Kinetic analysis of a molecular model of the budding yeast cell cycle

The bistable mitotic switch in fission yeast

In favorable conditions, eukaryotic cells proceed irreversibly through the cell division cycle (G1-S-G2-M) in order to produce two daughter cells with the same number and identity of chromosomes of their progenitor. The integrity of this process is maintained by "checkpoints" that hold a cell at particular transition points of the cycle until all requisite events are completed. The crucial functions of these checkpoints seem to depend on irreversible bistability of the underlying checkpoint control systems. Bistability of cell cycle transitions has been confirmed experimentally in frog egg extracts, budding yeast cells and mammalian cells. For fission yeast cells, a recent paper by Patterson et al. (2021) provides experimental evidence for an abrupt transition from G2 phase into mitosis, and we show that these data are consistent with a stochastic model of a bistable switch governing the G2/M checkpoint. Interestingly, our model suggests that their experimental data could also be explained by a reversible/sigmoidal switch, and stochastic simulations confirm this supposition. We propose a simple modification of their experimental protocol that could provide convincing evidence for (or against) bistability of the G2/M transition in fission yeast.

The oscillation of mitotic kinase governs cell cycle latches in mammalian cells

The mammalian cell cycle alternates between two phases - S-G2-M with high levels of A- and B-type cyclins (CycA and CycB, respectively) bound to cyclin-dependent kinases (CDKs), and G1 with persistent degradation of CycA and CycB by an activated anaphase promoting complex/cyclosome (APC/C) bound to Cdh1 (also known as FZR1 in mammals; denoted APC/C:Cdh1). Because CDKs phosphorylate and inactivate Cdh1, these two phases are mutually exclusive. This 'toggle switch' is flipped from G1 to S by cyclin-E bound to a CDK (CycE:CDK), which is not degraded by APC/C:Cdh1, and from M to G1 by Cdc20-bound APC/C (APC/C:Cdc20), which is not inactivated by CycA:CDK or CycB:CDK. After flipping the switch, cyclin E is degraded and APC/C:Cdc20 is inactivated. Combining mathematical modelling with single-cell timelapse imaging, we show that dysregulation of CycB:CDK disrupts strict alternation of the G1-S and M-G1 switches. Inhibition of CycB:CDK results in Cdc20-independent Cdh1 'endocycles', and sustained activity of CycB:CDK drives Cdh1-independent Cdc20 endocycles. Our model provides a mechanistic explanation for how whole-genome doubling can arise, a common event in tumorigenesis that can drive tumour evolution.

Data integration strategies for whole-cell modeling

Data makes the world go round-and high quality data is a prerequisite for precise models, especially for whole-cell models (WCM). Data for WCM must be reusable, contain information about the exact experimental background, and should-in its entirety-cover all relevant processes in the cell. Here, we review basic requirements to data for WCM and strategies how to combine them. As a species-specific resource, we introduce the Yeast Cell Model Data Base (YCMDB) to illustrate requirements and solutions. We discuss recent standards for data as well as for computational models including the modeling process as data to be reported. We outline strategies for constructions of WCM despite their inherent complexity.

Reusable rule-based cell cycle model explains compartment-resolved dynamics of 16 observables in RPE-1 cells

The mammalian cell cycle is regulated by a well-studied but complex biochemical reaction system. Computational models provide a particularly systematic and systemic description of the mechanisms governing mammalian cell cycle control. By combining both state-of-the-art multiplexed experimental methods and powerful computational tools, this work aims at improving on these models along four dimensions: model structure, validation data, validation methodology and model reusability. We developed a comprehensive model structure of the full cell cycle that qualitatively explains the behaviour of human retinal pigment epithelial-1 cells. To estimate the model parameters, time courses of eight cell cycle regulators in two compartments were reconstructed from single cell snapshot measurements. After optimisation with a parallel global optimisation metaheuristic we obtained excellent agreements between simulations and measurements. The PEtab specification of the optimisation problem facilitates reuse of model, data and/or optimisation results. Future perturbation experiments will improve parameter identifiability and allow for testing model predictive power. Such a predictive model may aid in drug discovery for cell cycle-related disorders.

A yeast cell cycle pulse generator model shows consistency with multiple oscillatory and checkpoint mutant datasets

Modeling biological systems holds great promise for speeding up the rate of discovery in systems biology by predicting experimental outcomes and suggesting targeted interventions. However, this process is dogged by an identifiability issue, in which network models and their parameters are not sufficiently constrained by coarse and noisy data to ensure unique solutions. In this work, we evaluated the capability of a simplified yeast cell-cycle network model to reproduce multiple observed transcriptomic behaviors under genomic mutations. We matched time-series data from both cycling and checkpoint arrested cells to model predictions using an asynchronous multi-level Boolean approach. We showed that this single network model, despite its simplicity, is capable of exhibiting dynamical behavior similar to the datasets in most cases, and we demonstrated the drop in severity of the identifiability issue that results from matching multiple datasets.

Generalized Michaelis-Menten rate law with time-varying molecular concentrations

The Michaelis-Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, systems biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium (quasi-steady state) much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated time-delay effects in molecular complex formation. With particularly marked improvements in protein-protein and protein-DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover), which goes beyond the quasi-steady state assumption.

Implications of differential size-scaling of cell-cycle regulators on cell size homeostasis

Accurate timing of division and size homeostasis is crucial for cells. A potential mechanism for cells to decide the timing of division is the differential scaling of regulatory protein copy numbers with cell size. However, it remains unclear whether such a mechanism can lead to robust growth and division, and how the scaling behaviors of regulatory proteins influence the cell size distribution. Here we study a mathematical model combining gene expression and cell growth, in which the cell-cycle activators scale superlinearly with cell size while the inhibitors scale sublinearly. The cell divides once the ratio of their concentrations reaches a threshold value. We find that the cell can robustly grow and divide within a finite range of the threshold value with the cell size proportional to the ploidy. In a stochastic version of the model, the cell size at division is uncorrelated with that at birth. Also, the more differential the cell-size scaling of the cell-cycle regulators is, the narrower the cell-size distribution is. Intriguingly, our model with multiple regulators rationalizes the observation that after the deletion of a single regulator, the coefficient of variation of cell size remains roughly the same though the average cell size changes significantly. Our work reveals that the differential scaling of cell-cycle regulators provides a robust mechanism of cell size control.

An autonomous mathematical model for the mammalian cell cycle

A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. A novel feature of the model is inclusion of cycle tasks such as origin licensing and initiation, nuclear envelope breakdown and kinetochore attachment, and their interactions with controllers (molecular complexes involved in cycle control). Other key features are that the model is autonomous, except for a dependence on external growth factors; the variables are continuous in time, without instantaneous resets at phase boundaries; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: the Cyclin D1-Cdk4/6 complex, APC^Cdh1, SCF^βTrCP, Cdc25A, MPF, NuMA, the securin-separase complex, and separase. Five variables represent task completion, with four for the status of origins and one for kinetochore attachment. The model predicts distinct behaviors corresponding to the main phases of the cell cycle, showing that the principal features of the mammalian cell cycle, including restriction point behavior, can be accounted for in a quantitative mechanistic way based on known interactions among cycle controllers and their coupling to tasks. The model is robust to parameter changes, in that cycling is maintained over at least a five-fold range of each parameter when varied individually. The model is suitable for exploring how extracellular factors affect cell cycle progression, including responses to metabolic conditions and to anti-cancer therapies.

A continuous-time stochastic Boolean model provides a quantitative description of the budding yeast cell cycle

The cell division cycle is regulated by a complex network of interacting genes and proteins. The control system has been modeled in many ways, from qualitative Boolean switching-networks to quantitative differential equations and highly detailed stochastic simulations. Here we develop a continuous-time stochastic model using seven Boolean variables to represent the activities of major regulators of the budding yeast cell cycle plus one continuous variable representing cell growth. The Boolean variables are updated asynchronously by logical rules based on known biochemistry of the cell-cycle control system using Gillespie's stochastic simulation algorithm. Time and cell size are updated continuously. By simulating a population of yeast cells, we calculate statistical properties of cell cycle progression that can be compared directly to experimental measurements. Perturbations of the normal sequence of events indicate that the cell cycle is 91% robust to random 'flips' of the Boolean variables, but 9% of the perturbations induce lethal mistakes in cell cycle progression. This simple, hybrid Boolean model gives a good account of the growth and division of budding yeast cells, suggesting that this modeling approach may be as accurate as detailed reaction-kinetic modeling with considerably less demands on estimating rate constants.

CELLoGeNe - An energy landscape framework for logical networks controlling cell decisions

Experimental and computational efforts are constantly made to elucidate mechanisms controlling cell fate decisions during development and reprogramming. One powerful computational method is to consider cell commitment and reprogramming as movements in an energy landscape. Here, we develop Computation of Energy Landscapes of Logical Gene Networks (CELLoGeNe), which maps Boolean implementation of gene regulatory networks (GRNs) into energy landscapes. CELLoGeNe removes inadvertent symmetries in the energy landscapes normally arising from standard Boolean operators. Furthermore, CELLoGeNe provides tools to visualize and stochastically analyze the shapes of multi-dimensional energy landscapes corresponding to epigenetic landscapes for development and reprogramming. We demonstrate CELLoGeNe on two GRNs governing different aspects of induced pluripotent stem cells, identifying experimentally validated attractors and revealing potential reprogramming roadblocks. CELLoGeNe is a general framework that can be applied to various biological systems offering a broad picture of intracellular dynamics otherwise inaccessible with existing methods.

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CELLoGeNe – Computation of Energy Landscapes of Logical Gene Networks

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Cell states as landscape attractors

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Maintenance and acquisition of cell pluripotency applications

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Single cell stochastic landscape navigation and visualization tool

A yeast cell cycle model integrating stress, signaling, and physiology

The cell division cycle in eukaryotic cells is a series of highly coordinated molecular interactions that ensure that cell growth, duplication of genetic material, and actual cell division are precisely orchestrated to give rise to two viable progeny cells. Moreover, the cell cycle machinery is responsible for incorporating information about external cues or internal processes that the cell must keep track of to ensure a coordinated, timely progression of all related processes. This is most pronounced in multicellular organisms, but also a cardinal feature in model organisms such as baker's yeast. The complex and integrative behavior is difficult to grasp and requires mathematical modeling to fully understand the quantitative interplay of the single components within the entire system. Here, we present a self-oscillating mathematical model of the yeast cell cycle that comprises all major cyclins and their main regulators. Furthermore, it accounts for the regulation of the cell cycle machinery by a series of external stimuli such as mating pheromones and changes in osmotic pressure or nutrient quality. We demonstrate how the external perturbations modify the dynamics of cell cycle components and how the cell cycle resumes after adaptation to or relief from stress.

Mechanical limitation of bacterial motility mediated by growing cell chains

Contrasting most known bacterial motility mechanisms, a bacterial sliding motility discovered in at least two Gram-positive bacterial families does not depend on designated motors. Instead, the cells maintain end-to-end connections following cell divisions to form long chains and exploit cell growth and division to push the cells forward. To investigate the dynamics of this motility mechanism, we constructed a mechanical model that depicts the interplay of the forces acting on and between the cells comprising the chain. Due to the exponential growth of individual cells, the tips of the chains can, in principle, accelerate to speeds faster than any known single-cell motility mechanism can achieve. However, analysis of the mechanical model shows that the exponential acceleration comes at the cost of an exponential buildup in mechanical stress in the chain, making overly long chains prone to breakage. Additionally, the mechanical model reveals that the dynamics of the chain expansion hinges on a single non-dimensional parameter. Perturbation analysis of the mechanical model further predicts the critical stress leading to chain breakage and its dependence on the non-dimensional parameter. Finally, we developed a simplistic population expansion model that uses the predicted breaking behavior to estimate the physical limit of chain-mediated population expansion. Predictions from the models provide critical insights into how this motility depends on key physical properties of the cell and the substrate. Overall, our models present a generically applicable theoretical framework for cell chain-mediated bacterial sliding motility and provide guidance for future experimental studies on such motility.

Mitotic kinase oscillation governs the latching of cell cycle switches

In 1996, Kim Nasmyth¹ proposed that the eukaryotic cell cycle is an alternating sequence of transitions from G₁ to S-G₂-M and back again. These two phases correlate to high activity of cyclin-dependent kinases (CDKs) that trigger S-G₂-M events and CDK antagonists that stabilize G₁ phase. We associated these “alternative phases” with the coexistence of two stable steady states of the biochemical reactions among CDKs and their antagonists.^2,3 Transitions between these steady states (G₁-to-S and M-to-G₁) are driven by “helper” proteins. The fact that the transitions are irreversible is guaranteed by a “latching” property of the molecular switches, as we have argued in previous publications.^4,5 Here, we show that if the latch is broken, then the biochemical reactions can swing back-and-forth across the transitions; either G₁-S-G₁-S … (periodic DNA replication without mitosis or cell division) or M-(G₁)-M-(G₁) … (periodic Cdc14 release, without fully exiting mitosis). Using mathematical modeling of the molecular control circuit in budding yeast, we provide a fresh account of aberrant cell cycles in mutant strains: endoreplication in the clb1-5Δ strain⁶ and periodic release and resequestration of Cdc14 (an “exit” phosphatase) in the CLB2kdΔ strain.^7,8 In our opinion, these “endocycles” are not autonomous oscillatory modules that must be entrained by the CDK oscillator^6,7 but rather inadvertent and deleterious oscillations that are normally suppressed by the CDK latching-gate mechanism.⁸

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Mitotic kinases enforce once-per-cycle occurrence of cell cycle events

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Many cell cycle events can occur periodically in the absence of mitosis

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Are they autonomous oscillators or accidental consequences of faulty regulation?

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Regulatory mutations allow negative feedback loops to sustain oscillations

From the Belousov-Zhabotinsky reaction to biochemical clocks, traveling waves and cell cycle regulation

In the last 20 years, a growing army of systems biologists has employed quantitative experimental methods and theoretical tools of data analysis and mathematical modeling to unravel the molecular details of biological control systems with novel studies of biochemical clocks, cellular decision-making, and signaling networks in time and space. Few people know that one of the roots of this new paradigm in cell biology can be traced to a serendipitous discovery by an obscure Russian biochemist, Boris Belousov, who was studying the oxidation of citric acid. The story is told here from an historical perspective, tracing its meandering path through glycolytic oscillations, cAMP signaling, and frog egg development. The connections among these diverse themes are drawn out by simple mathematical models (nonlinear differential equations) that share common structures and properties.

Cyclin/Forkhead-mediated coordination of cyclin waves: an autonomous oscillator rationalizing the quantitative model of Cdk control for budding yeast

Networks of interacting molecules organize topology, amount, and timing of biological functions. Systems biology concepts required to pin down 'network motifs' or 'design principles' for time-dependent processes have been developed for the cell division cycle, through integration of predictive computer modeling with quantitative experimentation. A dynamic coordination of sequential waves of cyclin-dependent kinases (cyclin/Cdk) with the transcription factors network offers insights to investigate how incompatible processes are kept separate in time during the eukaryotic cell cycle. Here this coordination is discussed for the Forkhead transcription factors in light of missing gaps in the current knowledge of cell cycle control in budding yeast. An emergent design principle is proposed where cyclin waves are synchronized by a cyclin/Cdk-mediated feed-forward regulation through the Forkhead as a transcriptional timer. This design is rationalized by the bidirectional interaction between mitotic cyclins and the Forkhead transcriptional timer, resulting in an autonomous oscillator that may be instrumental for a well-timed progression throughout the cell cycle. The regulation centered around the cyclin/Cdk-Forkhead axis can be pivotal to timely coordinate cell cycle dynamics, thereby to actuate the quantitative model of Cdk control.

Two classes of functional connectivity in dynamical processes in networks

The relationship between network structure and dynamics is one of the most extensively investigated problems in the theory of complex systems of recent years. Understanding this relationship is of relevance to a range of disciplines-from neuroscience to geomorphology. A major strategy of investigating this relationship is the quantitative comparison of a representation of network architecture (structural connectivity, SC) with a (network) representation of the dynamics (functional connectivity, FC). Here, we show that one can distinguish two classes of functional connectivity-one based on simultaneous activity (co-activity) of nodes, the other based on sequential activity of nodes. We delineate these two classes in different categories of dynamical processes-excitations, regular and chaotic oscillators-and provide examples for SC/FC correlations of both classes in each of these models. We expand the theoretical view of the SC/FC relationships, with conceptual instances of the SC and the two classes of FC for various application scenarios in geomorphology, ecology, systems biology, neuroscience and socio-ecological systems. Seeing the organisation of dynamical processes in a network either as governed by co-activity or by sequential activity allows us to bring some order in the myriad of observations relating structure and function of complex networks.

Bistability in fatty-acid oxidation resulting from substrate inhibition

In this study we demonstrated through analytic considerations and numerical studies that the mitochondrial fatty-acid β-oxidation can exhibit bistable-hysteresis behavior. In an experimentally validated computational model we identified a specific region in the parameter space in which two distinct stable and one unstable steady state could be attained with different fluxes. The two stable states were referred to as low-flux (disease) and high-flux (healthy) state. By a modular kinetic approach we traced the origin and causes of the bistability back to the distributive kinetics and the conservation of CoA, in particular in the last rounds of the β-oxidation. We then extended the model to investigate various interventions that may confer health benefits by activating the pathway, including (i) activation of the last enzyme MCKAT via its endogenous regulator p46-SHC protein, (ii) addition of a thioesterase (an acyl-CoA hydrolysing enzyme) as a safety valve, and (iii) concomitant activation of a number of upstream and downstream enzymes by short-chain fatty-acids (SCFA), metabolites that are produced from nutritional fibers in the gut. A high concentration of SCFAs, thioesterase activity, and inhibition of the p46Shc protein led to a disappearance of the bistability, leaving only the high-flux state. A better understanding of the switch behavior of the mitochondrial fatty-acid oxidation process between a low- and a high-flux state may lead to dietary and pharmacological intervention in the treatment or prevention of obesity and or non-alcoholic fatty-liver disease.

Entropic analysis of bistability and the general evolution criterion

An open flow bistable Schlögl model in a well-stirred isothermal reaction volume V showing the balance of the entropy production and the exchange entropy on the non-equilibrium stationary states.

Mutual inhibition between Prkd2 and Bcl6 controls T follicular helper cell differentiation

T follicular helper cells (T_FH) participate in germinal center (GC) development and are necessary for B cell production of high-affinity, isotype-switched antibodies. In a forward genetic screen, we identified a missense mutation in Prkd2, encoding the serine/threonine kinase protein kinase D2, which caused elevated titers of immunoglobulin E (IgE) in the serum. Subsequent analysis of serum antibodies in mice with a targeted null mutation of Prkd2 demonstrated polyclonal hypergammaglobulinemia of IgE, IgG1, and IgA isotypes, which was exacerbated by the T cell-dependent humoral response to immunization. GC formation and GC B cells were increased in Prkd2^-/- spleens. These effects were the result of excessive cell-autonomous T_FH development caused by unrestricted Bcl6 nuclear translocation in Prkd2^-/- CD4⁺ T cells. Prkd2 directly binds to Bcl6, and Prkd2-dependent phosphorylation of Bcl6 is necessary to constrain Bcl6 to the cytoplasm, thereby limiting T_FH development. In response to immunization, Bcl6 repressed Prkd2 expression in CD4⁺ T cells, thereby committing them to T_FH development. Thus, Prkd2 and Bcl6 form a mutually inhibitory positive feedback loop that controls the stable transition from naïve CD4⁺ T cells to T_FH during the adaptive immune response.

Misuse of the Michaelis-Menten rate law for protein interaction networks and its remedy

For over a century, the Michaelis-Menten (MM) rate law has been used to describe the rates of enzyme-catalyzed reactions and gene expression. Despite the ubiquity of the MM rate law, it accurately captures the dynamics of underlying biochemical reactions only so long as it is applied under the right condition, namely, that the substrate is in large excess over the enzyme-substrate complex. Unfortunately, in circumstances where its validity condition is not satisfied, especially so in protein interaction networks, the MM rate law has frequently been misused. In this review, we illustrate how inappropriate use of the MM rate law distorts the dynamics of the system, provides mistaken estimates of parameter values, and makes false predictions of dynamical features such as ultrasensitivity, bistability, and oscillations. We describe how these problems can be resolved with a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA). Furthermore, we show that the tQSSA can be used for accurate stochastic simulations at a lower computational cost than using the full set of mass-action rate laws. This review describes how to use quasi-steady state approximations in the right context, to prevent drawing erroneous conclusions from in silico simulations.

A novel analysis of gene array data: yeast cell cycle

Many gene array studies of the yeast cell cycle have been performed (Cho RJ, Campbell MJ, Winzeler EA et al. A genome-wide transcriptional analysis of the mitotic cell cycle. Mol Cell 1998;2:65–73; Orlando DA, Lin CY, Bernard A et al. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 2008;453:944–7; Pramila T, Wu W, Miles S et al. The Forkhead transcription factor Hcm1 regulates chromosome segregation genes and fills the S-phase gap in the transcriptional circuitry of the cell cycle. Genes Dev 2006;20:2266–78; Spellman PT, Sherlock G, Zhang MQ et al. Comprehensive identification of cell cycle–regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. MBoC 1998;9:3273–97). Largely, these studies contain elements drawn from laboratory experiments. The present investigation determines cell division cycle (CDC) genes solely from the data (Orlando DA, Lin CY, Bernard A et al. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 2008;453:944–7). It is shown by simple reasoning that the dynamics of the approximately 6000 yeast genes are described by an approximately six-dimensional space. This leads a precisely determined cell-cycle period, along with the quality and timing of the identified CDC genes. Convincing evidence for the role of the identified genes is obtained. While these show good agreement with standard CDC gene representatives (Orlando DA, Lin CY, Bernard A et al. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 2008;453:944–7; Spellman PT, Sherlock G, Zhang MQ et al. Comprehensive identification of cell cycle–regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. MBoC 1998;9:3273–97; de Lichtenberg U, Jensen LJ, Fausbøll A et al. Comparison of computational methods for the identification of cell cycle-regulated genes. Bioinformatics 2005;21:1164–71) several hundred newly revealed CDC genes appear, which merit attention. The present approach employs an adaptation of a method introduced to study turbulent flows (Schmid PJ. Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 2010;656:5–28), “dynamic mode decomposition” (DMD). From this, one can infer that singular value decomposition, analysis of the data entangles the underlying (gene) dynamics implicit in the data; and that DMD produces the disentangling transformation. It is the assertion of this study that a new tool now exists for the analysis of the gene array signals, and in particular for investigating the yeast cell cycle.

A systems biology approach to discovering pathway signaling dysregulation in metastasis

Total metastatic burden is the primary cause of death for many cancer patients. While the process of metastasis has been studied widely, much remains to be understood. Moreover, few agents have been developed that specifically target the major steps of the metastatic cascade. Many individual genes and pathways have been implicated in metastasis but a holistic view of how these interact and cooperate to regulate and execute the process remains somewhat rudimentary. It is unclear whether all of the signaling features that regulate and execute metastasis are yet fully understood. Novel features of a complex system such as metastasis can often be discovered by taking a systems-based approach. We introduce the concepts of systems modeling and define some of the central challenges facing the application of a multidisciplinary systems-based approach to understanding metastasis and finding actionable targets therein. These challenges include appreciating the unique properties of the high-dimensional omics data often used for modeling, limitations in knowledge of the system (metastasis), tumor heterogeneity and sampling bias, and some of the issues key to understanding critical features of molecular signaling in the context of metastasis. We also provide a brief introduction to integrative modeling that focuses on both the nodes and edges of molecular signaling networks. Finally, we offer some observations on future directions as they relate to developing a systems-based model of the metastatic cascade.

Extended Robust Boolean Network of Budding Yeast Cell Cycle

Background:

How to explore the dynamics of transition probabilities between phases of budding yeast cell cycle (BYCC) network based on the dynamics of protein activities that control this network? How to identify the robust structure of protein interactions of BYCC Boolean network (BN)? Budding yeast allows scientists to put experiments into effect in order to discover the intracellular cell cycle regulating structures which are well simulated by mathematical modeling.

Methods:

We extended an available deterministic BN of proteins responsible for the cell cycle to a Markov chain model containing apoptosis besides G1, S, G2, M, and stationary G1. Using genetic algorithm (GA), we estimated the kinetic parameters of the extended BN model so that the subsequent transition probabilities derived using Markov chain model of cell states as normal cell cycle becomes the maximum while the structure of chemical interactions of extended BN of cell cycle becomes more stable.

Results:

Using kinetic parameters optimized by GA, the probability of the subsequent transitions between cell cycle phases is maximized. The relative basin size of stationary G1 increased from 86% to 96.48% while the number of attractors decreased from 7 in the original model to 5 in the extended one. Hence, an increase in the robustness of the system has been achieved.

Conclusion:

The structure of interacting proteins in cell cycle network affects its robustness and probabilities of transitions between different cell cycle phases. Markov chain and BN are good approaches to study the stability and dynamics of the cell cycle network.

Random Parametric Perturbations of Gene Regulatory Circuit Uncover State Transitions in Cell Cycle

Many biological processes involve precise cellular state transitions controlled by complex gene regulation. Here, we use budding yeast cell cycle as a model system and explore how a gene regulatory circuit encodes essential information of state transitions. We present a generalized random circuit perturbation method for circuits containing heterogeneous regulation types and its usage to analyze both steady and oscillatory states from an ensemble of circuit models with random kinetic parameters. The stable steady states form robust clusters with a circular structure that are associated with cell cycle phases. This circular structure in the clusters is consistent with single-cell RNA sequencing data. The oscillatory states specify the irreversible state transitions along cell cycle progression. Furthermore, we identify possible mechanisms to understand the irreversible state transitions from the steady states. We expect this approach to be robust and generally applicable to unbiasedly predict dynamical transitions of a gene regulatory circuit.

Critical slowing down and attractive manifold: A mechanism for dynamic robustness in the yeast cell-cycle process

Biological processes that execute complex multiple functions, such as the cell cycle, must ensure the order of sequential events and maintain dynamic robustness against various fluctuations. Here, we examine the mechanisms and fundamental structure that achieve these properties in the cell cycle of the budding yeast Saccharomyces cerevisiae. We show that this process behaves like an excitable system containing three well-decoupled saddle-node bifurcations to execute DNA replication and mitosis events. The yeast cell-cycle regulatory network can be divided into three modules-the G1/S phase, early M phase, and late M phase-wherein both positive feedback loops in each module and interactions among modules play important roles. Specifically, when the cell-cycle process operates near the critical points of the saddle-node bifurcations, a critical slowing down effect takes place. Such interregnum then allows for an attractive manifold and sufficient duration for cell-cycle events, within which to assess the completion of DNA replication and mitosis, e.g., spindle assembly. Moreover, such arrangement ensures that any fluctuation in an early module or event will not transmit to a later module or event. Thus, our results suggest a possible dynamical mechanism of the cell-cycle process to ensure event order and dynamic robustness and give insight into the evolution of eukaryotic cell-cycle processes.

Nonequilibrium Thermodynamics in Cell Biology: Extending Equilibrium Formalism to Cover Living Systems

We discuss new developments in the nonequilibrium dynamics and thermodynamics of living systems, giving a few examples to demonstrate the importance of nonequilibrium thermodynamics for understanding biological dynamics and functions. We study single-molecule enzyme dynamics, in which the nonequilibrium thermodynamic and dynamic driving forces of chemical potential and flux are crucial for the emergence of non-Michaelis-Menten kinetics. We explore single-gene expression dynamics, in which nonequilibrium dissipation can suppress fluctuations. We investigate the cell cycle and identify the nutrition supply as the energy input that sustains the stability, speed, and coherence of cell cycle oscillation, from which the different vital phases of the cell cycle emerge. We examine neural decision-making processes and find the trade-offs among speed, accuracy, and thermodynamic costs that are important for neural function. Lastly, we consider the thermodynamic cost for specificity in cellular signaling and adaptation.

Bayesian inference using qualitative observations of underlying continuous variables

MOTIVATION

Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of a lack of a statistical interpretation of the objective functions used in optimization.

RESULTS

We formulated likelihood functions suitable for performing Bayesian UQ using qualitative observations of underlying continuous variables or a combination of qualitative and quantitative data. To demonstrate the resulting UQ capabilities, we analyzed a published model for immunoglobulin E (IgE) receptor signaling using synthetic qualitative and quantitative datasets. Remarkably, estimates of parameter values derived from the qualitative data were nearly as consistent with the assumed ground-truth parameter values as estimates derived from the lower throughput quantitative data. These results provide further motivation for leveraging qualitative data in biological modeling.

AVAILABILITY AND IMPLEMENTATION

The likelihood functions presented here are implemented in a new release of PyBioNetFit, an open-source application for analyzing Systems Biology Markup Language- and BioNetGen Language-formatted models, available online at www.github.com/lanl/PyBNF.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Clb3-centered regulations are recurrent across distinct parameter regions in minimal autonomous cell cycle oscillator designs

Some biological networks exhibit oscillations in their components to convert stimuli to time-dependent responses. The eukaryotic cell cycle is such a case, being governed by waves of cyclin-dependent kinase (cyclin/Cdk) activities that rise and fall with specific timing and guarantee its timely occurrence. Disruption of cyclin/Cdk oscillations could result in dysfunction through reduced cell division. Therefore, it is of interest to capture properties of network designs that exhibit robust oscillations. Here we show that a minimal yeast cell cycle network is able to oscillate autonomously, and that cyclin/Cdk-mediated positive feedback loops (PFLs) and Clb3-centered regulations sustain cyclin/Cdk oscillations, in known and hypothetical network designs. We propose that Clb3-mediated coordination of cyclin/Cdk waves reconciles checkpoint and oscillatory cell cycle models. Considering the evolutionary conservation of the cyclin/Cdk network across eukaryotes, we hypothesize that functional ("healthy") phenotypes require the capacity to oscillate autonomously whereas dysfunctional (potentially "diseased") phenotypes may lack this capacity.

A hybrid stochastic model of the budding yeast cell cycle

The growth and division of eukaryotic cells are regulated by complex, multi-scale networks. In this process, the mechanism of controlling cell-cycle progression has to be robust against inherent noise in the system. In this paper, a hybrid stochastic model is developed to study the effects of noise on the control mechanism of the budding yeast cell cycle. The modeling approach leverages, in a single multi-scale model, the advantages of two regimes: (1) the computational efficiency of a deterministic approach, and (2) the accuracy of stochastic simulations. Our results show that this hybrid stochastic model achieves high computational efficiency while generating simulation results that match very well with published experimental measurements.

Complex Stability and an Irrevertible Transition Reverted by Peptide and Fibroblasts in a Dynamic Model of Innate Immunity

We here apply a control analysis and various types of stability analysis to an in silico model of innate immunity that addresses the management of inflammation by a therapeutic peptide. Motivation is the observation, both in silico and in experiments, that this therapy is not robust. Our modeling results demonstrate how (1) the biological phenomena of acute and chronic modes of inflammation may reflect an inherently complex bistability with an irrevertible flip between the two modes, (2) the chronic mode of the model has stable, sometimes unique, steady states, while its acute-mode steady states are stable but not unique, (3) as witnessed by TNF levels, acute inflammation is controlled by multiple processes, whereas its chronic-mode inflammation is only controlled by TNF synthesis and washout, (4) only when the antigen load is close to the acute mode's flipping point, many processes impact very strongly on cells and cytokines, (5) there is no antigen exposure level below which reduction of the antigen load alone initiates a flip back to the acute mode, and (6) adding healthy fibroblasts makes the transition from acute to chronic inflammation revertible, although (7) there is a window of antigen load where such a therapy cannot be effective. This suggests that triple therapies may be essential to overcome chronic inflammation. These may comprise (1) anti-immunoglobulin light chain peptides, (2) a temporarily reduced antigen load, and (3a) fibroblast repopulation or (3b) stem cell strategies.

Parameter Estimation and Uncertainty Quantification for Systems Biology Models

Mathematical models can provide quantitative insights into immunoreceptor signaling, and other biological processes, but require parameterization and uncertainty quantification before reliable predictions become possible. We review currently available methods and software tools to address these problems. We consider gradient-based and gradient-free methods for point estimation of parameter values, and methods of profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification. We consider recent and potential future applications of these methods to systems-level modeling of immune-related phenomena.

Advanced Modeling of Cellular Proliferation: Toward a Multi-scale Framework Coupling Cell Cycle to Metabolism by Integrating Logical and Constraint-Based Models

Biological functions require a coherent cross talk among multiple layers of regulation within the cell. Computational efforts that aim to understand how these layers are integrated across spatial, temporal, and functional scales represent a challenge in Systems Biology. We have developed a computational, multi-scale framework that couples cell cycle and metabolism networks in the budding yeast cell. Here we describe the methodology at the basis of this framework, which integrates on off-the-shelf logical (Boolean) models of a minimal yeast cell cycle with a constraint-based model of metabolism (i.e., the Yeast 7 metabolic network reconstruction). Models are implemented in Python code using the BooleanNet and COBRApy packages, respectively, and are connected through the Boolean logic. The methodology allows for incorporation of interaction data, and validation through -omics data. Furthermore, evolutionary strategies may be incorporated to explore regulatory structures underlying coherent cross talks among regulatory layers.

PyBioNetFit and the Biological Property Specification Language

In systems biology modeling, important steps include model parameterization, uncertainty quantification, and evaluation of agreement with experimental observations. To help modelers perform these steps, we developed the software PyBioNetFit, which in addition supports checking models against known system properties and solving design problems. PyBioNetFit introduces Biological Property Specification Language (BPSL) for the formal declaration of system properties. BPSL allows qualitative data to be used alone or in combination with quantitative data. PyBioNetFit performs parameterization with parallelized metaheuristic optimization algorithms that work directly with existing model definition standards: BioNetGen Language (BNGL) and Systems Biology Markup Language (SBML). We demonstrate PyBioNetFit's capabilities by solving various example problems, including the challenging problem of parameterizing a 153-parameter model of cell cycle control in yeast based on both quantitative and qualitative data. We demonstrate the model checking and design applications of PyBioNetFit and BPSL by analyzing a model of targeted drug interventions in autophagy signaling.

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 model for positive feedback control of the transformation of fibroblasts to myofibroblasts

The phenotypic conversion of normal fibroblasts to myofibroblasts is central to normal wound healing and to pathological fibrosis that can occur in the heart and many other tissues. The transformation occurs in two stages. The first stage is driven mainly by mechanical changes such as increased stiffness of the heart due to hypertension and cellular contractility. The second stage requires both increasing stiffness and biochemical factors such as the growth factor, TGFβ. As more and more cells convert from weakly contractile fibroblasts to strongly contractile myofibroblasts, the stiffness of the ventricular muscle increases. We propose a simple model for the establishment of non-equilibrium steady states with different compositions of fibroblasts and myofibroblasts. Under some conditions a positive feedback loop resulting from the increasing stiffness caused by increasing numbers of myofibroblasts can produce a bifurcation between steady states with low and high myofibroblast content. We illustrate the large mechanical differences between normal fibroblasts and myofibroblasts with measurements in engineered tissue constructs.

A stochastic model of size control in the budding yeast cell cycle

BACKGROUND

Cell size is a key characteristic that significantly affects many aspects of cellular physiology. There are specific control mechanisms during cell cycle that maintain the cell size within a range from generation to generation. Such control mechanisms introduce substantial variabilities to important properties of the cell cycle such as growth and division. To quantitatively study the effect of such variability in progression through cell cycle, detailed stochastic models are required.

RESULTS

In this paper, a new hybrid stochastic model is proposed to study the effect of molecular noise and size control mechanism on the variabilities in cell cycle of the budding yeast Saccharomyces cerevisiae. The proposed model provides an accurate, yet computationally efficient approach for simulation of an intricate system by integrating the deterministic and stochastic simulation schemes. The developed hybrid stochastic model can successfully capture several key features of the cell cycle observed in experimental data. In particular, the proposed model: 1) confirms that the majority of noise in size control stems from low copy numbers of transcripts in the G1 phase, 2) identifies the size and time regulation modules in the size control mechanism, and 3) conforms with phenotypes of early G1 mutants in exquisite detail.

CONCLUSIONS

Hybrid stochastic modeling approach can be used to provide quantitative descriptions for stochastic properties of the cell cycle within a computationally efficient framework.

Exploring the underlying mechanisms of the coupling between cell differentiation and cell cycle

Differentiation and replication are the two major fates of the cells. They are the fundamental processes for completing the cellular functions. Although the underlying biological processes have been considerably explored for each of these processes and significant progresses have been made, global quantification and physical understanding are still challenging, especially for the relationship among them. In this study, we developed a theoretical framework for both the cell cycle and cell differentiation by exploring the associated global dynamics and their underlying relationship. We found that the dynamics of the cell cycle and cell differentiation is governed by both the landscape gradient and rotational curl flux. While landscape attracts the system down to the stable state basins, the curl flux drives the stable oscillation flow. We uncovered the irregular sombrero-shaped landscapes of the cell cycle at different developmental stages. We studied how the cells develop from undifferentiated cells to differentiated cells and how the cell cycle proceeds at different developmental stages. We investigated how the cell differentiation can influence the cell cycle where more progressive differentiation can lead to the changes of the cell cycle oscillations. In contrast, we can also quantitatively illustrate how the cell cycle can influence the cell differentiation where cell cycle regulation can lead to the changes of the differentiation processes. Through the landscape and flux analysis, we uncovered the key regulatory elements controlling the progression of the cell differentiation and cell cycle. This can help to design an effective strategy for drug discovery against associated diseases.

A comprehensive, mechanistically detailed, and executable model of the cell division cycle in Saccharomyces cerevisiae

Understanding how cellular functions emerge from the underlying molecular mechanisms is a key challenge in biology. This will require computational models, whose predictive power is expected to increase with coverage and precision of formulation. Genome-scale models revolutionised the metabolic field and made the first whole-cell model possible. However, the lack of genome-scale models of signalling networks blocks the development of eukaryotic whole-cell models. Here, we present a comprehensive mechanistic model of the molecular network that controls the cell division cycle in Saccharomyces cerevisiae. We use rxncon, the reaction-contingency language, to neutralise the scalability issues preventing formulation, visualisation and simulation of signalling networks at the genome-scale. We use parameter-free modelling to validate the network and to predict genotype-to-phenotype relationships down to residue resolution. This mechanistic genome-scale model offers a new perspective on eukaryotic cell cycle control, and opens up for similar models-and eventually whole-cell models-of human cells.

Modeling cell population dynamics

 Quantitative modeling is quickly becoming an integral part of biology, due to the ability of mathematical models and computer simulations to generate insights and predict the behavior of living systems. Single-cell models can be incapable or misleading for inferring population dynamics, as they do not consider the interactions between cells via metabolites or physical contact, nor do they consider competition for limited resources such as nutrients or space. Here we examine methods that are commonly used to model and simulate cell populations. First, we cover simple models where analytic solutions are available, and then move on to more complex scenarios where computational methods are required. Overall, we present a summary of mathematical models used to describe cell population dynamics, which may aid future model development and highlights the importance of population modeling in biology.

Modeling cell population dynamics

 Quantitative modeling is quickly becoming an integral part of biology, due to the ability of mathematical models and computer simulations to generate insights and predict the behavior of living systems. Single-cell models can be incapable or misleading for inferring population dynamics, as they do not consider the interactions between cells via metabolites or physical contact, nor do they consider competition for limited resources such as nutrients or space. Here we examine methods that are commonly used to model and simulate cell populations. First, we cover simple models where analytic solutions are available, and then move on to more complex scenarios where computational methods are required. Overall, we present a summary of mathematical models used to describe cell population dynamics, which may aid future model development and highlights the importance of population modeling in biology.

Using both qualitative and quantitative data in parameter identification for systems biology models

In systems biology, qualitative data are often generated, but rarely used to parameterize models. We demonstrate an approach in which qualitative and quantitative data can be combined for parameter identification. In this approach, qualitative data are converted into inequality constraints imposed on the outputs of the model. These inequalities are used along with quantitative data points to construct a single scalar objective function that accounts for both datasets. To illustrate the approach, we estimate parameters for a simple model describing Raf activation. We then apply the technique to a more elaborate model characterizing cell cycle regulation in yeast. We incorporate both quantitative time courses (561 data points) and qualitative phenotypes of 119 mutant yeast strains (1647 inequalities) to perform automated identification of 153 model parameters. We quantify parameter uncertainty using a profile likelihood approach. Our results indicate the value of combining qualitative and quantitative data to parameterize systems biology models.

Much of the data generated in biology is qualitative, but exploiting such data to inform models of biological systems remains a challenge. Here, the authors demonstrate an approach that allows use of both quantitative and qualitative data for parameterising dynamical models.

Computing with biological switches and clocks

The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch-like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing.

Kinetic models of hematopoietic differentiation

As cell and molecular biology is becoming increasingly quantitative, there is an upsurge of interest in mechanistic modeling at different levels of resolution. Such models mostly concern kinetics and include gene and protein interactions as well as cell population dynamics. The final goal of these models is to provide experimental predictions, which is now taking on. However, even without matured predictions, kinetic models serve the purpose of compressing a plurality of experimental results into something that can empower the data interpretation, and importantly, suggesting new experiments by turning "knobs" in silico. Once formulated, kinetic models can be executed in terms of molecular rate equations for concentrations or by stochastic simulations when only a limited number of copies are involved. Developmental processes, in particular those of stem and progenitor cell commitments, are not only topical but also particularly suitable for kinetic modeling due to the finite number of key genes involved in cellular decisions. Stem and progenitor cell commitment processes have been subject to intense experimental studies over the last decade with some emphasis on embryonic and hematopoietic stem cells. Gene and protein interactions governing these processes can be modeled by binary Boolean rules or by continuous-valued models with interactions set by binding strengths. Conceptual insights along with tested predictions have emerged from such kinetic models. Here we review kinetic modeling efforts applied to stem cell developmental systems with focus on hematopoiesis. We highlight the future challenges including multi-scale models integrating cell dynamical and transcriptional models. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Developmental Biology > Stem Cell Biology and Regeneration.

Exploring the Underlying Mechanisms of the Xenopus laevis Embryonic Cell Cycle

The cell cycle is an indispensable process in proliferation and development. Despite significant efforts, global quantification and physical understanding are still challenging. In this study, we explored the mechanisms of the Xenopus laevis embryonic cell cycle by quantifying the underlying landscape and flux. We uncovered the Mexican hat landscape of the Xenopus laevis embryonic cell cycle with several local basins and barriers on the oscillation path. The local basins characterize the different phases of the Xenopus laevis embryonic cell cycle, and the local barriers represent the checkpoints. The checkpoint mechanism of the cell cycle is revealed by the landscape basins and barriers. While landscape shape determines the stabilities of the states on the oscillation path, the curl flux force determines the stability of the cell cycle flow. Replication is fundamental for biology of living cells. We quantify the input energy (through the entropy production) as the thermodynamic requirement for initiation and sustainability of single cell life (cell cycle). Furthermore, we also quantify curl flux originated from the input energy as the dynamical requirement for the emergence of a new stable phase (cell cycle). This can provide a new quantitative insight for the origin of single cell life. In fact, the curl flux originated from the energy input or nutrition supply determines the speed and guarantees the progression of the cell cycle. The speed of the cell cycle is a hallmark of cancer. We characterized the quality of the cell cycle by the coherence time and found it is supported by the flux and energy cost. We are also able to quantify the degree of time irreversibility by the cross correlation function forward and backward in time from the stochastic traces in the simulation or experiments, providing a way for the quantification of the time irreversibility and the flux. Through global sensitivity analysis upon landscape and flux, we can identify the key elements for controlling the cell cycle speed. This can help to design an effective strategy for drug discovery against cancer.

Secondary Metabolites Produced during the Germination of Streptomyces coelicolor

Spore awakening is a series of actions that starts with purely physical processes and continues via the launching of gene expression and metabolic activities, eventually achieving a vegetative phase of growth. In spore-forming microorganisms, the germination process is controlled by intra- and inter-species communication. However, in the Streptomyces clade, which is capable of developing a plethora of valuable compounds, the chemical signals produced during germination have not been systematically studied before. Our previously published data revealed that several secondary metabolite biosynthetic genes are expressed during germination. Therefore, we focus here on the secondary metabolite production during this developmental stage. Using high-performance liquid chromatography-mass spectrometry, we found that the sesquiterpenoid antibiotic albaflavenone, the polyketide germicidin A, and chalcone are produced during germination of the model streptomycete, S. coelicolor. Interestingly, the last two compounds revealed an inhibitory effect on the germination process. The secondary metabolites originating from the early stage of microbial growth may coordinate the development of the producer (quorum sensing) and/or play a role in competitive microflora repression (quorum quenching) in their nature environments.

Identifying Noise Sources governing cell-to-cell variability

Phenotypic differences often occur even in clonal cell populations. Many potential sources of such variation have been identified, from biophysical rate variance intrinsic to all chemical processes to asymmetric division of molecular components extrinsic to any particular signaling pathway. Identifying the sources of phenotypic variation and quantifying their contributions to cell fate variation is not possible without accurate single cell data. By combining such data with mathematical models of potential noise sources it is possible to characterize the impact of varying levels of each noise source and identify which sources of variation best explain the experimental observations. The mathematical framework of information theory provides metrics of the impact of noise on the reliability of a cell to sense its environment. While the presence of noise in a single cellular system reduces the reliability of signal transduction its impact on a population of varied single cells remains unclear.

A Waking Review: Old and Novel Insights into the Spore Germination in Streptomyces

The complex development undergone by Streptomyces encompasses transitions from vegetative mycelial forms to reproductive aerial hyphae that differentiate into chains of single-celled spores. Whereas their mycelial life – connected with spore formation and antibiotic production – is deeply investigated, spore germination as the counterpoint in their life cycle has received much less attention. Still, germination represents a system of transformation from metabolic zero point to a new living lap. There are several aspects of germination that may attract our attention: (1) Dormant spores are strikingly well-prepared for the future metabolic restart; they possess stable transcriptome, hydrolytic enzymes, chaperones, and other required macromolecules stabilized in a trehalose milieu; (2) Germination itself is a specific sequence of events leading to a complete morphological remodeling that include spore swelling, cell wall reconstruction, and eventually germ tube emergences; (3) Still not fully unveiled are the strategies that enable the process, including a single cell’s signal transduction and gene expression control, as well as intercellular communication and the probability of germination across the whole population. This review summarizes our current knowledge about the germination process in Streptomyces, while focusing on the aforementioned points.

Systems Level Modeling of the Cell Cycle Using Budding Yeast

Proteins involved in the regulation of the cell cycle are highly conserved across all eukaryotes, and so a relatively simple eukaryote such as yeast can provide insight into a variety of cell cycle perturbations including those that occur in human cancer. To date, the budding yeast Saccharomyces cerevisiae has provided the largest amount of experimental and modeling data on the progression of the cell cycle, making it a logical choice for in-depth studies of this process. Moreover, the advent of methods for collection of high-throughput genome, transcriptome, and proteome data has provided a means to collect and precisely quantify simultaneous cell cycle gene transcript and protein levels, permitting modeling of the cell cycle on the systems level. With the appropriate mathematical framework and sufficient and accurate data on cell cycle components, it should be possible to create a model of the cell cycle that not only effectively describes its operation, but can also predict responses to perturbations such as variation in protein levels and responses to external stimuli including targeted inhibition by drugs. In this review, we summarize existing data on the yeast cell cycle, proteomics technologies for quantifying cell cycle proteins, and the mathematical frameworks that can integrate this data into representative and effective models. Systems level modeling of the cell cycle will require the integration of high-quality data with the appropriate mathematical framework, which can currently be attained through the combination of dynamic modeling based on proteomics data and using yeast as a model organism.

A simple molecular mechanism explains multiple patterns of cell-size regulation

Increasingly accurate and massive data have recently shed light on the fundamental question of how cells maintain a stable size trajectory as they progress through the cell cycle. Microbes seem to use strategies ranging from a pure sizer, where the end of a given phase is triggered when the cell reaches a critical size, to pure adder, where the cell adds a constant size during a phase. Yet the biological origins of the observed spectrum of behavior remain elusive. We analyze a molecular size-control mechanism, based on experimental data from the yeast S. cerevisiae, that gives rise to behaviors smoothly interpolating between adder and sizer. The size-control is obtained from the accumulation of an activator protein that titrates an inhibitor protein. Strikingly, the size-control is composed of two different regimes: for small initial cell size, the size-control is a sizer, whereas for larger initial cell size, it is an imperfect adder, in agreement with recent experiments. Our model thus indicates that the adder and critical size behaviors may just be different dynamical regimes of a single simple biophysical mechanism.

Decoding early myelopoiesis from dynamics of core endogenous network

A decade ago mainstream molecular biologists regarded it impossible or biologically ill-motivated to understand the dynamics of complex biological phenomena, such as cancer genesis and progression, from a network perspective. Indeed, there are numerical difficulties even for those who were determined to explore along this direction. Undeterred, seven years ago a group of Chinese scientists started a program aiming to obtain quantitative connections between tumors and network dynamics. Many interesting results have been obtained. In this paper we wish to test such idea from a different angle: the connection between a normal biological process and the network dynamics. We have taken early myelopoiesis as our biological model. A standard roadmap for the cell-fate diversification during hematopoiesis has already been well established experimentally, yet little was known for its underpinning dynamical mechanisms. Compounding this difficulty there were additional experimental challenges, such as the seemingly conflicting hematopoietic roadmaps and the cell-fate inter-conversion events. With early myeloid cell-fate determination in mind, we constructed a core molecular endogenous network from well-documented gene regulation and signal transduction knowledge. Turning the network into a set of dynamical equations, we found computationally several structurally robust states. Those states nicely correspond to known cell phenotypes. We also found the states connecting those stable states. They reveal the developmental routes-how one stable state would most likely turn into another stable state. Such interconnected network among stable states enabled a natural organization of cell-fates into a multi-stable state landscape. Accordingly, both the myeloid cell phenotypes and the standard roadmap were explained mechanistically in a straightforward manner. Furthermore, recent challenging observations were also explained naturally. Moreover, the landscape visually enables a prediction of a pool of additional cell states and developmental routes, including the non-sequential and cross-branch transitions, which are testable by future experiments. In summary, the endogenous network dynamics provide an integrated quantitative framework to understand the heterogeneity and lineage commitment in myeloid progenitors.