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

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

The impact of underreported infections on vaccine effectiveness estimates derived from retrospective cohort studies.

BACKGROUND: Surveillance data and vaccination registries are widely used to provide real-time vaccine effectiveness (VE) estimates, which can be biased due to underreported (i.e. under-ascertained and under-notified) infections. Here, we investigate how the magnitude and direction of this source of bias in retrospective cohort studies vary under different circumstances, including different levels of underreporting, heterogeneities in underreporting across vaccinated and unvaccinated, and different levels of pathogen circulation. METHODS: We developed a stochastic individual-based model simulating the transmission dynamics of a respiratory virus and a large-scale vaccination campaign. Considering a baseline scenario with 22.5% yearly attack rate and 30% reporting ratio, we explored fourteen alternative scenarios, each modifying one or more baseline assumptions. Using synthetic individual-level surveillance data and vaccination registries produced by the model, we estimated the VE against documented infection taking as reference either unvaccinated or recently vaccinated individuals (within 14 days post-administration). Bias was quantified by comparing estimates to the known VE assumed in the model. RESULTS: VE estimates were accurate when assuming homogeneous reporting ratios, even at low levels (10%), and moderate attack rates (<50%). A substantial downward bias in the estimation arose with homogeneous reporting and attack rates exceeding 50%. Mild heterogeneities in reporting ratios between vaccinated and unvaccinated strongly biased VE estimates, downward if cases in vaccinated were more likely to be reported and upward otherwise, particularly when taking as reference unvaccinated individuals. CONCLUSIONS: In observational studies, high attack rates or differences in underreporting between vaccinated and unvaccinated may result in biased VE estimates. This study underscores the critical importance of monitoring data quality and understanding biases in observational studies, to more adequately inform public health decisions.

A branching stochastic evolutionary model of the B-cell repertoire.

We propose a stochastic framework to describe the evolution of the B-cell repertoire during germinal center (GC) reactions. Our model is formulated as a multitype age-dependent branching process with time-varying immigration. The immigration process captures the mechanism by which founder B cells initiate clones by gradually seeding GC over time, while the branching process describes the temporal evolution of the composition of these clones. The model assigns a type to each cell to represent attributes of interest. Examples of attributes include the binding affinity class of the B cells, their clonal family, or the nucleotide sequence of the heavy and light chains of their receptors. The process is generally non-Markovian. We present its properties, including as t → ∞ when the process is supercritical, the most relevant case to study expansion of GC B cells. We introduce temporal alpha and beta diversity indices for multitype branching processes. We focus on the dynamics of clonal dominance, highlighting its non-stationarity, and the accumulation of somatic hypermutations in the context of sequential immunization. We evaluate the impact of the ongoing seeding of GC by founder B cells on the dynamics of the B-cell repertoire, and quantify the effect of precursor frequency and antigen availability on the timing of GC entry. An application of the model illustrates how it may help with interpretation of BCR sequencing data.

Dynamic modes of Notch transcription hubs conferring memory and stochastic activation revealed by live imaging the co-activator Mastermind.

Developmental programming involves the accurate conversion of signalling levels and dynamics to transcriptional outputs. The transcriptional relay in the Notch pathway relies on nuclear complexes containing the co-activator Mastermind (Mam). By tracking these complexes in real time, we reveal that they promote the formation of a dynamic transcription hub in Notch ON nuclei which concentrates key factors including the Mediator CDK module. The composition of the hub is labile and persists after Notch withdrawal conferring a memory that enables rapid reformation. Surprisingly, only a third of Notch ON hubs progress to a state with nascent transcription, which correlates with polymerase II and core Mediator recruitment. This probability is increased by a second signal. The discovery that target-gene transcription is probabilistic has far-reaching implications because it implies that stochastic differences in Notch pathway output can arise downstream of receptor activation.

To correctly give rise to future tissues, cells in an embryo must receive and respond to the right signals, at the right time, in the right way. This involves genes being switched on quickly, with cells often ensuring that a range of molecular actors physically come together at 'transcription hubs' in the nucleus ­ the compartment that houses genetic information. These hubs are thought to foster a microenvironment that facilitates the assembly of the machinery that will activate and copy the required genes into messenger RNA molecules. The resulting 'mRNAs' act as templates for producing the corresponding proteins, allowing cells to adequately respond to signals. For example, the activation at the cell surface of a molecule called Notch triggers a series of events that lead to important developmental genes being transcribed within minutes. This process involves a dedicated group of proteins, known as Notch nuclear complexes, quickly getting together in the nucleus and interacting with the transcriptional machinery. How they do this efficiently at the right gene locations is, however, still poorly understood. In particular, it remained unclear whether Notch nuclear complexes participate in the formation of transcription hubs, as well as how these influence mRNA production and the way cells 'remember' having been exposed to Notch activity. To investigate these questions, DeHaro-Arbona et al. genetically engineered fruit flies so that their Notch nuclear complexes and Notch target genes both carried visible tags that could be tracked in living cells in real time. Microscopy imaging of fly tissues revealed that, due to their characteristics, Notch complexes clustered with the transcription machinery and formed transcription hubs near their target genes. All cells exposed to Notch exhibited these hubs, but only a third produced the mRNAs associated with Notch target genes; adding a second signal (an insect hormone) significantly increased the proportion. This illustrates how 'chance' and collaboration influence the way the organism responds to Notch signalling. Finally, the experiments revealed that the hubs persisted for at least a day after removing the Notch signal. This 'molecular memory' led to cells responding faster when presented with Notch activity again. The work by DeHaro-Arbona sheds light on how individual cells respond to Notch signalling, and the factors that influence the activation of its target genes. This knowledge may prove useful when trying to better understand diseases in which this pathway is implicated, such as cancer.

A stochastic approach for co-evolution process of virus and human immune system.

Infectious diseases have long been a shaping force in human history, necessitating a comprehensive understanding of their dynamics. This study introduces a co-evolution model that integrates both epidemiological and evolutionary dynamics. Utilizing a system of differential equations, the model represents the interactions among susceptible, infected, and recovered populations for both ancestral and evolved viral strains. Methodologically rigorous, the model's existence and uniqueness have been verified, and it accommodates both deterministic and stochastic cases. A myriad of graphical techniques have been employed to elucidate the model's dynamics. Beyond its theoretical contributions, this model serves as a critical instrument for public health strategy, particularly predicting future outbreaks in scenarios where viral mutations compromise existing interventions.

A stochastic world model on gravity for stability inference.

The fact that objects without proper support will fall to the ground is not only a natural phenomenon, but also common sense in mind. Previous studies suggest that humans may infer objects' stability through a world model that performs mental simulations with a priori knowledge of gravity acting upon the objects. Here we measured participants' sensitivity to gravity to investigate how the world model works. We found that the world model on gravity was not a faithful replica of the physical laws, but instead encoded gravity's vertical direction as a Gaussian distribution. The world model with this stochastic feature fit nicely with participants' subjective sense of objects' stability and explained the illusion that taller objects are perceived as more likely to fall. Furthermore, a computational model with reinforcement learning revealed that the stochastic characteristic likely originated from experience-dependent comparisons between predictions formed by internal simulations and the realities observed in the external world, which illustrated the ecological advantage of stochastic representation in balancing accuracy and speed for efficient stability inference. The stochastic world model on gravity provides an example of how a priori knowledge of the physical world is implemented in mind that helps humans operate flexibly in open-ended environments.

On the validity of the state space correspondence strategy based on k-nearest neighbor cross-predictability in assessing directionality in stochastic systems: Application to cardiorespiratory coupling estimation.

We tested the validity of the state space correspondence (SSC) strategy based on k-nearest neighbor cross-predictability (KNNCP) to assess the directionality of coupling in stochastic nonlinear bivariate autoregressive (NBAR) processes. The approach was applied to assess closed-loop cardiorespiratory interactions between heart period (HP) variability and respiration (R) during a controlled respiration (CR) protocol in 19 healthy humans (aged from 27 to 35 yrs, 11 females) and during active standing (STAND) in 25 athletes (aged from 20 to 40 yrs, all men) and 25 non-athletes (aged from 20 to 40 yrs, all men). Over simulated NBAR processes, we found that (i) the SSC approach can detect the correct causal relationship as the direction leads to better KNNCP from the past of the driver to the future state of the target and (ii) simulations suggest that the ability of the method is preserved in any condition of complexity of the interacting series. Over CR and STAND protocols, we found that (a) slowing the breathing rate increases the strength of the causal relationship in both temporal directions in a balanced modality; (b) STAND is more powerful in modulating the coupling strength on the pathway from HP to R; (c) regardless of protocol and experimental condition, the strength of the link from HP to R is stronger than that from R to HP; (d) significant causal relationships in both temporal directions are found regardless of the level of complexity of HP variability and R. The SSC strategy is useful to disentangle closed-loop cardiorespiratory interactions.

Statistically inferred neuronal connections in subsampled neural networks strongly correlate with spike train covariances.

Statistically inferred neuronal connections from observed spike train data are often skewed from ground truth by factors such as model mismatch, unobserved neurons, and limited data. Spike train covariances, sometimes referred to as "functional connections," are often used as a proxy for the connections between pairs of neurons, but reflect statistical relationships between neurons, not anatomical connections. Moreover, covariances are not causal: spiking activity is correlated in both the past and the future, whereas neurons respond only to synaptic inputs in the past. Connections inferred by maximum likelihood inference, however, can be constrained to be causal. However, we show in this work that the inferred connections in spontaneously active networks modeled by stochastic leaky integrate-and-fire networks strongly correlate with the covariances between neurons, and may reflect noncausal relationships, when many neurons are unobserved or when neurons are weakly coupled. This phenomenon occurs across different network structures, including random networks and balanced excitatory-inhibitory networks. We use a combination of simulations and a mean-field analysis with fluctuation corrections to elucidate the relationships between spike train covariances, inferred synaptic filters, and ground-truth connections in partially observed networks.

Stochastic modeling of cascade dynamics: A unified approach for simple and complex contagions across homogeneous and heterogeneous threshold distributions on networks.

The COVID-19 pandemic has underscored the importance of understanding, forecasting, and avoiding infectious processes, as well as the necessity for understanding the diffusion and acceptance of preventative measures. Simple contagions, like virus transmission, can spread with a single encounter, while complex contagions, such as preventive social measures (e.g., wearing masks, social distancing), may require multiple interactions to propagate. This disparity in transmission mechanisms results in differing contagion rates and contagion patterns between viruses and preventive measures. Furthermore, the dynamics of complex contagions are significantly less understood than those of simple contagions. Stochastic models, integrating inherent variability and randomness, offer a way to elucidate complex contagion dynamics. This paper introduces a stochastic model for both simple and complex contagions and assesses its efficacy against ensemble simulations for homogeneous and heterogeneous threshold configurations. The model provides a unified framework for analyzing both types of contagions, demonstrating promising outcomes across various threshold setups on Erds-Rényi graphs.

Vesicle and reaction-diffusion hybrid modeling with STEPS.

Vesicles carry out many essential functions within cells through the processes of endocytosis, exocytosis, and passive and active transport. This includes transporting and delivering molecules between different parts of the cell, and storing and releasing neurotransmitters in neurons. To date, computational simulation of these key biological players has been rather limited and has not advanced at the same pace as other aspects of cell modeling, restricting the realism of computational models. We describe a general vesicle modeling tool that has been designed for wide application to a variety of cell models, implemented within our software STochastic Engine for Pathway Simulation (STEPS), a stochastic reaction-diffusion simulator that supports realistic reconstructions of cell tissue in tetrahedral meshes. The implementation is validated in an extensive test suite, parallel performance is demonstrated in a realistic synaptic bouton model, and example models are visualized in a Blender extension module.

The Stability of Competitive Metacommunities Is Insensitive to Dispersal Connectivity in a Fluctuating Environment.

AbstractMaintaining the stability of ecological communities is critical for conservation, yet we lack a clear understanding of what attributes of metacommunity structure control stability. Some theories suggest that greater dispersal promotes metacommunity stability by stabilizing local populations, while others suggest that dispersal synchronizes fluctuations across patches and leads to global instability. These effects of dispersal on stability may be mediated by metacommunity structure: the number of patches, the pattern of connections across patches, and levels of spatiotemporal correlation in the environment. Thus, we need theory to investigate metacommunity dynamics under different spatial structures and ecological scenarios. Here, we use simulations to investigate whether stability is primarily affected by connectivity, including dispersal rate and topology of connectivity network, or by mechanisms related to the number of patches. We find that in competitive metacommunities with environmental stochasticity, network topology has little effect on stability on the metacommunity scale even while it could change spatial diversity patterns. In contrast, the number of connected patches is the dominant factor promoting stability through averaging stochastic fluctuations across more patches, rather than due to more habitat heterogeneity per se. These results broaden our understanding of how metacommunity structure changes metacommunity stability, which is relevant for designing effective conservation strategies.

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations.

Information dissemination has a significant impact on social development. This paper considers that there are many stochastic factors in the social system, which will result in the phenomena of information cross-dissemination and variation. The dual-system stochastic susceptible-infectious-mutant-recovered model of information cross-dissemination and variation is derived from this problem. Afterward, the existence of the global positive solution is demonstrated, sufficient conditions for the disappearance of information and its stationary distribution are calculated, and the optimal control strategy for the stochastic model is proposed. The numerical simulation supports the results of the theoretical analysis and is compared to the parameter variation of the deterministic model. The results demonstrate that cross-dissemination of information can result in information variation and diffusion. Meanwhile, white noise has a positive effect on information dissemination, which can be improved by adjusting the perturbation parameters.

Stochasticity, determinism, and contingency shape genome evolution of endosymbiotic bacteria.

Evolution results from the interaction of stochastic and deterministic processes that create a web of historical contingency, shaping gene content and organismal function. To understand the scope of this interaction, we examine the relative contributions of stochasticity, determinism, and contingency in shaping gene inactivation in 34 lineages of endosymbiotic bacteria, Sodalis, found in parasitic lice, Columbicola, that are independently undergoing genome degeneration. Here we show that the process of genome degeneration in this system is largely deterministic: genes involved in amino acid biosynthesis are lost while those involved in providing B-vitamins to the host are retained. In contrast, many genes encoding redundant functions, including components of the respiratory chain and DNA repair pathways, are subject to stochastic loss, yielding historical contingencies that constrain subsequent losses. Thus, while selection results in functional convergence between symbiont lineages, stochastic mutations initiate distinct evolutionary trajectories, generating diverse gene inventories that lack the functional redundancy typically found in free-living relatives.

Unsupervised lung CT image registration via stochastic decomposition of deformation fields.

We address the problem of lung CT image registration, which underpins various diagnoses and treatments for lung diseases. The main crux of the problem is the large deformation that the lungs undergo during respiration. This physiological process imposes several challenges from a learning point of view. In this paper, we propose a novel training scheme, called stochastic decomposition, which enables deep networks to effectively learn such a difficult deformation field during lung CT image registration. The key idea is to stochastically decompose the deformation field, and supervise the registration by synthetic data that have the corresponding appearance discrepancy. The stochastic decomposition allows for revealing all possible decompositions of the deformation field. At the learning level, these decompositions can be seen as a prior to reduce the ill-posedness of the registration yielding to boost the performance. We demonstrate the effectiveness of our framework on Lung CT data. We show, through extensive numerical and visual results, that our technique outperforms existing methods.

Stochastic processes shape microbial community assembly in biofilters: Hidden role of rare taxa.

Stochastic and deterministic processes are the major themes governing microbial community assembly; however, their roles in bioreactors are poorly understood. Herein, the mechanisms underlying microbial assembly and the effect of rare taxa were studied in biofilters. Phylogenetic tree analysis revealed differences in microbial communities at various stages. Null model analysis showed that stochastic processes shaped the community assembly, and deterministic processes emerged only in the inoculated activated sludge after domestication. This finding indicates the dominant role of stochastic factors (biofilm formation, accumulation, and aging). The Sloan neutral model corroborated the advantages of stochastic processes and mainly attributed these advantages to rare taxa. Cooccurrence networks revealed the importance of rare taxa, which accounted for more than 85% of the keystones. Overall, these results provide good foundations for understanding community assembly, especially the role of rare taxa, and offer theoretical support for future community design and reactor regulation.

Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions.

Many imaging techniques for biological systems-like fixation of cells coupled with fluorescence microscopy-provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

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

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

Feedback between stochastic gene networks and population dynamics enables cellular decision-making.

Phenotypic selection occurs when genetically identical cells are subject to different reproductive abilities due to cellular noise. Such noise arises from fluctuations in reactions synthesizing proteins and plays a crucial role in how cells make decisions and respond to stress or drugs. We propose a general stochastic agent-based model for growing populations capturing the feedback between gene expression and cell division dynamics. We devise a finite state projection approach to analyze gene expression and division distributions and infer selection from single-cell data in mother machines and lineage trees. We use the theory to quantify selection in multi-stable gene expression networks and elucidate that the trade-off between phenotypic switching and selection enables robust decision-making essential for synthetic circuits and developmental lineage decisions. Using live-cell data, we demonstrate that combining theory and inference provides quantitative insights into bet-hedging-like response to DNA damage and adaptation during antibiotic exposure in Escherichia coli.

Polynomial chaos expansion of SAR and temperature increase variability in 3 T MRI due to stochastic input data.

Objective.Numerical simulations are largely adopted to estimate dosimetric quantities, e.g. specific absorption rate (SAR) and temperature increase, in tissues to assess the patient exposure to the radiofrequency (RF) field generated during magnetic resonance imaging (MRI). Simulations rely on reference anatomical human models and tabulated data of electromagnetic and thermal properties of biological tissues. However, concerns may arise about the applicability of the computed results to any phenotype, introducing a significant degree of freedom in the simulation input data. In addition, simulation input data can be affected by uncertainty in relative positioning of the anatomical model with respect to the RF coil. The objective of this work is the to estimate the variability of SAR and temperature increase at 3 T head MRI due to different sources of variability in input data, with the final aim to associate a global uncertainty to the dosimetric outcomes.Approach.A stochastic approach based on arbitrary Polynomial Chaos Expansion is used to evaluate the effects of several input variability's (anatomy, tissue properties, body position) on dosimetric outputs, referring to head imaging with a 3 T MRI scanner.Main results.It is found that head anatomy is the prevailing source of variability for the considered dosimetric quantities, rather than the variability due to tissue properties and head positioning. From knowledge of the variability of the dosimetric quantities, an uncertainty can be attributed to the results obtained using a generic anatomical head model when SAR and temperature increase values are compared with safety exposure limits.Significance.This work associates a global uncertainty to SAR and temperature increase predictions, to be considered when comparing the numerically evaluated dosimetric quantities with reference exposure limits. The adopted methodology can be extended to other exposure scenarios for MRI safety purposes.

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

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