A kinetic model of the cyclin E/Cdk2 developmental timer in Xenopus laevis embryos

Learning in Transcriptional Network Models: Computational Discovery of Pathway-Level Memory and Effective Interventions

Trainability, in any substrate, refers to the ability to change future behavior based on past experiences. An understanding of such capacity within biological cells and tissues would enable a particularly powerful set of methods for prediction and control of their behavior through specific patterns of stimuli. This top-down mode of control (as an alternative to bottom-up modification of hardware) has been extensively exploited by computer science and the behavioral sciences; in biology however, it is usually reserved for organism-level behavior in animals with brains, such as training animals towards a desired response. Exciting work in the field of basal cognition has begun to reveal degrees and forms of unconventional memory in non-neural tissues and even in subcellular biochemical dynamics. Here, we characterize biological gene regulatory circuit models and protein pathways and find them capable of several different kinds of memory. We extend prior results on learning in binary transcriptional networks to continuous models and identify specific interventions (regimes of stimulation, as opposed to network rewiring) that abolish undesirable network behavior such as drug pharmacoresistance and drug sensitization. We also explore the stability of created memories by assessing their long-term behavior and find that most memories do not decay over long time periods. Additionally, we find that the memory properties are quite robust to noise; surprisingly, in many cases noise actually increases memory potential. We examine various network properties associated with these behaviors and find that no one network property is indicative of memory. Random networks do not show similar memory behavior as models of biological processes, indicating that generic network dynamics are not solely responsible for trainability. Rational control of dynamic pathway function using stimuli derived from computational models opens the door to empirical studies of proto-cognitive capacities in unconventional embodiments and suggests numerous possible applications in biomedicine, where behavior shaping of pathway responses stand as a potential alternative to gene therapy.

Mathematical modeling of the female reproductive system: from oocyte to delivery

From ovulation to delivery, and through the menstrual cycle, the female reproductive system undergoes many dynamic changes to provide an optimal environment for the embryo to implant, and to develop successfully. It is difficult ethically and practically to observe the system over the timescales involved in growth and development (often hours to days). Even in carefully monitored conditions clinicians and biologists can only see snapshots of the development process. Mathematical models are emerging as a key means to supplement our knowledge of the reproductive process, and to tease apart complexity in the reproductive system. These models have been used successfully to test existing hypotheses regarding the mechanisms of female infertility and pathological fetal development, and also to provide new experimentally testable hypotheses regarding the process of development. This new knowledge has allowed for improvements in assisted reproductive technologies and is moving toward translation to clinical practice via multiscale assessments of the dynamics of ovulation, development in pregnancy, and the timing and mechanics of delivery. WIREs Syst Biol Med 2017, 9:e1353. doi: 10.1002/wsbm.1353 For further resources related to this article, please visit the WIREs website.

Crosstalks between cytokines and Sonic Hedgehog in Helicobacter pylori infection: a mathematical model

Helicobacter pylori infection of gastric tissue results in an immune response dominated by Th1 cytokines and has also been linked with dysregulation of Sonic Hedgehog (SHH) signaling pathway in gastric tissue. However, since interactions between the cytokines and SHH during H. pylori infection are not well understood, any mechanistic understanding achieved through interpretation of the statistical analysis of experimental results in the context of currently known circuit must be carefully scrutinized. Here, we use mathematical modeling aided by restraints of experimental data to evaluate the consistency between experimental results and temporal behavior of H. pylori activated cytokine circuit model. Statistical analysis of qPCR data from uninfected and H. pylori infected wild-type and parietal cell-specific SHH knockout (PC-SHH^KO) mice for day 7 and 180 indicate significant changes that suggest role of SHH in cytokine regulation. The experimentally observed changes are further investigated using a mathematical model that examines dynamic crosstalks among pro-inflammatory (IL1β, IL-12, IFNγ, MIP-2) cytokines, anti-inflammatory (IL-10) cytokines and SHH during H. pylori infection. Response analysis of the resulting model demonstrates that circuitry, as currently known, is inadequate for explaining of the experimental observations; suggesting the need for additional specific regulatory interactions. A key advantage of a computational model is the ability to propose putative circuit models for in-silico experimentation. We use this approach to propose a parsimonious model that incorporates crosstalks between NFĸB, SHH, IL-1β and IL-10, resulting in a feedback loop capable of exhibiting cyclic behavior. Separately, we show that analysis of an independent time-series GEO microarray data for IL-1β, IFNγ and IL-10 in mock and H. pylori infected mice further supports the proposed hypothesis that these cytokines may follow a cyclic trend. Predictions from the in-silico model provide useful insights for generating new hypothesis and design of subsequent experimental studies.

Phosphorylation of Claspin is triggered by the nucleocytoplasmic ratio at the Xenopus laevis midblastula transition

At the Xenopus midblastula transition (MBT), cell cycles lengthen, and checkpoints that respond to damaged or unreplicated DNA are established. The MBT is triggered by a critical nucleocytoplasmic (N/C) ratio; however, the molecular basis for its initiation remains unknown. In egg extracts, activation of Chk1 checkpoint kinase requires the adaptor protein Claspin, which recruits Chk1 for phosphorylation by ATR. At the MBT in embryos, Chk1 is transiently activated to lengthen the cell cycle. We show that Xenopus Claspin is phosphorylated at the MBT at both DNA replication checkpoint-dependent and -independent sites. Further, in egg extracts, Claspin phosphorylation depends on a threshold N/C ratio, but occurs even when ATR is inhibited. Not all phosphorylation that occurs at the MBT is reproduced in egg extracts. Our results identify Claspin as the most upstream molecule in the signaling pathway that responds to the N/C ratio and indicate that Claspin may also respond to an independent timer to trigger the MBT and activation of cell cycle checkpoints.

Computational systems biology of the cell cycle

One of the early success stories of computational systems biology was the work done on cell-cycle regulation. The earliest mathematical descriptions of cell-cycle control evolved into very complex, detailed computational models that describe the regulation of cell division in many different cell types. On the way these models predicted several dynamical properties and unknown components of the system that were later experimentally verified/identified. Still, research on this field is far from over. We need to understand how the core cell-cycle machinery is controlled by internal and external signals, also in yeast cells and in the more complex regulatory networks of higher eukaryotes. Furthermore, there are many computational challenges what we face as new types of data appear thanks to continuing advances in experimental techniques. We have to deal with cell-to-cell variations, revealed by single cell measurements, as well as the tremendous amount of data flowing from high throughput machines. We need new computational concepts and tools to handle these data and develop more detailed, more precise models of cell-cycle regulation in various organisms. Here we review past and present of computational modeling of cell-cycle regulation, and discuss possible future directions of the field.

Wee1 kinase alters cyclin E/Cdk2 and promotes apoptosis during the early embryonic development of Xenopus laevis

Background

The cell cycles of the Xenopus laevis embryo undergo extensive remodeling beginning at the midblastula transition (MBT) of early development. Cell divisions 2–12 consist of rapid cleavages without gap phases or cell cycle checkpoints. Some remodeling events depend upon a critical nucleo-cytoplasmic ratio, whereas others rely on a maternal timer controlled by cyclin E/Cdk2 activity. One key event that occurs at the MBT is the degradation of maternal Wee1, a negative regulator of cyclin-dependent kinase (Cdk) activity.

Results

In order to assess the effect of Wee1 on embryonic cell cycle remodeling, Wee1 mRNA was injected into one-cell stage embryos. Overexpression of Wee1 caused cell cycle delay and tyrosine phosphorylation of Cdks prior to the MBT. Furthermore, overexpression of Wee1 disrupted key developmental events that normally occur at the MBT such as the degradation of Cdc25A, cyclin E, and Wee1. Overexpression of Wee1 also resulted in post-MBT apoptosis, tyrosine phosphorylation of Cdks and persistence of cyclin E/Cdk2 activity. To determine whether Cdk2 was required specifically for the survival of the embryo, the cyclin E/Cdk2 inhibitor, Δ34-Xic1, was injected in embryos and also shown to induce apoptosis.

Conclusion

Taken together, these data suggest that Wee1 triggers apoptosis through the disruption of the cyclin E/Cdk2 timer. In contrast to Wee1 and Δ34-Xic1, altering Cdks by expression of Chk1 and Chk2 kinases blocks rather than promotes apoptosis and causes premature degradation of Cdc25A. Collectively, these data implicate Cdc25A as a key player in the developmentally regulated program of apoptosis in X. laevis embryos.

Modeling biochemical transformation processes and information processing with Narrator

Background

Software tools that model and simulate the dynamics of biological processes and systems are becoming increasingly important. Some of these tools offer sophisticated graphical user interfaces (GUIs), which greatly enhance their acceptance by users. Such GUIs are based on symbolic or graphical notations used to describe, interact and communicate the developed models. Typically, these graphical notations are geared towards conventional biochemical pathway diagrams. They permit the user to represent the transport and transformation of chemical species and to define inhibitory and stimulatory dependencies. A critical weakness of existing tools is their lack of supporting an integrative representation of transport, transformation as well as biological information processing.

Results

Narrator is a software tool facilitating the development and simulation of biological systems as Co-dependence models. The Co-dependence Methodology complements the representation of species transport and transformation together with an explicit mechanism to express biological information processing. Thus, Co-dependence models explicitly capture, for instance, signal processing structures and the influence of exogenous factors or events affecting certain parts of a biological system or process. This combined set of features provides the system biologist with a powerful tool to describe and explore the dynamics of life phenomena. Narrator's GUI is based on an expressive graphical notation which forms an integral part of the Co-dependence Methodology. Behind the user-friendly GUI, Narrator hides a flexible feature which makes it relatively easy to map models defined via the graphical notation to mathematical formalisms and languages such as ordinary differential equations, the Systems Biology Markup Language or Gillespie's direct method. This powerful feature facilitates reuse, interoperability and conceptual model development.

Conclusion

Narrator is a flexible and intuitive systems biology tool. It is specifically intended for users aiming to construct and simulate dynamic models of biology without recourse to extensive mathematical detail. Its design facilitates mappings to different formal languages and frameworks. The combined set of features makes Narrator unique among tools of its kind. Narrator is implemented as Java software program and available as open-source from .

The ups and downs of biological timers

BACKGROUND

The need to execute a sequence of events in an orderly and timely manner is central to many biological processes, including cell cycle progression and cell differentiation. For self-perpetuating systems, such as the cell cycle oscillator, delay times between events are defined by the network of interacting proteins that propagates the system. However, protein levels inside cells are subject to genetic and environmental fluctuations, raising the question of how reliable timing is maintained.

RESULTS

We compared the robustness of different mechanisms for encoding delay times to fluctuations in protein expression levels. Gradual accumulation and gradual decay of a regulatory protein have an equivalent capacity for defining delay times. Yet, we find that the former is highly sensitive to fluctuations in gene dosage, while the latter can buffer such perturbations. In particular, a positive feedback where the degrading protein auto-enhances its own degradation may render delay times practically insensitive to gene dosage.

CONCLUSION

While our understanding of biological timing mechanisms is still rudimentary, it is clear that there is an ample use of degradation as well as self-enhanced degradation in processes such as cell cycle and circadian clocks. We propose that degradation processes, and specifically self-enhanced degradation, will be preferred in processes where maintaining the robustness of timing is important.

Multisite phosphorylation and network dynamics of cyclin-dependent kinase signaling in the eukaryotic cell cycle

Multisite phosphorylation of regulatory proteins has been proposed to underlie ultrasensitive responses required to generate nontrivial dynamics in complex biological signaling networks. We used a random search strategy to analyze the role of multisite phosphorylation of key proteins regulating cyclin-dependent kinase (CDK) activity in a model of the eukaryotic cell cycle. We show that multisite phosphorylation of either CDK, CDC25, wee1, or CDK-activating kinase is sufficient to generate dynamical behaviors including bistability and limit cycles. Moreover, combining multiple feedback loops based on multisite phosphorylation do not destabilize the cell cycle network by inducing complex behavior, but rather increase the overall robustness of the network. In this model we find that bistability is the major dynamical behavior of the CDK signaling network, and that negative feedback converts bistability into limit cycle behavior. We also compare the dynamical behavior of several simplified models of CDK regulation to the fully detailed model. In summary, our findings suggest that multisite phosphorylation of proteins is a critical biological mechanism in generating the essential dynamics and ensuring robust behavior of the cell cycle.

Hysteresis and cell cycle transitions: how crucial is it?

Recently, experiments have shown that cyclin-dependent kinase (CDK) activity exhibits hysteresis in its response to total cyclin when cyclin is made nondegradable and controlled externally. This observation was taken to support mathematical modeling predictions regarding the underlying dynamics of the cell cycle. However, cell cycle dynamics can also be generated by other nonhysteretic mechanisms. To examine the robustness of the hysteretic response of CDK activity to total cyclin, we simulated various cell cycle signal transduction networks, and correlated the dynamics to the response function of CDK activity versus total cyclin. By randomly searching the parameter space, we assessed robustness by estimating the frequency of hysteretic versus nonhysteretic dynamical mechanisms. When the dynamical instabilities were caused by feedback loops in CDK phosphorylation and dephosphorylation or by feedback between cyclin and the CDK inhibitor, the response function of CDK activity versus total cyclin correlated well with the dynamical instabilities. However, when the dynamical instabilities originated from feedback between cyclin and APC-CDH1 or RB-E2F, the response function did not correlate with dynamical instabilities. Thus, although a hysteretic response is neither necessary nor sufficient, it is in general a much more robust mechanism for generating cell cycle dynamics than nonhysteretic mechanisms.

Modeling regulatory networks at Virginia Tech

The life of a cell is governed by the physicochemical properties of a complex network of interacting macromolecules (primarily genes and proteins). Hence, a full scientific understanding of and rational engineering approach to cell physiology require accurate mathematical models of the spatial and temporal dynamics of these macromolecular assemblies, especially the networks involved in integrating signals and regulating cellular responses. The Virginia Tech Consortium is involved in three specific goals of DARPA's computational biology program (Bio-COMP): to create effective software tools for modeling gene-protein-metabolite networks, to employ these tools in creating a new generation of realistic models, and to test and refine these models by well-conceived experimental studies. The special emphasis of this group is to understand the mechanisms of cell cycle control in eukaryotes (yeast cells and frog eggs). The software tools developed at Virginia Tech are designed to meet general requirements of modeling regulatory networks and are collected in a problem-solving environment called JigCell.