Low-frequency ERK and Akt activity dynamics are predictive of stochastic cell division events.

Understanding the dynamics of intracellular signaling pathways, such as ERK1/2 (ERK) and Akt1/2 (Akt), in the context of cell fate decisions is important for advancing our knowledge of cellular processes and diseases, particularly cancer. While previous studies have established associations between ERK and Akt activities and proliferative cell fate, the heterogeneity of single-cell responses adds complexity to this understanding. This study employed a data-driven approach to address this challenge, developing machine learning models trained on a dataset of growth factor-induced ERK and Akt activity time courses in single cells, to predict cell division events. The most predictive models were developed by applying discrete wavelet transforms (DWTs) to extract low-frequency features from the time courses, followed by using Ensemble Integration, a data integration and predictive modeling framework. The results demonstrated that these models effectively predicted cell division events in MCF10A cells (F-measure=0.524, AUC=0.726). ERK dynamics were found to be more predictive than Akt, but the combination of both measurements further enhanced predictive performance. The ERK model`s performance also generalized to predicting division events in RPE cells, indicating the potential applicability of these models and our data-driven methodology for predicting cell division across different biological contexts. Interpretation of these models suggested that ERK dynamics throughout the cell cycle, rather than immediately after growth factor stimulation, were associated with the likelihood of cell division. Overall, this work contributes insights into the predictive power of intra-cellular signaling dynamics for cell fate decisions, and highlights the potential of machine learning approaches in unraveling complex cellular behaviors.

Morphological Stability for in silico Models of Avascular Tumors.

The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to sharpen experimental procedures and, in the longer run, even for applications in personalized medicine. One of the greatest challenges is to balance model realism and detail with experimental data to eventually produce useful data-driven models. We contribute to this quest by developing a transparent, highly parsimonious, first principle in silico model of a growing avascular tumor. We initially formulate the physiological considerations and the specific model within a stochastic cell-based framework. We next formulate a corresponding mean-field model using partial differential equations which is amenable to mathematical analysis. Despite a few notable differences between the two models, we are in this way able to successfully detail the impact of all parameters in the stability of the growth process and on the eventual tumor fate of the stochastic model. This facilitates the deduction of Bayesian priors for a given situation, but also provides important insights into the underlying mechanism of tumor growth and progression. Although the resulting model framework is relatively simple and transparent, it can still reproduce the full range of known emergent behavior. We identify a novel model instability arising from nutrient starvation and we also discuss additional insight concerning possible model additions and the effects of those. Thanks to the framework's flexibility, such additions can be readily included whenever the relevant data become available.

DNA lesion bypass and the stochastic dynamics of transcription-coupled repair.

DNA base damage is a major source of oncogenic mutations and disruption to gene expression. The stalling of RNA polymerase II (RNAP) at sites of DNA damage and the subsequent triggering of repair processes have major roles in shaping the genome-wide distribution of mutations, clearing barriers to transcription, and minimizing the production of miscoded gene products. Despite its importance for genetic integrity, key mechanistic features of this transcription-coupled repair (TCR) process are controversial or unknown. Here, we exploited a well-powered in vivo mammalian model system to explore the mechanistic properties and parameters of TCR for alkylation damage at fine spatial resolution and with discrimination of the damaged DNA strand. For rigorous interpretation, a generalizable mathematical model of DNA damage and TCR was developed. Fitting experimental data to the model and simulation revealed that RNA polymerases frequently bypass lesions without triggering repair, indicating that small alkylation adducts are unlikely to be an efficient barrier to gene expression. Following a burst of damage, the efficiency of transcription-coupled repair gradually decays through gene bodies with implications for the occurrence and accurate inference of driver mutations in cancer. The reinitation of transcription from the repair site is not a general feature of transcription-coupled repair, and the observed data is consistent with reinitiation never taking place. Collectively, these results reveal how the directional but stochastic activity of TCR shapes the distribution of mutations following DNA damage.

Simple model to incorporate statistical noise based on a modified hodgkin-huxley approach for external electrical field driven neural responses.

Noise activity is known to affect neural networks, enhance the system response to weak external signals, and lead to stochastic resonance phenomenon that can effectively amplify signals in nonlinear systems. In most treatments, channel noise has been modeled based on multi-state Markov descriptions or the use stochastic differential equation models. Here we probe a computationally simple approach based on a minor modification of the traditional Hodgkin-Huxley approach to embed noise in neural response. Results obtained from numerous simulations with different excitation frequencies and noise amplitudes for the action potential firing show very good agreement with output obtained from well-established models. Furthermore, results from the Mann-Whitney U Test reveal a statistically insignificant difference. The distribution of the time interval between successive potential spikes obtained from this simple approach compared very well with the results of complicated Fox and Lu type methods at much reduced computational cost. This present method could also possibly be applied to the analysis of spatial variations and/or differences in characteristics of random incident electromagnetic signals.

A Genuinely Hybrid, Multiscale 3D Cancer Invasion and Metastasis Modelling Framework.

We introduce in this paper substantial enhancements to a previously proposed hybrid multiscale cancer invasion modelling framework to better reflect the biological reality and dynamics of cancer. These model updates contribute to a more accurate representation of cancer dynamics, they provide deeper insights and enhance our predictive capabilities. Key updates include the integration of porous medium-like diffusion for the evolution of Epithelial-like Cancer Cells and other essential cellular constituents of the system, more realistic modelling of Epithelial-Mesenchymal Transition and Mesenchymal-Epithelial Transition models with the inclusion of Transforming Growth Factor beta within the tumour microenvironment, and the introduction of Compound Poisson Process in the Stochastic Differential Equations that describe the migration behaviour of the Mesenchymal-like Cancer Cells. Another innovative feature of the model is its extension into a multi-organ metastatic framework. This framework connects various organs through a circulatory network, enabling the study of how cancer cells spread to secondary sites.

Effective vaccination strategies for human papillomavirus (HPV) infection and cervical cancer based on the mathematical model with a stochastic process.

Human papillomavirus (HPV) infection poses a significant risk to women's health by causing cervical cancer. In addition to HPV, cervical cancer incidence rates can be influenced by various factors, including human immunodeficiency virus and herpes, as well as screening policy. In this study, a mathematical model with stochastic processes was developed to analyze HPV transmission between genders and its subsequent impact on cervical cancer incidence. The model simulations suggest that both-gender vaccination is far more effective than female-only vaccination in preventing an increase in cervical cancer incidence. With increasing stochasticity, the difference between the number of patients in the vaccinated group and the number in the nonvaccinated group diminishes. To distinguish the patient population distribution of the vaccinated from the nonvaccinated, we calculated effect size (Cohen's distance) in addition to Student's t-test. The model analysis suggests a threshold vaccination rate for both genders for a clear reduction of cancer incidence when significant stochastic factors are present.

Longtime evolution and stationary response of a stochastic tumor-immune system with resting T cells.

In this paper, we take the resting T cells into account and interpret the progression and regression of tumors by a predator-prey like tumor-immune system. First, we construct an appropriate Lyapunov function to prove the existence and uniqueness of the global positive solution to the system. Then, by utilizing the stochastic comparison theorem, we prove the moment boundedness of tumor cells and two types of T cells. Furthermore, we analyze the impact of stochastic perturbations on the extinction and persistence of tumor cells and obtain the stationary probability density of the tumor cells in the persistent state. The results indicate that when the noise intensity of tumor perturbation is low, tumor cells remain in a persistent state. As this intensity gradually increases, the population of tumors moves towards a lower level, and the stochastic bifurcation phenomena occurs. When it reaches a certain threshold, instead the number of tumor cells eventually enter into an extinct state, and further increasing of the noise intensity will accelerate this process.

Chronic arsenic exposure induces malignant transformation of human HaCaT cells through both deterministic and stochastic changes in transcriptome expression.

Biological processes are inherently stochastic, i.e., are partially driven by hard to predict random probabilistic processes. Carcinogenesis is driven both by stochastic and deterministic (predictable non-random) changes. However, very few studies systematically examine the contribution of stochastic events leading to cancer development. In differential gene expression studies, the established data analysis paradigms incentivize expression changes that are uniformly different across the experimental versus control groups, introducing preferential inclusion of deterministic changes at the expense of stochastic processes that might also play a crucial role in the process of carcinogenesis. In this study, we applied simple computational techniques to quantify: (i) The impact of chronic arsenic (iAs) exposure as well as passaging time on stochastic gene expression and (ii) Which genes were expressed deterministically and which were expressed stochastically at each of the three stages of cancer development. Using biological coefficient of variation as an empirical measure of stochasticity we demonstrate that chronic iAs exposure consistently suppressed passaging related stochastic gene expression at multiple time points tested, selecting for a homogenous cell population that undergo transformation. Employing multiple balanced removal of outlier data, we show that chronic iAs exposure induced deterministic and stochastic changes in the expression of unique set of genes, that populate largely unique biological pathways. Together, our data unequivocally demonstrate that both deterministic and stochastic changes in transcriptome-wide expression are critical in driving biological processes, pathways and networks towards clonal selection, carcinogenesis, and tumor heterogeneity.

A stochastic framework for evaluating CAR T cell therapy efficacy and variability.

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy.

MIDOS: a novel stochastic model towards a treatment planning system for microsphere dosimetry in liver tumors.

PURPOSE: Transarterial radioembolization (TARE) procedures treat liver tumors by injecting radioactive microspheres into the hepatic artery. Currently, there is a critical need to optimize TARE towards a personalized dosimetry approach. To this aim, we present a novel microsphere dosimetry (MIDOS) stochastic model to estimate the activity delivered to the tumor(s), normal liver, and lung. METHODS: MIDOS incorporates adult male/female liver computational phantoms with the hepatic arterial, hepatic portal venous, and hepatic venous vascular trees. Tumors can be placed in both models at user discretion. The perfusion of microspheres follows cluster patterns, and a Markov chain approach was applied to microsphere navigation, with the terminal location of microspheres determined to be in either normal hepatic parenchyma, hepatic tumor, or lung. A tumor uptake model was implemented to determine if microspheres get lodged in the tumor, and a probability was included in determining the shunt of microspheres to the lung. A sensitivity analysis of the model parameters was performed, and radiation segmentectomy/lobectomy procedures were simulated over a wide range of activity perfused. Then, the impact of using different microspheres, i.e., SIR-Sphere®, TheraSphere®, and QuiremSphere®, on the tumor-to-normal ratio (TNR), lung shunt fraction (LSF), and mean absorbed dose was analyzed. RESULTS: Highly vascularized tumors translated into increased TNR. Treatment results (TNR and LSF) were significantly more variable for microspheres with high particle load. In our scenarios with 1.5 GBq perfusion, TNR was maximum for TheraSphere® at calibration time in segmentectomy/lobar technique, for SIR-Sphere® at 1-3 days post-calibration, and regarding QuiremSphere® at 3 days post-calibration. CONCLUSION: This novel approach is a decisive step towards developing a personalized dosimetry framework for TARE. MIDOS assists in making clinical decisions in TARE treatment planning by assessing various delivery parameters and simulating different tumor uptakes. MIDOS offers evaluation of treatment outcomes, such as TNR and LSF, and quantitative scenario-specific decisions.

Controlling smoking: A smoking epidemic model with different smoking degrees in deterministic and stochastic environments.

Engaging in smoking not only leads to substantial health risks but also imposes considerable financial burdens. To deepen our understanding of the mechanisms behind smoking transmission and to address the tobacco epidemic, we examined a five-dimensional smoking epidemic model that accounts for different degrees of smoking under both deterministic and stochastic conditions. In the deterministic case, we determine the basic reproduction number, analyze the stability of equilibria with and without smoking, and investigate the existence of saddle-node bifurcation. Our analysis reveals that the basic reproduction number cannot completely determine the existence of smoking, and the model possesses bistability, indicating its dynamic is susceptible to interference from environmental noises. In the stochastic case, we establish sufficient conditions for the ergodic stationary distribution and the elimination of smokers by constructing appropriate Lyapunov functions. Numerical simulations suggest that the effects of inevitable random fluctuations in the natural environment on controlling the smoking epidemic may be beneficial, harmful, or negligible, which are closely related to the noise intensities, initial smoking population sizes, and the effective exposure rate of smoking transmission (ß). Given the uncontrollable nature of environmental random effects, effective smoking control strategies can be achieved by: (1) accurate monitoring of initial smoking population sizes, and (2) implementing effective measures to reduce ß. Therefore, it is both effective and feasible to implement a complete set of strong MPOWER measures to control smoking prevalence.

Stochastic tumor-immune interaction model with external treatments and time delays: An optimal control problem.

Herein, we discuss an optimal control problem (OC-P) of a stochastic delay differential model to describe the dynamics of tumor-immune interactions under stochastic white noises and external treatments. The required criteria for the existence of an ergodic stationary distribution and possible extinction of tumors are obtained through Lyapunov functional theory. A stochastic optimality system is developed to reduce tumor cells using some control variables. The study found that combining white noises and time delays greatly affected the dynamics of the tumor-immune interaction model. Based on numerical results, it can be shown which variables are optimal for controlling tumor growth and which controls are effective for reducing tumor growth. With some conditions, white noise reduces tumor cell growth in the optimality problem. Some numerical simulations are conducted to validate the main results.

Modeling and analysis of a stochastic giving-up-smoking model with quit smoking duration.

Smoking has gradually become a very common behavior, and the related situation in different groups also presents different forms. Due to the differences of individual smoking cessation time and the interference of environmental factors in the spread of smoking behavior, we establish a stochastic giving up smoking model with quit-smoking duration. We also consider the saturated incidence rate. The total population is composed of potential smokers, smokers, quitters and removed. By using Itô's formula and constructing appropriate Lyapunov functions, we first ensure the existence of a unique global positive solution of the stochastic model. In addition, a threshold condition for extinction and permanence of smoking behavior is deduced. If the intensity of white noise is small, and $ \widetilde{\mathcal{R}}_0 < 1 $, smokers will eventually become extinct. If $ \widetilde{\mathcal{R}}_0 > 1 $, smoking will last. Then, the sufficient condition for the existence of a unique stationary distribution of the smoking phenomenon is studied as $ R_0/ > 1 $. Finally, conclusions are explained by numerical simulations.

Stochastic dynamics of human papillomavirus delineates cervical cancer progression.

Starting from a deterministic model, we propose and study a stochastic model for human papillomavirus infection and cervical cancer progression. Our analysis shows that the chronic infection state as random variables which have the ergodic invariant probability measure is necessary for progression from infected cell population to cervical cancer cells. It is shown that small progression rate from infected cells to precancerous cells and small microenvironmental noises associated with the progression rate and viral infection help to establish such chronic infection states. It implicates that large environmental noises associated with viral infection and the progression rate in vivo can reduce chronic infection. We further show that there will be a cervical cancer if the noise associated with precancerous cell growth is large enough. In addition, comparable numerical studies for the deterministic model and stochastic model, together with Hopf bifurcations in both deterministic and stochastic systems, highlight our analytical results.

Stochastic competitive release and adaptive chemotherapy.

We develop a finite-cell model of tumor natural selection dynamics to investigate the stochastic fluctuations associated with multiple rounds of adaptive chemotherapy. The adaptive cycles are designed to avoid chemoresistance in the tumor by managing the ecological mechanism of competitive release of a resistant subpopulation. Our model is based on a three-component evolutionary game played among healthy (H), sensitive (S), and resistant (R) populations of N cells, with a chemotherapy control parameter, C(t), which we use to dynamically impose selection pressure on the sensitive subpopulation to slow tumor growth and manage competitive release of the resistant population. The adaptive chemoschedule is designed based on the deterministic (N→∞) adjusted replicator dynamical system, then implemented using the finite-cell stochastic frequency dependent Moran process model (N=10K-50K) to ascertain the cumulative effect of the stochastic fluctuations on the efficacy of the adaptive schedules over multiple rounds. We quantify the stochastic fixation probability regions of the R and S populations in the HSR trilinear phase plane as a function of the control parameter C∈[0,1], showing that the size of the R region increases with increasing C. We then implement an adaptive time-dependent schedule C(t) for the stochastic model and quantify the variances (using principal component coordinates) associated with the evolutionary cycles over multiple rounds of adaptive therapy. The variances increase subquadratically through several rounds before the evolutionary cycle begins to break down. Despite this, we show the stochastic adaptive schedules are more effective at delaying resistance than standard maximum tolerated dose and low-dose metronomic schedules. The simplified low-dimensional model provides some insights on how well multiple rounds of adaptive therapies are likely to perform over a range of tumor sizes (i.e., different values of N) if the goal is to maintain a sustained balance among competing subpopulations of cells to avoid chemoresistance via competitive release in a stochastic environment.

Cusp bifurcation in a metastatic regulatory network.

Understanding the potential for cancers to metastasize is still relatively unknown. While many predictive methods may use deep learning or stochastic processes, we highlight a long standing mathematical concept that may be useful for modeling metastatic breast cancer systems. Ordinary differential equations (ODEs) can model cell state transitions by considering the pertinent environmental variables as well as the paths systems take over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. Many studies have applied concepts in one-parameter bifurcation theory to model biological network dynamics, and cell division. However, studies of two-parameter bifurcations are much more rare. Two-parameter bifurcations have not been studied in metastatic systems. Here we show how a specific two-parameter bifurcation phenomenon called a cusp bifurcation separates two qualitatively different metastatic cell state transitions modalities and propose a new perspective on defining such transitions based on mathematical theory. We hope the observations and verification methods detailed here may help in the understanding of metastatic potential from a basic biological perspective and in clinical settings.

De novo hematopoietic (stem) cell generation - A differentiation or stochastic process?

The hematopoietic system is one of the earliest tissues to develop. De novo generation of hematopoietic progenitor and stem cells occurs through a transdifferentiation of (hemogenic) endothelial cells to hematopoietic identity, resulting in the formation of intra-aortic hematopoietic cluster (IAHC) cells. Heterogeneity of IAHC cell phenotypes and functions has stymied the field in its search for the transcriptional program of emerging hematopoietic stem cells (HSCs), given that an individual IAHC cannot be simultaneously examined for function and transcriptome. Several models could account for this heterogeneity, including a novel model suggesting that the transcriptomes of individual emerging IAHC cells are in an unstable/metastable state, with pivotal hematopoietic transcription factors expressed dynamically due to transcriptional pulsing and combinatorial activities. The question remains - how is functional hematopoietic cell fate established - is the process stochastic? This article touches upon these important issues, which may be relevant to the field's inability to make HSCs ex vivo.

Macrophage phenotype transitions in a stochastic gene-regulatory network model.

Polarization is the process by which a macrophage cell commits to a phenotype based on external signal stimulation. To know how this process is affected by random fluctuations and events within a cell is of utmost importance to better understand the underlying dynamics and predict possible phenotype transitions. For this purpose, we develop a stochastic modeling approach for the macrophage polarization process. We classify phenotype states using the Robust Perron Cluster Analysis and quantify transition pathways and probabilities by applying Transition Path Theory. Depending on the model parameters, we identify four bistable and one tristable phenotype configuration. We find that bistable transitions are fast but their states less robust. In contrast, phenotype transitions in the tristable situation have a comparatively long time duration, which reflects the robustness of the states. The results indicate parallels in the overall transition behavior of macrophage cells with other heterogeneous and plastic cell types, such as cancer cells. Our approach allows for a probabilistic interpretation of macrophage phenotype transitions and biological inference on phenotype robustness. In general, the methodology can easily be adapted to other systems where random state switches are known to occur.

Cell population growth kinetics in the presence of stochastic heterogeneity of cell phenotype.

Recent studies at individual cell resolution have revealed phenotypic heterogeneity in nominally clonal tumor cell populations. The heterogeneity affects cell growth behaviors, which can result in departure from the idealized uniform exponential growth of the cell population. Here we measured the stochastic time courses of growth of an ensemble of populations of HL60 leukemia cells in cultures, starting with distinct initial cell numbers to capture a departure from the uniform exponential growth model for the initial growth ("take-off"). Despite being derived from the same cell clone, we observed significant variations in the early growth patterns of individual cultures with statistically significant differences in growth dynamics, which could be explained by the presence of inter-converting subpopulations with different growth rates, and which could last for many generations. Based on the hypothesis of existence of multiple subpopulations, we developed a branching process model that was consistent with the experimental observations.

A stochastic hierarchical model for low grade glioma evolution.

A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using a piecewise diffusion Markov process (PDifMP) at the cellular level, we derive an equation for the density of the transition probability of this Markov process based on the generalised Fokker-Planck equation. Then, a macroscopic model is derived via parabolic limit and Hilbert expansions in the moment equations. After setting up the model, we perform several numerical tests to study the role of the local characteristics and the extended generator of the PDifMP in the process of tumour progression. The main aim focuses on understanding how the variations of the jump rate function of this process at the microscopic scale and the diffusion coefficient at the macroscopic scale are related to the diffusive behaviour of the glioma cells and to the onset of malignancy, i.e., the transition from low-grade to high-grade gliomas.