Biosensors based on peptide exposure show single molecule conformations in live cells.

We describe an approach to study the conformation of individual proteins during single particle tracking (SPT) in living cells. "Binder/tag" is based on incorporation of a 7-mer peptide (the tag) into a protein where its solvent exposure is controlled by protein conformation. Only upon exposure can the peptide specifically interact with a reporter protein (the binder). Thus, simple fluorescence localization reflects protein conformation. Through direct excitation of bright dyes, the trajectory and conformation of individual proteins can be followed. Simple protein engineering provides highly specific biosensors suitable for SPT and FRET. We describe tagSrc, tagFyn, tagSyk, tagFAK, and an orthogonal binder/tag pair. SPT showed slowly diffusing islands of activated Src within Src clusters and dynamics of activation in adhesions. Quantitative analysis and stochastic modeling revealed in vivo Src kinetics. The simplicity of binder/tag can provide access to diverse proteins.

The effectiveness of moderating harmful online content.

In 2022, the European Union introduced the Digital Services Act (DSA), a new legislation to report and moderate harmful content from online social networks. Trusted flaggers are mandated to identify harmful content, which platforms must remove within a set delay (currently 24 h). Here, we analyze the likely effectiveness of EU-mandated mechanisms for regulating highly viral online content with short half-lives. We deploy self-exciting point processes to determine the relationship between the regulated moderation delay and the likely harm reduction achieved. We find that harm reduction is achievable for the most harmful content, even for fast-paced platforms such as Twitter. Our method estimates moderation effectiveness for a given platform and provides a rule of thumb for selecting content for investigation and flagging, managing flaggers' workload.

Modeling kinematic variability reveals displacement and velocity based dual control of saccadic eye movements.

Noise is a ubiquitous component of motor systems that leads to behavioral variability of all types of movements. Nonetheless, systems-based models investigating human movements are generally deterministic and explain only the central tendencies like mean trajectories. In this paper, a novel approach to modeling kinematic variability of movements is presented and tested on the oculomotor system. This approach reconciles the two prominent philosophies of saccade control: displacement-based control versus velocity-based control. This was achieved by quantifying the variability in saccadic eye movements and developing a stochastic model of its control. The proposed stochastic dual model generated significantly better fits of inter-trial variances of the saccade trajectories compared to existing models. These results suggest that the saccadic system can flexibly use the information of both desired displacement and velocity for its control. This study presents a potential framework for investigating computational principles of motor control in the presence of noise utilizing stochastic modeling of kinematic variability.

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.

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.

Remaining Useful Life Estimation of Hollow Worn Railway Vehicle Wheels via On-Board Random Vibration-Based Wheel Tread Depth Estimation.

The problem of remaining useful life estimation (RULE) of hollow worn railway vehicle wheels in terms of remaining mileage via wheel tread depth estimation using on-board vibration signals from a single accelerometer on the bogie frame is presently investigated. This is achieved based on the introduction of a statistical time series method that employs: (i) advanced data-driven stochastic Functionally Pooled models for the modeling of the vehicle dynamics under different wheel tread depths in a range of interest until a critical limit, as well as tread depth estimation through a proper optimization procedure, and (ii) a wheel tread depth evolution function with respect to the vehicle running mileage that interconnects the estimated hollow wear with the remaining useful mileage. The method's RULE performance is investigated via hundreds of Simpack-based Monte Carlo simulations with an Attiko Metro S.A. vehicle and many hollow worn wheels scenarios which are not used for the method's training. The obtained results indicate the accurate estimation of the wheels tread depth with a mean absolute error of ∼0.07 mm that leads to a corresponding small error of ∼3% with respect to the wheels remaining useful mileage. In addition, the comparison with a recently introduced Multiple Model (MM)-based multi-health state classification method for RULE, demonstrates the better performance of the postulated method that achieves 81.17% True Positive Rate (TPR) which is significantly higher than the 45.44% of the MM method.

Quantifying future carbon emissions uncertainties under stochastic modeling and Monte Carlo simulation: Insights for environmental policy consideration for the Belt and Road Initiative Region.

This study critically examines future carbon (CO2) emissions in the Belt & Road Initiative (BRI) region, considering factors such as energy consumption, economic growth, population growth, and population density. The objective of this study is to identify critical areas of higher emissions, which require policy intervention capable of strengthening sustainability in the BRI compact. A combined approach of stochastic modeling and Monte Carlo simulations was employed, utilizing panel data from 45 countries in the BRI region from 1990 to 2021. Results confirm that emissions are higher in all scenarios in direct proportion to electric power consumption, population growth, and Gross Domestic Product (GDP) growth. In scenarios with high emissions, a continuous and significant upward trend in CO2 emissions was observe. The medium emissions scenario exhibited a more moderated rise in emissions, suggesting a balance between economic development and environmental considerations. Critical areas for future environmental policy-making resides in electric power consumption, population growth, and GDP growth. The study strongly recommends for a shift from the current focus on road and railway infrastructure to renewable energy infrastructure, green innovations and efficient technology transfer to member countries. Without this, the BRI region is likely to face increased emissions, posing significant challenges to future sustainable development and global environmental sustainability.

A Mechanistic Model of Perceptual Binding Predicts That Binding Mechanism Is Robust against Noise.

The concept of the brain's own time and space is central to many models and theories that aim to explain how the brain generates consciousness. For example, the temporo-spatial theory of consciousness postulates that the brain implements its own inner time and space for conscious processing of the outside world. Furthermore, our perception and cognition of time and space can be different from actual time and space. This study presents a mechanistic model of mutually connected processes that encode phenomenal representations of space and time. The model is used to elaborate the binding mechanism between two sets of processes representing internal space and time, respectively. Further, a stochastic version of the model is developed to investigate the interplay between binding strength and noise. Spectral entropy is used to characterize noise effects on the systems of interacting processes when the binding strength between them is varied. The stochastic modeling results reveal that the spectral entropy values for strongly bound systems are similar to those for weakly bound or even decoupled systems. Thus, the analysis performed in this study allows us to conclude that the binding mechanism is noise-resilient.

Estimation of monkeypox spread in a nonendemic country considering contact tracing and self-reporting: A stochastic modeling study.

In May 2022, monkeypox started to spread in nonendemic countries. To investigate contact tracing and self-reporting of the primary case in the local community, a stochastic model is developed. An algorithm based on Gillespie's stochastic chemical kinetics is used to quantify the number of infections, contacts, and duration from the arrival of the primary case to the detection of the index case (or until there are no more local infections). Different scenarios were set considering the delay in contact tracing and behavior of infectors. We found that the self-reporting behavior of a primary case is the most significant factor affecting outbreak size and duration. Scenarios with a self-reporting primary case have an 86% reduction in infections (average: 5-7, in a population of 10 000) and contacts (average: 27-72) compared with scenarios with a non-self-reporting primary case (average number of infections and contacts: 27-72 and 197-537, respectively). Doubling the number of close contacts per day is less impactful compared with the self-reporting behavior of the primary case as it could only increase the number of infections by 45%. Our study emphasizes the importance of the prompt detection of the primary case.

A comparative probabilistic analysis of human and chimpanzee rotator cuff functional capacity.

Computational musculoskeletal modeling represents a valuable approach to examining biological systems in physical anthropology. Probabilistic modeling builds on computational musculoskeletal models by associating mathematical distributions of specific musculoskeletal features within known ranges of biological variability with functional outcomes. The purpose of this study was to determine if overlap in rotator cuff muscle force predictions would occur between species during the performance of an evolutionarily relevant horizontal bimanual arm suspension task. This necessitated creating novel probabilistic models of the human and chimpanzee glenohumeral joint through augmentation of previously published deterministic models. Glenohumeral musculoskeletal features of anthropological interest were probabilistically modeled to produce distributions of predicted human and chimpanzee rotator cuff muscle force that were representative of the specific anatomical manipulations. Musculoskeletal features modeled probabilistically included rotator cuff origins and deltoid insertion, glenoid inclination, and joint stability. Predicted human rotator cuff muscle force distributions were mostly limited to alternating between infraspinatus and teres minor, with both 100% and 0% muscle force predicted for both muscles. The chimpanzee model predicted low-to-moderate muscle force across all rotator cuff muscles. Rotator cuff muscle force predictions were most sensitive to changes of muscle origins and insertions. Results indicate that functional rotator cuff overlap is unlikely between chimpanzees and humans without greater modifications of the glenohumeral musculoskeletal phenotypes. The results also highlight the low efficacy of the human upper extremity in overhead, weight-bearing tasks, and propensity for rotator cuff injury.

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.

Non-homogeneous continuous-time Markov chain with covariates: Applications to ambulatory hypertension monitoring.

Hypertension significantly increases the risk for many health conditions including heart disease and stroke. Hypertensive patients often have continuous measurements of their blood pressure to better understand how it fluctuates over the day. The continuous-time Markov chain (CTMC) is commonly used to study repeated measurements with categorical outcomes. However, the standard CTMC may be restrictive, because the rates of transitions between states are assumed to be constant through time, while the transition rates for describing the dynamics of hypertension are likely to be changing over time. In addition, the applications of CTMC rarely account for the effects of other covariates on state transitions. In this article, we considered a non-homogeneous continuous-time Markov chain with two states to analyze changes in hypertension while accounting for multiple covariates. The explicit formulas for the transition probability matrix as well as the corresponding likelihood function were derived. In addition, we proposed a maximum likelihood estimation algorithm for estimating the parameters in the time-dependent rate function. Lastly, the model performance was demonstrated through both a simulation study and application to ambulatory blood pressure data.

Internal Biofilm Heterogeneities Enhance Solute Mixing and Chemical Reactions in Porous Media.

Bacterial biofilms can form in porous media that are of interest in industrial applications ranging from medical implants to biofilters as well as in environmental applications such as in situ groundwater remediation, where they can be critical locations for biogeochemical reactions. The presence of biofilms modifies porous media topology and hydrodynamics by clogging pores and consequently solutes transport and reactions kinetics. The interplay between highly heterogeneous flow fields found in porous media and microbial behavior, including biofilm growth, results in a spatially heterogeneous biofilm distribution in the porous media as well as internal heterogeneity across the thickness of the biofilm. Our study leverages highly resolved three-dimensional X-ray computed microtomography images of bacterial biofilms in a tubular reactor to numerically compute pore-scale fluid flow and solute transport by considering multiple equivalent stochastically generated internal permeability fields for the biofilm. We show that the internal heterogeneous permeability mainly impacts intermediate velocities when compared with homogeneous biofilm permeability. While the equivalent internal permeability fields of the biofilm do not impact fluid-fluid mixing, they significantly control a fast reaction. For biologically driven reactions such as nutrient or contaminant uptake by the biofilm, its internal permeability field controls the efficiency of the process. This study highlights the importance of considering the internal heterogeneity of biofilms to better predict reactivity in industrial and environmental bioclogged porous systems.

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 robust scenario analysis approach to water recycling quantitative microbial risk assessment.

AIMS: The growing need to access recycled water as a source for drinking water supply necessitates management of perceived risks. This study aimed to use quantitative microbial risk analysis (QMRA) to evaluate microbiological risks of indirect water recycling. METHODS AND RESULTS: Scenario analyses of risk probabilities of pathogen infection were conducted to investigate four key quantitative microbial risk assessment model assumptions: treatment process failure, drinking water consumption events per day, inclusion or exclusion of an engineered storage buffer, and treatment process redundancy. Results demonstrated that the proposed water recycling scheme could meet WHO pathogen risk guidelines of ∼10-3 annual risk of infection under 18 simulated scenarios.

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.

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.

Filtering input fluctuations in intensity and in time underlies stochastic transcriptional pulses without feedback.

Stochastic pulsatile dynamics have been observed in an increasing number of biological circuits with known mechanism involving feedback control and bistability. Surprisingly, recent single-cell experiments in Escherichia coli flagellar synthesis showed that flagellar genes are activated in stochastic pulses without the means of feedback. However, the mechanism for pulse generation in these feedbackless circuits has remained unclear. Here, by developing a system-level stochastic model constrained by a large set of single-cell E. coli flagellar synthesis data from different strains and mutants, we identify the general underlying design principles for generating stochastic transcriptional pulses without feedback. Our study shows that an inhibitor (YdiV) of the transcription factor (FlhDC) creates a monotonic ultrasensitive switch that serves as a digital filter to eliminate small-amplitude FlhDC fluctuations. Furthermore, we find that the high-frequency (fast) fluctuations of FlhDC are filtered out by integration over a timescale longer than the timescale of the input fluctuations. Together, our results reveal a filter-and-integrate design for generating stochastic pulses without feedback. This filter-and-integrate mechanism enables a general strategy for cells to avoid premature activation of the expensive downstream gene expression by filtering input fluctuations in both intensity and time so that the system only responds to input signals that are both strong and persistent.

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.

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.