Mechanisms that enhance sustainability of p53 pulses

Beyond microtubules: The cellular environment at the endoplasmic reticulum attracts proteins to the nucleus, enabling nuclear transport

All proteins are translated in the cytoplasm, yet many, including transcription factors, play vital roles in the nucleus. While previous research has concentrated on molecular motors for the transport of these proteins to the nucleus, recent observations reveal perinuclear accumulation even in the absence of an energy source, hinting at alternative mechanisms. Here, we propose that structural properties of the cellular environment, specifically the endoplasmic reticulum (ER), can promote molecular transport to the perinucleus without requiring additional energy expenditure. Specifically, physical interaction between proteins and the ER impedes their diffusion and leads to their accumulation near the nucleus. This result explains why larger proteins, more frequently interacting with the ER membrane, tend to accumulate at the perinucleus. Interestingly, such diffusion in a heterogeneous environment follows Chapman's law rather than the popular Fick's law. Our findings suggest a novel protein transport mechanism arising solely from characteristics of the intracellular environment.

Emerging role and therapeutic implications of p53 in intervertebral disc degeneration

Lower back pain (LBP) is a common degenerative musculoskeletal disease that imposes a huge economic burden on both individuals and society. With the aggravation of social aging, the incidence of LBP has increased globally. Intervertebral disc degeneration (IDD) is the primary cause of LBP. Currently, IDD treatment strategies include physiotherapy, medication, and surgery; however, none can address the root cause by ending the degeneration of intervertebral discs (IVDs). However, in recent years, targeted therapy based on specific molecules has brought hope for treating IDD. The tumor suppressor gene p53 produces a transcription factor that regulates cell metabolism and survival. Recently, p53 was shown to play an important role in maintaining IVD microenvironment homeostasis by regulating IVD cell senescence, apoptosis, and metabolism by activating downstream target genes. This study reviews research progress regarding the potential role of p53 in IDD and discusses the challenges of targeting p53 in the treatment of IDD. This review will help to elucidate the pathogenesis of IDD and provide insights for the future development of precision treatments.

Dynamic behavior of the p53-Mdm2 core module under the action of drug Nutlin and dual delays

Nutlin is a family of p53-targeting drugs. It is able to bind to Mdm2, thereby accelerate the accumulation of p53 that is a prominent tumor suppressor. An integrated module of the Nutlin PBK and p53 pathway is composed of positive feedback mediated by Mdm2 mRNA as well as the drug Nutlin and negative feedback mediated by Mdm2 protein. The main research content of our paper is how the time delay of protein synthesis, response time delay of Nutlin drug, the degradation rate of Mdm2, the degradation rate of p53 depended on Mdm2 and the actual dose of Nutlin in the cell affect the oscillatory behavior caused by Hopf bifurcation in the integrated network system of Nutlin PBK and p53 pathways. The stability of the unique positive equilibrium point and the existence of Hopf bifurcation are studied by taking the time delays as the bifurcation parameters and applying bifurcation theory. Based on the normal form theory and central manifold theorem, explicit criteria to determine the Hopf bifurcation direction and stability of the bifurcated periodic solution are established. It is found that the time delays and key parameters in the integrated network system of Nutlin PBK and p53 pathways play an important role in the amplitude and period of p53 oscillation according to the results from the numerical simulation and theoretical calculation. These results may provide us with a better understanding of the biological functions of the p53 pathway and some clues for cancer treatment.

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

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

Towards DNA-damage induced autophagy: A Boolean model of p53-induced cell fate mechanisms

How a cell determines a given phenotype upon damaged DNA is an open problem. Cell fate decisions happen at cell cycle checkpoints and it is becoming clearer that the p53 pathway is a major regulator of cell fate decisions involving apoptosis or senescence upon DNA damage, especially at G1/S. However, recent results suggest that this pathway is also involved in autophagy induction upon DNA damage. To our knowledge, in this work we propose the first model of the DNA damage-induced G1/S checkpoint contemplating the decision between three phenotypes: apoptosis, senescence, and autophagy. The Boolean model is proposed based on experiments with U87 glioblastoma cells using the transfection of miR-16 that can induce a DNA damage response. The wild-type case of the model shows that DNA damage induces the checkpoint and the coexistence of the three phenotypes (tristable dynamics), each with a different probability. We also predict that the positive feedback involving ATM, miR-16, and Wip1 has an influence on the tristable state. The model predictions were compared to experiments of gain and loss of function in other three different cell lines (MCF-7, A549, and U2OS) presenting agreement. For p53-deficient cell lines such as HeLa, H1299, and PC-3, our model contemplates the experimental observation that the alternative AMPK pathway can compensate this deficiency. We conclude that at the G1/S checkpoint the p53 pathway (or, in its absence, the AMPK pathway) can regulate the induction of different phenotypes in a stochastic manner in the U87 cell line and others.

Coupling of cell fate selection model enhances DNA damage response and may underlie BE phenomenon

Double-strand break-induced (DSB) cells send signal that induces DSBs in neighbour cells, resulting in the interaction among cells sharing the same medium. Since p53 network gives oscillatory response to DSBs, such interaction among cells could be modelled as an excitatory coupling of p53 network oscillators. This study proposes a plausible coupling model of three-mode two-dimensional oscillators, which models the p53-mediated cell fate selection in globally coupled DSB-induced cells. The coupled model consists of ATM and Wip1 proteins as variables. The coupling mechanism is realised through ATM variable via a mean-field modelling the bystander signal in the intercellular medium. Investigation of the model reveals that the coupling generates more sensitive DNA damage response by affecting cell fate selection. Additionally, the authors search for the cause-effect relationship between coupled p53 network oscillators and bystander effect (BE) endpoints. For this, they search for the possible values of uncertain parameters that may replicate BE experiments' results. At certain parametric regions, there is a correlation between the outcomes of cell fate and endpoints of BE, suggesting that the intercellular coupling of p53 network may manifest itself as the form of observed BEs.

Integrative data modeling from lung and lymphatic cancer predicts functional roles for miR-34a and miR-16 in cell fate regulation

MiR-34a and miR-16 coordinately control cell cycle checkpoint in non-small cell lung cancer (NSCLC) cells. In cutaneous T-cell lymphoma (CTCL) cells miR-16 regulates a switch between apoptosis and senescence, however the role of miR-34a in this process is unclear. Both miRNAs share many common targets and experimental evidences suggest that they synergistically control the cell-fate regulation of NSCLC. In this work we investigate whether the coordinate action between miR-34a and miR-16 can explain experimental results in multiple cell lines of NSCLC and CTCL. For that we propose a Boolean model of the G1/S checkpoint regulation contemplating the regulatory influences of both miRNAs. Model validation was performed by comparisons with experimental information from the following cell lines: A549, H460, H1299, MyLa and MJ presenting excellent agreement. The model integrates in a single logical framework the mechanisms responsible for cell fate decision in NSCLC and CTCL cells. From the model analysis we suggest that miR-34a is the main controller of miR-16 activity in these cells. The model also allows to investigate perturbations of single or more molecules with the purpose to intervene in cell fate mechanisms of NSCLC and CTCL cells.

Roles of cellular heterogeneity, intrinsic and extrinsic noise in variability of p53 oscillation

The p53 protein is a key mediator of the cellular response to various stress signals. In response to DNA damage, the concentration of p53 can temporally oscillate with fluctuations in both the amplitude and period. The underlying mechanism for p53 variability is not fully understood. Here, we construct a core regulatory network of p53 dynamics comprising the ATM-p53-Wip1 and p53-Mdm2 negative feedback loops. We dissect the contributions of cellular heterogeneity, intrinsic noise, and multiple forms of extrinsic noise to p53 variability in terms of the coefficients of variation of four quantities. Cellular heterogeneity greatly determines the fraction of oscillating cells among a population of isogenic cells. Intrinsic noise-fluctuation in biochemical reactions-has little impact on p53 variability given large amounts of molecules, whereas extrinsic colored noise with proper strength and correlation time contributes much to oscillatory variability in individual cells. With the three sources of noise combined, our results reproduce the experimental observations, suggesting that the long correlation time of colored noise is essential to p53 variability. Compared with previous studies, the current work reveals both the individual and integrated effects of distinct noise sources on p53 variability. This study provides a framework for exploring the variability in oscillations in cellular signaling pathways.

The effect of stochasticity on repair of DNA double strand breaks throughout non-homologous end joining pathway

DNA double strand breaks (DSBs) are the most lethal lesions of DNA induced by ionizing radiation, industrial chemicals and a wide variety of drugs used in chemotherapy. In the context of DNA damage response system modelling, uncertainty may arise in several ways such as number of induced DSBs, kinetic rates and measurement error in observable quantities. Therefore, using the stochastic approaches is imperative to gain further insight into the dynamic behaviour of DSBs repair process. In this article, a continuous-time Markov chain (CTMC) model of the non-homologous end joining (NHEJ) mechanism is formulated according to the DSB complexity. Additionally, a Metropolis Monte Carlo method is used to perform maximum likelihood estimation of the kinetic rate constants. Here, the effects of fluctuating kinetic rates and DSBs induction rate of the NHEJ mechanism are investigated. The stochastic realizations of the total yield of simple and complex DSBs ligation are simulated to compare their asymptotic dynamics. Furthermore, it has been proved that the total yield of DSBs has a normal distribution for sufficiently large number of DSBs. In order to estimate the expected duration of repairing DSBs, the probability distribution of DSBs lifetime is calculated based on the CTMC NHEJ model. Moreover, the variability of total yield of DSBs during constant low-dose radiation is evaluated in the presented model. The findings indicate that in stochastic NHEJ model, when there is no new DSBs induction through the repair process, all DSBs are eventually repaired. However, when DSBs are induced by constant low-dose radiation, a number of DSBs remains un-repaired.

Protein sequestration versus Hill-type repression in circadian clock models

Circadian (∼24 h) clocks are self-sustained endogenous oscillators with which organisms keep track of daily and seasonal time. Circadian clocks frequently rely on interlocked transcriptional-translational feedback loops to generate rhythms that are robust against intrinsic and extrinsic perturbations. To investigate the dynamics and mechanisms of the intracellular feedback loops in circadian clocks, a number of mathematical models have been developed. The majority of the models use Hill functions to describe transcriptional repression in a way that is similar to the Goodwin model. Recently, a new class of models with protein sequestration-based repression has been introduced. Here, the author discusses how this new class of models differs dramatically from those based on Hill-type repression in several fundamental aspects: conditions for rhythm generation, robust network designs and the periods of coupled oscillators. Consistently, these fundamental properties of circadian clocks also differ among Neurospora, Drosophila, and mammals depending on their key transcriptional repression mechanisms (Hill-type repression or protein sequestration). Based on both theoretical and experimental studies, this review highlights the importance of careful modelling of transcriptional repression mechanisms in molecular circadian clocks.

Modeling the role of microRNA-449a in the regulation of the G2/M cell cycle checkpoint in prostate LNCaP cells under ionizing radiation

Recent studies showed that induced microRNA-449a (miR-449a) enhances a G2/M cell cycle checkpoint arrest in prostate cancer (LNCaP) and lung adenocarcinoma cell lines. In the case of LNCaP cells, upregulated miR-449a directly downregulates c-Myc that is required to induce the cell cycle regulators Cdc25A and Cdc2/CyclinB whose inactivation blocks G2 to M phase transition. However, the molecular mechanisms involved are yet unclear, although in other prostate cancer cells the interactions among p53, miR-449a and Sirt-1 can affect the induction of the G2/M arrest. In order to clarify these molecular mechanisms, in this work we propose a boolean model of the G2/M checkpoint arrest regulation contemplating the influence of miR-449a. The model shows that the cell fate determination between two cellular phenotypes: G2/M-Arrest for DNA repair and G2/M-induced apoptosis is stochastic and influenced by miR-449a state of activation. The results were compared with experimental data available presenting agreement. We also found that several feedback loops are involved in this cell fate regulation and we indicate, through in silico gain or loss of function perturbations of genes, which of these feedback loops are more efficient to favor a specific phenotype.

System-based strategies for p53 recovery

The authors have proposed a systems theory-based novel drug design approach for the p53 pathway. The pathway is taken as a dynamic system represented by ordinary differential equations-based mathematical model. Using control engineering practices, the system analysis and subsequent controller design is performed for the re-activation of wild-type p53. p53 revival is discussed for both modes of operation, i.e. the sustained and oscillatory. To define the problem in control system paradigm, modification in the existing mathematical model is performed to incorporate the effect of Nutlin. Attractor point analysis is carried out to select the suitable domain of attraction. A two-loop negative feedback control strategy is devised to drag the system trajectories to the attractor point and to regulate cellular concentration of Nutlin, respectively. An integrated framework is constituted to incorporate the pharmacokinetic effects of Nutlin in the cancerous cells. Bifurcation analysis is also performed on the p53 model to see the conditions for p53 oscillation.

Understanding non-linear effects from Hill-type dynamics with application to decoding of p53 signaling

Analytical equations are derived depicting four possible scenarios resulting from pulsed signaling of a system subject to Hill-type dynamics. Pulsed Hill-type dynamics involves the binding of multiple signal molecules to a receptor and occurs e.g., when transcription factor p53 orchestrates cancer prevention, during calcium signaling, and during circadian rhythms. The scenarios involve: (i) enhancement of high-affinity binders compared to low-affinity ones, (ii) slowing reactions involving high-affinity binders, (iii) transfer of the clocking of low-affinity binders from the signal molecule to the products, and (iv) a unique clocking process that produces incremental increases in the activity of high-affinity binders with each signal pulse. In principle, these mostly non-linear effects could control cellular outcomes. An applications to p53 signaling is developed, with binding to most gene promoters identified as category (iii) responses. However, currently unexplained enhancement of high-affinity promoters such as CDKN1a (p21) by pulsed signaling could be an example of (i). In general, provision for all possible scenarios is required in the design of mathematical models incorporating pulsed Hill-type signaling as some aspect.

Revealing determinants of two-phase dynamics of P53 network under gamma irradiation based on a reduced 2D relaxation oscillator model

This study proposes a two-dimensional (2D) oscillator model of p53 network, which is derived via reducing the multidimensional two-phase dynamics model into a model of ataxia telangiectasia mutated (ATM) and Wip1 variables, and studies the impact of p53-regulators on cell fate decision. First, the authors identify a 6D core oscillator module, then reduce this module into a 2D oscillator model while preserving the qualitative behaviours. The introduced 2D model is shown to be an excitable relaxation oscillator. This oscillator provides a mechanism that leads diverse modes underpinning cell fate, each corresponding to a cell state. To investigate the effects of p53 inhibitors and the intrinsic time delay of Wip1 on the characteristics of oscillations, they introduce also a delay differential equation version of the 2D oscillator. They observe that the suppression of p53 inhibitors decreases the amplitudes of p53 oscillation, though the suppression increases the sustained level of p53. They identify Wip1 and P53DINP1 as possible targets for cancer therapies considering their impact on the oscillator, supported by biological findings. They model some mutations as critical changes of the phase space characteristics. Possible cancer therapeutic strategies are then proposed for preventing these mutations' effects using the phase space approach.

Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation

Biochemical reaction networks (BRNs) in a cell frequently consist of reactions with disparate timescales. The stochastic simulations of such multiscale BRNs are prohibitively slow due to high computational cost for the simulations of fast reactions. One way to resolve this problem uses the fact that fast species regulated by fast reactions quickly equilibrate to their stationary distribution while slow species are unlikely to be changed. Thus, on a slow timescale, fast species can be replaced by their quasi-steady state (QSS): their stationary conditional expectation values for given slow species. As the QSS are determined solely by the state of slow species, such replacement leads to a reduced model, where fast species are eliminated. However, it is challenging to derive the QSS in the presence of nonlinear reactions. While various approximation schemes for the QSS have been developed, they often lead to considerable errors. Here, we propose two classes of multiscale BRNs which can be reduced by deriving an exact QSS rather than approximations. Specifically, if fast species constitute either a feedforward network or a complex balanced network, the reduced model based on the exact QSS can be derived. Such BRNs are frequently observed in a cell as the feedforward network is one of fundamental motifs of gene or protein regulatory networks. Furthermore, complex balanced networks also include various types of fast reversible bindings such as bindings between transcriptional factors and gene regulatory sites. The reduced models based on exact QSS, which can be calculated by the computational packages provided in this work, accurately approximate the slow scale dynamics of the original full model with much lower computational cost.

Dynamics of p53: A Master Decider of Cell Fate

Cellular stress-induced temporal alterations—i.e., dynamics—are typically exemplified by the dynamics of p53 that serve as a master to determine cell fate. p53 dynamics were initially identified as the variations of p53 protein levels. However, a growing number of studies have shown that p53 dynamics are also manifested in variations in the activity, spatial location, and posttranslational modifications of p53 proteins, as well as the interplay among all p53 dynamical features. These are essential in determining a specific outcome of cell fate. In this review, we discuss the importance of the multifaceted features of p53 dynamics and their roles in the cell fate decision process, as well as their potential applications in p53-based cancer therapy. The review provides new insights into p53 signaling pathways and their potentials in the development of new strategies in p53-based cancer therapy.

Screening of Intestinal Crypt Organoids: A Simple Readout for Complex Biology

Oral and intestinal mucositis is a debilitating side effect of radiation treatment. A mouse model of radiation-induced mucositis leads to weight loss and tissue damage, reflecting the human ailment as it responds to keratinocyte growth factor (KGF), the standard-of-care treatment. Cultured intestinal crypt organoids allowed the development of an assay monitoring the effect of treatments of intestinal epithelium to radiation-induced damage. This in vitro assay resembles the mouse model as KGF and roof plate-specific spondin-1 (RSPO1) enhanced crypt organoid recovery following radiation. Screening identified compounds that increased the survival of organoids postradiation. Testing of these compounds revealed that the organoids changed their responses over time. Unbiased transcriptome analysis was performed on crypt organoid cultures at various time points in culture to investigate this adaptive behavior. A number of genes and pathways were found to be modulated over time, providing a rationale for the altered sensitivity of the organoid cultures. This report describes an in vitro assay that reflects aspects of human disease. The assay was used to identify bioactive compounds, which served as probes to interrogate the biology of crypt organoids over prolonged culture. The pathways that are changing over time may offer potential targets for treatment of mucositis.

A reaction-diffusion model for radiation-induced bystander effects

We develop and analyze a reaction-diffusion model to investigate the dynamics of the lifespan of a bystander signal emitted when cells are exposed to radiation. Experimental studies by Mothersill and Seymour 1997, using malignant epithelial cell lines, found that an emitted bystander signal can still cause bystander effects in cells even 60 h after its emission. Several other experiments have also shown that the signal can persist for months and even years. Also, bystander effects have been hypothesized as one of the factors responsible for the phenomenon of low-dose hyper-radiosensitivity and increased radioresistance (HRS/IRR). Here, we confirm this hypothesis with a mathematical model, which we fit to Joiner's data on HRS/IRR in a T98G glioma cell line. Furthermore, we use phase plane analysis to understand the full dynamics of the signal's lifespan. We find that both single and multiple radiation exposure can lead to bystander signals that either persist temporarily or permanently. We also found that, in an heterogeneous environment, the size of the domain exposed to radiation and the number of radiation exposures can determine whether a signal will persist temporarily or permanently. Finally, we use sensitivity analysis to identify those cell parameters that affect the signal's lifespan and the signal-induced cell death the most.

On p53 revival using system oriented drug dosage design

We propose a new paradigm in the drug design for the revival of the p53 pathway in cancer cells. It is shown that the current strategy of using small molecule based Mdm2 inhibitors is not enough to adequately revive p53 in cancerous cells, especially when it comes to the extracting pulsating behavior of p53. This fact has come to notice when a novel method for the drug dosage design is introduced using system oriented concepts. As a test case, small molecule drug Mdm2 repressor Nutlin 3a is considered. The proposed method determines the dose of Nutlin to revive p53 pathway functionality. For this purpose, PBK dynamics of Nutlin have also been integrated with p53 pathway model. The p53 pathway is the focus of researchers for the last thirty years for its pivotal role as a frontline cancer suppressant protein due to its effect on cell cycle checkpoints and cell apoptosis in response to a DNA strand break. That is the reason for finding p53 being absent in more than 50% of tumor cancers. Various drugs have been proposed to revive p53 in cancer cells. Small molecule based drugs are at the foremost and are the subject of advanced clinical trials. The dosage design of these drugs is an important issue. We use control systems concepts to develop the drug dosage so that the cancer cells can be treated in appropriate time. We investigate by using a computational model how p53 protein responds to drug Nutlin 3a, an agent that interferes with the MDM2-mediated p53 regulation. The proposed integrated model describes in some detail the regulation network of p53 including the negative feedback loop mediated by MDM2 and the positive feedback loop mediated by Mdm2 mRNA as well as the reversible represses of MDM2 caused by Nutlin. The reported PBK dynamics of Nutlin 3a are also incorporated to see the full effect. It has been reported that p53 response to stresses in two ways. Either it has a sustained (constant) p53 response, or there are oscillations in p53 concentration. The claimed dosage strategy achieves the p53 response in the first case. However, for the induction of oscillations, it is shown through bifurcation analysis that to achieve oscillating behavior of p53 inhibition of Mdm2 is not enough, rather antirepression of the p53-Mdm2 complex is also needed which leads to the need of a new drug design paradigm.

Comparison of cellular oscillations driven by noise or deterministic mechanisms under cell-size scaling

Ultradian cycles are frequently observed in biological systems. They serve important roles in regulating, for example, cell fate and the development of the organism. Many mathematical models have been developed to analyze their behavior. Generally, these models can be classified into two classes: Deterministic models that generate oscillatory behavior by incorporating time delays or Hopf bifurcations, and stochastic models that generate oscillatory behavior by noise driven resonance. However, it is still unclear which of these two mechanisms applies to cellular oscillations. In this paper, we show through theoretical analysis and numerical simulation that we can distinguish which of these two mechanisms govern cellular oscillations, by measuring statistics of oscillation amplitudes for cells of different sizes. We found that, for oscillations driven deterministically, the normalized average amplitude is constant with respect to cell size, while the coefficient of variation of the amplitude scales with cell size with an exponent of -0.5. On the other hand, for oscillations driven stochastically, the coefficient of variation of the amplitude is constant with respect to cell size, while the normalized average amplitude scales with cell size with an exponent of -0.5. Our results provide a theoretical basis to discern whether a particular oscillatory behavior is governed by a deterministic or stochastic mechanism.

Model-driven experimental approach reveals the complex regulatory distribution of p53 by the circadian factor Period 2

The circadian clock and cell cycle networks are interlocked on the molecular level, with the core clock loop exerting a multilevel regulatory role over cell cycle components. This is particularly relevant to the circadian factor Period 2 (Per2), which modulates the stability of the tumor suppressor p53 in unstressed cells and transcriptional activity in response to genotoxic stress. Per2 binding prevents Mdm2-mediated ubiquitination of p53 and, therefore, its degradation, and oscillations in the peaks of Per2 and p53 were expected to correspond. However, our findings showed that Per2 and p53 rhythms were significantly out-of-phase relative to each other in cell lysates and in purified cytoplasmic fractions. These seemingly conflicting experimental data motivated the use of a combined theoretical and experimental approach focusing on the role played by Per2 in dictating the phase of p53 oscillations. Systematic modeling of all possible regulatory scenarios predicted that the observed phase relationship between Per2 and p53 could be simulated if (i) p53 was more stable in the nucleus than in the cytoplasm, (ii) Per2 associates to various ubiquitinated forms of p53, and (iii) Per2 mediated p53 nuclear import. These predictions were supported by a sevenfold increase in p53's half-life in the nucleus and by in vitro binding of Per2 to the various ubiquitinated forms of p53. Last, p53's nuclear shuttling was significantly favored by ectopic expression of Per2 and reduced because of Per2 down-regulation. Our combined theoretical/mathematical approach reveals how clock regulatory nodes can be inferred from oscillating time course data.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype.

DNA Damage Response Is Involved in the Developmental Toxicity of Mebendazole in Zebrafish Retina

Intestinal helminths cause iron-deficiency anemia in pregnant women, associated with premature delivery, low birth weight, maternal ill health, and maternal death. Although benzimidazole compounds such as mebendazole (MBZ) are highly efficacious against helminths, there are limited data on its use during pregnancy. In this study, we performed in vivo imaging of the retinas of zebrafish larvae exposed to MBZ, and found that exposure to MBZ during 2 and 3 days post-fertilization caused malformation of the retinal layers. To identify the molecular mechanism underlying the developmental toxicity of MBZ, we performed transcriptome analysis of zebrafish eyes. The analysis revealed that the DNA damage response was involved in the developmental toxicity of MBZ. We were also able to demonstrate that inhibition of ATM significantly attenuated the apoptosis induced by MBZ in the zebrafish retina. These results suggest that MBZ causes developmental toxicity in the zebrafish retina at least partly by activating the DNA damage response, including ATM signaling, providing a potential adverse outcome pathway in the developmental toxicity of MBZ in mammals.

Modeling the heterogeneity of p53 dynamics in DNA damage response

The tumor suppressor p53 can be activated by DNA damage and exhibits undamped pulses. Recent reports have demonstrated a non-threshold mechanism for p53 dynamics. However, no related theoretical studies have been proposed. Here, we constructed a refined DNA damage repair model that incorporated both intrinsic and extrinsic DNA lesions. We proposed that the basal DNA damage may trigger significant fractions of p53 pulses. We also reproduced the heterogeneity of p53 dynamics in experiments. The number of p53 pulses showed no correlations with DNA damage. We also replicated the linear correlation between DNA damage and the probability of igniting a pulse. Our model has unraveled the heterogeneous p53 responses.

Multiscale modeling of tumor growth induced by circadian rhythm disruption in epithelial tissue

We propose a multiscale chemo-mechanical model of cancer tumor development in epithelial tissue. The model is based on the transformation of normal cells into a cancerous state triggered by a local failure of spatial synchronization of the circadian rhythm. The model includes mechanical interactions and a chemical signal exchange between neighboring cells, as well as a division of cells and intercalation that allows for modification of the respective parameters following transformation into the cancerous state. The numerical simulations reproduce different dephasing patterns--spiral waves and quasistationary clustering, with the latter being conducive to cancer formation. Modification of mechanical properties reproduces a distinct behavior of invasive and localized carcinoma.

MiR-192-Mediated Positive Feedback Loop Controls the Robustness of Stress-Induced p53 Oscillations in Breast Cancer Cells

The p53 tumor suppressor protein plays a critical role in cellular stress and cancer prevention. A number of post-transcriptional regulators, termed microRNAs, are closely connected with the p53-mediated cellular networks. While the molecular interactions among p53 and microRNAs have emerged, a systems-level understanding of the regulatory mechanism and the role of microRNAs-forming feedback loops with the p53 core remains elusive. Here we have identified from literature that there exist three classes of microRNA-mediated feedback loops revolving around p53, all with the nature of positive feedback coincidentally. To explore the relationship between the cellular performance of p53 with the microRNA feedback pathways, we developed a mathematical model of the core p53-MDM2 module coupled with three microRNA-mediated positive feedback loops involving miR-192, miR-34a, and miR-29a. Simulations and bifurcation analysis in relationship to extrinsic noise reproduce the oscillatory behavior of p53 under DNA damage in single cells, and notably show that specific microRNA abrogation can disrupt the wild-type cellular phenotype when the ubiquitous cell-to-cell variability is taken into account. To assess these in silico results we conducted microRNA-perturbation experiments in MCF7 breast cancer cells. Time-lapse microscopy of cell-population behavior in response to DNA double-strand breaks, together with image classification of single-cell phenotypes across a population, confirmed that the cellular p53 oscillations are compromised after miR-192 perturbations, matching well with the model predictions. Our study via modeling in combination with quantitative experiments provides new evidence on the role of microRNA-mediated positive feedback loops in conferring robustness to the system performance of stress-induced response of p53.

DNA damage triggered activities of the tumor suppressor protein p53 could be significantly dynamical. The functional role of p53 oscillations in cellular decision making during cancer development has been appreciated. A set of recent studies have revealed extensive crosstalk between the p53 network and microRNAs, but the specifics of the participation of microRNAs in the regulation of the p53 signaling pathway remains largely elusive. Here we investigated microRNAs that form feedback regulation with p53. We enumerated the molecular interactions among these microRNAs and the p53 core and developed a mathematical model to reproduce the DNA damage induced p53 oscillations in single cells. We performed computer simulations and system analysis in combination with experimental assessment to probe the behavior of p53 under microRNA-inhibited conditions. We show that the robust cellular performance of the stress response of p53 in a breast cancer cell line is controlled by miR-192, which forms positive feedback loops with p53.

The relationship between stochastic and deterministic quasi-steady state approximations

Background

The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case.

Results

Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations.

Conclusions

The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0218-3) contains supplementary material, which is available to authorized users.

Disorder, oscillatory dynamics and state switching: the role of c-Myc

In this paper, using the intrinsically disordered oncoprotein Myc as an example, we present a mathematical model to help explain how protein oscillatory dynamics can influence state switching. Earlier studies have demonstrated that, while Myc overexpression can facilitate state switching and transform a normal cell into a cancer phenotype, its downregulation can reverse state-switching. A fundamental aspect of the model is that a Myc threshold determines cell fate in cells expressing p53. We demonstrate that a non-cooperative positive feedback loop coupled with Myc sequestration at multiple binding sites can generate bistable Myc levels. Normal quiescent cells with Myc levels below the threshold can respond to mitogenic signals to activate the cyclin/cdk oscillator for limited cell divisions but the p53/Mdm2 oscillator remains nonfunctional. In response to stress, the p53/Mdm2 oscillator is activated in pulses that are critical to DNA repair. But if stress causes Myc levels to cross the threshold, Myc inactivates the p53/Mdm2 oscillator, abrogates p53 pulses, and pushes the cyclin/cdk oscillator into overdrive sustaining unchecked proliferation seen in cancer. However, if Myc is downregulated, the cyclin/cdk oscillator is inactivated and the p53/Mdm2 oscillator is reset and the cancer phenotype is reversed.

The validity of quasi-steady-state approximations in discrete stochastic simulations

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.

Bystander communication and cell cycle decisions after DNA damage

The DNA damage response (DDR) has two main goals, to repair the damaged DNA and to communicate the presence of damaged DNA. This communication allows the adaptation of cellular behavior to minimize the risk associated with DNA damage. In particular, cell cycle progression must be adapted after a DNA-damaging insult, and cells either pause or terminally exit the cell cycle during a DDR. As cells can accumulate mutations after a DDR due to error-prone DNA repair, terminal cell cycle exit may prevent malignant transformation. The tumor suppressor p53 plays a key role in promoting terminal cell cycle exit. Interestingly, p53 has been implicated in communication of a stress response to surrounding cells, known as the bystander response. Recently, surrounding cells have also been shown to affect the damaged cell, suggesting the presence of intercellular feedback loops. How such feedback may affect terminal cell cycle exit remains unclear, but its presence calls for caution in evaluating cellular outcome without controlling the cellular surrounding. In addition, such feedback may contribute to how the cellular environment affects malignant transformation after DNA damage.

The dynamics of p53 in single cells: physiologically based ODE and reaction-diffusion PDE models

The intracellular signalling network of the p53 protein plays important roles in genome protection and the control of cell cycle phase transitions. Recently observed oscillatory behaviour in single cells under stress conditions has inspired several research groups to simulate and study the dynamics of the protein with the aim of gaining a proper understanding of the physiological meanings of the oscillations. We propose compartmental ODE and PDE models of p53 activation and regulation in single cells following DNA damage and we show that the p53 oscillations can be retrieved by plainly involving p53-Mdm2 and ATM-p53-Wip1 negative feedbacks, which are sufficient for oscillations experimentally, with no further need to introduce any delays into the protein responses and without considering additional positive feedback.

Mathematical modeling for novel cancer drug discovery and development

INTRODUCTION

Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments.

AREAS COVERED

This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment.

EXPERT OPINION

Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

Reaction-diffusion systems for spatio-temporal intracellular protein networks: A beginner's guide with two examples

Spatio-temporal dynamics of a variety of proteins is, among other things, regulated by post-translational modifications of these proteins. Such modifications can thus influence stability and biochemical activities of the proteins, activity and stability of their upstream targets within specific signalling pathways. Commonly used mathematical tools for such protein–protein (and/or protein-mRNA) interactions in single cells, namely, Michaelis–Menten and Hill kinetics, yielding a system of ordinary differential equations, are extended here into (non-linear) partial differential equations by taking into account a more realistic spatial representation of the environment where these reactions occur. In the modelling framework under consideration, all interactions occur in a cell divided into two compartments, the nucleus and the cytoplasm, connected by the semipermeable nuclear membrane and bounded by the impermeable cell membrane. Passive transport mechanism, modelled by the so-called Kedem–Katchalsky boundary conditions, is used here to represent migration of species throughout the nuclear membrane. Nonlinear systems of partial differential equations are solved by the semi-implicit Rothe method. Examples of two spatial oscillators are shown. Namely, these are the circadian rhythm for concentration of the FRQ protein in Neurospora crassa and oscillatory dynamics observed in the activation and regulation of the p53 protein following DNA damage in mammalian cells.

A plausible model for bimodal p53 switch in DNA damage response

p53 is a tumor suppressor and the p53 dynamics displays stimulus dependent patterns. Recent evidence suggests a bimodal p53 switch in cell fate decision. However, no theoretical studies have been proposed to investigate bimodal p53 induction. Here we constructed a model and showed that MDM2-p53 mRNA binding might contribute to bimodal p53 switch through an intrinsic positive feedback loop. Lower damage favored pulsing while monotonic increasing was generated with higher damage. Bimodal p53 dynamics was largely influenced by cellular MDM2 and elevated p53/MDM2 ratios with increasing etoposide favor mono-ubiquitination. Our model replicated recent experiments and provided potential insights into dynamic mechanisms of bimodal switch.

The p53 protein and its molecular network: modelling a missing link between DNA damage and cell fate

Various molecular pharmacokinetic-pharmacodynamic (PK-PD) models have been proposed in the last decades to represent and predict drug effects in anticancer chemotherapies. Most of these models are cell population based since clearly measurable effects of drugs can be seen much more easily on populations of cells, healthy and tumour, than in individual cells. The actual targets of drugs are, however, cells themselves. The drugs in use either disrupt genome integrity by causing DNA strand breaks, and consequently initiate programmed cell death, or block cell proliferation mainly by inhibiting factors that enable cells to proceed from one cell cycle phase to the next through checkpoints in the cell division cycle. DNA damage caused by cytotoxic drugs (and also cytostatic drugs at high concentrations) activates, among others, the p53 protein-modulated signalling pathways that directly or indirectly force the cell to make a decision between survival and death. The paper aims to become the first-step in a larger scale enterprise that should bridge the gap between intracellular and population PK-PD models, providing oncologists with a rationale to predict and optimise the effects of anticancer drugs in the clinic. So far, it only sticks at describing p53 activation and regulation in single cells following their exposure to DNA damaging stress agents. We show that p53 oscillations that have been observed in individual cells can be reconstructed and predicted by compartmentalising cellular events occurring after DNA damage, either in the nucleus or in the cytoplasm, and by describing network interactions, using ordinary differential equations (ODEs), between the ATM, p53, Mdm2 and Wip1 proteins, in each compartment, nucleus or cytoplasm, and between the two compartments. This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications.