The dynamics of cell cycle regulation

Synthetic gene circuit evolution: Insights and opportunities at the mid-scale

Directed evolution focuses on optimizing single genetic components for predefined engineering goals by artificial mutagenesis and selection. In contrast, experimental evolution studies the adaptation of entire genomes in serially propagated cell populations, to provide an experimental basis for evolutionary theory. There is a relatively unexplored gap at the middle ground between these two techniques, to evolve in vivo entire synthetic gene circuits with nontrivial dynamic function instead of single parts or whole genomes. We discuss the requirements for such mid-scale evolution, with hypothetical examples for evolving synthetic gene circuits by appropriate selection and targeted shuffling of a seed set of genetic components in vivo. Implementing similar methods should aid the rapid generation, functionalization, and optimization of synthetic gene circuits in various organisms and environments, accelerating both the development of biomedical and technological applications and the understanding of principles guiding regulatory network evolution.

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.

Equations describing semi-confluent cell growth (I) Analytical approximations

A set of differential equations with analytical solutions are presented that can quantitatively account for variable degrees of contact inhibition on cell growth in two- and three-dimensional cultures. The developed equations can be used for comparative purposes when assessing contribution of higher-order effects, such as culture geometry and nutrient depletion, on mean cell growth rate. These equations also offer experimentalists the opportunity to characterize cell culture experiments using a single reductive parameter.

The Dual Role of Sulforaphane-Induced Cellular Stress-A Systems Biological Study

The endoplasmic reticulum (ER) plays a crucial role in cellular homeostasis. When ER stress is generated, an autophagic self-digestive process is activated to promote cell survival; however, cell death is induced in the case of excessive levels of ER stress. The aim of the present study was to investigate the effect of a natural compound called sulforaphane (SFN) upon ER stress. Our goal was to investigate how SFN-dependent autophagy activation affects different stages of ER stress induction. We approached our scientific analysis from a systems biological perspective using both theoretical and molecular biological techniques. We found that SFN induced the various cell-death mechanisms in a concentration- and time-dependent manner. The short SFN treatment at low concentrations promoted autophagy, whereas the longer treatment at higher concentrations activated cell death. We proved that SFN activated autophagy in a mTORC1-dependent manner and that the presence of ULK1 was required for its function. A low concentration of SFN pre- or co-treatment combined with short and long ER stress was able to promote cell survival via autophagy induction in each treatment, suggesting the potential medical importance of SFN in ER stress-related diseases.

Combining formal methods and Bayesian approach for inferring discrete-state stochastic models from steady-state data

Stochastic population models are widely used to model phenomena in different areas such as cyber-physical systems, chemical kinetics, collective animal behaviour, and beyond. Quantitative analysis of stochastic population models easily becomes challenging due to the combinatorial number of possible states of the population. Moreover, while the modeller easily hypothesises the mechanistic aspects of the model, the quantitative parameters associated to these mechanistic transitions are difficult or impossible to measure directly. In this paper, we investigate how formal verification methods can aid parameter inference for population discrete-time Markov chains in a scenario where only a limited sample of population-level data measurements-sample distributions among terminal states-are available. We first discuss the parameter identifiability and uncertainty quantification in this setup, as well as how the existing techniques of formal parameter synthesis and Bayesian inference apply. Then, we propose and implement four different methods, three of which incorporate formal parameter synthesis as a pre-computation step. We empirically evaluate the performance of the proposed methods over four representative case studies. We find that our proposed methods incorporating formal parameter synthesis as a pre-computation step allow us to significantly enhance the accuracy, precision, and scalability of inference. Specifically, in the case of unidentifiable parameters, we accurately capture the subspace of parameters which is data-compliant at a desired confidence level.

Organoids and metastatic orthotopic mouse model for mismatch repair-deficient colorectal cancer

Background

Genome integrity is essential for the survival of an organism. DNA mismatch repair (MMR) genes (e.g., MLH1, MSH2, MSH6, and PMS2) play a critical role in the DNA damage response pathway for genome integrity maintenance. Germline mutations of MMR genes can lead to Lynch syndrome or constitutional mismatch repair deficiency syndrome, resulting in an increased lifetime risk of developing cancer characterized by high microsatellite instability (MSI-H) and high mutation burden. Although immunotherapy has been approved for MMR-deficient (MMRd) cancer patients, the overall response rate needs to be improved and other management options are needed.

Methods

To better understand the biology of MMRd cancers, elucidate the resistance mechanisms to immune modulation, and develop vaccines and therapeutic testing platforms for this high-risk population, we generated organoids and an orthotopic mouse model from intestine tumors developed in a Msh2-deficient mouse model, and followed with a detailed characterization.

Results

The organoids were shown to be of epithelial origin with stem cell features, to have a high frameshift mutation frequency with MSI-H and chromosome instability, and intra- and inter-tumor heterogeneity. An orthotopic model using intra-cecal implantation of tumor fragments derived from organoids showed progressive tumor growth, resulting in the development of adenocarcinomas mixed with mucinous features and distant metastasis in liver and lymph node.

Conclusions

The established organoids with characteristics of MSI-H cancers can be used to study MMRd cancer biology. The orthotopic model, with its distant metastasis and expressing frameshift peptides, is suitable for evaluating the efficacy of neoantigen-based vaccines or anticancer drugs in combination with other therapies.

The fitness value of ecological information in a variable world

Information processing is increasingly recognized as a fundamental component of life in variable environments, including the evolved use of environmental cues, biomolecular networks, and social learning. Despite this, ecology lacks a quantitative framework for understanding how population, community, and ecosystem dynamics depend on information processing. Here, we review the rationale and evidence for 'fitness value of information' (FVOI), and synthesize theoretical work in ecology, information theory, and probability behind this general mathematical framework. The FVOI quantifies how species' per capita population growth rates can depend on the use of information in their environment. FVOI is a breakthrough approach to linking information processing and ecological and evolutionary outcomes in a changing environment, addressing longstanding questions about how information mediates the effects of environmental change and species interactions.

Rule-based modelling of biological systems using regulated rewriting

In systems biology, models play a crucial role in understanding studied systems. There are many modelling approaches, among which rewriting systems provide a framework for describing systems on a mechanistic level. Describing biochemical processes often requires incorporating knowledge on an abstract level to simplify the system description or substitute the missing details. For this purpose, we present regulation mechanisms, an extension of this formalism with additional controls on the rewriting process. We introduce several regulation mechanisms and apply them to a rule-based language, a notation suitable for modelling biological phenomena. Finally, we demonstrate the usage of such regulations on several case studies from the biochemical domain.

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.

Network inference from perturbation time course data

Networks underlie much of biology from subcellular to ecological scales. Yet, understanding what experimental data are needed and how to use them for unambiguously identifying the structure of even small networks remains a broad challenge. Here, we integrate a dynamic least squares framework into established modular response analysis (DL-MRA), that specifies sufficient experimental perturbation time course data to robustly infer arbitrary two and three node networks. DL-MRA considers important network properties that current methods often struggle to capture: (i) edge sign and directionality; (ii) cycles with feedback or feedforward loops including self-regulation; (iii) dynamic network behavior; (iv) edges external to the network; and (v) robust performance with experimental noise. We evaluate the performance of and the extent to which the approach applies to cell state transition networks, intracellular signaling networks, and gene regulatory networks. Although signaling networks are often an application of network reconstruction methods, the results suggest that only under quite restricted conditions can they be robustly inferred. For gene regulatory networks, the results suggest that incomplete knockdown is often more informative than full knockout perturbation, which may change experimental strategies for gene regulatory network reconstruction. Overall, the results give a rational basis to experimental data requirements for network reconstruction and can be applied to any such problem where perturbation time course experiments are possible.

Intrinsic nonlinear dynamics drive single-species systems

The importance of oscillations and deterministic chaos in natural biological systems has been discussed for several decades and was originally based on discrete-time population growth models (May 1974). Recently, all types of nonlinear dynamics were shown for experimental communities where several species interact. Yet, there are no data exhibiting the whole range of nonlinear dynamics for single-species systems without trophic interactions. Up until now, ecological experiments and models ignored the intracellular dimension, which includes multiple nonlinear processes even within one cell type. Here, we show that dynamics of single-species systems of protists in continuous experimental chemostat systems and corresponding continuous-time models reveal typical characteristics of nonlinear dynamics and even deterministic chaos, a very rare discovery. An automatic cell registration enabled a continuous and undisturbed analysis of dynamic behavior with a high temporal resolution. Our simple and general model considering the cell cycle exhibits a remarkable spectrum of dynamic behavior. Chaos-like dynamics were shown in continuous single-species populations in experimental and modeling data on the level of a single type of cells without any external forcing. This study demonstrates how complex processes occurring in single cells influence dynamics on the population level. Nonlinearity should be considered as an important phenomenon in cell biology and single-species dynamics and also, for the maintenance of high biodiversity in nature, a prerequisite for nature conservation.

Human β defensins-1, an antimicrobial peptide, kills Candida glabrata by generating oxidative stress and arresting the cell cycle in G0/G1 phase

Candida glabrata is the most frequently isolated non-albicans Candida species in clinical samples and is known to develop resistance to commonly used antifungal drugs. Human β defensins (hBDs) are antimicrobial peptides of immune systems and are active against a broad range of pathogens including Candida species. Herein, the antifungal effect of hBD-1 and its mechanism of action in C. glabrata was studied. The antifungal susceptibility of hBD-1 against C. glabrata was calculated by broth microdilution assay. To study the mechanism of antifungal action, the impact of hBD-1 on cell cycle, expression of oxidative stress enzymes, and membrane disintegration were assessed. The susceptibility results confirmed that hBD-1 possessed the minimum inhibitory concentration of 3.12 µg/mL and prevented the growth and caused yeast cell death to various extents. The peptide at subinhibitory and inhibitory concentrations blocked the cell cycle in C. glabrata in G0/G1 phase and disturbed the activity of primary and secondary antioxidant enzymes. Furthermore, at higher concentrations disruption of membrane integrity was observed. Altogether, hBD-1 showed candidicidal activity against C. glabrata and was able to induce oxidative stress and arrested cell cycle in C. auris and therefore has a potential to be developed as an antifungal drug against C. glabrata.

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.

Polygenic and Network-Based Studies in Risk Identification and Demystification of cancer

INTRODUCTION

Diseases were initially thought to be the consequence of a single gene mutation. Advances in DNA sequencing tools and our understanding of gene behavior have revealed that complex diseases, such as cancer, are the product of genes cooperating with each other and with their environment in orchestrated communication networks. Seeing that the function of individual genes is still used to analyze cancer, the shift to using functionally interacting groups of genes as a new unit of study holds promise for demystifying cancer.

AREAS COVERED

The literature search focused on three types of cancer, namely breast, lung, and prostate, but arguments from other cancers were also included. The aim was to prove that multigene analyses can accurately predict and prognosticate cancer risk, subtype cancer for more personalized and effective treatments, and discover anti-cancer therapies. Computational intelligence is being harnessed to analyze this type of data and is proving indispensable to scientific progress.

EXPERT OPINION

In the future, comprehensive profiling of all kinds of patient data (e.g., serum molecules, environmental exposures) can be used to build universal networks that should help us elucidate the molecular mechanisms underlying diseases and provide appropriate preventive measures, ensuring lifelong health and longevity.

WebMaBoSS: A Web Interface for Simulating Boolean Models Stochastically

WebMaBoSS is an easy-to-use web interface for conversion, storage, simulation and analysis of Boolean models that allows to get insight from these models without any specific knowledge of modeling or coding. It relies on an existing software, MaBoSS, which simulates Boolean models using a stochastic approach: it applies continuous time Markov processes over the Boolean network. It was initially built to fill the gap between Boolean and continuous formalisms, i.e., providing semi-quantitative results using a simple representation with a minimum number of parameters to fit. The goal of WebMaBoSS is to simplify the use and the analysis of Boolean models coping with two main issues: 1) the simulation of Boolean models of intracellular processes with MaBoSS, or any modeling tool, may appear as non-intuitive for non-experts; 2) the simulation of already-published models available in current model databases (e.g., Cell Collective, BioModels) may require some extra steps to ensure compatibility with modeling tools such as MaBoSS. With WebMaBoSS, new models can be created or imported directly from existing databases. They can then be simulated, modified and stored in personal folders. Model simulations are performed easily, results visualized interactively, and figures can be exported in a preferred format. Extensive model analyses such as mutant screening or parameter sensitivity can also be performed. For all these tasks, results are stored and can be subsequently filtered to look for specific outputs. This web interface can be accessed at the address: https://maboss.curie.fr/webmaboss/ and deployed locally using docker. This application is open-source under LGPL license, and available at https://github.com/sysbio-curie/WebMaBoSS.

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.

Strategic Developments & Future Perspective on Gene Therapy for Breast Cancer: Role of mTOR and Brk/ PTK6 as Molecular Targets

Breast cancer is a serious health issue and a major concern in biomedical research. Alteration in major signaling (viz. PI3K-AKT-mTOR, Ras-Raf-MEK-Erk, NF-kB, cyclin D1, JAK-STAT, Wnt, Notch, Hedgehog signaling and apoptotic pathway) contributes to the development of major subtypes of mammary carcinoma such as HER2 positive, TNBC, luminal A and B and normal-like breast cancer. Further, mutation and expression parameters of different genes involved in the growth and development of cells play an important role in the progress of different types of carcinoma, making gene therapy an emerging new therapeutic approach for the management of life-threatening diseases like cancer. The genetic targets (oncogenes and tumor suppressor genes) play a major role in the formation of a tumor. Brk/PTK6 and mTOR are two central molecules that are involved in the regulation of numerous signaling related to cell growth, proliferation, angiogenesis, survival, invasion, metastasis, apoptosis, and autophagy. Since these two proteins are highly upregulated in mammary carcinogenesis, this can be used as targeted genes for the treatment of breast cancer. However, not much work has been done on them. This review highlights the therapeutic significance of Brk and mTOR and their associated signaling in mammary carcinogenesis, which may provide a strategy to develop gene therapy for breast cancer management.

Evolution of opposing regulatory interactions underlies the emergence of eukaryotic cell cycle checkpoints

In eukaryotes the entry into mitosis is initiated by activation of cyclin-dependent kinases (CDKs), which in turn activate a large number of protein kinases to induce all mitotic processes. The general view is that kinases are active in mitosis and phosphatases turn them off in interphase. Kinases activate each other by cross- and self-phosphorylation, while phosphatases remove these phosphate groups to inactivate kinases. Crucial exceptions to this general rule are the interphase kinase Wee1 and the mitotic phosphatase Cdc25. Together they directly control CDK in an opposite way of the general rule of mitotic phosphorylation and interphase dephosphorylation. Here we investigate why this opposite system emerged and got fixed in almost all eukaryotes. Our results show that this reversed action of a kinase-phosphatase pair, Wee1 and Cdc25, on CDK is particularly suited to establish a stable G2 phase and to add checkpoints to the cell cycle. We show that all these regulators appeared together in LECA (Last Eukaryote Common Ancestor) and co-evolved in eukaryotes, suggesting that this twist in kinase-phosphatase regulation was a crucial step happening at the emergence of eukaryotes.

Upregulation of Chemoresistance by Mg2+ Deficiency through Elevation of ATP Binding Cassette Subfamily B Member 1 Expression in Human Lung Adenocarcinoma A549 Cells

Several anticancer drugs including cisplatin (CDDP) induce hypomagnesemia. However, it remains fully uncertain whether Mg²⁺ deficiency affects chemosensitivity of cancer cells. Here, we investigated the effect of low Mg²⁺ concentration (LM) on proliferation and chemosensitivity using human lung adenocarcinoma A549 cells. Cell proliferation was reduced by continuous culture with LM accompanied with the elevation of G1 phase proportion. The amounts of reactive oxygen species (ROS) and stress makers such as phosphorylated-ataxia telangiectasia mutated and phosphorylated-p53 were increased by LM. Cell injury was dose-dependently increased by anticancer drugs such as CDDP and doxorubicin (DXR), which were suppressed by LM. Similar results were obtained by roscovitine, a cell cycle inhibitor. These results suggest that LM induces chemoresistance mediated by ROS production and G1 arrest. The mRNA and protein levels of ATP binding cassette subfamily B member 1 (ABCB1) were increased by LM and roscovitine. The LM-induced elevation of ABCB1 and nuclear p38 expression was suppressed by SB203580, a p38 MAPK inhibitor. PSC833, an ABCB1 inhibitor, and SB203580 rescued the sensitivity to anticancer drugs. In addition, cancer stemness properties were suppressed by SB203580. We suggest that Mg²⁺ deficiency reduces the chemotherapy sensitivity of A549 cells, although it suppresses cell proliferation.

Therapeutic Approach of KRAS Mutant Tumours by the Combination of Pharmacologic Ascorbate and Chloroquine

The Warburg effect has been considered a potential therapeutic target to fight against cancer progression. In KRAS mutant cells, PKM2 (pyruvate kinase isozyme M2) is hyper-activated, and it induces GLUT1 expression; therefore, KRAS has been closely involved in the initiation of Warburg metabolism. Although mTOR (mammalian target of rapamycin), a well-known inhibitor of autophagy-dependent survival in physiological conditions, is also activated in KRAS mutants, many recent studies have revealed that autophagy becomes hyper-active in KRAS mutant cancer cells. In the present study, a mathematical model was built containing the main elements of the regulatory network in KRAS mutant cancer cells to explore the further possible therapeutic strategies. Our dynamical analysis suggests that the downregulation of KRAS, mTOR and autophagy are crucial in anti-cancer therapy. PKM2 has been assumed to be the key switch in the stress response mechanism. We predicted that the addition of both pharmacologic ascorbate and chloroquine is able to block both KRAS and mTOR pathways: in this case, no GLUT1 expression is observed, meanwhile autophagy, essential for KRAS mutant cancer cells, is blocked. Corresponding to our system biological analysis, this combined pharmacologic ascorbate and chloroquine treatment in KRAS mutant cancers might be a therapeutic approach in anti-cancer therapies.

Dynamical analysis of the fission yeast cell cycle via Markov chain

The cell cycle is a complex network involved in the regulation of cell growth and proliferation. Intrinsic molecular noise in gene expression in the cell cycle network can generate fluctuations in protein concentration. How the cell cycle network maintains its robust transitions between cell cycle phases in the presence of these fluctuations remains unclear. To understand the complex and robust behavior of the cell cycle system in the presence of intrinsic noise, we developed a Markov model for the fission yeast cell cycle system. We quantified the effect of noise on gene and protein activity and on the probability of transition between different phases of the cell cycle. Our analysis shows how network perturbations decide the fate of the cell. Our model predicts that the cell cycle pathway (subsequent transitions from [Formula: see text]) is the most robust and probable pathway among all possible trajectories in the cell cycle network. We performed a sensitivity analysis to find correlations between protein interaction weights and transition probabilities between cell cycle phases. The sensitivity analysis predicts how network perturbations affect the transition probability between different cell cycle phases and, consequently, affect different cell fates, thus, forming testable in vitro/in vivo hypotheses. Our simulation results agree with published experimental findings and reveal how noise in the cell cycle regulatory network can affect cell cycle progression.

Computational modeling of chromosome re-replication in mutant strains of fission yeast

Typically cells replicate their genome only once per division cycle, but under some circumstances, both natural and unnatural, cells synthesize an overabundance of DNA, either in a disorganized manner (“overreplication”) or by a systematic doubling of chromosome number (“endoreplication”). These variations on the theme of DNA replication and division have been studied in strains of fission yeast, Schizosaccharomyces pombe, carrying mutations that interfere with the function of mitotic cyclin-dependent kinase (Cdk1:Cdc13) without impeding the roles of DNA-replication loading factor (Cdc18) and S-phase cyclin-dependent kinase (Cdk1:Cig2). Some of these mutations support endoreplication, and some overreplication. In this paper, we propose a dynamical model of the interactions among the proteins governing DNA replication and cell division in fission yeast. By computational simulations of the mathematical model, we account for the observed phenotypes of these re-replicating mutants, and by theoretical analysis of the dynamical system, we provide insight into the molecular distinctions between overreplicating and endoreplicating cells. In the case of induced overproduction of regulatory proteins, our model predicts that cells first switch from normal mitotic cell cycles to growth-controlled endoreplication, and ultimately to disorganized overreplication, parallel to the slow increase of protein to very high levels.

Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.

Many systems in nature show bistability, which means they can evolve to one of two stable steady states under exactly the same conditions. Which state they evolve to depends on where the system comes from. Such bistability underlies the switching behavior that is essential for cells to progress in the cell division cycle. A quick switch happens when the cell jumps from one steady state to another steady state. Typical of this switching behavior is its robustness and irreversibility. In this paper, we expand this viewpoint of the dynamics of the cell cycle by considering bistable switches which themselves are changing in time. This gives the cell an extra layer of control over transitions both in time and in space, and can make those transitions more robust. Such dynamically changing bistability can appear very naturally. We show this in a model of mitotic entry, in which we include a nuclear and cytoplasmic compartment. The activity of a crucial cell cycle protein follows a bistable switch in each compartment, but the shape of its response is changing in time as proteins are imported into and exported from the nucleus.

Single Cell Characterization of a Synthetic Bacterial Clock with a Hybrid Feedback Loop Containing dCas9-sgRNA

Genetic networks that generate oscillations in gene expression activity are found in a wide range of organisms throughout all kingdoms of life. Oscillatory dynamics facilitates the temporal orchestration of metabolic and growth processes inside cells and organisms, as well as the synchronization of such processes with periodically occurring changes in the environment. Synthetic oscillator gene circuits such as the "repressilator" can perform similar functions in bacteria. Until recently, such circuits were mainly based on a relatively small set of well-characterized transcriptional repressors and activators. A promising, sequence-programmable alternative for gene regulation is given by CRISPR interference (CRISPRi), which enables transcriptional repression of nearly arbitrary gene targets directed by short guide RNA molecules. In order to demonstrate the use of CRISPRi in the context of dynamic gene circuits, we here replaced one of the nodes of a repressilator circuit by the RNA-guided dCas9 protein. Using single cell experiments in microfluidic reactors we show that this system displays robust relaxation oscillations over multiple periods and over several days. With a period of ≈14 bacterial generations, our oscillator is similar in speed as previously reported oscillators. Using an information-theoretic approach for the analysis of the single cell data, the potential of the circuit to act as a synthetic pacemaker for cellular processes is evaluated. We also observe that the oscillator appears to affect cellular growth, leading to variations in growth rate with the oscillator's frequency.

Gene expression oscillations in C. elegans underlie a new developmental clock

During C. elegans larval development, thousands of genes, accounting for >20% of the transcriptome, exhibit oscillatory expression with large amplitudes. The time of peaking varies for different genes, but expression generally peaks once per larval stage, with both the oscillation period and larval stage duration varying in concert with temperature. This and other evidence support the existence of a gene expression oscillator that functions as a developmental clock. In this article, we review what is known about the biology, architecture and possible mechanisms of this clock. We compare it to other oscillators, and highlight tools and approaches suited to its study. Finally, we point out implications of these wide-spread and dynamic changes of gene expression on any type of gene expression profiling experiment in C. elegans larvae and how such experiments need to be controlled.

Carvone Decreases Melanin Content by Inhibiting Melanoma Cell Proliferation via the Cyclic Adenosine Monophosphate (cAMP) Pathway

Melanin, which determines the color of the skin and hair, is initially synthesized to protect the skin from ultraviolet light; however, excessive melanin pigmentation caused by abnormal cell proliferation can result in various melanocytic lesions. Cyclic adenosine monophosphate (cAMP) is known to regulate cell cycle progression and consequently to inhibit the division of abnormally proliferating cells. In this work, we aimed to test whether carvone, a scent compound from plants, inhibits proliferation and subsequently reduces melanin content of melanoma cells and to determine whether its beneficial effects are mediated by the cAMP pathway. We found that carvone decreases melanin content and inhibits melanoma cell proliferation in a concentration-dependent manner. Meanwhile, it inhibited the activation of cell cycle-associated proteins such as cyclin-dependent kinase 1 (CDK1). Of note, the beneficial effects of carvone were abrogated by cAMP inhibition. Our findings indicate potential benefits of carvone for the treatment of melanomas and presumably other hyperpigmentation-related dermatological disorders such as melasmas, lentigines, and excessive freckles.

Modeling the Control of Meiotic Cell Divisions: Entry, Progression, and Exit

Upon nitrogen starvation, Schizosaccharomyces pombe exit the mitotic cell cycle and become irreversibly committed to the completion of meiosis program. Meiotic cell divisions are coordinated with sporulation events to produce haploid spores. In the last few decades, experiments on fission yeast have revealed different molecular players involved in two meiotic cell divisions, meiosis I (MI) and meiosis II (MII). How the MI entry, MI-to-MII transition, and MII exit occur because of the dynamics of the regulatory network is not well understood. In this work, we developed a comprehensive mathematical model of the network that describes the temporal dynamics of meiotic progression. The model accounts for the phenotypes of several experimental data (single and multiple mutations). We demonstrate the control strategy involving multiple feedback loops to yield two successive division cycles. The differential regulation of anaphase-promoting complex/cyclosome (APC/C) coactivators and its inhibitors is crucial for the dynamics of both MI-to-MII transition and MII exit. This model generates mechanistic insights that help in further experiments and modeling.

Developmental function and state transitions of a gene expression oscillator in Caenorhabditis elegans

Gene expression oscillators can structure biological events temporally and spatially. Different biological functions benefit from distinct oscillator properties. Thus, finite developmental processes rely on oscillators that start and stop at specific times, a poorly understood behavior. Here, we have characterized a massive gene expression oscillator comprising > 3,700 genes in Caenorhabditis elegans larvae. We report that oscillations initiate in embryos, arrest transiently after hatching and in response to perturbation, and cease in adults. Experimental observation of the transitions between oscillatory and non-oscillatory states at high temporal resolution reveals an oscillator operating near a Saddle Node on Invariant Cycle (SNIC) bifurcation. These findings constrain the architecture and mathematical models that can represent this oscillator. They also reveal that oscillator arrests occur reproducibly in a specific phase. Since we find oscillations to be coupled to developmental processes, including molting, this characteristic of SNIC bifurcations endows the oscillator with the potential to halt larval development at defined intervals, and thereby execute a developmental checkpoint function.

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.

Porcine Epidemic Diarrhoea Virus Induces Cell-cycle Arrest through the DNA Damage-signalling Pathway

Introduction

Porcine epidemic diarrhoea virus (PEDV) infection causes watery diarrhoea, vomiting, anorexia, and weight loss, especially among neonatal piglets, inflicting on them morbidity and mortality potentially reaching 90%–100%. Despite it being known that certain mammalian cell phases are arrested by PEDV, the mechanisms have not been elucidated, and PEDV pathogenesis is poorly understood. This study determined the effect of an epidemic PEDV strain on cell cycle progression.

Material and Methods

We observed the effect of the PEDV SHpd/2012 strain on an infected Vero cell cycle through flow cytometry and Western blot, investigating the interrelationships of cell-cycle arrest, the DNA damage–signalling pathway caused by PEDV and the phosphorylation levels of the key molecules Chk.2 and H2A.X involved upstream and downstream in this pathway.

Results

PEDV induced Vero cell-cycle arrest at the G1/G0 phase. The phosphorylation levels of Chk.2 and H2A.X increased with the prolongation of PEDV infection, and no significant cell-cycle arrest was observed after treatment with ATM or Chk.2 inhibitors. The proliferation of PEDV was also inhibited by treatment with ATM or Chk.2 inhibitors.

Conclusion

PEDV-induced cell-cycle arrest is associated with activation of DNA damage–signalling pathways. Our findings elucidate the molecular basis of PEDV replication and provide evidence to support further evaluation of PEDV pathogenesis.

A Mathematical Model for the Effect of Low-Dose Radiation on the G2/M Transition

We develop a mathematical model to study the immediate effect of low-dose radiation on the G2 checkpoint and the G2/M transition of the cell cycle via a radiation pathway (the ATM-Chk2 pathway) of an individual mammalian cell. The model consists of a system of nonlinear differential equations describing the dynamics of a network of regulatory proteins that play key roles in the G2/M transition, cell cycle oscillations, and the radiation pathway. We simulate the application of a single pulse of low-dose radiation at different intensities ([Formula: see text] 0-0.4 Gy) and times during the latter part of the G2-phase. We use bifurcation analysis to characterize the effect of radiation on the G2/M transition via the ATM-Chk2 pathway. We show that radiation between 0.1 and 0.3 Gy can delay the G2/M transition, and radiation higher than 0.3 Gy can fully activate the G2 checkpoint. Also, our results show that radiation can be low enough to neither delay the G2/M transition nor activate the G2 checkpoint ([Formula: see text] 0.1 Gy). Our model supports the idea that the cell response to radiation during G2-phase explains hyper-radiosensitivity and increased radioresistance (HRS/IRR) observed at low dose.

An Inactivation Switch Enables Rhythms in a Neurospora Clock Model

Autonomous endogenous time-keeping is ubiquitous across many living organisms, known as the circadian clock when it has a period of about 24 h. Interestingly, the fundamental design principle with a network of interconnected negative and positive feedback loops is conserved through evolution, although the molecular components differ. Filamentous fungus Neurospora crassa is a well-established chrono-genetics model organism to investigate the underlying mechanisms. The core negative feedback loop of the clock of Neurospora is composed of the transcription activator White Collar Complex (WCC) (heterodimer of WC1 and WC2) and the inhibitory element called FFC complex, which is made of FRQ (Frequency protein), FRH (Frequency interacting RNA Helicase) and CK1a (Casein kinase 1a). While exploring their temporal dynamics, we investigate how limit cycle oscillations arise and how molecular switches support self-sustained rhythms. We develop a mathematical model of 10 variables with 26 parameters to understand the interactions and feedback among WC1 and FFC elements in nuclear and cytoplasmic compartments. We performed control and bifurcation analysis to show that our novel model produces robust oscillations with a wild-type period of 22.5 h. Our model reveals a switch between WC1-induced transcription and FFC-assisted inactivation of WC1. Using the new model, we also study the possible mechanisms of glucose compensation. A fairly simple model with just three nonlinearities helps to elucidate clock dynamics, revealing a mechanism of rhythms' production. The model can further be utilized to study entrainment and temperature compensation.

Parameter estimation in models of biological oscillators: an automated regularised estimation approach

BACKGROUND

Dynamic modelling is a core element in the systems biology approach to understanding complex biosystems. Here, we consider the problem of parameter estimation in models of biological oscillators described by deterministic nonlinear differential equations. These problems can be extremely challenging due to several common pitfalls: (i) a lack of prior knowledge about parameters (i.e. massive search spaces), (ii) convergence to local optima (due to multimodality of the cost function), (iii) overfitting (fitting the noise instead of the signal) and (iv) a lack of identifiability. As a consequence, the use of standard estimation methods (such as gradient-based local ones) will often result in wrong solutions. Overfitting can be particularly problematic, since it produces very good calibrations, giving the impression of an excellent result. However, overfitted models exhibit poor predictive power. Here, we present a novel automated approach to overcome these pitfalls. Its workflow makes use of two sequential optimisation steps incorporating three key algorithms: (1) sampling strategies to systematically tighten the parameter bounds reducing the search space, (2) efficient global optimisation to avoid convergence to local solutions, (3) an advanced regularisation technique to fight overfitting. In addition, this workflow incorporates tests for structural and practical identifiability.

RESULTS

We successfully evaluate this novel approach considering four difficult case studies regarding the calibration of well-known biological oscillators (Goodwin, FitzHugh-Nagumo, Repressilator and a metabolic oscillator). In contrast, we show how local gradient-based approaches, even if used in multi-start fashion, are unable to avoid the above-mentioned pitfalls.

CONCLUSIONS

Our approach results in more efficient estimations (thanks to the bounding strategy) which are able to escape convergence to local optima (thanks to the global optimisation approach). Further, the use of regularisation allows us to avoid overfitting, resulting in more generalisable calibrated models (i.e. models with greater predictive power).

Adding phosphorylation events to the core oscillator driving the cell cycle of fission yeast

Much is known about the regulatory elements controlling the cell cycle in fission yeast (Schizosaccharomyces pombe). This regulation is mainly done by the (cyclin-dependent kinase/cyclin) complex (Cdc2/Cdc13) that activates specific target genes and proteins via phosphorylation events during the cell cycle in a time-dependent manner. However, more work is still needed to complement the existing gaps in the current fission yeast gene regulatory network to be able to overcome abnormalities in its growth, repair and development, i.e. explain many phenomena including mitotic catastrophe. In this work we complement the previously presented core oscillator of the cell cycle of fission yeast by selected phosphorylation events and study their effects on the temporal evolution of the core oscillator based Boolean network. Thereby, we attempt to establish a regulatory link between the autonomous cell cycle oscillator and the remainder of the cell. We suggest the unclear yet regulatory effect of phosphorylation on the added components, and discuss many unreported points regarding the temporal evolution of the cell cycle and its components. To better visualize the results regardless of the programming background we developed an Android application that can be used to run the core and extended model of the fission yeast cell cycle step by step.

A theoretical study on the cross-talk of stress regulatory pathways in root cells

The plants developed more dedicated regulatory pathways than the animals did to response various environment stresses, since they could not run away. The cross-talk among the pathways generally introduce non-trivial regulatory behaviors, from which the plants may benefit. For better understanding the regulatory mechanism due to cross-talk, we study in this work two entangled stress regulatory pathways in root cells. A quantitative model of the regulatory network is constructed in the simplest fashion. An analytic parameter-free approach is then employed to analyse the response tendencies. It leads us to a simple constraint on the non-linear regulatory exponents. Under the constraint, a transition to the non-monotonic growth inhibition happens at finite concentration of ABA, due to which the plants could survive from cold/heat stress. The parameter-free tendency analysis would also be applied to further experiments, especially in the case of insufficient data for multi-parameter fitting.

A toolbox for discrete modelling of cell signalling dynamics

We present a library of network motifs for the development of complex and realistic biological network models using the BioModelAnalyzer, and demonstrate their wider value by using them to construct a model of the cell cycle.

Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation

A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change. An oscillatory protein synthesis model whose properties are modulated by RNA interference is used as an example. This model consists of a set of coupled delay-differential equations involving three delays. Sensitivity analyses are carried out at several operating points. Comments on the evolutionary implications of the results are offered.

Molecular Network Dynamics of Cell Cycle Control: Periodicity of Start and Finish

The cell division cycle is controlled by a complex regulatory network which ensures that the phases of the cell cycle are executed in the right order. This regulatory network receives signals from the environment, monitors the state of the DNA, and decides timings of cell cycle events. The underlying transcriptional and post-translational regulatory interactions lead to complex dynamical responses, such as the oscillations in the levels of cell cycle proteins driven by intertwined biochemical reactions. A cell moves between different phases of its cycle similar to a dynamical system switching between its steady states. The complex molecular network driving these phases has been investigated in previous computational systems biology studies. Here, we review the critical physiological and molecular transitions that occur in the cell cycle and discuss the role of mathematical modeling in elucidating these transitions and understand cell cycle synchronization.

Recurrent neural network based hybrid model for reconstructing gene regulatory network

One of the exciting problems in systems biology research is to decipher how genome controls the development of complex biological system. The gene regulatory networks (GRNs) help in the identification of regulatory interactions between genes and offer fruitful information related to functional role of individual gene in a cellular system. Discovering GRNs lead to a wide range of applications, including identification of disease related pathways providing novel tentative drug targets, helps to predict disease response, and also assists in diagnosing various diseases including cancer. Reconstruction of GRNs from available biological data is still an open problem. This paper proposes a recurrent neural network (RNN) based model of GRN, hybridized with generalized extended Kalman filter for weight update in backpropagation through time training algorithm. The RNN is a complex neural network that gives a better settlement between biological closeness and mathematical flexibility to model GRN; and is also able to capture complex, non-linear and dynamic relationships among variables. Gene expression data are inherently noisy and Kalman filter performs well for estimation problem even in noisy data. Hence, we applied non-linear version of Kalman filter, known as generalized extended Kalman filter, for weight update during RNN training. The developed model has been tested on four benchmark networks such as DNA SOS repair network, IRMA network, and two synthetic networks from DREAM Challenge. We performed a comparison of our results with other state-of-the-art techniques which shows superiority of our proposed model. Further, 5% Gaussian noise has been induced in the dataset and result of the proposed model shows negligible effect of noise on results, demonstrating the noise tolerance capability of the model.

A self-regulating biomolecular comparator for processing oscillatory signals

While many cellular processes are driven by biomolecular oscillators, precise control of a downstream on/off process by a biochemical oscillator signal can be difficult: over an oscillator's period, its output signal varies continuously between its amplitude limits and spends a significant fraction of the time at intermediate values between these limits. Further, the oscillator's output is often noisy, with particularly large variations in the amplitude. In electronic systems, an oscillating signal is generally processed by a downstream device such as a comparator that converts a potentially noisy oscillatory input into a square wave output that is predominantly in one of two well-defined on and off states. The comparator's output then controls downstream processes. We describe a method for constructing a synthetic biochemical device that likewise produces a square-wave-type biomolecular output for a variety of oscillatory inputs. The method relies on a separation of time scales between the slow rate of production of an oscillatory signal molecule and the fast rates of intermolecular binding and conformational changes. We show how to control the characteristics of the output by varying the concentrations of the species and the reaction rates. We then use this control to show how our approach could be applied to process different in vitro and in vivo biomolecular oscillators, including the p53-Mdm2 transcriptional oscillator and two types of in vitro transcriptional oscillators. These results demonstrate how modular biomolecular circuits could, in principle, be combined to build complex dynamical systems. The simplicity of our approach also suggests that natural molecular circuits may process some biomolecular oscillator outputs before they are applied downstream.

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.

Nutritional Control of Cell Size by the Greatwall-Endosulfine-PP2A·B55 Pathway

Proliferating cells adjust their cell size depending on the nutritional environment. Cells are large in rich media and small in poor media. This physiological response has been demonstrated in both unicellular and multicellular organisms. Here we show that the greatwall-endosulfine (Ppk18-Igo1 in fission yeast) pathway couples the nutritional environment to the cell-cycle machinery by regulating the activity of PP2A·B55. In the presence of nutrients, greatwall (Ppk18) protein kinase is inhibited by TORC1 and PP2A·B55 is active. High levels of PP2A·B55 prevent the activation of mitotic Cdk1·Cyclin B, and cells increase in size in G2 before they undergo mitosis. When nutrients are limiting, TORC1 activity falls off, and the activation of greatwall (Ppk18) leads to the phosphorylation of endosulfine (Igo1) and inhibition of PP2A·B55, which in turn allows full activation of Cdk1·CyclinB and entry into mitosis with a smaller cell size. Given the conservation of this pathway, it is reasonable to assume that this mechanism operates in higher eukaryotes, as well.