Theoretical Prediction of Disrupted Min Oscillation in Flattened Escherichia coli

The dynamics of the Min-protein system help Escherichia coli regulate the process of cell division by identifying the center of the cell. While this system exhibits robust bipolar oscillations in wild-type cell shapes, recent experiments have shown that when the cells are mechanically deformed into wide, flattened out, irregular shapes, the spatial regularity of these oscillations breaks down. We employ widely used stochastic and deterministic models of the Min system to simulate cells with flattened shapes. The deterministic model predicts strong bipolar oscillations, in contradiction with the experimentally observed behavior, while the stochastic model, which is based on the same reaction-diffusion equations, predicts more spatially irregular oscillations. We further report simulations of flattened but more symmetric shapes, which suggest that the flattening and lateral expansion may contribute as much to the irregular oscillation behavior as the asymmetry of the cell shapes.     

Division synchrony and the dynamics of microbial populations: A size-specific model

A discrete, environmentally coupled, size-specific model of microbial population dynamics in continuous culture is presented. It is mathematically simpler than other models based on similar assumptions and lends itself to numerical and analytic solutions. It displays several phenomena which have been reported in the experimental literature but which are not well understood; specifically, a loose relationship between biomass and numbers (i.e., a time lag between mass growth and cell division) and a critical damping of biomass while numbers continue to oscillate. In addition, the model provides several new predictions: The stable biomass distribution is independent of the environmental factors considered in the model and uniformly distributes the biomass among the size classes. The rate of approach to stability and the frequency of waves through the size distributions are a function of the flow rate and the variance in rate of growth and size at division. The model should provide a useful basis for studying the effects of size specificity on the dynamics of microbial populations cultured in chemostats.     

Highly canalized MinD transfer and MinE sequestration explain the origin of robust MinCDE-protein dynamics

Min-protein oscillations in Escherichia coli are characterized by the remarkable robustness with which spatial patterns dynamically adapt to variations of cell geometry. Moreover, adaption, and therefore proper cell division, is independent of temperature. These observations raise fundamental questions about the mechanisms establishing robust Min oscillations, and about the role of spatial cues, as they are at odds with present models. Here, we introduce a robust model based on experimental data, consistently explaining the mechanisms underlying pole-to-pole, striped, and circular patterns, as well as the observed temperature dependence of the oscillation period. Contrary to prior conjectures, the model predicts that MinD and cardiolipin domains are not colocalized. The transient sequestration of MinE and highly canalized transfer of MinD between polar zones are the key mechanisms underlying oscillations. MinD channeling enhances midcell localization and facilitates stripe formation, revealing the potential optimization process from which robust Min-oscillations originally arose.     

Membrane Binding of MinE Allows for a Comprehensive Description of Min-Protein Pattern Formation

The rod-shaped bacterium Escherichia coli selects the cell center as site of division with the help of the proteins MinC, MinD, and MinE. This protein system collectively oscillates between the two cell poles by alternately binding to the membrane in one of the two cell halves. This dynamic behavior, which emerges from the interaction of the ATPase MinD and its activator MinE on the cell membrane, has become a paradigm for protein self-organization. Recently, it has been found that not only the binding of MinD to the membrane, but also interactions of MinE with the membrane contribute to Min-protein self-organization. Here, we show that by accounting for this finding in a computational model, we can comprehensively describe all observed Min-protein patterns in vivo and in vitro. Furthermore, by varying the system''s geometry, our computations predict patterns that have not yet been reported. We confirm these predictions experimentally.     

IL-2 regulates expansion of CD4+ T cell populations by affecting cell death: insights from modeling CFSE data

It is generally accepted that IL-2 influences the dynamics of populations of T cells in vitro and in vivo. However, which parameters for cell division and/or death are affected by IL-2 is not well understood. To get better insights into the potential ways of how IL-2 may influence the population dynamics of T cells, we analyze data on the dynamics of CFSE-labeled polyclonal CD4(+) T lymphocytes in vitro after anti-CD3 stimulation at different concentrations of exogenous IL-2. Inferring cell division and death rates from CFSE-delabeling experiments is not straightforward and requires the use of mathematical models. We find that to adequately describe the dynamics of T cells at low concentrations of exogenous IL-2, the death rate of divided cells has to increase with the number of divisions cells have undergone. IL-2 hardly affects the average interdivision time. At low IL-2 concentrations 1) fewer cells are recruited into the response and successfully complete their first division; 2) the stochasticity of cell division is increased; and 3) the rate, at which the death rate increases with the division number, increases. Summarizing, our mathematical reinterpretation suggests that the main effect of IL-2 on the in vitro dynamics of naive CD4(+) T cells occurs by affecting the rate of cell death and not by changing the rate of cell division.     

Topological solution for cell proliferation in intestinal crypt. I. Elastic growth without cell loss

The cells of an intestinal crypt are tightly packed and, consequently, cell renewal must proceed in accordance with topological laws implicit in the hexagonal cell patterns. The division wave is proposed as the simplest way of proliferation, satisfying topological requirements in steady state. Six pentagonal cells, persisting by topological necessity in the crypt bottom, are the sources of division waves for the whole crypt. The positions of the six pentagonal cells specify the order of cell division. The division, reciprocally, changes the positions of the pentagons which, in turn, specify the order of division in the new cells, and so on. The resulting order of cell division accounts for maintenance of the crypt structure, cell movement toward the villus and cessation of division. Since the pattern of elastic growth is dictated entirely by topological considerations, it does not depend on the genetic constitution of the organism. This model is different from conventional models in which the crypt is assumed to be composed of fixed longitudinal cell columns, the cells of the bottom contributing collectively to the proliferative potential of the whole crypt.     

Cell surface glycoproteins I: Accumulation of a glycoprotein on the outer surface of mouse LS cells during mitosis

Surface glycopeptides derived from vertebrate cells have been separated into 4 classes by chromatography on DEAE cellulose columns. Among different cell types tested, significant differences were observed in the relative amounts of these 4 glycopeptide classes present on the cell surface. This type of heterogeneity is consistent with the expected biological role of cell surface glycoproteins. One glycopeptide, as revealed by the DEAE column analysis, was found to have a characteristic metabolic pattern in mouse LS cells. New accumulation of this structure, called glycopeptide 4, on the cell surface was detected only around the period of cell division (M phase) and not at other times during the cell cycle.     

Cell cycle modelling

Models able to describe the events of cellular growth and division and the dynamics of cell populations are useful for the understanding of functional control mechanisms and for the theoretical support for automated analysis of flow cytometric data and of cell volume distributions. This paper reports on models that we have developed with this aim for different kinds of cells. The models are composed by two subsystems: one describes the growth dynamics of RNA and protein, and the second accounts for DNA replication and cell division, and describe in a rather unitary frame the cell cycle of eukaryotic cells, like mammalian cells and yeast, and of prokaryotic cells. The model is also used to study the effects of various sources of variability on the statistical properties of cell populations, and we find that in microbial cells the main source of variability appears to be an inaccuracy of the molecular mechanism that monitors cell size. In normal mammalian cells another source of variability, that depends upon the interaction with growth factors which give competence, is apparent. An extended version of the model, which comprises also this additional variability, is presented and used to describe the properties of mammalian cell growth.     

Microtubule Dynamics may Embody a Stationary Bipolarity Forming Mechanism Related to the Prokaryotic Division Site Mechanism (Pole-to-Pole Oscillations)

Cell division mechanisms in eukaryotes and prokaryotes have until recently been seen as being widely different. However, pole-to-pole oscillations of proteins like MinE in prokaryotes are now known to determine the division plane. These protein waves arise through spontaneous pattern forming reaction—diffusion mechanisms, based on cooperative binding of the proteins to a quasistationary matrix (like the cell membrane or DNA). Rather than waves, stationary bipolar pattern formation may arise as well. Some of the involved proteins have eukaryotic homologs (e.g. FtsZ and tubulin), pointing to a possible ancient shared mechanism. Tubulin polymerizes to microtubules in the spindle. Mitotic microtubules are in a highly dynamical state, frequently undergoing rapid shortening (catastrophe), and fragments formed from the microtubule ends are inferred to enhance the destabilization. Here, we show that cooperative binding of such fragments to microtubules may set up a similar pattern forming mechanism as seen in prokaryotes. The result is a spontaneously formed, well controllable, bipolar state of microtubule dynamics in the cell, which may contribute to defining the bipolar spindle.     

Spatial dynamics of feedback and feedforward regulation in cell lineages

Feedback mechanisms within cell lineages are thought to be important for maintaining tissue homeostasis. Mathematical models that assume well-mixed cell populations, together with experimental data, have suggested that negative feedback from differentiated cells on the stem cell self-renewal probability can maintain a stable equilibrium and hence homeostasis. Cell lineage dynamics, however, are characterized by spatial structure, which can lead to different properties. Here, we investigate these dynamics using spatially explicit computational models, including cell division, differentiation, death, and migration / diffusion processes. According to these models, the negative feedback loop on stem cell self-renewal fails to maintain homeostasis, both under the assumption of strong spatial restrictions and fast migration / diffusion. Although homeostasis cannot be maintained, this feedback can regulate cell density and promote the formation of spatial structures in the model. Tissue homeostasis, however, can be achieved if spatially restricted negative feedback on self-renewal is combined with an experimentally documented spatial feedforward loop, in which stem cells regulate the fate of transit amplifying cells. This indicates that the dynamics of feedback regulation in tissue cell lineages are more complex than previously thought, and that combinations of spatially explicit control mechanisms are likely instrumental.     

Linking cell division to cell growth in a spatiotemporal model of the cell cycle

Cell division must be tightly coupled to cell growth in order to maintain cell size, yet the mechanisms linking these two processes are unclear. It is known that almost all proteins involved in cell division shuttle between cytoplasm and nucleus during the cell cycle; however, the implications of this process for cell cycle dynamics and its coupling to cell growth remains to be elucidated. We developed mathematical models of the cell cycle which incorporate protein translocation between cytoplasm and nucleus. We show that protein translocation between cytoplasm and nucleus not only modulates temporal cell cycle dynamics, but also provides a natural mechanism coupling cell division to cell growth. This coupling is mediated by the effect of cytoplasmic-to-nuclear size ratio on the activation threshold of critical cell cycle proteins, leading to the size-sensing checkpoint (sizer) and the size-independent clock (timer) observed in many cell cycle experiments.     

Sic1 as a timer of Clb cyclin waves in the yeast cell cycle - design principle of not just an inhibitor

Cellular systems biology aims to uncover design principles that describe the properties of biological networks through interaction of their components in space and time. The cell cycle is a complex system regulated by molecules that are integrated into functional modules to ensure genome integrity and faithful cell division. In budding yeast, cyclin-dependent kinases (Cdk1/Clb) drive cell cycle progression, being activated and inactivated in a precise temporal sequence. In this module, which we refer to as the 'Clb module', different Cdk1/Clb complexes are regulated to generate waves of Clb activity, a functional property of cell cycle control. The inhibitor Sic1 plays a critical role in the Clb module by binding to and blocking Cdk1/Clb activity, ultimately setting the timing of DNA replication and mitosis. Fifteen years of research subsequent to the identification of Sic1 have lead to the development of an integrative approach that addresses its role in regulating the Clb module. Sic1 is an intrinsically disordered protein and achieves its inhibitory function by cooperative binding, where different structural regions stretch on the Cdk1/Clb surface. Moreover, Sic1 promotes S?phase entry, facilitating Cdk1/Clb5 nuclear transport, and therefore revealing a double function of inhibitor/activator that rationalizes a mechanism to prevent precocious DNA replication. Interestingly, the investigation of Clb temporal dynamics by mathematical modelling and experimental validation provides evidence that Sic1 acts as a timer to coordinate oscillations of Clb cyclin waves. Here we review these findings, focusing on the design principle underlying the Clb module, which highlights the role of Sic1 in regulating phase-specific Cdk1/Clb activities.     

Modeling cell proliferation for simulating three-dimensional tissue morphogenesis based on a reversible network reconnection framework

Tissue morphogenesis in multicellular organisms is accompanied by proliferative cell behaviors: cell division (increase in cell number after each cell cycle) and cell growth (increase in cell volume during each cell cycle). These proliferative cell behaviors can be regulated by multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze multicellular dynamics, a reversible network reconnection (RNR) model has been suggested, in which each cell shape is expressed by a single polyhedron. In this study, to apply the RNR model to simulate tissue morphogenesis involving proliferative cell behaviors, we model cell proliferation based on a RNR model framework. In this model, cell division was expressed by dividing a polyhedron at a planar surface for which cell division behaviors were characterized by three quantities: timing, intracellular position, and normal direction of the dividing plane. In addition, cell growth was expressed by volume growth as a function of individual cell times within their respective cell cycles. Numerical simulations using the proposed model showed that tissues grew during successive cell divisions with several cell cycle times. During these processes, the cell number in tissues increased while maintaining individual cell size and shape. Furthermore, tissue morphology dramatically changed based on different regulations of cell division directions. Thus, the proposed model successfully provided a basis for expressing proliferative cell behaviors during morphogenesis based on a RNR model framework.     

Key Events of the Cell Cycle: Regulation and Organization

The review surveys the studies of molecular genetic mechanisms of the cell cycle control on various eukaryotic models. The major cell cycle phenomena are considered: (1) checkpoints and their role in preserving DNA integrity and fidelity of mitosis, (2) the cell oscillator model, and (3) the role of cyclins in timing of cell division and coordination of mitotic events. The main classes of regulatory proteins involved in the cell cycle are discussed in detail.     

Dissipative particle dynamics simulations for biological tissues: rheology and competition

In this work, we model biological tissues using a simple, mechanistic simulation based on dissipative particle dynamics. We investigate the continuum behavior of the simulated tissue and determine its dependence on the properties of the individual cell. Cells in our simulation adhere to each other, expand in volume, divide after reaching a specific size checkpoint and undergo apoptosis at a constant rate, leading to a steady-state homeostatic pressure in the tissue. We measure the dependence of the homeostatic state on the microscopic parameters of our model and show that homeostatic pressure, rather than the unconfined rate of cell division, determines the outcome of tissue competitions. Simulated cell aggregates are cohesive and round up due to the effect of tissue surface tension, which we measure for different tissues. Furthermore, mixtures of different cells unmix according to their adhesive properties. Using a variety of shear and creep simulations, we study tissue rheology by measuring yield stresses, shear viscosities, complex viscosities as well as the loss tangents as a function of model parameters. We find that cell division and apoptosis lead to a vanishing yield stress and fluid-like tissues. The effects of different adhesion strengths and levels of noise on the rheology of the tissue are also measured. In addition, we find that the level of cell division and apoptosis drives the diffusion of cells in the tissue. Finally, we present a method for measuring the compressibility of the tissue and its response to external stress via cell division and apoptosis.     

The motility of mollicutes

Recent experiments show that the conformation of filament proteins play a role in the motility and morphology of many different types of bacteria. Conformational changes in the protein subunits may produce forces to drive propulsion and cell division. Here we present a molecular mechanism by which these forces can drive cell motion. Coupling of a biochemical cycle, such as ATP hydrolysis, to the dynamics of elastic filaments enable elastic filaments to propagate deformations that generate propulsive forces. We demonstrate this possibility for two classes of wall-less bacteria called mollicutes: the swimming of helical-shaped Spiroplasma, and the gliding motility of Mycoplasma.     

Key events in the cell cycle, their regulation and organization

The review surveys the studies of molecular genetic mechanisms of the cell cycle control on various eukaryotic models. The major cell cycle phenomena are considered: (1) checkpoints and their role in preserving DNA integrity and fidelity of mitosis, (2) the cell oscillator model, and (3) the role of cyclins in timing of cell division and coordination of mitotic events. The main classes of regulatory proteins involved in the cell cycle are discussed in detail.     

Live cell division dynamics monitoring in 3D large spheroid tumor models using light sheet microscopy

Background

Multicellular tumor spheroids are models of increasing interest for cancer and cell biology studies. They allow considering cellular interactions in exploring cell cycle and cell division mechanisms. However, 3D imaging of cell division in living spheroids is technically challenging and has never been reported.

Results

Here, we report a major breakthrough based on the engineering of multicellular tumor spheroids expressing an histone H2B fluorescent nuclear reporter protein, and specifically designed sample holders to monitor live cell division dynamics in 3D large spheroids using an home-made selective-plane illumination microscope.

Conclusions

As illustrated using the antimitotic drug, paclitaxel, this technological advance paves the way for studies of the dynamics of cell divion processes in 3D and more generally for the investigation of tumor cell population biology in integrated system as the spheroid model.