Data-driven Stochastic Model for Quantifying the Interplay Between Amyloid-beta and Calcium Levels in Alzheimer's Disease.

The abnormal aggregation of extracellular amyloid-ß(Aß) in senile plaques resulting in calcium Ca+2 dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in the past to better understand the underlying molecular mechanisms driving Aß deposition and Ca+2 dysregulation. Importantly, synaptic impairments, neuronal loss, and cognitive failure in AD patients are all related to the buildup of intraneuronal Aß accumulation. Moreover, increasing evidence show a feed-forward loop between Aß and Ca+2 levels, i.e. Aß disrupts neuronal Ca+2 levels, which in turn affects the formation of Aß. To better understand this interaction, we report a novel stochastic model where we analyze the positive feedback loop between Aß and Ca+2 using ADNI data. A good therapeutic treatment plan for AD requires precise predictions. Stochastic models offer an appropriate framework for modelling AD since AD studies are observational in nature and involve regular patient visits. The etiology of AD may be described as a multi-state disease process using the approximate Bayesian computation method. So, utilizing ADNI data from 2-year visits for AD patients, we employ this method to investigate the interplay between Aß and Ca+2 levels at various disease development phases. Incorporating the ADNI data in our physics-based Bayesian model, we discovered that a sufficiently large disruption in either Aß metabolism or intracellular Ca+2 homeostasis causes the relative growth rate in both Ca+2 and Aß, which corresponds to the development of AD. The imbalance of Ca+2 ions causes Aß disorders by directly or indirectly affecting a variety of cellular and subcellular processes, and the altered homeostasis may worsen the abnormalities of Ca+2 ion transportation and deposition. This suggests that altering the Ca+2 balance or the balance between Aß and Ca+2 by chelating them may be able to reduce disorders associated with AD and open up new research possibilities for AD therapy.

Choice of friction coefficient deeply affects tissue behaviour in stochastic epithelial vertex models.

To understand the mechanisms that coordinate the formation of biological tissues, the use of numerical implementations is necessary. The complexity of such models involves many assumptions and parameter choices that result in unpredictable consequences, obstructing the comparison with experimental data. Here, we focus on vertex models, a family of spatial models used extensively to simulate the dynamics of epithelial tissues. Usually, in the literature, the choice of the friction coefficient is not addressed using quasi-static deformation arguments that generally do not apply to realistic scenarios. In this manuscript, we discuss the role that the choice of friction coefficient has on the relaxation times and consequently in the conditions of cell cycle progression and division. We explore the effects that these changes have on the morphology, growth rate and topological transitions of the tissue dynamics. These results provide a deeper understanding of the role that an accurate mechanical description plays in the use of vertex models as inference tools. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.

Infectious Disease in the Workplace: Quantifying Uncertainty in Transmission.

Understanding disease transmission in the workplace is essential for protecting workers. To model disease outbreaks, the small populations in many workplaces require that stochastic effects are considered, which results in higher uncertainty. The aim of this study was to quantify and interpret the uncertainty inherent in such circumstances. We assessed how uncertainty of an outbreak in workplaces depends on i) the infection dynamics in the community, ii) the workforce size, iii) spatial structure in the workplace, iv) heterogeneity in susceptibility of workers, and v) heterogeneity in infectiousness of workers. To address these questions, we developed a multiscale model: A deterministic model to predict community transmission, and a stochastic model to predict workplace transmission. We extended this basic workplace model to allow for spatial structure, and heterogeneity in susceptibility and infectiousness in workers. We found a non-monotonic relationship between the workplace transmission rate and the coefficient of variation (CV), which we use as a measure of uncertainty. Increasing community transmission, workforce size and heterogeneity in susceptibility decreased the CV. Conversely, increasing the level of spatial structure and heterogeneity in infectiousness increased the CV. However, when the model predicts bimodal distributions, for example when community transmission is low and workplace transmission is high, the CV fails to capture this uncertainty. Overall, our work informs modellers and policy makers on how model complexity impacts outbreak uncertainty. In particular: workforce size, community and workplace transmission, spatial structure and individual heterogeneity contribute in a specific and individual manner to the predicted workplace outbreak size distribution.

Order from chaos: cellular asymmetries explained with modelling.

Molecules inside cells are subject to physical forces and undergo biochemical interactions, continuously changing their physical properties and dynamics. Despite this, cells achieve highly ordered molecular patterns that are crucial to regulate various cellular functions and to specify cell fate. In the Caenorhabditis elegans one-cell embryo, protein asymmetries are established in the narrow time window of a cell division. What are the mechanisms that allow molecules to establish asymmetries, defying the randomness imposed by Brownian motion? Mathematical and computational models have paved the way to the understanding of protein dynamics up to the 'single-molecule level' when resolution represents an issue for precise experimental measurements. Here we review the models that interpret cortical and cytoplasmic asymmetries in the one-cell C. elegans embryo.

An approach for considering the object surface properties in a TLS stochastic model.

The interaction between laser beams and backscattering object surfaces lies at the fundamental working principle of any Terrestrial Laser Scanning (TLS) system. Optical properties of surfaces such as concrete, metals, wood, etc., which are commonly encountered in structural health monitoring of buildings and structures, constitute an important category of systematic and random TLS errors. This paper presents an approach for considering the random errors caused by object surfaces. Two surface properties are considered: roughness and reflectance. The effects on TLS measurements are modeled stepwise in form of a so-called synthetic variance-covariance matrix (SVCM) based on the elementary error theory. A line of work is continued for the TLS stochastic model by introducing a new approach for determining variances and covariances in the SVCM. Real measurements of cast stone façade elements of a tall building are used to validate this approach and show that the quality of the estimation can be improved with the appropriate SVCM.

Quantitative microbial spoilage risk assessment caused by fungi in sports drinks through multilevel modelling.

The risk of fungal spoilage of sports drinks produced in the beverage industry was assessed using quantitative microbial spoilage risk assessment (QMSRA). The most relevant pathway was the contamination of the bottles during packaging by mould spores in the air. Mould spores' concentration was estimated by longitudinal sampling for 6 years (936 samples) in different production areas and seasons. This data was analysed using a multilevel model that separates the natural variability in spore concentration (as a function of sampling year, season, and area) and the uncertainty of the sampling method. Then, the expected fungal contamination per bottle was estimated by Monte Carlo simulation, considering their settling velocity and the time and exposure area. The product's shelf life was estimated through the inoculation of bottles with mould spores, following the determination of the probability of visual spoilage as a function of storage time at 20 and 30 °C using logistic regression. The Monte Carlo model estimated low expected spore contamination in the product (1.7 × 10-6 CFU/bottle). Nonetheless, the risk of spoilage is still relevant due to the large production volume and because, as observed experimentally, even a single spore has a high spoilage potential. The applicability of the QMSRA during daily production was made possible through the simplification of the model under the hypothesis that no bottle will be contaminated by more than one spore. This simplification allows the calculation of a two-dimensional performance objective that combines the spore concentration in the air and the exposure time, defining "acceptable combinations" according to an acceptable level of spoilage (ALOS; the proportion of spoiled bottles). The implementation of the model at the operational level was done through the representation of the simplified model as a two-dimensional diagram that defines acceptable and unacceptable areas. The innovative methodology employed here for defining and simplifying QMSRA models can be a blueprint for future studies aiming to quantify the risk of spoilage of other beverages with a similar scope.

Enhancing Insights into Australia's Gonococcal Surveillance Programme through Stochastic Modelling.

Continued surveillance of antimicrobial resistance is critical as a feedback mechanism for the generation of concerted public health action. A characteristic of importance in evaluating disease surveillance systems is representativeness. Scenario tree modelling offers an approach to quantify system representativeness. This paper utilises the modelling approach to assess the Australian Gonococcal Surveillance Programme's representativeness as a case study. The model was built by identifying the sequence of events necessary for surveillance output generation through expert consultation and literature review. A scenario tree model was developed encompassing 16 dichotomous branches representing individual system sub-components. Key classifications included biological sex, clinical symptom status, and location of healthcare service access. The expected sensitivities for gonococcal detection and antibiotic status ascertainment were 0.624 (95% CI; 0.524, 0.736) and 0.144 (95% CI; 0.106, 0.189), respectively. Detection capacity of the system was observed to be high overall. The stochastic modelling approach has highlighted the need to consider differential risk factors such as sex, health-seeking behaviours, and clinical behaviour in sample generation. Actionable points generated by this study include modification of clinician behaviour and supplementary systems to achieve a greater contextual understanding of the surveillance data generation process.

Intraday dynamic rescheduling under patient no-shows.

Patient no-shows are a major source of uncertainty for outpatient clinics. A common approach to hedge against the effect of no-shows is to overbook. The trade-off between patient's waiting costs and provider idling/overtime costs determines the optimal level of overbooking. Existing work on appointment scheduling assumes that appointment times cannot be updated once they have been assigned. However, advances in communication technology and the adoption of online (as opposed to in-person) appointments make it possible for appointments to be flexible. In this paper, we describe an intraday dynamic rescheduling model that adjusts upcoming appointments based on observed no-shows. We formulate the problem as a Markov Decision Process in order to compute the optimal pre-day schedule and the optimal policy to update the schedule for every scenario of no-shows. We also propose an alternative formulation based on the idea of 'atomic' actions that allows us to apply a shortest path algorithm to solve for the optimal policy more efficiently. Based on a numerical study using parameter estimates from existing literature, we find that intraday dynamic rescheduling can reduce expected cost by 15% compared to static scheduling.

Strategic and flexible LNG production under uncertain future demand and natural gas prices.

The expectation in global demand for liquified natural gas (LNG) remains bullish in the coming years. Despite the unprecedented impact of the COVID-19 pandemic, and the oil price wars between OPEC and Russia in 2020, causing oversupply and falling prices, the LNG markets continue to demonstrate flexibility and resilience in delivering the needs of different sectors, whilst helping achieve the emissions targets. This is attributed to the high competitiveness amongst LNG producers and suppliers, providing greater confidence for medium-to-long term demand. However, the uncertainties in the current outlook for the return of demand and price growth in the post-COVID period pose difficulty for new liquefaction project investment decisions in the pre-Investment Decision Phase (pre-FID). Accordingly, the consideration of new production and selling strategies is needed in the early design stages of projects to cope with the shift in buyers' sentiments favouring increased reliance on spot and short-term uncontracted volumes, as well as incorporating additional flexibility into long-term contracts. In this study, the economic valuation of the flexible Air Product's AP-X liquefaction technology was investigated considering the modelling of price volatilities, using the mean-reverting jump-diffusion pricing model and Monte Carlo simulation, assuming different demand level scenarios in the high-income Asia Pacific markets based on historical trends. The results clearly demonstrate that embedding flexibility within an LNG production system allows producers and suppliers to diversify selling strategies, and take advantage of the lucrative market conditions when demand and prices increase, and hedge against market risks when demand and prices are low.

A model for malaria treatment evaluation in the presence of multiple species.

Plasmodium falciparum and P. vivax are the two most common causes of malaria. While the majority of deaths and severe morbidity are due to P. falciparum, P. vivax poses a greater challenge to eliminating malaria outside of Africa due to its ability to form latent liver stage parasites (hypnozoites), which can cause relapsing episodes within an individual patient. In areas where P. falciparum and P. vivax are co-endemic, individuals can carry parasites of both species simultaneously. These mixed infections complicate dynamics in several ways: treatment of mixed infections will simultaneously affect both species, P. falciparum can mask the detection of P. vivax, and it has been hypothesised that clearing P. falciparum may trigger a relapse of dormant P. vivax. When mixed infections are treated for only blood-stage parasites, patients are at risk of relapse infections due to P. vivax hypnozoites. We present a stochastic mathematical model that captures interactions between P. falciparum and P. vivax, and incorporates both standard schizonticidal treatment (which targets blood-stage parasites) and radical cure treatment (which additionally targets liver-stage parasites). We apply this model via a hypothetical simulation study to assess the implications of different treatment coverages of radical cure for mixed and P. vivax infections and a "unified radical cure" treatment strategy where P. falciparum, P. vivax, and mixed infections all receive radical cure after screening glucose-6-phosphate dehydrogenase (G6PD) normal. In addition, we investigated the impact of mass drug administration (MDA) of blood-stage treatment. We find that a unified radical cure strategy leads to a substantially lower incidence of malaria cases and deaths overall. MDA with schizonticidal treatment was found to decrease P. falciparum with little effect on P. vivax. We perform a univariate sensitivity analysis to highlight important model parameters.

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.

Modelling the structural disorder in trigonal-prismatic coordinated transition metal dichalcogenides.

Trigonal-prismatic coordinated transition metal dichalcogenides (TMDCs) are formed from stacked (chalcogen)-(transition metal)-(chalcogen) triple layers, where the chemical bond is covalent within the triple layers and van der Waals (vdW) forces are effective between the layers. Bonding is at the origin of the great interest in these compounds, which are used as 2D materials in applications such as catalysis, electronics, photoelectronics, sensors, batteries and thermoelectricity. This paper addresses the issue of modelling the structural disorder in multilayer TMDCs. The structural model takes into account stacking faults, correlated displacement of atoms and average crystallite size/shape, and is assessed by simulation of the X-ray diffraction pattern and fitting to the experimental data relative to a powdered sample of MoS2 exfoliated and restacked via lithiation. From fitting, an average crystallite size of about 50 Å, nearly spherical crystallites and a definite probability of deviation from the fully eclipsed atomic arrangement present in the ordered structure are determined. The increased interlayer distance and correlated intralayer and interlayer atomic displacement are attributed to the presence of lithium intercalated in the vdW gap between triple layers (Li/Mo molar ratio of about 0.06). The model holds for the whole class of trigonal-prismatic coordinated TMDCs, and is suitably flexible to take into account different preparation routes.

Patterns of interdivision time correlations reveal hidden cell cycle factors.

The time taken for cells to complete a round of cell division is a stochastic process controlled, in part, by intracellular factors. These factors can be inherited across cellular generations which gives rise to, often non-intuitive, correlation patterns in cell cycle timing between cells of different family relationships on lineage trees. Here, we formulate a framework of hidden inherited factors affecting the cell cycle that unifies known cell cycle control models and reveals three distinct interdivision time correlation patterns: aperiodic, alternator, and oscillator. We use Bayesian inference with single-cell datasets of cell division in bacteria, mammalian and cancer cells, to identify the inheritance motifs that underlie these datasets. From our inference, we find that interdivision time correlation patterns do not identify a single cell cycle model but generally admit a broad posterior distribution of possible mechanisms. Despite this unidentifiability, we observe that the inferred patterns reveal interpretable inheritance dynamics and hidden rhythmicity of cell cycle factors. This reveals that cell cycle factors are commonly driven by circadian rhythms, but their period may differ in cancer. Our quantitative analysis thus reveals that correlation patterns are an emergent phenomenon that impact cell proliferation and these patterns may be altered in disease.

On predicting heterogeneity in nanoparticle dosage.

Nanoparticles are increasingly employed as a vehicle for the targeted delivery of therapeutics to specific cell types. However, much remains to be discovered about the fundamental biology that dictates the interactions between nanoparticles and cells. Accordingly, few nanoparticle-based targeted therapeutics have succeeded in clinical trials. One element that hinders our understanding of nanoparticle-cell interactions is the presence of heterogeneity in nanoparticle dosage data obtained from standard experiments. It is difficult to distinguish between heterogeneity that arises from stochasticity in nanoparticle-cell interactions, and that which arises from heterogeneity in the cell population. Mathematical investigations have revealed that both sources of heterogeneity contribute meaningfully to the heterogeneity in nanoparticle dosage. However, these investigations have relied on simplified models of nanoparticle internalisation. Here we present a stochastic mathematical model of nanoparticle internalisation that incorporates a suite of relevant biological phenomena such as multistage internalisation, cell division, asymmetric nanoparticle inheritance and nanoparticle saturation. Critically, our model provides information about nanoparticle dosage at an individual cell level. We perform model simulations to examine the influence of specific biological phenomena on the heterogeneity in nanoparticle dosage in the absence of heterogeneity in the cell population. Under certain modelling assumptions, we derive analytic approximations of the nanoparticle dosage distribution. We demonstrate that the analytic approximations are accurate, and show that nanoparticle dosage can be described by a Poisson mixture distribution with rate parameters that are a function of Beta-distributed random variables. We discuss the implications of the analytic results with respect to parameter estimation and model identifiability from standard experimental data. Finally, we highlight extensions and directions for future research.

Eco-hydrological modelling of channel network dynamics-part 1: stochastic simulation of active stream expansion and retraction.

Dynamic changes in the active portion of stream networks represent a phenomenon common to diverse climates and geologic settings. However, mechanistically describing these processes at the relevant spatiotemporal scales without huge computational burdens remains challenging. Here, we present a novel stochastic framework for the effective simulation of channel network dynamics capitalizing on the concept of 'hierarchical structuring of temporary streams'-a general principle to identify the activation/deactivation order of network nodes. The framework allows the long-term description of event-based changes of the river network configuration starting from widely available climatic data (mainly rainfall and evapotranspiration). Our results indicate that climate strongly controls temporal variations of the active length, influencing not only the preferential configuration of the active channels but also the speed of network retraction during drying. Moreover, we observed that-while the statistics of wet length are mainly dictated by the underlying climatic conditions-the spatial patterns of active reaches and the size of the largest connected patch of the network are strongly controlled by the spatial correlation of local persistency. The proposed framework provides a robust mathematical set-up for analysing the multi-faceted ecological legacies of channel network dynamics, as discussed in a companion paper.

Locally correlated kinetics of post-replication DNA methylation reveals processivity and region specificity in DNA methylation maintenance.

DNA methylation occurs predominantly on cytosine-phosphate-guanine (CpG) dinucleotides in the mammalian genome, and the methylation landscape is maintained over mitotic cell division. It has been posited that coupling of maintenance methylation activity among neighbouring CpGs is critical to stability over cellular generations; however, the mechanism is unclear. We used mathematical models and stochastic simulation to analyse data from experiments that probe genome-wide methylation of nascent DNA post-replication in cells. We find that DNA methylation maintenance rates on individual CpGs are locally correlated, and the degree of this correlation varies by genomic regional context. By using theory of protein diffusion along DNA, we show that exponential decay of methylation rate correlation with genomic distance is consistent with enzyme processivity. Our results provide quantitative evidence of genome-wide methyltransferase processivity in vivo. We further developed a method to disentangle different mechanistic sources of kinetic correlations. From the experimental data, we estimate that an individual methyltransferase methylates neighbour CpGs processively if they are 36 basepairs apart, on average. But other mechanisms of coupling dominate for longer inter-CpG distances. Our study demonstrates that quantitative insights into enzymatic mechanisms can be obtained from replication-associated, cell-based genome-wide measurements, by combining data-driven statistical analyses with hypothesis-driven mathematical modelling.

The stochastic θ -SEIHRD model: Adding randomness to the COVID-19 spread.

In this article we mainly extend a newly introduced deterministic model for the COVID-19 disease to a stochastic setting. More precisely, we incorporated randomness in some coefficients by assuming that they follow a prescribed stochastic dynamics. In this way, the model variables are now represented by stochastic process, that can be simulated by appropriately solving the system of stochastic differential equations. Thus, the model becomes more complete and flexible than the deterministic analogous, as it incorporates additional uncertainties which are present in more realistic situations. In particular, confidence intervals for the main variables and worst case scenarios can be computed.

Predicting the Tensile Behaviour of Ultra-High Performance Fibre-Reinforced Concrete from Single-Fibre Pull-Out Tests.

In this paper, a prediction model for the tensile behaviour of ultra-high performance fibre-reinforced concrete is proposed. It is based on integrating force contributions of all fibres crossing the crack plane. Piecewise linear models for the force contributions depending on fibre orientation and embedded length are fitted to force-slip curves obtained in single-fibre pull-out tests. Fibre characteristics in the crack are analysed in a micro-computed tomography image of a concrete sample. For more general predictions, a stochastic fibre model with a one-parametric orientation distribution is introduced. Simple estimators for the orientation parameter are presented, which only require fibre orientations in the crack plane. Our prediction method is calibrated to fit experimental tensile curves.

Characterizing outbreak vulnerability in a stochastic SIS model with an external disease reservoir.

In this article, we take a mathematical approach to the study of population-level disease spread, performing a quantitative and qualitative investigation of an SISκ model which is a susceptible-infectious-susceptible (SIS) model with exposure to an external disease reservoir. The external reservoir is non-dynamic, and exposure from the external reservoir is assumed to be proportional to the size of the susceptible population. The full stochastic system is modelled using a master equation formalism. A constant population size assumption allows us to solve for the stationary probability distribution, which is then used to investigate the predicted disease prevalence under a variety of conditions. By using this approach, we quantify outbreak vulnerability by performing the sensitivity analysis of disease prevalence to changing population characteristics. In addition, the shape of the probability density function is used to understand where, in parameter space, there is a transition from disease free, to disease present, and to a disease endemic system state. Finally, we use Kullback-Leibler divergence to compare our semi-analytical results for the SISκ model with more complex susceptible-infectious-recovered (SIR) and susceptible-exposed-infectious-recovered (SEIR) models.

Inference and uncertainty quantification of stochastic gene expression via synthetic models.

Estimating uncertainty in model predictions is a central task in quantitative biology. Biological models at the single-cell level are intrinsically stochastic and nonlinear, creating formidable challenges for their statistical estimation which inevitably has to rely on approximations that trade accuracy for tractability. Despite intensive interest, a sweet spot in this trade-off has not been found yet. We propose a flexible procedure for uncertainty quantification in a wide class of reaction networks describing stochastic gene expression including those with feedback. The method is based on creating a tractable coarse-graining of the model that is learned from simulations, a synthetic model, to approximate the likelihood function. We demonstrate that synthetic models can substantially outperform state-of-the-art approaches on a number of non-trivial systems and datasets, yielding an accurate and computationally viable solution to uncertainty quantification in stochastic models of gene expression.