Dynamics of P53 in response to DNA damage: Mathematical modeling and perspective

Dynamic behavior of P53-Mdm2-Wip1 gene regulatory network under the influence of time delay and noise

The tumor suppressor protein P53 can regulate the cell cycle, thereby preventing cell abnormalities. In this paper, we study the dynamic characteristics of the P53 network under the influence of time delay and noise, including stability and bifurcation. In order to study the influence of several factors on the concentration of P53, bifurcation analysis on several important parameters is conducted; the results show that the important parameters could induce P53 oscillations within an appropriate range. Then we study the stability of the system and the existing conditions of Hopf bifurcation by using Hopf bifurcation theory with time delays as the bifurcation parameter. It is found that time delay plays a key role in inducing Hopf bifurcation and regulating the period and amplitude of system oscillation. Meanwhile, the combination of time delays can not only promote the oscillation of the system but it also provides good robustness. Changing the parameter values appropriately can change the bifurcation critical point and even the stable state of the system. In addition, due to the low copy number of the molecules and the environmental fluctuations, the influence of noise on the system is also considered. Through numerical simulation, it is found that noise not only promotes system oscillation but it also induces system state switching. The above results may help us to further understand the regulation mechanism of the P53-Mdm2-Wip1 network in the cell cycle.

Robust p53 recovery using chattering free sliding mode control and a gain-scheduled modified Utkin observer

p53 protein plays an essential role in protecting the genomic integrity of mammalian cells. A drastic decrease in the amount of p53 protein has been observed in cancerous cells. By using Nutlin-based small molecule drugs, the concentration of p53 can be restored to the desired level. This paper presents the drug-dosage design for p53 pathway, based on a control-oriented nonlinear model. A chattering free sliding mode control (CFSMC) strategy is employed to track the desired trajectory of p53 concentration for both of its dynamic behaviors, i.e., sustained and oscillatory responses. A gain-scheduled modified Utkin observer (GSMUO) is designed for robust state reconstruction and disturbance estimation. The simulation results show that CFSMC and GSMUO exhibit desired robustness and performance properties in the presence of parametric variations, an input disturbance and measurement noise. Moreover, a comprehensive simulation study, along with a detailed quantitative analysis is performed to compare CFSMC-GSMUO with four different techniques: a sliding mode control (SMC) with an equivalent control based sliding mode observer (SMO) and GSMUO, respectively, and a dynamic sliding mode control (DSMC) with SMO and GSMUO, respectively. The analysis demonstrates that the tracking error and utilization of the control energy is the least in the case of CFSMC-GSMUO as compared to its counterparts.

Molecular-Genetic Portrait of Breast Cancer with Triple Negative Phenotype

Simple Summary

Breast cancer is a genetically heterogeneous disease with different molecular biological and clinical characteristics. The available knowledge about the genetic heterogeneity of the most aggressive molecular subtype of breast cancer—triple-negative—has led to discoveries in drug treatment. Identification of the molecular-genetic phenotype of breast cancer is an important prognostic factor of the disease and allows personalization of the patient’s treatment.

Abstract

Understanding of the genetic mechanisms and identification of the biological markers of tumor progression that form the individual molecular phenotype of transformed cells can characterize the degree of tumor malignancy, the ability to metastasize, the hormonal sensitivity, and the effectiveness of chemotherapy, etc. Breast cancer (BC) is a genetically heterogeneous disease with different molecular biological and clinical characteristics. The available knowledge about the genetic heterogeneity of the most aggressive molecular subtype of breast cancer—triple-negative (TN)—has led to discoveries in drug treatment, including the use of DNA damaging agents (platinum and PARP inhibitors) for these tumors, as well as the use of immunotherapy. Most importantly, the ability to prescribe optimal drug treatment regimens for patients with TNBC based on knowledge of the molecular-genetic characteristics of this subtype of BC will allow the achievement of high rates of overall and disease-free survival. Thus, identification of the molecular-genetic phenotype of breast cancer is an important prognostic factor of the disease and allows personalization of the patient’s treatment.

Mathematical Modelling of p53 Signalling during DNA Damage Response: A Survey

No gene has garnered more interest than p53 since its discovery over 40 years ago. In the last two decades, thanks to seminal work from Uri Alon and Ghalit Lahav, p53 has defined a truly synergistic topic in the field of mathematical biology, with a rich body of research connecting mathematic endeavour with experimental design and data. In this review we survey and distill the extensive literature of mathematical models of p53. Specifically, we focus on models which seek to reproduce the oscillatory dynamics of p53 in response to DNA damage. We review the standard modelling approaches used in the field categorising them into three types: time delay models, spatial models and coupled negative-positive feedback models, providing sample model equations and simulation results which show clear oscillatory dynamics. We discuss the interplay between mathematics and biology and show how one informs the other; the deep connections between the two disciplines has helped to develop our understanding of this complex gene and paint a picture of its dynamical response. Although yet more is to be elucidated, we offer the current state-of-the-art understanding of p53 response to DNA damage.

Effect of pharmacodynamical interaction between nutlin-3a and aspirin in the activation of p53

BACKGROUND AND OBJECTIVE

p53, an anti-tumour protein, is significantly inactivated in most tumours. A small molecule of nutlin-3a is used to activate its function by repressing (Mouse double minute 2 homolog) Mdm2 protein which inhibits its activity. In cancer patients, a high risk of drug-drug interactions (DDIs) is observed owing to their multi-dosing prescriptions, which may lead them to harmful effects. In the presented work, we have aimed to investigate the effect of pharmacodynamical interaction between two anti-cancer drugs, nutlin-3a and aspirin in the activation of p53 protein.

METHODS

We have adapted control system techniques and designed a Proportional-Integral-Derivative (PID) controller. This controller is used to activate p53 protein. A drug interaction parameter is used to incorporate the effect of both drugs. Extensive simulation is performed using two different doses of aspirin, i.e. a low and a high dose of aspirin.

RESULTS

The result shows no harmful effects of pharmacodynamical interaction when a low dose is administered along with nutlin-3a. When a high dose of aspirin is administered it acts as input disturbance and leads to undesirable over-expression of p53 protein. This can further harm other growth cells, thus inducing harmful effects. A comparative analysis is also tabulated with different dosing regimens which shows that a combination of nutlin-3a and a low dose of aspirin provides better results than a high dose of aspirin.

CONCLUSION

Overall, the work provides an insight to the activation of p53 protein in cancer patients under the presence of pharmacodynamical interaction and might contribute to the effective management of cancer patients.

The role of cooperativity in a p53-miR34 dynamical mathematical model

The objective of this study is to evaluate the role of cooperativity, captured by the Hill coefficient, in a minimal mathematical model describing the interactions between p53 and miR-34a. The model equations are analyzed for negative, none and normal cooperativity using a specific version of bifurcation theory and they are solved numerically. Special attention is paid to the sign of so-called first Lyapunov value. Interpretations of the results are given, both according to dynamic theory and in biological terms. In terms of cell signaling, we propose the hypothesis that when the outgoing signal of a system spends a physiologically significant amount of time outside of its equilibrium state, then the value of that signal can be sampled at any point along the trajectory towards that equilibrium and indeed, at multiple points. Coupled with non-linear behavior, such as that caused by cooperativity, this feature can account for a complex and varied response, which p53 is known for. From dynamical point of view, we found that when cooperativity is negative, the system has only one stable equilibrium point. In the absence of cooperativity, there is a single unstable equilibrium point with a critical boundary of stability. In the case with normal cooperativity, the system can have one, two, or three steady states with both, bi-stability and bi-instability occurring.

Recent treatment progress of triple negative breast cancer

Breast cancer (BC) is a serious worldwide disease that threatens women's health. Particularly, the morbidity of triple-negative breast cancer (TNBC) is higher than that of other BC types due to its high molecular heterogeneity, metastatic potential and poor prognosis. TNBC lacks of estrogen receptor (ER), progesterone receptor (PR) and human epidermal growth factor receptor 2 (HER2), so there are still no effective treatment methods for TNBC. Here, we reviewed the classification of TNBC, its molecular mechanisms of pathogenesis, treatment methods and prognosis. Finding effective targets is critical for the treatment of TNBC. Also, refining the classification of TNBC is benefited to choose the treatment of TNBC, because the sensitivity of chemotherapy is different in different TNBC. Some new treatment methods have been proposed in recent years, such as nutritional therapy and noncoding RNA treatment methods. There are some disadvantages, such as the side effect on normal cells after nutrient deprivation, low specificity and instability of noncoding RNA. More studies are necessary to improve the treatment of TNBC.

Mathematical Modeling of p53 Pathways

Cells have evolved balanced systems that ensure an appropriate response to stress. The systems elicit repair responses in temporary or moderate stress but eliminate irreparable cells via apoptosis in detrimental conditions of prolonged or severe stress. The tumor suppressor p53 is a central player in these stress response systems. When activated under DNA damage stress, p53 regulates hundreds of genes that are involved in DNA repair, cell cycle, and apoptosis. Recently, increasing studies have demonstrated additional regulatory roles of p53 in metabolism and mitochondrial physiology. Due to the inherent complexity of feedback loops between p53 and its target genes, the application of mathematical modeling has emerged as a novel approach to better understand the multifaceted functions and dynamics of p53. In this review, we discuss several mathematical modeling approaches in exploring the p53 pathways.

Sliding mode controller-observer pair for p53 pathway

A significant loss of p53 protein, an anti-tumour agent, is observed in early cancerous cells. Induction of small molecules based drug is by far the most prominent technique to revive and maintain wild-type p53 to the desired level. In this study, a sliding mode control (SMC) based robust non-linear technique is presented for the drug design of a control-oriented p53 model. The control input generated by conventional SMC is discontinuous; however, depending on the physical nature of the system, drug infusion needs to be continuous. Therefore, to obtain a smooth control signal, a dynamic SMC (DSMC) is designed. Moreover, the boundedness of the zero-dynamics is also proved. To make the model-based control design possible, the unknown states of the system are estimated using an equivalent control based, reduced-order sliding mode observer. The robustness of the proposed technique is assessed by introducing input disturbance and parametric uncertainty in the system. The effectiveness of the proposed control scheme is witnessed by performing in-silico trials, revealing that the sustained level of p53 can be achieved by controlled drug administration. Moreover, a comparative quantitative analysis shows that both controllers yield similar performance. However, DSMC consumes less control energy.

Two-dimensional polynomial type canonical relaxation oscillator model for p53 dynamics

p53 network, which is responsible for DNA damage response of cells, exhibits three distinct qualitative behaviours; low state, oscillation and high state, which are associated with normal cell cycle progression, cell cycle arrest and apoptosis, respectively. The experimental studies demonstrate that these dynamics of p53 are due to the ATM and Wip1 interaction. This paper proposes a simple two-dimensional canonical relaxation oscillator model based on the identified topological structure of ATM and Wip1 interaction underlying these qualitative behaviours of p53 network. The model includes only polynomial terms that have the interpretability of known ATM and Wip1 interaction. The introduced model is useful for understanding relaxation oscillations in gene regulatory networks. Through mathematical analysis, we investigate the roles of ATM and Wip1 in forming of these three essential behaviours, and show that ATM and Wip1 constitute the core mechanism of p53 dynamics. In agreement with biological findings, we show that Wip1 degradation term is a highly sensitive parameter, possibly related to mutations. By perturbing the corresponding parameters, our model characterizes some mutations such as ATM deficiency and Wip1 overexpression. Finally, we provide intervention strategies considering our observation that Wip1 seems to be an important target to conduct therapies for these mutations.

Programmed cell death: the battlefield between the host and alpha-herpesviruses and a potential avenue for cancer treatment

Programed cell death is an antiviral mechanism by which the host limits viral replication and protects uninfected cells. Many viruses encode proteins resistant to programed cell death to escape the host immune defenses, which indicates that programed cell death is more favorable for the host immune defense. Alpha-herpesviruses are pathogens that widely affect the health of humans and animals in different communities worldwide. Alpha-herpesviruses can induce apoptosis, autophagy and necroptosis through different molecular mechanisms. This review concisely illustrates the different pathways of apoptosis, autophagy, and necroptosis induced by alpha-herpesviruses. These pathways influence viral infection and replication and are a potential avenue for cancer treatment. This review will increase our understanding of the role of programed cell death in the host immune defense and provides new possibilities for cancer treatment.

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.

Diepoxybutane-induced apoptosis is mediated through the ERK1/2 pathway

Diepoxybutane (DEB) is the most potent active metabolite of butadiene, a regulated air pollutant. We previously reported the occurrence of DEB-induced, p53-dependent, mitochondrial-mediated apoptosis in human lymphoblasts. The present study investigated the role of the extracellular signal-regulated protein kinases 1 and 2 (ERK1/2) pathway in DEB-induced apoptotic signaling in exposed human lymphoblasts. Activated ERK1/2 and mitogen-activated protein (MAP) kinase/ERK1/2 kinase (MEK) levels were significantly upregulated in DEB-exposed human lymphoblasts. The MEK inhibitor PD98059 and ERK1/2 siRNA significantly inhibited apoptosis, ERK1/2 activation, as well as p53 and phospho-p53 (serine-15) levels in human lymphoblasts undergoing DEB-induced apoptosis. Collectively, these results demonstrate that DEB induces apoptotic signaling through the MEK-ERK1/2-p53 pathway in human lymphoblasts. This is the first report implicating the activation of the ERK1/2 pathway and its subsequent role in mediating DEB-induced apoptotic signaling in human lymphoblasts. These findings contribute towards the understanding of DEB toxicity, as well as the signaling pathways mediating DEB-induced apoptosis in human lymphoblasts.

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.

Stress and the nonsense-mediated RNA decay pathway

Cells respond to internal and external cellular stressors by activating stress-response pathways that re-establish homeostasis. If homeostasis is not achieved in a timely manner, stress pathways trigger programmed cell death (apoptosis) to preserve organism integrity. A highly conserved stress pathway is the unfolded protein response (UPR), which senses excessive amounts of unfolded proteins in the ER. While a physiologically beneficial pathway, the UPR requires tight regulation to provide a beneficial outcome and avoid deleterious consequences. Recent work has demonstrated that a conserved and highly selective RNA degradation pathway-nonsense-mediated RNA decay (NMD)-serves as a major regulator of the UPR pathway. NMD degrades mRNAs encoding UPR components to prevent UPR activation in response to innocuous ER stress. In response to strong ER stress, NMD is inhibited by the UPR to allow for a full-magnitude UPR response. Recent studies have indicated that NMD also has other stress-related functions, including promoting the timely termination of the UPR to avoid apoptosis; NMD also regulates responses to non-ER stressors, including hypoxia, amino-acid deprivation, and pathogen infection. NMD regulates stress responses in species across the phylogenetic scale, suggesting that it has conserved roles in shaping stress responses. Stress pathways are frequently constitutively activated or dysregulated in human disease, raising the possibility that "NMD therapy" may provide clinical benefit by downmodulating stress responses.

Significance of Wild-Type p53 Signaling in Suppressing Apoptosis in Response to Chemical Genotoxic Agents: Impact on Chemotherapy Outcome

Our genomes are subject to potentially deleterious alterations resulting from endogenous sources (e.g., cellular metabolism, routine errors in DNA replication and recombination), exogenous sources (e.g., radiation, chemical agents), and medical diagnostic and treatment applications. Genome integrity and cellular homeostasis are maintained through an intricate network of pathways that serve to recognize the DNA damage, activate cell cycle checkpoints and facilitate DNA repair, or eliminate highly injured cells from the proliferating population. The wild-type p53 tumor suppressor and its downstream effector p21^WAF1 (p21) are key regulators of these responses. Although extensively studied for its ability to control cell cycle progression, p21 has emerged as a multifunctional protein capable of downregulating p53, suppressing apoptosis, and orchestrating prolonged growth arrest through stress-induced premature senescence. Studies with solid tumors and solid tumor-derived cell lines have revealed that such growth-arrested cancer cells remain viable, secrete growth-promoting factors, and can give rise to progeny with stem-cell-like properties. This article provides an overview of the mechanisms by which p53 signaling suppresses apoptosis following genotoxic stress, facilitating repair of genomic injury under physiological conditions but having the potential to promote tumor regrowth in response to cancer chemotherapy.

Modeling amplified p53 responses under DNA-PK inhibition in DNA damage response

During DNA double strand breaks (DSBs) repair, coordinated activation of phosphatidylinositol 3-kinase (PI3K)-like kinases can activate p53 signaling pathway. Recent findings have identified novel interplays among these kinases demonstrating amplified first p53 pulses under DNA-PK inhibition. However, no theoretical model has been developed to characterize such dynamics. In current work, we modeled the prolonged p53 pulses with DNA-PK inhibitor. We could identify a dose-dependent increase in the first pulse amplitude and width. Meanwhile, weakened DNA-PK mediated ATM inhibition was insufficient to reproduce such dynamic behavior. Moreover, the information flow was shifted predominantly to the first pulse under DNA-PK inhibition. Furthermore, the amplified p53 responses were relatively robust. Taken together, our model can faithfully replicate amplified p53 responses under DNA-PK inhibition and provide insights into cell fate decision by manipulating p53 dynamics.

Kinetic aspects of enzyme-mediated repair of DNA single-strand breaks

In cells and bacteria, DNA can be damaged in different ways. The efficient damage repair, mediated by various enzymes, is crucial for their survival. Most frequently, the damage is reduced to single-strand breaks. In human cells, according to the experiments, the repair of such breaks can mechanistically be divided into four steps including (i) the break detection, (ii) processing of damaged ends, (iii) gap filling, and (iv) ligation of unbound ends of the broken strand. The first and second steps run in parallel while the third and fourth steps are sequential. The author proposes a kinetic model describing these steps. It allows one to understand the likely dependence of the number of breaks in different states on enzyme concentrations. The dependence of these concentrations on the rate of the formation of breaks can be understood as well. In addition, the likely role of unzipping and zipping of the fragments of broken ends of the strand in the ligation step has been scrutinized taking the specifics of binding of DNA stands into account.