, but, surprisingly, exhibits long saturation plateaus above certain concentrations of those factors. Similar saturation observed for Spitzenkörper components in much faster growing fungal hyphae suggests that elements independent of canonical surface remodelers may limit single tip growth. This work provides standardized methods and resources to decipher the complex mechanisms that control cell growth.This article has an associated First Person interview with Sarah Taheraly, joint first author of the paper.

Strongly oversized fission yeast cells lack any size control and tend to grow linearly rather than bilinearly

During the mitotic cycle, the rod-shaped fission yeast cells grow only at their tips. The newly born cells grow first unipolarly at their old end, but later in the cycle, the 'new end take-off' event occurs, resulting in bipolar growth. Photographs were taken of several steady-state and induction synchronous cultures of different cell cycle mutants of fission yeast, generally larger than wild type. Length measurements of many individual cells were performed from birth to division. For all the measured growth patterns, three different functions (linear, bilinear and exponential) were fitted, and the most adequate one was chosen by using specific statistical criteria, considering the altering parameter numbers. Although the growth patterns were heterogeneous in all the cultures studied, we could find some tendencies. In cultures with sufficiently wide size distribution, cells large enough at birth tend to grow linearly, whereas the other cells generally tend to grow bilinearly. We have found that among bilinearly growing cells, the larger they are at birth, the rate change point during their bilinear pattern occurs earlier in the cycle. This shifting near to the beginning of the cycle might finally cause a linear pattern, if the cells are even larger. In all of the steady-state cultures studied, a size control mechanism operates to maintain homeostasis. By contrast, strongly oversized cells of induction synchronous cultures lack any sizer, and their cycle rather behaves like an adder. We could determine the critical cell size for both the G1 and G2 size controls, where these mechanisms become cryptic. TAKE AWAY: Most individual fission yeast cells in steady-state cultures grow bilinearly. In strongly oversized fission yeast cells, linear growth dominates over bilinear. Above birth length thresholds, both the G1 and G2 size controls become cryptic.

Decoupling of Rates of Protein Synthesis from Cell Expansion Leads to Supergrowth

Cell growth is a complex process in which cells synthesize cellular components while they increase in size. It is generally assumed that the rate of biosynthesis must somehow be coordinated with the rate of growth in order to maintain intracellular concentrations. However, little is known about potential feedback mechanisms that could achieve proteome homeostasis or the consequences when this homeostasis is perturbed. Here, we identify conditions in which fission yeast cells are prevented from volume expansion but nevertheless continue to synthesize biomass, leading to general accumulation of proteins and increased cytoplasmic density. Upon removal of these perturbations, this biomass accumulation drove cells to undergo a multi-generational period of "supergrowth" wherein rapid volume growth outpaced biosynthesis, returning proteome concentrations back to normal within hours. These findings demonstrate a mechanism for global proteome homeostasis based on modulation of volume growth and dilution.

Fission yeast cells grow approximately exponentially

How the rate of cell growth is influenced by cell size is a fundamental question of cell biology. The simple model that cell growth is proportional to cell size, based on the proposition that larger cells have proportionally greater synthetic capacity than smaller cells, leads to the prediction that the rate of cell growth increases exponentially with cell size. However, other modes of cell growth, including bilinear growth, have been reported. The distinction between exponential and bilinear growth has been explored in particular detail in the fission yeast Schizosaccharomyces pombe. We have revisited the mode of fission yeast cell growth using high-resolution time-lapse microscopy and find, as previously reported, that these two growth models are difficult to distinguish both because of the similarity in shapes between exponential and bilinear curves over the two-fold change in length of a normal cell cycle and because of the substantial biological and experimental noise inherent to these experiments. Therefore, we contrived to have cells grow more than twofold, by holding them in G2 for up to 8 h. Over this extended growth period, in which cells grow up to 5.5-fold, the two growth models diverge to the point that we can confidently exclude bilinear growth as a general model for fission yeast growth. Although the growth we observe is clearly more complicated than predicted by simple exponential growth, we find that exponential growth is a robust approximation of fission yeast growth, both during an unperturbed cell cycle and during extended periods of growth.

Biphasic decline of β-cell function with age in euglycemic nonobese diabetic mice parallels diabetes onset

A gradual decline in insulin response is known to precede the onset of type 1 diabetes (T1D). To track age-related changes in the β-cell function of nonobese diabetic (NOD) mice, the most commonly used animal model for T1D, and to establish differences between those who do and do not become hyperglycemic, we performed a long-term longitudinal oral glucose tolerance test (OGTT) study (10-42 weeks) in combination with immunofluorescence imaging of islet morphology and cell proliferation. We observed a clear biphasic decline in insulin secretion (AUC0-30 min ) even in euglycemic animals. A first phase (10-28 weeks) consisted of a relatively rapid decline and paralleled diabetes development in the same cohort of animals. This was followed by a second phase (29-42 weeks) during which insulin secretion declined much slower while no additional animals became diabetic. Blood glucose profiles showed a corresponding, but less pronounced change: the area under the concentration curve (AUC0-150 min ) increased with age, and fit with a bilinear model indicated a rate-change in the trendline around 28 weeks. In control NOD scids, no such changes were observed. Islet morphology also changed with age as islets become surrounded by mononuclear infiltrates, and, in all mice, islets with immune cell infiltration around them showed increased β-cell proliferation. In conclusion, insulin secretion declines in a biphasic manner in all NOD mice. This trend, as well as increased β-cell proliferation, is present even in the NODs that never become diabetic, whereas, it is absent in control NOD scid mice.

Activity-limiting role of molecular size: size-dependency of maximum activity for P450 inhibition as revealed by qHTS data

Analysis of a large number of data on cytochrome P450 (P450) inhibition obtained from quantitative high-throughput screening assays from the PubChem BioAssay Database clearly indicates that molecular size has an important activity-limiting role for datasets focused on drug-like compounds (PubChem BioAssay Identifier [AID] 1851) as well as for datasets also incorporating a wider range of environmental chemicals (AIDs 410, 899, 883, 891, and 884). Maximum inhibitory activity increases with size for small enough structures then plateaus and begins to show a decreasing trend for larger structures. Log-scaled maximum median inhibitory concentration (pIC50) as a function of molecular size could be fitted well with a bilinear model (LinBiExp), and the shape of the curve is quite similar across five P450 isozymes (CYP1A2, 2C9, 2C19, 2D6, and 3A4) with a turning-point of maximum inhibition around 300-500 Da. While the present size-based approach cannot account for the variability of activity in general, using data for a very large number of compounds, it still provides an intuitive interpretation of the maximum P450-inhibitory activity obtainable for a given molecular size and highlights the presence of an "optimum" size range.

Repair rather than segregation of damage is the optimal unicellular aging strategy

BACKGROUND

How aging, being unfavourable for the individual, can evolve is one of the fundamental problems of biology. Evidence for aging in unicellular organisms is far from conclusive. Some studies found aging even in symmetrically dividing unicellular species; others did not find aging in the same, or in different, unicellular species, or only under stress. Mathematical models suggested that segregation of non-genetic damage, as an aging strategy, would increase fitness. However, these models failed to consider repair as an alternative strategy or did not properly account for the benefits of repair. We used a new and improved individual-based model to examine rigorously the effect of a range of aging strategies on fitness in various environments.

RESULTS

Repair of damage emerges as the best strategy despite its fitness costs, since it immediately increases growth rate. There is an optimal investment in repair that outperforms damage segregation in well-mixed, lasting and benign environments over a wide range of parameter values. Damage segregation becomes beneficial, and only in combination with repair, when three factors are combined: (i) the rate of damage accumulation is high, (ii) damage is toxic and (iii) efficiency of repair is low. In contrast to previous models, our model predicts that unicellular organisms should have active mechanisms to repair damage rather than age by segregating damage. Indeed, as predicted, all organisms have evolved active mechanisms of repair whilst aging in unicellular organisms is absent or minimal under benign conditions, apart from microorganisms with a different ecology, inhabiting short-lived environments strongly favouring early reproduction rather than longevity.

CONCLUSIONS

Aging confers no fitness advantage for unicellular organisms in lasting environments under benign conditions, since repair of non-genetic damage is better than damage segregation.