Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle

A perturbation approach for refining Boolean models of cell cycle regulation

Considerable effort is required to build mathematical models of large protein regulatory networks. Utilizing computational algorithms that guide model development can significantly streamline the process and enhance the reliability of the resulting models. In this article, we present a perturbation approach for developing data-centric Boolean models of cell cycle regulation. To evaluate networks, we assign a score based on their steady states and the dynamical trajectories corresponding to the initial conditions. Then, perturbation analysis is used to find new networks with lower scores, in which dynamical trajectories traverse through the correct cell cycle path with high frequency. We apply this method to refine Boolean models of cell cycle regulation in budding yeast and mammalian cells.

Mechanistic modeling of cell viability assays with in silico lineage tracing

Data from cell viability assays, which measure cumulative division and death events in a population and reflect substantial cellular heterogeneity, are widely available. However, interpreting such data with mechanistic computational models is hindered because direct model/data comparison is often muddled. We developed an algorithm that tracks simulated division and death events in mechanistically detailed single-cell lineages to enable such a model/data comparison and suggest causes of cell-cell drug response variability. Using our previously developed model of mammalian single-cell proliferation and death signaling, we simulated drug dose response experiments for four targeted anti-cancer drugs (alpelisib, neratinib, trametinib and palbociclib) and compared them to experimental data. Simulations are consistent with data for strong growth inhibition by trametinib (MEK inhibitor) and overall lack of efficacy for alpelisib (PI-3K inhibitor), but are inconsistent with data for palbociclib (CDK4/6 inhibitor) and neratinib (EGFR inhibitor). Model/data inconsistencies suggest (i) the importance of CDK4/6 for driving the cell cycle may be overestimated, and (ii) that the cellular balance between basal (tonic) and ligand-induced signaling is a critical determinant of receptor inhibitor response. Simulations show subpopulations of rapidly and slowly dividing cells in both control and drug-treated conditions. Variations in mother cells prior to drug treatment all impinging on ERK pathway activity are associated with the rapidly dividing phenotype and trametinib resistance. This work lays a foundation for the application of mechanistic modeling to large-scale cell viability assay datasets and better understanding determinants of cellular heterogeneity in drug response.

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Transient Zn2+ deficiency induces replication stress and compromises daughter cell proliferation

Cells must replicate their genome quickly and accurately, and they require metabolites and cofactors to do so. Ionic zinc (Zn2+) is an essential micronutrient that is required for hundreds of cellular processes, including DNA synthesis and adequate proliferation. Deficiency in this micronutrient impairs DNA synthesis and inhibits proliferation, but the mechanism is unknown. Using fluorescent reporters to track single cells via long-term live-cell imaging, we find that Zn2+ is required at the G1/S transition and during S phase for timely completion of S phase. A short pulse of Zn2+ deficiency impairs DNA synthesis and increases markers of replication stress. These markers of replication stress are reversed upon resupply of Zn2+. Finally, we find that if Zn2+ is chelated during the mother cell's S phase, daughter cells enter a transient quiescent state, maintained by sustained expression of p21, which disappears upon reentry into the cell cycle. In summary, short pulses of mild Zn2+ deficiency in S phase specifically induce replication stress, which causes downstream proliferation impairments in daughter cells.

Regulation of myogenic cell proliferation and differentiation during mammalian skeletal myogenesis

Mammalian skeletal myogenesis is a complex process that allows precise control of myogenic cells' proliferation, differentiation, and fusion to form multinucleated, contractile, and functional muscle fibers. Typically, myogenic progenitors continue growth and division until acquiring a differentiated state, which then permanently leaves the cell cycle and enters terminal differentiation. These processes have been intensively studied using the skeletal muscle developing models in vitro and in vivo, uncovering a complex cellular intrinsic network during mammalian skeletal myogenesis containing transcription factors, translation factors, extracellular matrix, metabolites, and mechano-sensors. Examining the events and how they are knitted together will better understand skeletal myogenesis's molecular basis. This review describes various regulatory mechanisms and recent advances in myogenic cell proliferation and differentiation during mammalian skeletal myogenesis. We focus on significant cell cycle regulators, myogenic factors, and chromatin regulators impacting the coordination of the cell proliferation versus differentiation decision, which will better clarify the complex signaling underlying skeletal myogenesis.

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.

Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach

Quantitative understanding of cellular processes, such as cell cycle and differentiation, is impeded by various forms of complexity ranging from myriad molecular players and their multilevel regulatory interactions, cellular evolution with multiple intermediate stages, lack of elucidation of cause-effect relationships among the many system players, and the computational complexity associated with the profusion of variables and parameters. In this paper, we present a modeling framework based on the cybernetic concept that biological regulation is inspired by objectives embedding rational strategies for dimension reduction, process stage specification through the system dynamics, and innovative causal association of regulatory events with the ability to predict the evolution of the dynamical system. The elementary step of the modeling strategy involves stage-specific objective functions that are computationally determined from experiments, augmented with dynamical network computations involving endpoint objective functions, mutual information, change-point detection, and maximal clique centrality. We demonstrate the power of the method through application to the mammalian cell cycle, which involves thousands of biomolecules engaged in signaling, transcription, and regulation. Starting with a fine-grained transcriptional description obtained from RNA sequencing measurements, we develop an initial model, which is then dynamically modeled using the cybernetic-inspired method, based on the strategies described above. The cybernetic-inspired method is able to distill the most significant interactions from a multitude of possibilities. In addition to capturing the complexity of regulatory processes in a mechanistically causal and stage-specific manner, we identify the functional network modules, including novel cell cycle stages. Our model is able to predict future cell cycles consistent with experimental measurements. We posit that this innovative framework has the promise to extend to the dynamics of other biological processes, with a potential to provide novel mechanistic insights.

Transient Zn2+ deficiency induces replication stress and compromises daughter cell proliferation

Cells must replicate their genome quickly and accurately, and they require metabolites and cofactors to do so. Ionic zinc (Zn2+) is an essential micronutrient that is required for hundreds of cellular processes, including DNA synthesis and adequate proliferation. Deficiency in this micronutrient impairs DNA synthesis and inhibits proliferation, but the mechanism is unknown. Using fluorescent reporters to track single cells via long-term live-cell imaging, we find that Zn2+ is required at the G1/S transition and during S-phase for timely completion of S-phase. A short pulse of Zn2+ deficiency impairs DNA synthesis and increases markers of replication stress. These markers of replication stress are reversed upon resupply of Zn2+. Finally, we find that if Zn2+ is removed during the mother cell's S-phase, daughter cells enter a transient quiescent state, maintained by sustained expression of p21, which disappears upon reentry into the cell cycle. In summary, short pulses of mild Zn2+ deficiency in S-phase specifically induce replication stress, which causes downstream proliferation impairments in daughter cells.

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.

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.

An improved approach for calculating energy landscape of gene networks from moment equations

The energy landscape theory has widely been applied to study the stochastic dynamics of biological systems. Different methods have been developed to quantify the energy landscape for gene networks, e.g., using Gaussian approximation (GA) approach to calculate the landscape by solving the diffusion equation approximately from the first two moments. However, how high-order moments influence the landscape construction remains to be elucidated. Also, multistability exists extensively in biological networks. So, how to quantify the landscape for a multistable dynamical system accurately, is a paramount problem. In this work, we prove that the weighted summation from GA (WSGA), provides an effective way to calculate the landscape for multistable systems and limit cycle systems. Meanwhile, we proposed an extended Gaussian approximation (EGA) approach by considering the effects of the third moments, which provides a more accurate way to obtain probability distribution and corresponding landscape. By applying our generalized EGA approach to two specific biological systems: multistable genetic circuit and synthetic oscillatory network, we compared EGA with WSGA by calculating the KL divergence of the probability distribution between these two approaches and simulations, which demonstrated that the EGA provides a more accurate approach to calculate the energy landscape.

NetAct: a computational platform to construct core transcription factor regulatory networks using gene activity

A major question in systems biology is how to identify the core gene regulatory circuit that governs the decision-making of a biological process. Here, we develop a computational platform, named NetAct, for constructing core transcription factor regulatory networks using both transcriptomics data and literature-based transcription factor-target databases. NetAct robustly infers regulators' activity using target expression, constructs networks based on transcriptional activity, and integrates mathematical modeling for validation. Our in silico benchmark test shows that NetAct outperforms existing algorithms in inferring transcriptional activity and gene networks. We illustrate the application of NetAct to model networks driving TGF-β-induced epithelial-mesenchymal transition and macrophage polarization.

Transcriptional Fluctuations Govern the Serum-Dependent Cell Cycle Duration Heterogeneities in Mammalian Cells

Mammalian cells exhibit a high degree of intercellular variability in cell cycle period and phase durations. However, the factors orchestrating the cell cycle duration heterogeneities remain unclear. Herein, by combining cell cycle network-based mathematical models with live single-cell imaging studies under varied serum conditions, we demonstrate that fluctuating transcription rates of cell cycle regulatory genes across cell lineages and during cell cycle progression in mammalian cells majorly govern the robust correlation patterns of cell cycle period and phase durations among sister, cousin, and mother-daughter lineage pairs. However, for the overall cellular population, alteration in the serum level modulates the fluctuation and correlation patterns of cell cycle period and phase durations in a correlated manner. These heterogeneities at the population level can be fine-tuned under limited serum conditions by perturbing the cell cycle network using a p38-signaling inhibitor without affecting the robust lineage-level correlations. Overall, our approach identifies transcriptional fluctuations as the key controlling factor for the cell cycle duration heterogeneities and predicts ways to reduce cell-to-cell variabilities by perturbing the cell cycle network regulations.

Understanding the mechanisms of HPV-related carcinogenesis: Implications for cell cycle dynamics

The role of human papillomavirus (HPV) as a causative agent for epithelial cancers is well-known, but many open questions remain regarding the downstream gene regulatory effects of viral proteins E6 and E7 on the cell cycle. Here, we extend a cell cycle model originally presented by Gérard and Goldbeter (2009) in order to capture the effects of E6 and E7 on key actors in the cell cycle. Results suggest that E6 is sufficient to reverse p53-induced quiescence, while E7 is sufficient to reverse p16INK4a-induced quiescence; both E6 and E7 are necessary when p53 and p16INK4a are both active. Moreover, E7 appears to play a role as a "growth factor substitute", inducing cell division in the absence of growth factor. Low levels of E7 may permit regular cell division, but the results suggest that higher levels of E7 dysregulate the cell cycle in ways that may destabilize the cellular genome. The mechanisms explored here provide opportunities for developing new treatment targets that take advantage of the cell cycle regulatory system to prevent HPV-related cancer effects.

Computational modeling of protracted HCMV replication using genome substrates and protein temporal profiles

Human cytomegalovirus (HCMV) is a major cause of illness in immunocompromised individuals. The HCMV lytic cycle contributes to the clinical manifestations of infection. The lytic cycle occurs over ∼96 h in diverse cell types and consists of viral DNA (vDNA) genome replication and temporally distinct expression of hundreds of viral proteins. Given its complexity, understanding this elaborate system can be facilitated by the introduction of mechanistic computational modeling of temporal relationships. Therefore, we developed a multiplicity of infection (MOI)-dependent mechanistic computational model that simulates vDNA kinetics and late lytic replication based on in-house experimental data. The predictive capabilities were established by comparison to post hoc experimental data. Computational analysis of combinatorial regulatory mechanisms suggests increasing rates of protein degradation in association with increasing vDNA levels. The model framework also allows expansion to account for additional mechanisms regulating the processes. Simulating vDNA kinetics and the late lytic cycle for a wide range of MOIs yielded several unique observations. These include the presence of saturation behavior at high MOIs, inefficient replication at low MOIs, and a precise range of MOIs in which virus is maximized within a cell type, being 0.382 IU to 0.688 IU per fibroblast. The predicted saturation kinetics at high MOIs are likely related to the physical limitations of cellular machinery, while inefficient replication at low MOIs may indicate a minimum input material required to facilitate infection. In summary, we have developed and demonstrated the utility of a data-driven and expandable computational model simulating lytic HCMV infection.

Bilateral Feedback in Oscillator Model Is Required to Explain the Coupling Dynamics of Hes1 with the Cell Cycle

Biological processes are governed by the expression of proteins, and for some proteins, their level of expression can fluctuate periodically over time (i.e., they oscillate). Many oscillatory proteins (e.g., cell cycle proteins and those from the HES family of transcription factors) are connected in complex ways, often within large networks. This complexity can be elucidated by developing intuitive mathematical models that describe the underlying critical aspects of the relationships between these processes. Here, we provide a mathematical explanation of a recently discovered biological phenomenon: the phasic position of the gene Hes1’s oscillatory expression at the beginning of the cell cycle of an individual human breast cancer stem cell can have a predictive value on how long that cell will take to complete a cell cycle. We use a two-component model of coupled oscillators to represent Hes1 and the cell cycle in the same cell with minimal assumptions. Inputting only the initial phase angles, we show that this model is capable of predicting the dynamic mitosis to mitosis behaviour of Hes1 and predicting cell cycle length patterns as found in real-world experimental data. Moreover, we discover that bidirectional coupling between Hes1 and the cell cycle is critical within the system for the data to be reproduced and that nonfixed asymmetry in the interactions between the oscillators is required. The phase dynamics we present here capture the complex interplay between Hes1 and the cell cycle, helping to explain nongenetic cell cycle variability, which has critical implications in cancer treatment contexts.

Differential methods for assessing sensitivity in biological models

Differential sensitivity analysis is indispensable in fitting parameters, understanding uncertainty, and forecasting the results of both thought and lab experiments. Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to determine which method is best suited for a particular model. In this paper, we explain a variety of differential sensitivity methods and assess their value in some typical biological models. First, we explain the mathematical basis for three numerical methods: adjoint sensitivity analysis, complex perturbation sensitivity analysis, and forward mode sensitivity analysis. We then carry out four instructive case studies. (a) The CARRGO model for tumor-immune interaction highlights the additional information that differential sensitivity analysis provides beyond traditional naive sensitivity methods, (b) the deterministic SIR model demonstrates the value of using second-order sensitivity in refining model predictions, (c) the stochastic SIR model shows how differential sensitivity can be attacked in stochastic modeling, and (d) a discrete birth-death-migration model illustrates how the complex perturbation method of differential sensitivity can be generalized to a broader range of biological models. Finally, we compare the speed, accuracy, and ease of use of these methods. We find that forward mode automatic differentiation has the quickest computational time, while the complex perturbation method is the simplest to implement and the most generalizable.

CDK1-cyclin-B1-induced kindlin degradation drives focal adhesion disassembly at mitotic entry

The disassembly of integrin-containing focal adhesions (FAs) at mitotic entry is essential for cell rounding, mitotic retraction fibre formation, bipolar spindle positioning and chromosome segregation. The mechanism that drives FA disassembly at mitotic entry is unknown. Here, we show that the CDK1–cyclin B1 complex phosphorylates the integrin activator kindlin, which results in the recruitment of the cullin 9–FBXL10 ubiquitin ligase complex that mediates kindlin ubiquitination and degradation. This molecular pathway is essential for FA disassembly and cell rounding, as phospho-inhibitory mutations of the CDK1 motif prevent kindlin degradation, FA disassembly and mitotic cell rounding. Conversely, phospho-mimetic mutations promote kindlin degradation in interphase, accelerate mitotic cell rounding and impair mitotic retraction fibre formation. Despite the opposing effects on kindlin stability, both types of mutations cause severe mitotic spindle defects, apoptosis and aneuploidy. Thus, the exquisite regulation of kindlin levels at mitotic entry is essential for cells to progress accurately through mitosis.

Chen et al. report that at mitotic entry, cyclin B1–CDK1 phosphorylates the focal adhesion protein kindlin to induce its proteasomal degradation and promote focal adhesion disassembly and mitotic rounding.

Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.

Principles, mechanisms and functions of entrainment in biological oscillators

Entrainment is a phenomenon in which two oscillators interact with each other, typically through physical or chemical means, to synchronize their oscillations. This phenomenon occurs in biology to coordinate processes from the molecular to organismal scale. Biological oscillators can be entrained within a single cell, between cells or to an external input. Using six illustrative examples of entrainable biological oscillators, we discuss the distinctions between entrainment and synchrony and explore features that contribute to a system's propensity to entrain. Entrainment can either enhance or reduce the heterogeneity of oscillations within a cell population, and we provide examples and mechanisms of each case. Finally, we discuss the known functions of entrainment and discuss potential functions from an evolutionary perspective.

A mathematical model for cell cycle control: graded response or quantized response

Cell cycle is an important and complex biological system. A lot of efforts have been put in understanding cell cycle arrest for its vital role in clinical therapies. The cell-cycle-arrest outcomes upon stimulation are complicated. The response could be stringent or relaxed, and graded or quantized. A model fully addressing various cell-cycle-arrest outcomes is to be developed. Here, we developed a mathematical model of cell cycle control incorporating distinct characteristics of various cell-cycle-arrest outcomes. The model can simulate two typical properties of cell cycle arrest, quantized and graded. We also characterized the inheritable quiescence and refractory state, which were crucial in long-term response of the population. Then, we monitored cells respond to multiple stimulations, and the results indicated that cells responded to stimulations with small interval did not induce significantly sustained cell cycle arrest as the existence of refractory state. Our work will benefit fundamental research and make efforts to predicting outcomes of clinical therapeutics.

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

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.

Unraveling the stochastic transition mechanism between oscillation states by landscape and minimum action path theory

Cell fate transitions have been studied from various perspectives, such as the transition between stable states, or the transition between stable states and oscillation states. However, there is a lack...

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.

Crosstalk between Plk1, p53, cell cycle, and G2/M DNA damage checkpoint regulation in cancer: computational modeling and analysis

Different cancer cell lines can have varying responses to the same perturbations or stressful conditions. Cancer cells that have DNA damage checkpoint-related mutations are often more sensitive to gene perturbations including altered Plk1 and p53 activities than cancer cells without these mutations. The perturbations often induce a cell cycle arrest in the former cancer, whereas they only delay the cell cycle progression in the latter cancer. To study crosstalk between Plk1, p53, and G2/M DNA damage checkpoint leading to differential cell cycle regulations, we developed a computational model by extending our recently developed model of mitotic cell cycle and including these key interactions. We have used the model to analyze the cancer cell cycle progression under various gene perturbations including Plk1-depletion conditions. We also analyzed mutations and perturbations in approximately 1800 different cell lines available in the Cancer Dependency Map and grouped lines by genes that are represented in our model. Our model successfully explained phenotypes of various cancer cell lines under different gene perturbations. Several sensitivity analysis approaches were used to identify the range of key parameter values that lead to the cell cycle arrest in cancer cells. Our resulting model can be used to predict the effect of potential treatments targeting key mitotic and DNA damage checkpoint regulators on cell cycle progression of different types of cancer cells.

Improving cancer treatments via dynamical biophysical models

Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.

A modular approach for modeling the cell cycle based on functional response curves

Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way.

Bistability plays an important role in many biochemical processes and typically emerges from complex interaction patterns such as positive and double negative feedback loops. Here, we propose to theoretically study the effect of bistability in a larger interaction network. We explicitly incorporate a functional expression describing an S-shaped input-output curve in the model equations, without the need for considering the underlying biochemical events. This expression can be converted into a functional module for an ultrasensitive response, and a time delay is easily included as well. Exploiting the fact that several of these modules can easily be combined in larger networks, we construct a cell cycle model consisting of multiple bistable switches and show how this approach can account for a number of known properties of the cell cycle.

A Dimension Reduction Approach for Energy Landscape: Identifying Intermediate States in Metabolism-EMT Network

Dimension reduction is a challenging problem in complex dynamical systems. Here, a dimension reduction approach of landscape (DRL) for complex dynamical systems is proposed, by mapping a high-dimensional system on a low-dimensional energy landscape. The DRL approach is applied to three biological networks, which validates that new reduced dimensions preserve the major information of stability and transition of original high-dimensional systems. The consistency of barrier heights calculated from the low-dimensional landscape and transition actions calculated from the high-dimensional system further shows that the landscape after dimension reduction can quantify the global stability of the system. The epithelial-mesenchymal transition (EMT) and abnormal metabolism are two hallmarks of cancer. With the DRL approach, a quadrastable landscape for metabolism-EMT network is identified, including epithelial (E), abnormal metabolic (A), hybrid E/M (H), and mesenchymal (M) cell states. The quantified energy landscape and kinetic transition paths suggest that for the EMT process, the cells at E state need to first change their metabolism, then enter the M state. The work proposes a general framework for the dimension reduction of a stochastic dynamical system, and advances the mechanistic understanding of the underlying relationship between EMT and cellular metabolism.

Building patient-specific models for receptor tyrosine kinase signaling networks

Cancer progresses due to changes in the dynamic interactions of multidimensional factors associated with gene mutations. Cancer research has actively adopted computational methods, including data-driven and mathematical model-driven approaches, to identify causative factors and regulatory rules that can explain the complexity and diversity of cancers. A data-driven, statistics-based approach revealed correlations between gene alterations and clinical outcomes in many types of cancers. A model-driven mathematical approach has elucidated the dynamic features of cancer networks and identified the mechanisms of drug efficacy and resistance. More recently, machine learning methods have emerged that can be used for mining omics data and classifying patient. However, as the strengths and weaknesses of each method becoming apparent, new analytical tools are emerging to combine and improve the methodologies and maximize their predictive power for classifying cancer subtypes and prognosis. Here, we introduce recent advances in cancer systems biology aimed at personalized medicine, with focus on the receptor tyrosine kinase signaling network.

A Computational Model for the Cold Response Pathway in Plants

Understanding the mechanism by which plants respond to cold stress and strengthen their tolerance to low temperatures is an important and challenging task in plant sciences. Experiments have established that the first step in the perception and transduction of the cold stress signal consists of a transient influx of Ca²⁺. This Ca²⁺ influx triggers the activation of a cascade of phosphorylation-dephosphorylation reactions that eventually affects the expression of C-repeat-binding factors (CBFs, notably CBF3), which were shown in many plants to control resistance to cold stress by regulating the expression of cold-regulated (COR) genes. Based on experimental observations mostly made on Arabidopsis thaliana, we build a computational model for the cold response pathway in plants, from the transduction of the cold signal via the transient influx of Ca²⁺ to the activation of the phosphorylation cascade leading to CBF3 expression. We explore the dynamics of this regulatory network by means of numerical simulations and compare the results with experimental observations on the dynamics of the cold response, both for the wild type and for mutants. The simulations show how, in response to cold stress, a brief Ca²⁺ influx, which is over in minutes, is transduced along the successive steps of the network to trigger the expression of cold response genes such as CBF3 within hours. Sometimes, instead of a single Ca²⁺ spike the decrease in temperature brings about a train of high-frequency Ca²⁺ oscillations. The model is applied to both types of Ca²⁺ signaling. We determine the dynamics of the network in response to a series of identical cold stresses, to account for the observation of desensitization and resensitization. The analysis of the model predicts the possibility of an oscillatory expression of CBF3 originating from the negative feedback exerted by ZAT12, a factor itself controlled by CBF3. Finally, we extend the model to incorporate the circadian control of CBF3 expression, to account for the gating of the response to cold stress by the plant circadian clock.

The transcriptome dynamics of single cells during the cell cycle

The cell cycle is among the most basic phenomena in biology. Despite advances in single-cell analysis, dynamics and topology of the cell cycle in high-dimensional gene expression space remain largely unknown. We developed a linear analysis of transcriptome data which reveals that cells move along a planar circular trajectory in transcriptome space during the cycle. Non-cycling gene expression adds a third dimension causing helical motion on a cylinder. We find in immortalized cell lines that cell cycle transcriptome dynamics occur largely independently from other cellular processes. We offer a simple method ("Revelio") to order unsynchronized cells in time. Precise removal of cell cycle effects from the data becomes a straightforward operation. The shape of the trajectory implies that each gene is upregulated only once during the cycle, and only two dynamic components represented by groups of genes drive transcriptome dynamics. It indicates that the cell cycle has evolved to minimize changes of transcriptional activity and the related regulatory effort. This design principle of the cell cycle may be of relevance to many other cellular differentiation processes.

The Greatwall kinase safeguards the genome integrity by affecting the kinome activity in mitosis

Progression through mitosis is balanced by the timely regulation of phosphorylation and dephosphorylation events ensuring the correct segregation of chromosomes before cytokinesis. This balance is regulated by the opposing actions of CDK1 and PP2A, as well as the Greatwall kinase/MASTL. MASTL is commonly overexpressed in cancer, which makes it a potential therapeutic anticancer target. Loss of Mastl induces multiple chromosomal errors that lead to the accumulation of micronuclei and multilobulated cells in mitosis. Our analyses revealed that loss of Mastl leads to chromosome breaks and abnormalities impairing correct segregation. Phospho-proteomic data for Mastl knockout cells revealed alterations in proteins implicated in multiple processes during mitosis including double-strand DNA damage repair. In silico prediction of the kinases with affected activity unveiled NEK2 to be regulated in the absence of Mastl. We uncovered that, RAD51AP1, involved in regulation of homologous recombination, is phosphorylated by NEK2 and CDK1 but also efficiently dephosphorylated by PP2A/B55. Our results suggest that MastlKO disturbs the equilibrium of the mitotic phosphoproteome that leads to the disruption of DNA damage repair and triggers an accumulation of chromosome breaks even in noncancerous cells.

The shifting shape and functional specializations of the cell cycle during lineage development

Essentially all cell cycling in multicellular organisms in vivo takes place in the context of lineage differentiation. This notwithstanding, the regulation of the cell cycle is often assumed to be generic, independent of tissue or developmental stage. Here we review developmental-stage-specific cell cycle adaptations that may influence developmental decisions, in mammalian erythropoiesis and in other lineages. The length of the cell cycle influences the balance between self-renewal and differentiation in multiple tissues, and may determine lineage fate. Shorter cycles contribute to the efficiency of reprogramming somatic cells into induced pluripotency stem cells and help maintain the pluripotent state. While the plasticity of G1 length is well established, the speed of S phase is emerging as a novel regulated parameter that may influence cell fate transitions in the erythroid lineage, in neural tissue and in embryonic stem cells. A slow S phase may stabilize the self-renewal state, whereas S phase shortening may favor a cell fate change. In the erythroid lineage, functional approaches and single-cell RNA-sequencing show that a key transcriptional switch, at the transition from self-renewal to differentiation, is synchronized with and dependent on S phase. This specific S phase is shorter, as a result of a genome-wide increase in the speed of replication forks. Furthermore, there is progressive shortening in G1 in the period preceding this switch. Together these studies suggest an integrated regulatory landscape of the cycle and differentiation programs, where cell cycle adaptations are controlled by, and in turn feed back on, the propagation of developmental trajectories. This article is categorized under: Biological Mechanisms > Cell Fates Developmental Biology > Stem Cell Biology and Regeneration Developmental Biology > Lineages.

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.

Resistin: An inflammatory cytokine with multi-faceted roles in cancer

Systemic and organ-confined inflammation has been associated with cancer development and progression. Resistin, initially described as an adipocyte-derived cytokine in mice, is mostly expressed by the macrophages in humans. It has potent pro-inflammatory properties, and its elevated serum levels are detected in cancer patients. Aberrant expression of resistin receptors is also reported in several malignancies and associated with aggressive clinicopathological features. Several lines of evidence demonstrate that resistin, acting through its different receptors, promotes tumor growth, metastasis, and chemoresistance by influencing a variety of cellular phenotypes as well as by modulating the tumor microenvironment. Racially disparate expression of resistin has also attracted much interest, considering prevalent cancer health disparities. This review discusses the aberrant expression of resistin and its receptors, its diverse downstream signaling and impact on tumor growth, metastasis, angiogenesis, and therapy resistance to support its clinical exploitation in biomarker and therapeutic development.

Quantifying the Landscape and Transition Paths for Proliferation-Quiescence Fate Decisions

The cell cycle, essential for biological functions, experiences delicate spatiotemporal regulation. The transition between G1 and S phase, which is called the proliferation–quiescence decision, is critical to the cell cycle. However, the stability and underlying stochastic dynamical mechanisms of the proliferation–quiescence decision have not been fully understood. To quantify the process of the proliferation–quiescence decision, we constructed its underlying landscape based on the relevant gene regulatory network. We identified three attractors on the landscape corresponding to the G0, G1, and S phases, individually, which are supported by single-cell data. By calculating the transition path, which quantifies the potential barrier, we built expression profiles in temporal order for key regulators in different transitions. We propose that the two saddle points on the landscape characterize restriction point (RP) and G1/S checkpoint, respectively, which provides quantitative and physical explanations for the mechanisms of Rb governing the RP while p21 controlling the G1/S checkpoint. We found that Emi1 inhibits the transition from G0 to G1, while Emi1 in a suitable range facilitates the transition from G1 to S. These results are partially consistent with previous studies, which also suggested new roles of Emi1 in the cell cycle. By global sensitivity analysis, we identified some critical regulatory factors influencing the proliferation–quiescence decision. Our work provides a global view of the stochasticity and dynamics in the proliferation–quiescence decision of the cell cycle.

Mathematical modelling of breast cancer cells in response to endocrine therapy and Cdk4/6 inhibition

Oestrogen receptor (ER)-positive breast cancer is responsive to a number of targeted therapies used clinically. Unfortunately, the continuous application of any targeted therapy often results in resistance to the therapy. Our ultimate goal is to use mathematical modelling to optimize alternating therapies that not only decrease proliferation but also stave off resistance. Toward this end, we measured levels of key proteins and proliferation over a 7-day time course in ER+ MCF-7 breast cancer cells. Treatments included endocrine therapy, either oestrogen deprivation, which mimics the effects of an aromatase inhibitor, or fulvestrant, an ER degrader. These data were used to calibrate a mathematical model based on key interactions between ER signalling and the cell cycle. We show that the calibrated model is capable of predicting the combination treatment of fulvestrant and oestrogen deprivation. Further, we show that we can add a new drug, palbociclib, to the model by measuring only two key proteins, cMyc and hyperphosphorylated RB1, and adjusting only parameters associated with the drug. The model is then able to predict the combination treatment of oestrogen deprivation and palbociclib. We illustrate the model's potential to explore protocols that limit proliferation and hold off resistance by not depending on any one therapy.

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.

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.

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.

Network mechanisms and dysfunction within an integrated computational model of progression through mitosis in the human cell cycle

The cellular protein-protein interaction network that governs cellular proliferation (cell cycle) is highly complex. Here, we have developed a novel computational model of human mitotic cell cycle, integrating diverse cellular mechanisms, for the purpose of generating new hypotheses and predicting new experiments designed to help understand complex diseases. The pathogenic state investigated is infection by a human herpesvirus. The model starts at mitotic entry initiated by the activities of Cyclin-dependent kinase 1 (CDK1) and Polo-like kinase 1 (PLK1), transitions through Anaphase-promoting complex (APC/C) bound to Cell division cycle protein 20 (CDC20), and ends upon mitotic exit mediated by APC/C bound to CDC20 homolog 1 (CDH1). It includes syntheses and multiple mechanisms of degradations of the mitotic proteins. Prior to this work, no such comprehensive model of the human mitotic cell cycle existed. The new model is based on a hybrid framework combining Michaelis-Menten and mass action kinetics for the mitotic interacting reactions. It simulates temporal changes in 12 different mitotic proteins and associated protein complexes in multiple states using 15 interacting reactions and 26 ordinary differential equations. We have defined model parameter values using both quantitative and qualitative data and using parameter values from relevant published models, and we have tested the model to reproduce the cardinal features of human mitosis determined experimentally by numerous laboratories. Like cancer, viruses create dysfunction to support infection. By simulating infection of the human herpesvirus, cytomegalovirus, we hypothesize that virus-mediated disruption of APC/C is necessary to establish a unique mitotic collapse with sustained CDK1 activity, consistent with known mechanisms of virus egress. With the rapid discovery of cellular protein-protein interaction networks and regulatory mechanisms, we anticipate that this model will be highly valuable in helping us to understand the network dynamics and identify potential points of therapeutic interventions.

Cell Cycle-Dependent Switch of TopBP1 Functions by Cdk2 and Akt

Cdk2-dependent TopBP1-treslin interaction is critical for DNA replication initiation. However, it remains unclear how this association is terminated after replication initiation is finished. Here, we demonstrate that phosphorylation of TopBP1 by Akt coincides with cyclin A activation during S and G₂ phases and switches the TopBP1-interacting partner from treslin to E2F1, which results in the termination of replication initiation. Premature activation of Akt in G₁ phase causes an early switch and inhibits DNA replication. TopBP1 is often overexpressed in cancer and can bypass control by Cdk2 to interact with treslin, leading to enhanced DNA replication. Consistent with this notion, reducing the levels of TopBP1 in cancer cells restores sensitivity to a Cdk2 inhibitor. Together, our study links Cdk2 and Akt pathways to the control of DNA replication through the regulation of TopBP1-treslin interaction. These data also suggest an important role for TopBP1 in driving abnormal DNA replication in cancer.

Towards abstraction of computational modelling of mammalian cell cycle: Model reduction pipeline incorporating multi-level hybrid petri nets

Cell cycle is a large biochemical network and it is crucial to simplify it to gain a clearer understanding and insights into the cell cycle. This is also true for other biochemical networks. In this study, we present a model abstraction scheme/pipeline to create a minimal abstract model of the whole mammalian cell cycle system from a large Ordinary Differential Equation model of cell cycle we published previously (Abroudi et al., 2017). The abstract model is developed in a way that it captures the main characteristics (dynamics of key controllers), responses (G1-S and G2-M transitions and DNA damage) and the signalling subsystems (Growth Factor, G1-S and G2-M checkpoints, and DNA damage) of the original model (benchmark). Further, our model exploits: (i) separation of time scales (slow and fast reactions), (ii) separation of levels of complexity (high-level and low-level interactions), (iii) cell-cycle stages (temporality), (iv) functional subsystems (as mentioned above), and (v) represents the whole cell cycle - within a Multi-Level Hybrid Petri Net (MLHPN) framework. Although hybrid Petri Nets is not new, the abstraction of interactions and timing we introduced here is new to cell cycle and Petri Nets. Importantly, our models builds on the significant elements, representing the core cell cycle system, found through a novel Global Sensitivity Analysis on the benchmark model, using Self Organising Maps and Correlation Analysis that we introduced in (Abroudi et al., 2017). Taken the two aspects together, our study proposes a 2-stage model reduction pipeline for large systems and the main focus of this paper is on stage 2, Petri Net model, put in the context of the pipeline. With the MLHPN model, the benchmark model with 61 continuous variables (ODEs) and 148 parameters were reduced to 14 variables (4 continuous (Cyc_Cdks - the main controllers of cell cycle) and 10 discrete (regulators of Cyc_Cdks)) and 31 parameters. Additional 9 discrete elements represented the temporal progression of cell cycle. Systems dynamics simulation results of the MLHPN model were in close agreement with the benchmark model with respect to the crucial metrics selected for comparison: order and pattern of Cyc_Cdk activation, timing of G1-S and G2-M transitions with or without DNA damage, efficiency of the two cell cycle checkpoints in arresting damaged cells and passing healthy cells, and response to two types of global parameter perturbations. The results show that the MLHPN provides a close approximation to the comprehensive benchmark model in robustly representing systems dynamics and emergent properties while presenting the core cell cycle controller in an intuitive, transparent and subsystems format.

Antitumor Activity of Ohmyungsamycin A through the Regulation of the Skp2-p27 Axis and MCM4 in Human Colorectal Cancer Cells

Ohmyungsamycin A (1), a novel cyclic peptide discovered from a marine Streptomyces sp., was previously reported with antibacterial and anticancer activities. However, the antitumor activities and the underlying molecular mechanisms of 1 remain to be elucidated. Compound 1 inhibited the proliferation and tumor growth of HCT116 human colorectal cancer cells based on both in vitro cell cultures and an in vivo animal model. A cDNA microarray analysis revealed that 1 downregulated genes involved in cell cycle checkpoint control. Compound 1 also induced G₀/G₁ cell cycle arrest that was mediated by the regulation of S-phase kinase-associated protein 2 (Skp2)-p27 axis and minichromosome maintenance protein 4 (MCM4). Furthermore, a longer exposure of 1 exhibited an accumulation of a sub-G₁ phase cell population, which is characteristic of apoptotic cells. The induction of apoptosis by 1 was also associated with the modulation of caspase family proteins. Compound 1 effectively suppressed tumor growth in a xenograft mouse model subcutaneously implanted with HCT116 cells. In addition, analysis of tumors revealed that 1 upregulated the expression of the CDK inhibitor p27 but downregulated the expression of Skp2 and MCM4. These findings demonstrate the involvement of 1 in cell cycle regulation and the induction of apoptosis in human colorectal cancer cells.

Multiple Targets of the Canonical WNT/β-Catenin Signaling in Cancers

Canonical WNT/β-catenin signaling is involved in most of the mechanisms that lead to the formation and development of cancer cells. It plays a central role in three cyclic processes, which are the cell division cycle, the immune cycle, and circadian rhythms. When the canonical WNT pathway is upregulated as in cancers, the increase in β-catenin in the nucleus leads to activation of the expression of numerous genes, in particular CYCLIN D1 and cMYC, where the former influences the G1 phase of the cell division cycle, and the latter, the S phase. Every stage of the immune cycle is disrupted by the canonical WNT signaling. In numerous cancers, the dysfunction of the canonical WNT pathway is accompanied by alterations of the circadian genes (CLOCK, BMAL1, PER). Induction of these cyclic phenomena leads to the genesis of thermodynamic mechanisms that operate far from equilibrium, and that have been called “dissipative structures.” Moreover, upregulation of the canonical WNT/β-catenin signaling is important in the myofibroblasts of the cancer stroma. Their differentiation is controlled by the canonical WNT /TGF-β1 signaling. Myofibroblasts present ultraslow contractile properties due to the presence of the non-muscle myosin IIA. Myofibroblats also play a role in the inflammatory processes, often found in cancers and fibrosis processes. Finally, upregulated canonical WNT deviates mitochondrial oxidative phosphorylation toward the Warburg glycolysis metabolism, which is characteristic of cancers. Among all these cancer-generating mechanisms, the upregulated canonical WNT pathway would appear to offer the best hope as a therapeutic target, particularly in the field of immunotherapy.

A feedback loop of conditionally stable circuits drives the cell cycle from checkpoint to checkpoint

We perform logic-based network analysis on a model of the mammalian cell cycle. This model is composed of a Restriction Switch driving cell cycle commitment and a Phase Switch driving mitotic entry and exit. By generalizing the concept of stable motif, i.e., a self-sustaining positive feedback loop that maintains an associated state, we introduce the concept of a conditionally stable motif, the stability of which is contingent on external conditions. We show that the stable motifs of the Phase Switch are contingent on the state of three nodes through which it receives input from the rest of the network. Biologically, these conditions correspond to cell cycle checkpoints. Holding these nodes locked (akin to a checkpoint-free cell) transforms the Phase Switch into an autonomous oscillator that robustly toggles through the cell cycle phases G1, G2 and mitosis. The conditionally stable motifs of the Phase Switch Oscillator are organized into an ordered sequence, such that they serially stabilize each other but also cause their own destabilization. Along the way they channel the dynamics of the module onto a narrow path in state space, lending robustness to the oscillation. Self-destabilizing conditionally stable motifs suggest a general negative feedback mechanism leading to sustained oscillations.

Robust synchronization of the cell cycle and the circadian clock through bidirectional coupling

The cell cycle and the circadian clock represent major cellular rhythms, which appear to be coupled. Thus the circadian factor BMAL1 controls the level of cell cycle proteins such as Cyclin E and WEE1, the latter of which inhibits the kinase CDK1 that governs the G2/M transition. In reverse the cell cycle impinges on the circadian clock through direct control by CDK1 of REV-ERBα, which negatively regulates BMAL1. These observations provide evidence for bidirectional coupling of the cell cycle and the circadian clock. By merging detailed models for the two networks in mammalian cells, we previously showed that unidirectional coupling to the circadian clock can entrain the cell cycle to 24 or 48 h, depending on the cell cycle autonomous period, while complex oscillations occur when entrainment fails. Here we show that the reverse unidirectional coupling via phosphorylation of REV-ERBα or via mitotic inhibition of transcription, both controlled by CDK1, can elicit entrainment of the circadian clock by the cell cycle. We then determine the effect of bidirectional coupling of the cell cycle and circadian clock as a function of their relative coupling strengths. In contrast to unidirectional coupling, bidirectional coupling markedly reduces the likelihood of complex oscillations. While the two rhythms oscillate independently as long as both couplings are weak, one rhythm entrains the other if one of the couplings dominates. If the couplings in both directions become stronger and of comparable magnitude, the two rhythms synchronize, generally at an intermediate period within the range defined by the two autonomous periods prior to coupling. More surprisingly, synchronization may also occur at a period slightly below or above this range, while in some conditions the synchronization period can even be much longer. Two or even three modes of synchronization may sometimes coexist, yielding examples of birhythmicity or trirhythmicity. Because synchronization readily occurs in the form of simple periodic oscillations over a wide range of coupling strengths and in the presence of multiple connections between the two oscillatory networks, the results indicate that bidirectional coupling favours the robust synchronization of the cell cycle and the circadian clock.