Minimal Mechanisms of Microtubule Length Regulation in Living Cells

The microtubule cytoskeleton is responsible for sustained, long-range intracellular transport of mRNAs, proteins, and organelles in neurons. Neuronal microtubules must be stable enough to ensure reliable transport, but they also undergo dynamic instability, as their plus and minus ends continuously switch between growth and shrinking. This process allows for continuous rebuilding of the cytoskeleton and for flexibility in injury settings. Motivated by in vivo experimental data on microtubule behavior in Drosophila neurons, we propose a mathematical model of dendritic microtubule dynamics, with a focus on understanding microtubule length, velocity, and state-duration distributions. We find that limitations on microtubule growth phases are needed for realistic dynamics, but the type of limiting mechanism leads to qualitatively different responses to plausible experimental perturbations. We therefore propose and investigate two minimally-complex length-limiting factors: limitation due to resource (tubulin) constraints and limitation due to catastrophe of large-length microtubules. We combine simulations of a detailed stochastic model with steady-state analysis of a mean-field ordinary differential equations model to map out qualitatively distinct parameter regimes. This provides a basis for predicting changes in microtubule dynamics, tubulin allocation, and the turnover rate of tubulin within microtubules in different experimental environments.

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.

How drug onset rate and duration of action affect drug forgiveness

Medication nonadherence is one of the largest problems in healthcare today, particularly for patients undergoing long-term pharmacotherapy. To combat nonadherence, it is often recommended to prescribe so-called "forgiving" drugs, which maintain their effect despite lapses in patient adherence. Nevertheless, drug forgiveness is difficult to quantify and compare between different drugs. In this paper, we construct and analyze a stochastic pharmacokinetic/pharmacodynamic (PK/PD) model to quantify and understand drug forgiveness. The model parameterizes a medication merely by an effective rate of onset of effect when the medication is taken (on-rate) and an effective rate of loss of effect when a dose is missed (off-rate). Patient dosing is modeled by a stochastic process that allows for correlations in missed doses. We analyze this "on/off" model and derive explicit formulas that show how treatment efficacy depends on drug parameters and patient adherence. As a case study, we compare the effects of nonadherence on the efficacy of various antihypertensive medications. Our analysis shows how different drugs can have identical efficacies under perfect adherence, but vastly different efficacies for adherence patterns typical of actual patients. We further demonstrate that complex PK/PD models can indeed be parameterized in terms of effective on-rates and off-rates. Finally, we have created an online app to allow pharmacometricians to explore the implications of our model and analysis.

A comparative environmental analysis of conventional and organic rice farming in Thailand in a life cycle perspective using a stochastic modeling approach

System stochasticity is an inherent characteristic of agricultural systems. Many studies have been conducted in Thailand to analyze the rice production systems. However, most of the prior work just focused on deterministic approach to investigate the rice production systems while disregarding the system variability. In this study, the conventional and organic rice farming systems in Thailand were compared considering the uncertainties associated with parameters. The system variability was taken into account by employing a stochastic modeling approach. The considered impact categories include global warming, ozone formation (human health), freshwater ecotoxicity, terrestrial acidification, fine particulate matter formation, freshwater eutrophication, and fossil resource scarcity. The results showed that yield had considerable influence on the environmental profiles of the two systems; organic and conventional farming showed similar results in terms of global warming on a per hectare basis, but the considerable difference was observed on a per tonne basis. The field emissions due to farm inputs were the most significant contributor to most of the impact categories. The fuel used for irrigation, land preparation, and harvesting also contributed significantly to several impact categories. On the other hand, the impacts of inputs production and material transportation were modest. Uncertainty analysis outcomes indicated that there was a noticeable deviation from the deterministic results in terms of global warming and freshwater ecotoxicity. However, when considering the associated uncertainties, no significant difference was observed between the environmental profiles of the two systems.

Inducing Homochirality Through Intermediary Catalytic Species: A Stochastic Approach

A new chiral amplification mechanism based on a stochastic approach is proposed. The mechanism includes five different chemical species, an achiral substrate (A), two chiral forms (L, D), and two intermediary species (LA, DA). The process occurs within a small, semipermeable compartment that can be diffusively coupled with the outside environment. The study considers two alternative primary sources for chiral species within the compartment, one chemical and the other diffusive. As a remarkable fact, the chiral amplification process occurs due to stochastic fluctuations of an intermediary catalytic species (LA, DA) produced in situ, given the interaction of the chiral species with the achiral substrate. The net process includes two different steps: the synthesis of the catalyst (LA and DA) and the catalytic production of new chiral species from the substrate. Stochastic simulations show that proper parameterization can induce a robust chiral state within the compartment regardless of whether the system is open or closed. We also show how an increase in the non-catalytic production of chiral species tends to negatively impact the homochirality degree of the system. By its conception, the proposed mechanism suggests a deeper connection with how most biochemical processes occur in living beings, a fact that could open new avenues for studying this fascinating phenomenon.

Modeling the effects of farming practices on bovine respiratory disease in a multi-batch cattle fattening farm

Bovine Respiratory Disease (BRD) affects young bulls, causing animal welfare and health concerns as well as economical costs. BRD is caused by an array of viruses and bacteria and also by environmental and abiotic factors. How farming practices influence the spread of these causal pathogens remains unclear. Our goal was to assess the impact of zootechnical practices on the spread of three causal agents of BRD, namely the bovine respiratory syncytial virus (BRSV), Mannheimia haemolytica and Mycoplasma bovis. In that extent, we used an individual based stochastic mechanistic model monitoring risk factors, infectious processes, detection and treatment in a farm possibly featuring several batches simultaneously. The model was calibrated with three sets of parameters relative to each of the three pathogens using data extracted from literature. Separated batches were found to be more effective than a unique large one for reducing the spread of pathogens, especially for BRSV and M.bovis. Moreover, it was found that allocating high risk and low risk individuals into separated batches participated in reducing cumulative incidence, epidemic peaks and antimicrobial usage, especially for M. bovis. Theses findings rise interrogations on the optimal farming practices in order to limit BRD occurrence and pave the way to models featuring coinfections and collective treatments p { line-height: 115%; margin-bottom: 0.25 cm; background: transparent}a:link { color: #000080; text-decoration: underline}a.cjk:link { so-language: zxx}a.ctl:link { solanguage: zxx}.

homFrom a coenzyme-like mechanism to homochirality

Inspired in a coenzyme-like behavior, an alternative mechanism to induce homochirality within a small vesicle is proposed. The system includes six different chemical species: an achiral substrate A, the enantiomeric forms L and D, a coenzyme E and two intermediate catalytic forms LE and DE. Whereas the coenzyme and the intermediate catalytic forms are trapped within the vesicle, the substrate and the two enantiomeric forms are able to diffuse selectively across the vesicle boundary. Instead of using autocatalysis, the production of new enantiomers includes two different steps, the production of intermediate catalytic species (LE, DE) and the catalytic production of new enantiomers from the substrate. Using a suitable parameterization, we found that the chiral evolution of the system is highly dependent on the total amount of coenzyme within the vesicle, regardless of whether the surrounding membrane is permeable or not. However, the existence of large flows from the outside can destabilize the homochiral state inside the vesicle. In general, homochiral states tend to arise when the amount of coenzyme is quite low, a value that can vary according to the parametrization. On the other hand, the system tends to decrease the enantiomeric excess when the coenzyme levels are high enough. In general, the appearance of homochirality is conditioned by stochastic fluctuations in coenzyme levels within the vesicle, an effect that is gradually amplified throughout the entire process of enantiomer synthesis.

The Mathematical modeling of Cancer growth and angiogenesis by an individual based interacting system

We present a mathematical model for the complex system for the growth of a solid tumor. The system embeds proliferation of cells depending on the surrounding oxygen field, hypoxia caused by insufficient oxygen when the tumor reaches a certain size, consequent VEGF release and angiogenic new vasculature growth, re-oxygenation of the tumor and subsequent tumor growth restart. Specifically cancerous cells are represented by individual units, interacting as proliferating particles of a solid body, oxygen, and VEGF are fields with a source and a sink, and new angiogenic vasculature is described by a network of growing curves. The model, as shown by numerical simulations, captures both the time-evolution of the tumor growth before and after angiogenesis and its spatial properties, with different distribution of proliferating and hypoxic cells in the external and deep layers of the tumor, and the spatial structure of the angiogenic network. The microscopic description of the growth opens the possibility of tuning the model to patient-specific scenarios.

Legacy pollutants in fractured aquifers: Analytical approximations for back diffusion to predict atrazine concentrations under uncertainty

We present novel analytical approximations for the estimation of travel distance and relative height of solute concentration peaks within a single fracture system for pollutants that have been temporarily applied at a constant rate in the past. These approximations are used to investigate the spatiotemporal evolution of the concentration of atrazine, as an example for many other so-called legacy compounds that are still found in the groundwater of fractured rock aquifers even decades after their application has stopped. This is done in a stochastic framework to account for the uncertainty in relevant parameters, focusing on probabilities of exceeding the given legal concentration limit and the expected length of the recovery period. We specifically consider the properties of the Muschelkalk limestone aquifer in the Ammer river catchment in SW Germany, and the three major types of carbonate rock facies: Shoal, Tempestite, and Basinal limestones. Atrazine sorption parameters have been determined in laboratory experiments. The simulations confirm that diffusion-limited sorption and desorption may cause considerable atrazine levels long after application stop. For the properties of the considered rock facies types, and corresponding parameter ranges, atrazine concentration above the legal limit is supposed to be limited to locations referring to only a few years of travel time. If the concentration exceeds the legal limit by the year 2022, it will take decades to centuries until recovery.

Native diffusion of fluorogenic turn-on dyes accurately report interfacial chemical reaction locations

Single-molecule fluorescence microscopy with "turn-on" dyes that change fluorescent state after a reaction report on the chemistry of interfaces relevant to analytical and bioanalytical chemistry. Paramount to accurately understanding the phenomena at the ultimate detection limit of a single molecule is ensuring fluorophore properties such as diffusion do not obscure the chemical reaction of interest. Here, we develop Monte Carlo simulations of a dye that undergoes reduction to turn-on at the cathode of a corroded iron surface taking into account the diffusion of the dye molecules in a total internal reflection fluorescence (TIRF) excitation volume, location of the cathode, and chemical reactions. We find, somewhat counterintuitively, that a fast diffusion coefficient of D = 10⁸ nm²/s, corresponding to the dye in aqueous solution, accurately reports the location of single reaction sites. The dyes turn on and are present for the acquisition of a single frame allowing for localization before diffusing out of the thin TIRF excitation volume axially. Previously turned-on (i.e., activated) dyes can also randomly hit the surface surrounding the reaction site leading to a uniform increase in the background. Using concentrations that lead to high turnover rates at the reaction site can achieve signal-to-background ratios of  ~100 in our simulation. Therefore, the interplay between diffusion, turn-on reaction rate, and concentration of the dye must be strategically considered to produce accurate images of reaction locations. This work demonstrates that modeling can assist in the design of single-molecule microscopy experiments to understand interfaces related to analytical chemistry such as electrode, nanoparticle, and sensor surfaces.

A simple model for viral decay dynamics and the distribution of infected cell life spans in SHIV-infected infant rhesus macaques

The dynamics of HIV viral load following the initiation of antiretroviral therapy is not well-described by simple, single-phase exponential decay. Several mathematical models have been proposed to describe its more complex behavior, the most popular of which is two-phase exponential decay. The underlying assumption in two-phase exponential decay is that there are two classes of infected cells with different lifespans. However, with the exception of CD4+ T cells, there is not a consensus on all of the cell types that can become productively infected, and the fit of the two-phase exponential decay to observed data from SHIV.C.CH505 infected infant rhesus macaques was relatively poor. Therefore, we propose a new model for viral decay, inspired by the Gompertz model where the decay rate itself is a dynamic variable. We modify the Gompertz model to include a linear term that modulates the decay rate. We show that this simple model performs as well as the two-phase exponential decay model on HIV and SIV data sets, and outperforms it for the infant rhesus macaque SHIV.C.CH505 infection data set. We also show that by using a stochastic differential equation formulation, the modified Gompertz model can be interpreted as being driven by a population of infected cells with a continuous distribution of cell lifespans, and estimate this distribution for the SHIV.C.CH505-infected infant rhesus macaques. Thus, we find that the dynamics of viral decay in this model of infant HIV infection and treatment may be explained by a distribution of cell lifespans, rather than two distinct cell types.

Modeling Cellular Signaling Variability Based on Single-Cell Data: The TGFβ-SMAD Signaling Pathway

Nongenetic heterogeneity is key to cellular decisions, as even genetically identical cells respond in very different ways to the same external stimulus, e.g., during cell differentiation or therapeutic treatment of disease. Strong heterogeneity is typically already observed at the level of signaling pathways that are the first sensors of external inputs and transmit information to the nucleus where decisions are made. Since heterogeneity arises from random fluctuations of cellular components, mathematical models are required to fully describe the phenomenon and to understand the dynamics of heterogeneous cell populations. Here, we review the experimental and theoretical literature on cellular signaling heterogeneity, with special focus on the TGFβ/SMAD signaling pathway.

Heteroclinic cycling and extinction in May-Leonard models with demographic stochasticity

May and Leonard (SIAM J Appl Math 29:243-253, 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each "cycle", passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic Escherichia coli), in the immune system, in neural information processing models ("winnerless competition"), and in models of neural central pattern generators. Yet as May and Leonard observed "Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two." Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard's ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length.

Deterministic Approach and Monte Carlo Simulation to Predict Listeria monocytogenes Time to Grow on Refrigerated Ham: A Study Supporting Risk-based Decisions for Consumers' Health

This study assessed the growth of Listeria monocytogenes in ready-to-eat (RTE) ham during storage under conditions simulating domestic practices with the intention to offer support in the elaboration of food safety policies that should better protect consumers against food poisoning at home. RTE ham, artificially contaminated at either medium (10²-10³ CFU/g) or high (10⁴-10⁵ CFU/g) concentration, was stored at both isothermal (4℃ in a refrigerator able to maintain a relatively constant temperature and 5℃ and 7℃ in a refrigerator with fluctuating temperature) and dynamic (5℃ and 7℃ with intermittent exposure to ambient temperature, e.g. 25℃) conditions. Under isothermal conditions, the increasing storage temperature determined a significantly increased (p < 0.05) capacity of L. monocytogenes to grow. The kinetic growth parameters were derived by fitting the Baranyi and Roberts model to the experimental data and, based on the maximum specific growth rates, it was estimated the temperature dependence of L. monocytogenes growth in RTE ham. At medium contamination level, sanitary risk time calculation revealed that, unlike storage at 5℃ and 7℃, storage at 4℃ of the RTE ham extends the time period during which the product is safe for consumption by ∼40 and 52%, respectively. However, the real temperature fluctuations included in the Monte Carlo simulations at low L. monocytogenes counts (1, 5 and 10 CFU/g) have shortened the safety margins. Stochastic models also proved to be useful tools for describing the pathogen's behavior when refrigeration of the RTE ham alternates with periods of ham being kept at room temperature, considered dynamic conditions of growth.

MoDLE: high-performance stochastic modeling of DNA loop extrusion interactions

DNA loop extrusion emerges as a key process establishing genome structure and function. We introduce MoDLE, a computational tool for fast, stochastic modeling of molecular contacts from DNA loop extrusion capable of simulating realistic contact patterns genome wide in a few minutes. MoDLE accurately simulates contact maps in concordance with existing molecular dynamics approaches and with Micro-C data and does so orders of magnitude faster than existing approaches. MoDLE runs efficiently on machines ranging from laptops to high performance computing clusters and opens up for exploratory and predictive modeling of 3D genome structure in a wide range of settings.

Modeling signaling pathways in biology with MaBoSS: From one single cell to a dynamic population of heterogeneous interacting cells

As a result of the development of experimental technologies and the accumulation of data, biological and molecular processes can be described as complex networks of signaling pathways. These networks are often directed and signed, where nodes represent entities (genes/proteins) and arrows interactions. They are translated into mathematical models by adding a dynamic layer onto them. Such mathematical models help to understand and interpret non-intuitive experimental observations and to anticipate the response to external interventions such as drug effects on phenotypes. Several frameworks for modeling signaling pathways exist. The choice of the appropriate framework is often driven by the experimental context. In this review, we present MaBoSS, a tool based on Boolean modeling using a continuous time approach, which predicts time-dependent probabilities of entities in different biological contexts. MaBoSS was initially built to model the intracellular signaling in non-interacting homogeneous cell populations. MaBoSS was then adapted to model heterogeneous cell populations (EnsembleMaBoSS) by considering families of models rather than a unique model. To account for more complex questions, MaBoSS was extended to simulate dynamical interacting populations (UPMaBoSS), with a precise spatial distribution (PhysiBoSS). To illustrate all these levels of description, we show how each of these tools can be used with a running example of a simple model of cell fate decisions. Finally, we present practical applications to cancer biology and studies of the immune response.

Modeling air emissions from complex facilities at detailed temporal and spatial resolution: The Methane Emission Estimation Tool (MEET)

Recent attention to methane emissions from oil and gas infrastructure has increased interest in comparing measurements with inventory emission estimates. While measurement methods typically estimate emissions over a few periods that are seconds to hours in length, current inventory methods typically produce long-term average emission estimates. This temporal mis-alignment complicates comparisons and leads to underestimates in the uncertainty of measurement methods. This study describes a new temporally and spatially resolved inventory emission model (MEET), and demonstrates the model by application to compressor station emissions - the key facility type in midstream natural gas operations The study looks at three common facility measurement methods: tracer flux methods for measuring station emissions, the use of ethane-methane ratios for source attribution of basin-scale estimates, and the behavior of continuous monitoring for leak detection at stations. Simulation results indicate that measurement methods likely underestimate uncertainties in emission estimates by failing to account for the variability in normal facility emissions and variations in ethane/methane ratios. A tracer-based measurement campaign could estimate emissions outside the 95% confidence interval of annual emissions 30% of the time, while ethane/methane ratios could be mis-estimated by as much as 50%. Use of MEET also highlights the need to improve data reporting from measurement campaigns to better capture the temporal and spatial variation in observed emissions.

Identifiability analysis for models of the translation kinetics after mRNA transfection

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. That is, whether parameters can be uniquely determined from perfect or realistic data in theory and practice. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

A stochastic approach to estimate intraocular pressure and dynamic corneal responses of the cornea

IntraOcular Pressure (IOP) is one of the most informative factors for monitoring the eye-health. This is usually measured by tonometers. However, the outputs of the tonometers depend on the physical and geometrical properties of the cornea. Therefore, the common practice is to develop a numerical model to generate some correction factors. The main challenge here is the accuracy and efficiency of a numerical model in predicting the IOP and Dynamic Corneal Response (DCR) of each patient. This study addresses this issue by developing a two-step surrogate model based on adaptive sparse Polynomial Chaos Expansion (PCE) for fast and accurate prediction of the IOP. In this regard, first, an FE model of the cornea has been developed to predict the DCR parameters. This FE model has been replaced with a PCE-based surrogate model to speed up the simulation step. The uncertainties in the geometry and material model of the cornea have been propagated through the surrogate model to estimate the distributions of the DCR parameters. In the second step, the combination of DCR parameters and the input parameters provide a proper parameter space for developing an efficient data-driven PCE model to predict the IOP. Moreover, sensitivity analysis by using PCE-based Sobol indices has been performed. The results demonstrate the accuracy and efficiency of the proposed method in predicting the IOP. Sensitivity analysis revealed that IOP measurement was influenced mostly by deflection amplitude and applanation time. The analysis indicates the importance of the interactions between the parameters.

A data-driven method to learn a jump diffusion process from aggregate biological gene expression data

Dynamic models of gene expression are urgently required. In this paper, we describe the time evolution of gene expression by learning a jump diffusion process to model the biological process directly. Our algorithm needs aggregate gene expression data as input and outputs the parameters of the jump diffusion process. The learned jump diffusion process can predict population distributions of gene expression at any developmental stage, obtain long-time trajectories for individual cells, and offer a novel approach to computing RNA velocity. Moreover, it studies biological systems from a stochastic dynamic perspective. Gene expression data at a time point, which is a snapshot of a cellular process, is treated as an empirical marginal distribution of a stochastic process. The Wasserstein distance between the empirical distribution and predicted distribution by the jump diffusion process is minimized to learn the dynamics. For the learned jump diffusion process, its trajectories correspond to the development process of cells, the stochasticity determines the heterogeneity of cells, its instantaneous rate of state change can be taken as "RNA velocity", and the changes in scales and orientations of clusters can be noticed too. We demonstrate that our method can recover the underlying nonlinear dynamics better compared to previous parametric models and the diffusion processes driven by Brownian motion for both synthetic and real world datasets. Our method is also robust to perturbations of data because the computation involves only population expectations.

Fast and scalable earth texture synthesis using spatially assembled generative adversarial neural networks

The earth texture with complex morphological geometry and compositions such as shale and carbonate rocks, is typically characterized with sparse field samples because of an expensive and time-consuming characterization process. Accordingly, generating arbitrary large size of the geological texture with similar topological structures at a low computation cost has become one of the key tasks for realistic geomaterial reconstruction and subsequent hydro-mechanical evaluation for science and engineering applications. Recently, generative adversarial neural networks (GANs) have demonstrated a potential of synthesizing input textural images and creating equiprobable geomaterial images for stochastic analysis of hydrogeological properties, for example, the feasibility of CO₂ storage sites and exploration of unconventional resources. However, the texture synthesis with the GANs framework is often limited by the computational cost and scalability of the output texture size. In this study, we proposed a spatially assembled GANs (SAGANs) that can generate output images of an arbitrary large size regardless of the size of training images with computational efficiency. The performance of the SAGANs was evaluated with two and three dimensional (2D and 3D) rock image samples widely used in geostatistical reconstruction of the earth texture and Lattice-Boltzmann (LB) simulations were performed to compare pore-scale flow patterns and upscaled permeabilities of training and generated geomaterial images. We demonstrate SAGANs can generate the arbitrary large size of statistical realizations with connectivity and structural properties and flow characteristics similar to training images, and also can generate a variety of realizations even on a single training image. In addition, the computational time was significantly improved compared to standard GANs frameworks.

Complementing femur model validation with a variability-focused approach

OBJECTIVE

This short communication presents an approach as an objective means to validate that population variability is potentially incorporated into human body models in an accurate way, complementing existing validation techniques based on individual experiment-simulation comparison. This shall provide a further option for the assessment of the quality of large-number statistical simulations with human body models regarding their biofidelic behavior.

METHODS

This population-based approach uses mathematical clustering methods to group similar curves of a combined population of numerical simulation results and experimental curves together. The resulting clusters can be used to assess the biofidelic behavior of numerical simulations, also with characteristics substantially differing from the experimental objects. This developed population-based approach was tested on a reference load case, the dynamic 3-point bending of the femur (Forman et al. 2012).

RESULTS

The clustering approach rendered a distinction into 4 groups of response curves. For this small number, the grouping can be manually assessed as plausible. All experimental, and most numerical responses were grouped into one cluster. Three result curves constitute a cluster of their own, with their meta-data ranking on the margins of the population in at least one of the crucial biomechanical parameters. Such a result can be considered in accordance with the included experimental and anthropometric data.

CONCLUSIONS

The feasibility of using such a cluster analysis without individual comparisons is demonstrated on a small set of results. It is used to judge whether a finite element model including aspects of the variation in a population is in agreement with experimental and anthropometric data. For experiments as the femur bending addressed here, it is of high importance to firstly ensure a gross match of curve shapes between experiments and simulation, i.e., capturing the relevant biomechanical aspects.

Machine learning-guided, big data-enabled, biomarker-based systems pharmacology: modeling the stochasticity of natural history and disease progression

The incidence of systemic and metabolic co-morbidities increases with aging. The purpose was to investigate a novel paradigm for modeling the orchestrated changes in many disease-related biomarkers that occur during aging. A hybrid strategy that integrates machine learning and stochastic modeling was evaluated for modeling the long-term dynamics of biomarker systems. Bayesian networks (BN) were used to identify quantitative systems pharmacology (QSP)-like models for the inter-dependencies for three disease-related datasets of metabolic (MB), metabolic with leptin (MB-L), and cardiovascular (CVB) biomarkers from the NHANES database. Biomarker dynamics were modeled using discrete stochastic vector autoregression (VAR) equations. BN were used to derive the topological order and connectivity of a data driven QSP model structure for inter-dependence of biomarkers across the lifespan. The strength and directionality of the connections in the QSP models were evaluated using bootstrapping. VAR models based on QSP model structures from BN were assessed for modeling biomarker system dynamics. BN-restricted VAR models of order 1 were identified as parsimonious and effective for characterizing biomarker system dynamics in the MB, MB-L and CVB datasets. Simulation of annual and triennial data for each biomarker provided good fits and predictions of the training and test datasets, respectively. The novel strategy harnesses machine learning to construct QSP model structures for inter-dependence of biomarkers. Stochastic modeling with the QSP models was effective for predicting the age-varying dynamics of disease-relevant biomarkers over the lifespan.

A stochastic micro to macro mechanical model for the evolution of bone-implant interface stiffness

Upon placement of an implant into living bone, an interface is formed through which various biochemical, biological, physical, and mechanical interactions take place. This interface evolves over time as the mechanical properties of peri-implant bone increase. Owing to the multifactorial nature of interfacial processes, it is challenging to devise a comprehensive model for predicting the mechanical behavior of the bone-implant interface. We propose a simple spatio-temporally evolving mechanical model - from an elementary unit cell comprising randomly oriented mineralized collagen fibrils having randomly assigned stiffness all the way up to a macroscopic bone-implant interface in a gap healing scenario. Each unit cell has an assigned Young's modulus value between 1.62 GPa and 25.73 GPa corresponding to minimum (i.e., 0) and maximum (i.e., 0.4) limits of mineral volume fraction, respectively, in the overlap region of the mineralized collagen fibril. Gap closure and subsequent stiffening are modeled to reflect the two main directions of peri-implant bone formation, i.e., contact osteogenesis and distance osteogenesis. The linear elastic stochastic finite element model reveals highly nonlinear temporal evolution of bone-implant interface stiffness, strongly dictated by the specific kinetics of contact osteogenesis and distance osteogenesis. The bone-implant interface possesses a small stiffness until gap closure, which subsequently evolves into a much higher stiffness, and this transition is reminiscent of a percolation transition whose threshold corresponds to gap closure. The model presented here, albeit preliminary, can be incorporated into future calculations of the bone-implant system where the interface is well-defined mechanically. STATEMENT OF SIGNIFICANCE: A simple, physically informed model for the mechanical characteristics of the bone-implant interface is still missing. Here, we start by extending the reported mechanical characteristics of a one cubic micrometre unit cell to a 250 µm long interface made of 1 µm thick layers. The stiffness of each cell (based on mineral content) is assigned randomly to mimic bone micro-heterogeneity. The numerical study of this interface representative structure allows for the simultaneous determination of the spatio-temporal evolution of the mechanical response at local (discrete element) and global (overall model) scales. The proposed model is the first of this kind that can easily be incorporated into realistic future models of bone-implant interaction with emphasis on implant stability and different loading conditions.

Development of a quantitative chemical risk assessment (QCRA) procedure for contaminants of emerging concern in drinking water supply

The uncertainties on the occurrence, fate and hazard of Contaminants of Emerging Concern (CECs) increasingly challenge drinking water (DW) utilities whether additional measures should be taken to reduce the health risk. This has led to the development and evaluation of risk-based approaches by the scientific community. DW guideline values are commonly derived based on deterministic chemical risk assessment (CRA). Here, we propose a new probabilistic procedure, that is a quantitative chemical risk assessment (QCRA), to assess potential health risk related to the occurrence of CECs in DW. The QCRA includes uncertainties in risk calculation in both exposure and hazard assessments. To quantify the health risk in terms of the benchmark quotient probabilistic distribution, the QCRA estimates the probabilistic distribution of CECs concentration in DW based on their concentration in source water and simulating the breakthrough curves of a granular activated carbon (GAC) treatment process. The model inputs and output uncertainties were evaluated by sensitivity and uncertainty analyses for each step of the risk assessment to identify the most relevant factors affecting risk estimation. Dominant factors resulted to be the concentration of CECs in water sources, GAC isotherm parameters and toxicological data. To stress the potential of this new QCRA approach, several case studies are considered with focus on bisphenol A as an example CEC and various GAC management options. QCRA quantifies the probabilistic risk, providing more insight compared to CRA. QCRA proved to be more effective in supporting the intervention prioritization for treatment optimization to pursue health risk minimization.

Computational modeling of the immune response in multiple sclerosis using epimod framework

BACKGROUND

Multiple Sclerosis (MS) represents nowadays in Europe the leading cause of non-traumatic disabilities in young adults, with more than 700,000 EU cases. Although huge strides have been made over the years, MS etiology remains partially unknown. Furthermore, the presence of various endogenous and exogenous factors can greatly influence the immune response of different individuals, making it difficult to study and understand the disease. This becomes more evident in a personalized-fashion when medical doctors have to choose the best therapy for patient well-being. In this optics, the use of stochastic models, capable of taking into consideration all the fluctuations due to unknown factors and individual variability, is highly advisable.

RESULTS

We propose a new model to study the immune response in relapsing remitting MS (RRMS), the most common form of MS that is characterized by alternate episodes of symptom exacerbation (relapses) with periods of disease stability (remission). In this new model, both the peripheral lymph node/blood vessel and the central nervous system are explicitly represented. The model was created and analysed using Epimod, our recently developed general framework for modeling complex biological systems. Then the effectiveness of our model was shown by modeling the complex immunological mechanisms characterizing RRMS during its course and under the DAC administration.

CONCLUSIONS

Simulation results have proven the ability of the model to reproduce in silico the immune T cell balance characterizing RRMS course and the DAC effects. Furthermore, they confirmed the importance of a timely intervention on the disease course.

Stochastic modeling of chlorophyll-a for probabilistic assessment and monitoring of algae blooms in the Lower Nakdong River, South Korea

Eutrophication is one of the critical water quality issues in the world nowadays. Various studies have been conducted to explore the contributing factors related to eutrophication symptoms. However, in the field of eutrophication modeling, the stochastic nature associated with the eutrophication process has not been sufficiently explored, especially in a multivariate stochastic modeling framework. In this study, a multivariate hidden Markov model (MHMM) that can consider the spatio-temporal dependence in chlorophyll-a concentration over the Nakdong River of South Korea was proposed. The MHMM can effectively cluster the intra-seasonal and inter-annual variability of chlorophyll-a, thereby enabling us to understand the spatio-temporal evolutions of algal blooms. The relationships between hydro-climatic conditions (e.g., temperature and river flow) and chlorophyll-a concentrations were evident, whereas a relatively weak relationship with water quality parameters was observed. The MHMM enables us to effectively infer the conditional probability of the eutrophication state for the following month. The self-transition likelihood of staying in the current state is substantially higher than the likelihood of moving to other states. Moreover, the proposed modeling approach can effectively offer a probabilistic decision-support framework for constructing an alert classification of the eutrophication. The potential use of the proposed modeling framework was also provided.

Stable tug-of-war between kinesin-1 and cytoplasmic dynein upon different ATP and roadblock concentrations

The maintenance of intracellular processes, like organelle transport and cell division, depend on bidirectional movement along microtubules. These processes typically require kinesin and dynein motor proteins, which move with opposite directionality. Because both types of motors are often simultaneously bound to the cargo, regulatory mechanisms are required to ensure controlled directional transport. Recently, it has been shown that parameters like mechanical motor activation, ATP concentration and roadblocks on the microtubule surface differentially influence the activity of kinesin and dynein motors in distinct manners. However, how these parameters affect bidirectional transport systems has not been studied. Here, we investigate the regulatory influence of these three parameters using in vitro gliding motility assays and stochastic simulations. We find that the number of active kinesin and dynein motors determines the transport direction and velocity, but that variations in ATP concentration and roadblock density have no significant effect. Thus, factors influencing the force balance between opposite motors appear to be important, whereas the detailed stepping kinetics and bypassing capabilities of the motors only have a small effect.

Modeling the intracellular dynamics of the dengue viral infection and the innate immune response

The interplay between the dengue virus and the innate immune response is not fully understood. Here, we use deterministic and stochastic approaches to investigate the dynamics of the interaction between the interferon-mediated innate immune response and the dengue virus. We aim to develop a quantitative representation of these complex interactions and predict their system-level dynamics. Our simulation results predict bimodal and bistable dynamics that represent viral clearance and virus-producing states. Under normal conditions, we determined that the viral infection outcome is modulated by the innate immune response and the positive-strand viral RNA concentration. Additionally, we tested system perturbations by external stimulation, such as the direct induction of the innate immune response by interferon, and a therapeutic intervention consisting of the direct application of mRNA encoding for several interferon-stimulated genes. Our simulation results suggest optimal regimes for the studied intervention approaches.

Estimation of parameters in biological species with several mating and reproduction alternatives

With the purpose of modeling the demographic dynamics of biological species in which different mating and reproduction alternatives are feasible, in Molina et al. (2014) we introduced a new mathematical model based on discrete-time branching processes. Assuming that the reproduction phase is governed by probability distributions belonging to the power series family, some reproductive parameters for such species were estimated. In this work, in a more general statistical context, we generalize this research. By considering observations, until a given generation, of the number of female and male individuals in each generation, we now investigate several inferential questions about the parameters of biological interest included in the mathematical model. We study such questions using procedures based on Bayesian statistical methodology. We apply the proposed methods to describe the dynamics of salmonid species.

An embedded element based 2D finite element model for the strength prediction of mineralized collagen fibril using Monte-Carlo type of simulations

A computationally efficient statistical model for the prediction of the strength of mineralized collagen fibril (a basic building block of bone) is presented by taking into account the uncertainties associated with the geometrical and material parameters of collagen and mineral phases. The mineral plates have been considered as one-dimensional bar elements embedded in the two-dimensional plane stress collagen matrix. The mineral phase is considered as linear elastic and a hyperelastic material model is adopted for the collagen phase. Further, the crack initiation and propagation in the collagen phase have been modeled using a damage plasticity approach. Different realizations of the arrangement of mineral plates have been generated to account for the associated geometrical uncertainties using an in-house MATLAB® code. Monte-Carlo type simulations have been performed on the different realizations of mineralized collagen fibril to predict its characteristic stress-strain response under tensile load. The characteristic strength of 3.64 GPa is obtained for mineralized collagen fibril using Weibull's analysis which is found to be in agreement with the molecular dynamics simulation data and numerical studies reported in the past. A parameter sensitivity analysis concluded that mineral modulus has a significant effect on the overall tangent modulus of mineralized collagen fibril in large strain regime.

Parameter estimation and treatment optimization in a stochastic model for immunotherapy of cancer

Adoptive Cell Transfer therapy of cancer is currently in full development and mathematical modeling is playing a critical role in this area. We study a stochastic model developed by Baar et al. (2015) for modeling immunotherapy against melanoma skin cancer. First, we estimate the parameters of the deterministic limit of the model based on biological data of tumor growth in mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic Approximation Expectation Maximization algorithm. With the estimated parameters, we return to the stochastic model and calculate the probability of complete T cells exhaustion. We show that for some relevant parameter values, an early relapse is due to stochastic fluctuations (complete T cells exhaustion) with a non negligible probability. Then, focusing on the relapse related to the T cell exhaustion, we propose to optimize the treatment plan (treatment doses and restimulation times) by minimizing the T cell exhaustion probability in the parameter estimation ranges.

Optimisation and control of the supply of blood bags in hemotherapic centres via Markov decision process with discounted arrival rate

Running a cost-effective human blood transfusion supply chain challenges decision makers in blood services world-wide. In this paper, we develop a Markov decision process with the objective of minimising the overall costs of internal and external collections, storing, producing and disposing of blood bags, whilst explicitly considering the probability that a donated blog bag will perish before demanded. The model finds an optimal policy to collect additional bags based on the number of bags in stock rather than using information about the age of the oldest item. Using data from the literature, we validate our model and carry out a case study based on data from a large blood supplier in South America. The study helped achieve an overall increase of 4.5% in blood donations in one year.

To lead or to herd: optimal strategies for 3D collective migration of cell clusters

Cells migrating in clusters play a significant role in a number of biological processes such as embryogenesis, wound healing, and tumor metastasis during cancer progression. A variety of environmental and biochemical factors can influence the collective migration of cells with differing degrees of cell autonomy and inter-cellular coupling strength. For example, weakly coupled cells can move collectively under the influence of contact guidance from neighboring cells or the environment. Alternatively strongly coupled cells might follow one or more leader cells to move as a single cohesive unit. Additionally, chemical and mechanical signaling between these cells may alter the degree of coupling and determine effective cluster sizes. Being able to understand this collective cell migration process is critical in the prediction and manipulation of outcomes of key biological processes. Here we focus on understanding how various environmental and cellular factors influence small clusters of cells migrating collectively within a 3D fibrous matrix. We combine existing knowledge of single-cell migration in 2D and 3D environments, prior experimental observations of cell-cell interactions and collective migration, and a newly developed stochastic model of cell migration in 3D matrices, to simulate the migration of cell clusters in different physiologically relevant environments. Our results show that based on the extracellular environment and the strength of cell-cell mechanical coupling, two distinct optimal approaches to driving collective cell migration emerge. The ability to effectively employ these two distinct migration strategies might be critical for cells to collectively migrate through the heterogeneous tissue environments within the body.

BAYESIAN INFERENCE OF STOCHASTIC REACTION NETWORKS USING MULTIFIDELITY SEQUENTIAL TEMPERED MARKOV CHAIN MONTE CARLO

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not directly measurable and must be inferred from experimental data. Bayesian inference provides a rigorous probabilistic framework for identifying these parameters by finding a posterior parameter distribution that captures their uncertainty. Traditional computational methods for solving inference problems such as Markov Chain Monte Carlo methods based on classical Metropolis-Hastings algorithm involve numerous serial evaluations of the likelihood function, which in turn requires expensive forward solutions of the chemical master equation (CME). We propose an alternate approach based on a multifidelity extension of the Sequential Tempered Markov Chain Monte Carlo (ST-MCMC) sampler. This algorithm is built upon Sequential Monte Carlo and solves the Bayesian inference problem by decomposing it into a sequence of efficiently solved subproblems that gradually increase both model fidelity and the influence of the observed data. We reformulate the finite state projection (FSP) algorithm, a well-known method for solving the CME, to produce a hierarchy of surrogate master equations to be used in this multifidelity scheme. To determine the appropriate fidelity, we introduce a novel information-theoretic criteria that seeks to extract the most information about the ultimate Bayesian posterior from each model in the hierarchy without inducing significant bias. This novel sampling scheme is tested with high performance computing resources using biologically relevant problems.

Distribution and origination of zinc contamination in newly reclaimed heterogeneous dredger fills: Field investigation and numerical simulation

Heavy metal elements, including Zn, Cd, As, Ni, Cu, Pb and Cr, were detected in soils (no deeper than 75 m) from newly reclaimed zones of Shanghai, China. The Zn concentration exceeded soil quality limits. The Zn contamination was tested in both dredger fills and sedimentary layers (①_3-3, ②₃, ④ and ⑤_1-1). However, it was not detected in layer ⑤_1-2-⑨. PCA and HCA analysis show that exogenous Zn probably was the contaminant source of dredger fills before the fills were dredged from the neighboring waters. Stochastic heterogeneity of the dredger fills affects the Zn-depollution remarkably. Numerical simulations show both acid precipitation and widespread drainage channels in the zones contributed to Zn-decrease in the dredger fills no deeper than 1.2 m. Acid rainstorms work better than acid constant precipitation in Zn-remediation for layers below 0.4 m. To remove Zn contamination in deep dredger fills, un-consolidation of the fills should be utilized.

Spatio-temporal dynamics of Host-Virus competition: A model study of influenza A

We present results of a study of the early-time response of the innate immune system to influenza virus infection in an agent-based model (ABM) of epithelial cell layers. We find that the competition between the anti-viral immune response and viral antagonism can lead to viral titers non-monotonic in the initial infection fraction as found in experiments. Our model includes a coarse-grained version of intra-cellular processes and inter-cellular communication via cytokine and virion diffusion. We use ABM to follow the propagation of viral infection in the layer and the increase of the viral load as a function of time for different values of the multiplicity of infection (MOI), the initial number of viruses added per cell. We find that for moderately strong host immune response, the number of infected cells and viral load for a smaller MOI exceeds that for larger MOI, as seen in experiments. We elucidate the mechanism underlying this result as the synergistic action of cytokines secreted by infected cells in controlling viral amplification for larger MOI. We investigate the length and time scales that determine this non-monotonic behavior within the ABM. We study the diffusive spread of virions and cytokines from a single infected cell in an absorbing medium analytically and numerically and deduce the length scale that yields a good estimate of the MOI at which we find non-monotonicity. Detailed computations of the temporal behavior of averaged quantities and spatial measures provide further insights into host-viral interactions and connections to experimental observations.

Enhancing images of shale formations by a hybrid stochastic and deep learning algorithm

Accounting for the morphology of shale formations, which represent highly heterogeneous porous media, is a difficult problem. Although two- or three-dimensional images of such formations may be obtained and analyzed, they either do not capture the nanoscale features of the porous media, or they are too small to be an accurate representative of the media, or both. Increasing the resolution of such images is also costly. While high-resolution images may be used to train a deep-learning network in order to increase the quality of low-resolution images, an important obstacle is the lack of a large number of images for the training, as the accuracy of the network's predictions depends on the extent of the training data. Generating a large number of high-resolution images by experimental means is, however, very time consuming and costly, hence limiting the application of deep-learning algorithms to such an important class of problems. To address the issue we propose a novel hybrid algorithm by which a stochastic reconstruction method is used to generate a large number of plausible images of a shale formation, using very few input images at very low cost, and then train a deep-learning convolutional network by the stochastic realizations. We refer to the method as hybrid stochastic deep-learning (HSDL) algorithm. The results indicate promising improvement in the quality of the images, the accuracy of which is confirmed by visual, as well as quantitative comparison between several of their statistical properties. The results are also compared with those obtained by the regular deep learning algorithm without using an enriched and large dataset for training, as well as with those generated by bicubic interpolation.

Exploring the information transmission properties of noise-induced dynamics: application to glioma differentiation

Background

Cells operate in an uncertain environment, where critical cell decisions must be enacted in the presence of biochemical noise. Information theory can measure the extent to which such noise perturbs normal cellular function, in which cells must perceive environmental cues and relay signals accurately to make timely and informed decisions. Using multivariate response data can greatly improve estimates of the latent information content underlying important cell fates, like differentiation.

Results

We undertake an information theoretic analysis of two stochastic models concerning glioma differentiation therapy, an alternative cancer treatment modality whose underlying intracellular mechanisms remain poorly understood. Discernible changes in response dynamics, as captured by summary measures, were observed at low noise levels. Mitigating certain feedback mechanisms present in the signaling network improved information transmission overall, as did targeted subsampling and clustering of response dynamics.

Conclusion

Computing the channel capacity of noisy signaling pathways present great probative value in uncovering the prevalent trends in noise-induced dynamics. Areas of high dynamical variation can provide concise snapshots of informative system behavior that may otherwise be overlooked. Through this approach, we can examine the delicate interplay between noise and information, from signal to response, through the observed behavior of relevant system components.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2970-7) contains supplementary material, which is available to authorized users.

A mathematical model to describe the demographic dynamics of long-lived raptor species

Population viability analysis of threatened large and long-lived raptor species has strong limitations due to the restricted demographic information available for these species. In this work, we mathematically model the demographic dynamics of these raptor species through time-indexed branching processes. By assuming the more general non-parametric statistical setting, we determine accurate estimates for the most relevant reproductive parameters involved in the model. To this end, we propose an algorithm based on approximate Bayesian computations methods. As illustration, by using real data of counts of the number of pairs in the population, we apply the proposed statistical and computational methods to describe the demographic dynamics of the Eurasian black vulture colony located at National Park of Monfragüe (Spain), which appears to be both the largest and densest breeding colony worldwide. In the scenario of these data-poor species, the class of time-indexed branching processes introduced appears to be appropriate and a more cost-effective method to evaluate dynamics and viability of the populations, applicable to the conservation of these taxa.

The role of stochastic sequestration dynamics for intrinsic noise filtering in signaling network motifs

The relation between design principles of signaling network motifs and their robustness against intrinsic noise still remains illusive. In this work we investigate the role of cascading for coping with intrinsic noise due to stochasticity in molecular reactions. We use stochastic approaches to quantify fluctuations in the terminal kinase of phosphorylation-dephosphorylation cascade motifs and demonstrate that cascading highly affects these fluctuations. We show that this purely stochastic effect can be explained by time-varying sequestration of upstream kinase molecules. In particular, we discuss conditions on time scales and parameter regimes which lead to a reduction of output fluctuations. Our results are put into biological context by adapting rate parameters of our modeling approach to biologically feasible ranges for general binding-unbinding and phosphorylation-dephosphorylation mechanisms. Overall, this study reveals a novel role of stochastic sequestration for dynamic noise filtering in signaling cascade motifs.

Hotspots and main drivers of fecal pollution in Neusiedler See, a large shallow lake in Central Europe

To minimize the risk of negative consequences for public health from fecal pollution in lakes, the continuous surveillance of microbiological water quality parameters, alongside other environmental variables, is necessary at defined bathing sites. Such routine surveillance may prove insufficient to elucidate the main drivers of fecal pollution in a complex lake/watershed ecosystem, and it may be that more comprehensive monitoring activities are required. In this study, the aims were to identify the hotspots and main driving factors of fecal pollution in a large shallow Central European lake, the Neusiedler See, and to determine to what degree its current monitoring network can be considered representative spatially. A stochastic and geostatistical analysis of a huge data set of water quality data (~ 164,000 data points, representing a 22-year time-series) of standard fecal indicator bacteria (SFIB), water quality and meteorological variables sampled at 26 sampling sites was conducted. It revealed that the hotspots of fecal pollution are exclusively related to sites with elevated anthropogenic activity. Background pollution from wildlife or diffuse agricultural run-off at more remote sites was comparatively low. The analysis also showed that variability in the incidence of SFIB was driven mainly by meteorological phenomena, above all, temperature, number of sunny hours, and wind (direction and speed). Due to antagonistic effects and temporal undersampling, the influence of precipitation on SFIB variance could not be clearly determined. Geostatistical analysis did reveal that the current spatial sampling density is insufficient to cover SFIB variance over the whole lake, and that the sites are therefore in the most part representative of local phenomena. Suggestions for the future monitoring and managing of fecal pollution are offered. The applied statistical approach may also serve as a model for the study of other such areas, and in general indicate a method for dealing with similarly large and spatiotemporally heterogeneous datasets.

Mathematical models for the effects of hypertension and stress on kidney and their uncertainty

Determining the future state of individual patients, with regard to the susceptibility to life-threatening condition is a crucial problem in the public health. Chronic Kidney Disease (CKD) is a perilous disease, which is characterized by gradual loss of kidney function. This paper presents a set of mathematical models for CKD by applying both deterministic and stochastic approaches. Specifically, hypertension and stress are considered as the main causes of damaging and removing of nephrons thereby reducing the Glomerular Filtration Rate (GFR), which leads to irreparable damages to the kidney function and may result in renal failure, or even kidney loss. This paper analyzes the equilibria for both deterministic and stochastic models. In this regard, mathematical theorems related to stability and stochastic stability of the models are provided. The other important issue, which is discussed in the presented work, is the uncertainty problem for stochastic models. We have used simulations in MATLAB to calculate the uncertainty of the stochastic models. In addition, we have provided a framework for the future prediction of proposed models in specific cases. Finally, the models and the theoretical results are verified in application by applying them to the real clinical data.

Another look at silent circulation of poliovirus in small populations

Background

Silent circulation of polioviruses complicates the polio endgame and motivates analyses that explore the probability of undetected circulation for different scenarios. A recent analysis suggested a relatively high probability of unusually long silent circulation of polioviruses in small populations (defined as 10,000 people or smaller).

Methods

We independently replicated the simple, hypothetical model by Vallejo et al. (2017) and repeated their analyses to explore the model behavior, interpretation of the results, and implications of simplifying assumptions.

Results

We found a similar trend of increasing times between detected cases with increasing basic reproduction number (R₀) and population size. However, we found substantially lower estimates of the probability of at least 3 years between successive polio cases than they reported, which appear more consistent with the prior literature. While small and isolated populations may sustain prolonged silent circulation, our reanalysis suggests that the existing rule of thumb of less than a 5% chance of 3 or more years of undetected circulation with perfect surveillance holds for most conditions of the model used by Vallejo et al. and most realistic conditions.

Conclusions

Avoiding gaps in surveillance remains critical to declaring wild poliovirus elimination with high confidence as soon as possible after the last detected poliovirus, but concern about transmission in small populations with adequate surveillance should not significantly change the criteria for the certification of wild polioviruses.

Slow update stochastic simulation algorithms for modeling complex biochemical networks

The stochastic simulation algorithm (SSA) based modeling is a well recognized approach to predict the stochastic behavior of biological networks. The stochastic simulation of large complex biochemical networks is a challenge as it takes a large amount of time for simulation due to high update cost. In order to reduce the propensity update cost, we proposed two algorithms: slow update exact stochastic simulation algorithm (SUESSA) and slow update exact sorting stochastic simulation algorithm (SUESSSA). We applied cache-based linear search (CBLS) in these two algorithms for improving the search operation for finding reactions to be executed. Data structure used for incorporating CBLS is very simple and the cost of maintaining this during propensity update operation is very low. Hence, time taken during propensity updates, for simulating strongly coupled networks, is very fast; which leads to reduction of total simulation time. SUESSA and SUESSSA are not only restricted to elementary reactions, they support higher order reactions too. We used linear chain model and colloidal aggregation model to perform a comparative analysis of the performances of our methods with the existing algorithms. We also compared the performances of our methods with the existing ones, for large biochemical networks including B cell receptor and FcϵRI signaling networks.

Analysis of lethal and sublethal impacts of environmental disasters on sperm whales using stochastic modeling

Mathematical models are essential for combining data from multiple sources to quantify population endpoints. This is especially true for species, such as marine mammals, for which data on vital rates are difficult to obtain. Since the effects of an environmental disaster are not fixed, we develop time-varying (nonautonomous) matrix population models that account for the eventual recovery of the environment to the pre-disaster state. We use these models to investigate how lethal and sublethal impacts (in the form of reductions in the survival and fecundity, respectively) affect the population's recovery process. We explore two scenarios of the environmental recovery process and include the effect of demographic stochasticity. Our results provide insights into the relationship between the magnitude of the disaster, the duration of the disaster, and the probability that the population recovers to pre-disaster levels or a biologically relevant threshold level. To illustrate this modeling methodology, we provide an application to a sperm whale population. This application was motivated by the 2010 Deepwater Horizon oil rig explosion in the Gulf of Mexico that has impacted a wide variety of species populations including oysters, fish, corals, and whales.

Intimate Partner Violence: A Stochastic Model

Intimate partner violence (IPV) has been a well-studied problem in the past psychological literature, especially through its classical methodology such as qualitative, quantitative and mixed methods. This article introduces two basic stochastic models as an alternative approach to simulate the short and long-term dynamics of a couple at risk of IPV. In both models, the members of the couple may assume a finite number of states, updating them in a probabilistic way at discrete time steps. After defining the transition probabilities, we first analyze the evolution of the couple in isolation and then we consider the case in which the individuals modify their behavior depending on the perceived violence from other couples in their environment or based on the perceived informal social support. While high perceived violence in other couples may converge toward the own presence of IPV by means a gender-specific transmission, the gender differences fade-out in the case of received informal social support. Despite the simplicity of the two stochastic models, they generate results which compare well with past experimental studies about IPV and they give important practical implications for prevention intervention in this field.

Optimal treatment and stochastic modeling of heterogeneous tumors

In this work we review past articles that have mathematically studied cancer heterogeneity and the impact of this heterogeneity on the structure of optimal therapy. We look at past works on modeling how heterogeneous tumors respond to radiotherapy, and take a particularly close look at how the optimal radiotherapy schedule is modified by the presence of heterogeneity. In addition, we review past works on the study of optimal chemotherapy when dealing with heterogeneous tumors.

REVIEWERS

This article was reviewed by Thomas McDonald, David Axelrod, and Leonid Hanin.

Stochastic modeling suggests that noise reduces differentiation efficiency by inducing a heterogeneous drug response in glioma differentiation therapy

Background

Glioma differentiation therapy is a novel strategy that has been used to induce glioma cells to differentiate into glia-like cells. Although some advances in experimental methods for exploring the molecular mechanisms involved in differentiation therapy have been made, a model-based comprehensive analysis is still needed to understand these differentiation mechanisms and improve the effects of anti-cancer therapeutics. This type of analysis becomes necessary in stochastic cases for two main reasons: stochastic noise inherently exists in signal transduction and phenotypic regulation during targeted therapy and chemotherapy, and the relationship between this noise and drug efficacy in differentiation therapy is largely unknown.

Results

In this study, we developed both an additive noise model and a Chemical-Langenvin-Equation model for the signaling pathways involved in glioma differentiation therapy to investigate the functional role of noise in the drug response. Our model analysis revealed an ultrasensitive mechanism of cyclin D1 degradation that controls the glioma differentiation induced by the cAMP inducer cholera toxin (CT). The role of cyclin D1 degradation in human glioblastoma cell differentiation was then experimentally verified. Our stochastic simulation demonstrated that noise not only renders some glioma cells insensitive to cyclin D1 degradation during drug treatment but also induce heterogeneous differentiation responses among individual glioma cells by modulating the ultrasensitive response of cyclin D1. As such, the noise can reduce the differentiation efficiency in drug-treated glioma cells, which was verified by the decreased evolution of differentiation potential, which quantified the impact of noise on the dynamics of the drug-treated glioma cell population.

Conclusion

Our results demonstrated that targeting the noise-induced dynamics of cyclin D1 during glioma differentiation therapy can increase anti-glioma effects, implying that noise is a considerable factor in assessing and optimizing anti-cancer drug interventions.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0316-x) contains supplementary material, which is available to authorized users.

What is a typical optic nerve head?

Whereas it is known that elevated intraocular pressure (IOP) increases the risk of glaucoma, it is not known why optic nerve heads (ONHs) vary so much in sensitivity to IOP and how this sensitivity depends on the characteristics of the ONH such as tissue mechanical properties and geometry. It is often assumed that ONHs with uncommon or atypical sensitivity to IOP, high sensitivity in normal tension glaucoma or high robustness in ocular hypertension, also have atypical ONH characteristics. Here we address two specific questions quantitatively: Do atypical ONH characteristics necessarily lead to atypical biomechanical responses to elevated IOP? And, do typical biomechanical responses necessarily come from ONHs with typical characteristics. We generated 100,000 ONH numerical models with randomly selected values for the characteristics, all falling within literature ranges of normal ONHs. The models were solved to predict their biomechanical response to an increase in IOP. We classified ONH characteristics and biomechanical responses into typical or atypical using a percentile-based threshold, and calculated the fraction of ONHs for which the answers to the two questions were true and/or false. We then studied the effects of varying the percentile threshold. We found that when we classified the extreme 5% of individual ONH characteristics or responses as atypical, only 28% of ONHs with an atypical characteristic had an atypical response. Further, almost 29% of typical responses came from ONHs with at least one atypical characteristic. Thus, the answer to both questions is no. This answer held irrespective of the threshold for classifying typical or atypical. Our results challenge the assumption that ONHs with atypical sensitivity to IOP must have atypical characteristics. This finding suggests that the traditional approach of identifying risk factors by comparing characteristics between patient groups (e.g. ocular hypertensive vs. primary open angle glaucoma) may not be a sound strategy.