Distinguishing between stochasticity and determinism: Examples from cell cycle duration variability

Coupling Cell Size Regulation and Proliferation Dynamics of C. glutamicum Reveals Cell Division Based on Surface Area

Single cells actively coordinate growth and division to regulate their size, yet how this size homeostasis at the single-cell level propagates over multiple generations to impact clonal expansion remains fundamentally unexplored. Classical timer models for cell proliferation (where the duration of the cell cycle is an independent variable) predict that the stochastic variation in colony size will increase monotonically over time. In stark contrast, implementing size control according to adder strategy (where on average a fixed size added from cell birth to division) leads to colony size variations that eventually decay to zero. While these results assume a fixed size of the colony-initiating progenitor cell, further analysis reveals that the magnitude of the intercolony variation in population number is sensitive to heterogeneity in the initial cell size. We validate these predictions by tracking the growth of isogenic microcolonies of Corynebacterium glutamicum in microfluidic chambers. Approximating their cell shape to a capsule, we observe that the degree of random variability in cell size is different depending on whether the cell size is quantified as per length, surface area, or volume, but size control remains an adder regardless of these size metrics. A comparison of the observed variability in the colony population with the predictions suggests that proliferation matches better with a cell division based on the cell surface. In summary, our integrated mathematical-experimental approach bridges the paradigms of single-cell size regulation and clonal expansion at the population levels. This innovative approach provides elucidation of the mechanisms of size homeostasis from the stochastic dynamics of colony size for rod-shaped microbes.

Modeling the Circadian Control of the Cell Cycle and Its Consequences for Cancer Chronotherapy

The mammalian cell cycle is governed by a network of cyclin/Cdk complexes which signal the progression into the successive phases of the cell division cycle. Once coupled to the circadian clock, this network produces oscillations with a 24 h period such that the progression into each phase of the cell cycle is synchronized to the day-night cycle. Here, we use a computational model for the circadian clock control of the cell cycle to investigate the entrainment in a population of cells characterized by some variability in the kinetic parameters. Our numerical simulations showed that successful entrainment and synchronization are only possible with a sufficient circadian amplitude and an autonomous period close to 24 h. Cellular heterogeneity, however, introduces some variability in the entrainment phase of the cells. Many cancer cells have a disrupted clock or compromised clock control. In these conditions, the cell cycle runs independently of the circadian clock, leading to a lack of synchronization of cancer cells. When the coupling is weak, entrainment is largely impacted, but cells maintain a tendency to divide at specific times of day. These differential entrainment features between healthy and cancer cells can be exploited to optimize the timing of anti-cancer drug administration in order to minimize their toxicity and to maximize their efficacy. We then used our model to simulate such chronotherapeutic treatments and to predict the optimal timing for anti-cancer drugs targeting specific phases of the cell cycle. Although qualitative, the model highlights the need to better characterize cellular heterogeneity and synchronization in cell populations as well as their consequences for circadian entrainment in order to design successful chronopharmacological protocols.

The fate of notch-1 transcript is linked to cell cycle dynamics by activity of a natural antisense transcript

A core imprint of metazoan life is that perturbations of cell cycle are offset by compensatory changes in successive cellular generations. This trait enhances robustness of multicellular growth and requires transmission of signaling cues within a cell lineage. Notably, the identity and mode of activity of transgenerational signals remain largely unknown. Here we report the discovery of a natural antisense transcript encoded in exon 25 of notch-1 locus (nAS25) by which mother cells control the fate of notch-1 transcript in daughter cells to buffer against perturbations of cell cycle. The antisense transcript is transcribed at G1 phase of cell cycle from a bi-directional E2F1-dependent promoter in the mother cell where the titer of nAS25 is calibrated to the length of G1. Transmission of the antisense transcript from mother to daughter cells stabilizes notch-1 sense transcript in G0 phase of daughter cells by masking it from RNA editing and resultant nonsense-mediated degradation. In consequence, nAS25-mediated amplification of notch-1 signaling reprograms G1 phase in daughter cells to compensate for the altered dynamics of the mother cell. The function of nAS25/notch-1 in integrating G1 phase history of the mother cell into that of daughter cells is compatible with the predicted activity of a molecular oscillator, slower than cyclins, that coordinates cell cycle within cell lineage.

Quantitative Studies for Cell-Division Cycle Control

The cell-division cycle (CDC) is driven by cyclin-dependent kinases (CDKs). Mathematical models based on molecular networks, as revealed by molecular and genetic studies, have reproduced the oscillatory behavior of CDK activity. Thus, one basic system for representing the CDC is a biochemical oscillator (CDK oscillator). However, genetically clonal cells divide with marked variability in their total duration of a single CDC round, exhibiting non-Gaussian statistical distributions. Therefore, the CDK oscillator model does not account for the statistical nature of cell-cycle control. Herein, we review quantitative studies of the statistical properties of the CDC. Over the past 70 years, studies have shown that the CDC is driven by a cluster of molecular oscillators. The CDK oscillator is coupled to transcriptional and mitochondrial metabolic oscillators, which cause deterministic chaotic dynamics for the CDC. Recent studies in animal embryos have raised the possibility that the dynamics of molecular oscillators underlying CDC control are affected by allometric volume scaling among the cellular compartments. Considering these studies, we discuss the idea that a cluster of molecular oscillators embedded in different cellular compartments coordinates cellular physiology and geometry for successful cell divisions.

A Two-Pulse Cellular Stimulation Test Elucidates Variability and Mechanisms in Signaling Pathways

Mammalian cells respond in a variable manner when provided with physiological pulses of ligand, such as low concentrations of acetylcholine present for just tens of seconds or TNFα for just tens of minutes. For a two-pulse stimulation, some cells respond to both pulses, some do not respond, and yet others respond to only one or the other pulse. Are these different response patterns the result of the small number of ligands being able to only stochastically activate the pathway at random times or an output pattern from a deterministic algorithm responding differently to different stimulation intervals? If the response is deterministic in nature, what parameters determine whether a response is generated or skipped? To answer these questions, we developed a two-pulse test that utilizes different rest periods between stimulation pulses. This "rest-period test" revealed that cells skip responses predictably as the rest period is shortened. By combining these experimental results with a mathematical model of the pathway, we further obtained mechanistic insight into potential sources of response variability. Our analysis indicates that in both intracellular calcium and NFκB signaling, response variability is consistent with extrinsic noise (cell-to-cell variability in protein levels), a short-term memory of stimulation, and high Hill coefficient processes. Furthermore, these results support recent works that have emphasized the role of deterministic processes for explaining apparently stochastic cellular response variability and indicate that even weak stimulations likely guide mammalian cells to appropriate fates rather than leaving outcomes to chance. We envision that the rest-period test can be applied to other signaling pathways to extract mechanistic insight.

Modeling the Influence of Seasonal Differences in the HPA Axis on Synchronization of the Circadian Clock and Cell Cycle

Synchronization of biological functions to environmental signals enables organisms to anticipate and appropriately respond to daily external fluctuations and is critical to the maintenance of homeostasis. Misalignment of circadian rhythms with environmental cues is associated with adverse health outcomes. Cortisol, the downstream effector of hypothalamic-pituitary-adrenal (HPA) activity, facilitates synchronization of peripheral biological processes to the environment. Cortisol levels exhibit substantial seasonal rhythmicity, with peak levels occurring during the short-photoperiod winter months and reduced levels occurring in the long-photoperiod summer season. Seasonal changes in cortisol secretion could therefore alter its entraining capabilities, resulting in a season-dependent modification in the alignment of biological activities with the environment. We develop a mathematical model to investigate the influence of photoperiod-induced seasonal differences in the circadian rhythmicity of the HPA axis on the synchronization of the peripheral circadian clock and cell cycle in a heterogeneous cell population. Model simulations predict that the high-amplitude cortisol rhythms in winter result in the greatest entrainment of peripheral oscillators. Furthermore, simulations predict a circadian gating of the cell cycle with respect to the expression of peripheral clock genes. Seasonal differences in cortisol rhythmicity are also predicted to influence mitotic synchrony, with a high-amplitude winter rhythm resulting in the greatest synchrony and a shift in timing of the cell cycle phases, relative to summer. Our results highlight the primary interactions among the HPA axis, the peripheral circadian clock, and the cell cycle and thereby provide an improved understanding of the implications of circadian misalignment on the synchronization of peripheral regulatory processes.

Investigating cell functioning by theoretical analysis of cell-to-cell variability

Here we discuss cell-to-cell variability in isogenic cell populations on the basis of an analogy between the processes of vesicle self-reproduction and cell self-replication. A short review of the theoretical analysis of vesicle self-reproduction is presented to indicate that this process only occurs under the fulfillment of specific criteria: causal relations between the values of vesicle variables involved in its growth and division, and the parameters of the environment. It is shown that when division is asymmetric, both vesicle birth size and interdivision times are variable. We argue that during cell self-replication, the balance between processes of cell growth and division also relies on causal relations between the corresponding cellular variables. A possible method is suggested to unravel previously unidentified causal relations between cell variables from the relationships between their variability parameters such as the widths of their probability distributions and their correlation coefficients. The method is outlined by reviewing the results of the corresponding analysis applied to a population of red blood cells. Some novel research directions are suggested that could lead from the analysis of cell-to-cell variability to a better understanding of the organizational structure of cells and possibly also their evolutionary origin.

Circadian Clock, Cell Division, and Cancer: From Molecules to Organism

As a response to environmental changes driven by the Earth's axial rotation, most organisms evolved an internal biological timer-the so called circadian clock-which regulates physiology and behavior in a rhythmic fashion. Emerging evidence suggests an intimate interplay between the circadian clock and another fundamental rhythmic process, the cell cycle. However, the precise mechanisms of this connection are not fully understood. Disruption of circadian rhythms has a profound impact on cell division and cancer development and, vice versa, malignant transformation causes disturbances of the circadian clock. Conventional knowledge attributes tumor suppressor properties to the circadian clock. However, this implication might be context-dependent, since, under certain conditions, the clock can also promote tumorigenesis. Therefore, a better understanding of the molecular links regulating the physiological balance between the two cycles will have potential significance for the treatment of cancer and associated disorders.