Random walk models in biology

Social information-mediated population dynamics in non-grouping prey

Abstract

Inadvertent social information (ISI) use, i.e., the exploitation of social cues including the presence and behaviour of others, has been predicted to mediate population-level processes even in the absence of cohesive grouping. However, we know little about how such effects may arise when the prey population lacks social structure beyond the spatiotemporal autocorrelation originating from the random movement of individuals. In this study, we built an individual-based model where predator avoidance behaviour could spread among randomly moving prey through the network of nearby observers. We qualitatively assessed how ISI use may affect prey population size when cue detection was associated with different probabilities and fitness costs, and characterised the structural properties of the emerging detection networks that would provide pathways for information spread in prey. We found that ISI use was among the most influential model parameters affecting prey abundance and increased equilibrium population sizes in most examined scenarios. Moreover, it could substantially contribute to population survival under high predation pressure, but this effect strongly depended on the level of predator detection ability. When prey exploited social cues in the presence of high predation risk, the observed detection networks consisted of a large number of connected components with small sizes and small ego networks; this resulted in efficient information spread among connected individuals in the detection networks. Our study provides hypothetical mechanisms about how temporary local densities may allow information diffusion about predation threats among conspecifics and facilitate population stability and persistence in non-grouping animals.

Significance statement

The exploitation of inadvertently produced social cues may not only modify individual behaviour but also fundamentally influence population dynamics and species interactions. Using an individual-based model, we investigated how the detection and spread of adaptive antipredator behaviour may cascade to changes in the demographic performance of randomly moving (i.e., non-grouping) prey. We found that social information use contributed to population stability and persistence by reducing predation-related per capita mortality and raising equilibrium population sizes when predator detection ability reached a sufficient level. We also showed that temporary detection networks had structural properties that allowed efficient information spread among prey under high predation pressure. Our work represents a general modelling approach that could be adapted to specific predator-prey systems and scrutinise how temporary local densities allow dynamic information diffusion about predation threats and facilitate population stability in non-grouping animals.

Unexpected advantages of exploitation for target searches in complex networks

Exploitation universally emerges in various decision-making contexts, e.g., animals foraging, web surfing, the evolution of scientists' research topics, and our daily lives. Despite its ubiquity, exploitation, which refers to the behavior of revisiting previous experiences, has often been considered to delay the search process of finding a target. In this paper, we investigate how exploitation affects search performance by applying a non-Markovian random walk model, where a walker randomly revisits a previously visited node using long-term memory. We analytically study two broad forms of network structures, namely, (i) clique-like networks and (ii) lollipop-like networks and find that exploitation can significantly improve search performance in lollipop-like networks, whereas it hinders target search in clique-like networks. Moreover, we numerically verify that exploitation can reduce the time needed to fully explore the underlying networks using 550 diverse real-world networks. Based on the analytic result, we define the lollipop-likeness of a network and observe a positive relationship between the advantage of exploitation and lollipop-likeness.

Attaining the recesses of the cognitive space

Existing neuropsychological tests of executive function often manifest a difficulty pinpointing cognitive deficits when these are intermittent and come in the form of omissions. We discuss the hypothesis that two partially interrelated reasons for this failure stem from relative inability of neuropsychological tests to explore the cognitive space and to explicitly take into account strategic and opportunistic resource allocation decisions, and to address the temporal aspects of both behaviour and task-related brain function in data analysis. Criteria for tasks suitable for neuropsychological assessment of executive function, as well as appropriate ways to analyse and interpret observed behavioural data are suggested. It is proposed that experimental tasks should be devised which emphasize typical rather than optimal performance, and that analyses should quantify path-dependent fluctuations in performance levels rather than averaged behaviour. Some implications for experimental neuropsychology are illustrated for the case of planning and problem-solving abilities and with particular reference to cognitive impairment in closed-head injury.

Follow that cell: leukocyte migration in L-plastin mutant zebrafish

Actin assemblies are important in motile cells such as leukocytes which form dynamic plasma membrane extensions or podia. L-plastin (LCP1) is a leukocyte-specific calcium-dependent actin-bundling protein that, in mammals, is known to affect immune cell migration. Previously, we generated CRISPR/Cas9 engineered zebrafish lacking L-plastin (lcp1-/-) and reported that they had reduced survival to adulthood, suggesting that lack of this actin-bundler might negatively affect the immune system. To test this hypothesis, we examined the distribution and migration of neutrophils and macrophages in the transparent tail of early zebrafish larvae using cell-specific markers and an established wound-migration assay. Knockout larvae were similar to their heterozygous siblings in having equal body sizes and comparable numbers of neutrophils in caudal hematopoietic tissue at two days post-fertilization, indicating no gross defect in neutrophil production or developmental migration. When stimulated by a tail wound, all genotypes of neutrophils were equally migratory in a two-hour window. However for macrophages we observed both migration defects and morphological differences. L-plastin knockout macrophages (lcp1 -/-) still homed to wounds but were slower, less directional and had a star-like morphology with many leading and trailing projections. In contrast, heterozygous macrophages lcp1 (+/-) were faster, more directional, and had a streamlined, slug-like morphology. Overall, these findings show that in larval zebrafish L-plastin knockout primarily affects the macrophage response with possible consequences for organismal immunity. Consistent with our observations, we propose a model in which cytoplasmic L-plastin negatively regulates macrophage integrin adhesion by holding these transmembrane heterodimers in a 'clasped', inactive form and is a necessary part of establishing macrophage polarity during chemokine-induced motility. This article is protected by copyright. All rights reserved.

Live imaging of the co-translational recruitment of XBP1 mRNA to the ER and its processing by diffuse, non-polarized IRE1α

Endoplasmic reticulum (ER) to nucleus homeostatic signaling, known as the unfolded protein response (UPR), relies on the non-canonical splicing of XBP1 mRNA. The molecular switch that initiates splicing is the oligomerization of the ER stress sensor and UPR endonuclease IRE1α (inositol-requiring enzyme 1 alpha). While IRE1α can form large clusters that have been proposed to function as XBP1 processing centers on the ER, the actual oligomeric state of active IRE1α complexes as well as the targeting mechanism that recruits XBP1 to IRE1α oligomers remains unknown. Here, we have developed a single-molecule imaging approach to monitor the recruitment of individual XBP1 transcripts to the ER surface. Using this methodology, we confirmed that stable ER association of unspliced XBP1 mRNA is established through HR2 (hydrophobic region 2)-dependent targeting and relies on active translation. In addition, we show that IRE1α-catalyzed splicing mobilizes XBP1 mRNA from the ER membrane in response to ER stress. Surprisingly, we find that XBP1 transcripts are not recruited into large IRE1α clusters, which are only observed upon overexpression of fluorescently tagged IRE1α during ER stress. Our findings support a model where ribosome-engaged, immobilized XBP1 mRNA is processed by small IRE1α assemblies that could be dynamically recruited for processing of mRNA transcripts on the ER.

Network meta-analysis and random walks

Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. In assessing the validity of an NMA, it is therefore important to know the proportion contributions of each direct treatment comparison to each network treatment effect. The construction of proportion contributions is based on the observation that each row of the hat matrix represents a so-called "evidence flow network" for each treatment comparison. However, the existing algorithm used to calculate these values is associated with ambiguity according to the selection of paths. In this article, we present a novel analogy between NMA and random walks. We use this analogy to derive closed-form expressions for the proportion contributions. A random walk on a graph is a stochastic process that describes a succession of random "hops" between vertices which are connected by an edge. The weight of an edge relates to the probability that the walker moves along that edge. We use the graph representation of NMA to construct the transition matrix for a random walk on the network of evidence. We show that the net number of times a walker crosses each edge of the network is related to the evidence flow network. By then defining a random walk on the directed evidence flow network, we derive analytically the matrix of proportion contributions. The random-walk approach has none of the associated ambiguity of the existing algorithm.

Guidance by followers ensures long-range coordination of cell migration through α-catenin mechanoperception

Morphogenesis, wound healing, and some cancer metastases depend upon the migration of cell collectives that need to be guided to their destination as well as coordinated with other cell movements. During zebrafish gastrulation, the extension of the embryonic axis is led by the mesendodermal polster that migrates toward the animal pole, followed by the axial mesoderm that undergoes convergence and extension. Here, we investigate how polster cells are guided toward the animal pole. Using a combination of precise laser ablations, advanced transplants, and functional as well as in silico approaches, we establish that each polster cell is oriented by its immediate follower cells. Each cell perceives the migration of followers, through E-cadherin/α-catenin mechanotransduction, and aligns with them. Therefore, directional information propagates from cell to cell over the whole tissue. Such guidance of migrating cells by followers ensures long-range coordination of movements and developmental robustness.

Slow wave synchronization and sleep state transitions

Spontaneous synchronization over large networks is ubiquitous in nature, ranging from inanimate to biological systems. In the human brain, neuronal synchronization and de-synchronization occur during sleep, with the greatest degree of neuronal synchronization during slow wave sleep (SWS). The current sleep classification schema is based on electroencephalography and provides common criteria for clinicians and researchers to describe stages of non-rapid eye movement (NREM) sleep as well as rapid eye movement (REM) sleep. These sleep stage classifications have been based on convenient heuristic criteria, with little consideration of the accompanying normal physiological changes across those same sleep stages. To begin to resolve those inconsistencies, first focusing only on NREM sleep, we propose a simple cluster synchronization model to explain the emergence of SWS in healthy people without sleep disorders. We apply the empirical mode decomposition (EMD) analysis to quantify slow wave activity in electroencephalograms, and provide quantitative evidence to support our model. Based on this synchronization model, NREM sleep can be classified as SWS and non-SWS, such that NREM sleep can be considered as an intrinsically bistable process. Finally, we develop an automated algorithm for SWS classification. We show that this new approach can unify brain wave dynamics and their corresponding physiologic changes.

Anomalous diffusion and asymmetric tempering memory in neutrophil chemotaxis

The motility of neutrophils and their ability to sense and to react to chemoattractants in their environment are of central importance for the innate immunity. Neutrophils are guided towards sites of inflammation following the activation of G-protein coupled chemoattractant receptors such as CXCR2 whose signaling strongly depends on the activity of Ca2+ permeable TRPC6 channels. It is the aim of this study to analyze data sets obtained in vitro (murine neutrophils) and in vivo (zebrafish neutrophils) with a stochastic mathematical model to gain deeper insight into the underlying mechanisms. The model is based on the analysis of trajectories of individual neutrophils. Bayesian data analysis, including the covariances of positions for fractional Brownian motion as well as for exponentially and power-law tempered model variants, allows the estimation of parameters and model selection. Our model-based analysis reveals that wildtype neutrophils show pure superdiffusive fractional Brownian motion. This so-called anomalous dynamics is characterized by temporal long-range correlations for the movement into the direction of the chemotactic CXCL1 gradient. Pure superdiffusion is absent vertically to this gradient. This points to an asymmetric 'memory' of the migratory machinery, which is found both in vitro and in vivo. CXCR2 blockade and TRPC6-knockout cause tempering of temporal correlations in the chemotactic gradient. This can be interpreted as a progressive loss of memory, which leads to a marked reduction of chemotaxis and search efficiency of neutrophils. In summary, our findings indicate that spatially differential regulation of anomalous dynamics appears to play a central role in guiding efficient chemotactic behavior.

Return Probability of Quantum and Correlated Random Walks

The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer lattice by the path counting method. We show that the return probability of both quantum and correlated random walks can be expressed in terms of the Legendre polynomial. Moreover, the generating function of the return probability can be written in terms of elliptic integrals of the first and second kinds for the quantum walk.

Pre-training graph neural networks for link prediction in biomedical networks

MOTIVATION

Graphs or networks are widely utilized to model the interactions between different entities (e.g. proteins, drugs, etc.) for biomedical applications. Predicting potential interactions/links in biomedical networks is important for understanding the pathological mechanisms of various complex human diseases, as well as screening compound targets for drug discovery. Graph neural networks (GNNs) have been utilized for link prediction in various biomedical networks, which rely on the node features extracted from different data sources, e.g. sequence, structure and network data. However, it is challenging to effectively integrate these data sources and automatically extract features for different link prediction tasks.

RESULTS

In this article, we propose a novel Pre-Training Graph Neural Networks-based framework named PT-GNN to integrate different data sources for link prediction in biomedical networks. First, we design expressive deep learning methods [e.g. convolutional neural network and graph convolutional network (GCN)] to learn features for individual nodes from sequence and structure data. Second, we further propose a GCN-based encoder to effectively refine the node features by modelling the dependencies among nodes in the network. Third, the node features are pre-trained based on graph reconstruction tasks. The pre-trained features can be used for model initialization in downstream tasks. Extensive experiments have been conducted on two critical link prediction tasks, i.e. synthetic lethality (SL) prediction and drug-target interaction (DTI) prediction. Experimental results demonstrate PT-GNN outperforms the state-of-the-art methods for SL prediction and DTI prediction. In addition, the pre-trained features benefit improving the performance and reduce the training time of existing models.

AVAILABILITY AND IMPLEMENTATION

Python codes and dataset are available at: https://github.com/longyahui/PT-GNN.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

The local burden of disease during the first wave of the COVID-19 epidemic in England: estimation using different data sources from changing surveillance practices

BACKGROUND

The COVID-19 epidemic has differentially impacted communities across England, with regional variation in rates of confirmed cases, hospitalisations and deaths. Measurement of this burden changed substantially over the first months, as surveillance was expanded to accommodate the escalating epidemic. Laboratory confirmation was initially restricted to clinical need ("pillar 1") before expanding to community-wide symptomatics ("pillar 2"). This study aimed to ascertain whether inconsistent measurement of case data resulting from varying testing coverage could be reconciled by drawing inference from COVID-19-related deaths.

METHODS

We fit a Bayesian spatio-temporal model to weekly COVID-19-related deaths per local authority (LTLA) throughout the first wave (1 January 2020-30 June 2020), adjusting for the local epidemic timing and the age, deprivation and ethnic composition of its population. We combined predictions from this model with case data under community-wide, symptomatic testing and infection prevalence estimates from the ONS infection survey, to infer the likely trajectory of infections implied by the deaths in each LTLA.

RESULTS

A model including temporally- and spatially-correlated random effects was found to best accommodate the observed variation in COVID-19-related deaths, after accounting for local population characteristics. Predicted case counts under community-wide symptomatic testing suggest a total of 275,000-420,000 cases over the first wave - a median of over 100,000 additional to the total confirmed in practice under varying testing coverage. This translates to a peak incidence of around 200,000 total infections per week across England. The extent to which estimated total infections are reflected in confirmed case counts was found to vary substantially across LTLAs, ranging from 7% in Leicester to 96% in Gloucester with a median of 23%.

CONCLUSIONS

Limitations in testing capacity biased the observed trajectory of COVID-19 infections throughout the first wave. Basing inference on COVID-19-related mortality and higher-coverage testing later in the time period, we could explore the extent of this bias more explicitly. Evidence points towards substantial under-representation of initial growth and peak magnitude of infections nationally, to which different parts of the country contribute unequally.

A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling

In vitro tumour spheroids have been used to study avascular tumour growth and drug design for over 50 years. Tumour spheroids exhibit heterogeneity within the growing population that is thought to be related to spatial and temporal differences in nutrient availability. The recent development of real-time fluorescent cell cycle imaging allows us to identify the position and cell cycle status of individual cells within the growing spheroid, giving rise to the notion of a four-dimensional (4D) tumour spheroid. We develop the first stochastic individual-based model (IBM) of a 4D tumour spheroid and show that IBM simulation data compares well with experimental data using a primary human melanoma cell line. The IBM provides quantitative information about nutrient availability within the spheroid, which is important because it is difficult to measure these data experimentally.

Efficient quantitative assessment of robot swarms: coverage and targeting Lévy strategies

Biologically inspiredstrategieshave long been adapted to swarm robotic systems, including biased random walks, reaction to chemotactic cues and long-range coordination. In this paper we applyanalysis toolsdeveloped for modeling biological systems, such as continuum descriptions, to the efficient quantitative characterization of robot swarms. As an illustration, both Brownian and Lévy strategies with a characteristic long-range movement are discussed. As a result we obtain computationally fast methods for the optimization of robot movement laws to achieve a prescribed collective behavior. We show how to compute performance metrics like coverage and hitting times, and illustrate the accuracy and efficiency of our approach for area coverage and search problems. Comparisons between the continuum model and robotic simulations confirm the quantitative agreement and speed up by a factor of over 100 of our approach. Results confirm and quantify the advantage of Lévy strategies over Brownian motion for search and area coverage problems in swarm robotics.

Fluorescence Recovery after Photobleaching in Colloidal Science: Introduction and Application

FRAP (fluorescence recovery after photo bleaching) is a method for determining diffusion in material science. In industrial applications such as medications, foods, Medtech, hygiene, and textiles, the diffusion process has a substantial influence on the overall qualities of goods. All these complex and heterogeneous systems have diffusion-based processes at the local level. FRAP is a fluorescence-based approach for detecting diffusion; in this method, a high-intensity laser is made for a brief period and then applied to the samples, bleaching the fluorescent chemical inside the region, which is subsequently filled up by natural diffusion. This brief Review will focus on the existing research on employing FRAP to measure colloidal system heterogeneity and explore diffusion into complicated structures. This description of FRAP will be followed by a discussion of how FRAP is intended to be used in colloidal science. When constructing the current Review, the most recent publications were reviewed for this assessment. Because of the large number of FRAP articles in colloidal research, there is currently a dearth of knowledge regarding the growth of FRAP's significance to colloidal science. Colloids make up only 2% of FRAP papers, according to ISI Web of Knowledge.

Limiting factors for queen conch (Lobatus gigas) reproduction: A simulation-based evaluation

Queen conch are among the most economically, socially, and culturally important fishery resources in the Caribbean. Despite a multitude of fisheries management measures enacted across the region, populations are depleted and failing to recover. It is believed that queen conch are highly susceptible to depensatory processes, impacting reproductive success and contributing to the lack of recovery. We developed a model of reproductive dynamics to evaluate how variations in biological factors such as population density, movement speeds, rest periods between mating events, scent tracking, visual perception of conspecifics, sexual facilitation, and barriers to movement affect reproductive success and overall reproductive output. We compared simulation results to empirical observations of mating and spawning frequencies from conch populations in the central Bahamas and Florida Keys. Our results confirm that low probability of mate finding associated with decreased population density is the primary driver behind observed breeding behavior in the field, but is insufficient to explain observed trends. Specifically, sexual facilitation coupled with differences in movement speeds and ability to perceive conspecifics may explain the observed lack of mating at low densities and differences between mating frequencies in the central Bahamas and Florida Keys, respectively. Our simulations suggest that effective management strategies for queen conch should aim to protect high-density reproductive aggregations and critical breeding habitats.

Towards predicting COVID-19 infection waves: A random-walk Monte Carlo simulation approach

Phenomenological and deterministic models are often used for the estimation of transmission parameters in an epidemic and for the prediction of its growth trajectory. Such analyses are usually based on single peak outbreak dynamics. In light of the present COVID-19 pandemic, there is a pressing need to better understand observed epidemic growth with multiple peak structures, preferably using first-principles methods. Along the lines of our previous work  [Physica A 574, 126014 (2021)], here we apply 2D random-walk Monte Carlo calculations to better understand COVID-19 spread through contact interactions. Lockdown scenarios and all other control interventions are imposed through mobility restrictions and a regulation of the infection rate within the stochastically interacting population. The susceptible, infected and recovered populations are tracked over time, with daily infection rates obtained without recourse to the solution of differential equations. The simulations were carried out for population densities corresponding to four countries, India, Serbia, South Africa and USA. In all cases our results capture the observed infection growth rates. More importantly, the simulation model is shown to predict secondary and tertiary waves of infections with reasonable accuracy. This predictive nature of multiple wave structures provides a simple and effective tool that may be useful in planning mitigation strategies during the present pandemic.

Dose distribution to a random walker moving in a two-dimensional surface around a radioactive source

BACKGROUND

Modeling of dose distribution of randomly moving population around a radioactive source is a complex problem.

OBJECTIVE

The objective is to develop a model and solution techniques to estimate radiation absorbed dose to the population randomly moving around a radioactive source.

METHODS

The problem is formulated using a second-order partial differential equation; different moments of the dose distribution function are defined related to physically realizable quantities, and solutions are obtained using standard moments methods. Alternatively, numerical simulations are performed to estimate the radiation doses using Monte Carlo approach for individual positions and random motions of the people around the source.

RESULTS

A good agreement is found between average doses obtained from moments method and numerical simulations. A typical application of this model to different exposure conditions shows that the average dose is highly dependent on the population density. The study results show that average dose decreases with increase in the population density and movement area of random walker.

SIGNIFICANCE

This mathematical model can be used as a rapid assessment tool by the emergency planners in resource optimization by providing quick estimates of likely exposures for triage and emergency response.

In silico framework to inform the design of repair constructs for peripheral nerve injury repair

Peripheral nerve injuries affect millions of people per year and cause loss of sensation and muscle control alongside chronic pain. The most severe injuries are treated through a nerve autograft; however, donor site morbidity and poor outcomes mean alternatives are required. One option is to engineer nerve replacement tissues to provide a supportive microenvironment to encourage nerve regeneration as an alternative to nerve grafts. Currently, progress is hampered due to a lack of consensus on how to arrange materials and cells in space to maximize rate of regeneration. This is compounded by a reliance on experimental testing, which precludes extensive investigations of multiple parameters due to time and cost limitations. Here, a computational framework is proposed to simulate the growth of repairing neurites, captured using a random walk approach and parameterized against literature data. The framework is applied to a specific scenario where the engineered tissue comprises a collagen hydrogel with embedded biomaterial fibres. The size and number of fibres are optimized to maximize neurite regrowth, and the robustness of model predictions is tested through sensitivity analyses. The approach provides an in silico tool to inform the design of engineered replacement tissues, with the opportunity for further development to multi-cue environments.

Brownian particles driven by spatially periodic noise

We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular, we find a very slow dynamics for the mean displacement, scaling as [Formula: see text] with time t. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker-Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient.

In silico evolution of nucleic acid-binding proteins from a nonfunctional scaffold

Directed evolution emulates the process of natural selection to produce proteins with improved or altered functions. These approaches have proven to be very powerful but are technically challenging and particularly time and resource intensive. To bypass these limitations, we constructed a system to perform the entire process of directed evolution in silico. We employed iterative computational cycles of mutation and evaluation to predict mutations that confer high-affinity binding activities for DNA and RNA to an initial de novo designed protein with no inherent function. Beneficial mutations revealed modes of nucleic acid recognition not previously observed in natural proteins, highlighting the ability of computational directed evolution to access new molecular functions. Furthermore, the process by which new functions were obtained closely resembles natural evolution and can provide insights into the contributions of mutation rate, population size and selective pressure on functionalization of macromolecules in nature.

Why Is the Grass the Best Surface to Prevent Lameness? Integrative Analysis of Functional Ranges as a Key for Dairy Cows’ Welfare

Simple Summary

Lameness is a highly prevalent clinical condition that causes movement disorders in dairy cows worldwide. With an estimated global population of one billion dairy cows, producing 522 million metric tons of milk per year, this problem affects food availability as well as the global economy. While grass is considered to be the best support surface for cattle, in many places it cannot be used, particularly when climate conditions are too harsh for grass to grow or be maintained. In this paper, we investigate whether grass is the best surface to prevent lameness. The answer to this question is fundamental to establishing better farming practices for cattle welfare. We built an integrative analysis of functional ranges to establish the minimum and maximum movement capacities that a cow has, according to the surfaces to which it is subjected in free housing systems. Using this analysis, we identified many aspects that make a grass surface the healthiest option for cattle. However, when grass is not available, this type of strategy can help to find the best characteristics for other possible surfaces. Our study applies movement analysis to one of the most critical problems in the world of livestock management and contributes towards finding the balance between animal welfare and production.

Abstract

Lameness is a painful clinical condition of the bovine locomotor system that results in alterations of movement. Together with mastitis and infertility, lameness is the main welfare, health, and production problem found in intensive dairy farms worldwide. The clinical assessment of lameness results in an imprecise diagnosis and delayed intervention. Hence, the current approach to the problem is palliative rather than preventive. The five main surfaces used in free housing systems in dairy farms are two natural (grass and sand) and three artificial (rubber, asphalt, and concrete). Each surface presents a different risk potential for lameness, with grass carrying the lowest threat. The aim of the present study is to evaluate the flooring type influences on cows’ movement capabilities, using all the available information relating to kinematics, kinetics, behavior, and posture in free-housed dairy cows. Inspired by a refurbished movement ecology concept, we conducted a literature review, taking into account kinematics, kinetics, behavior, and posture parameters by reference to the main surfaces used in free housing systems for dairy cows. We built an integrative analysis of functional ranges (IAFuR), which provides a combined welfare status diagram for the optimal (i.e., within the upper and lower limit) functional ranges for movement (i.e., posture, kinematics, and kinetics), navigation (i.e., behavior), and recovery capacities (i.e., metabolic cost). Our analysis confirms grass’ outstanding clinical performance, as well as for all of the movement parameters measured. Grass boosts pedal joint homeostasis; provides reliable, safe, and costless locomotion; promotes longer resting times. Sand is the best natural alternative surface, but it presents an elevated metabolic cost. Rubber is an acceptable artificial alternative surface, but it is important to consider the mechanical and design properties. Asphalt and concrete surfaces are the most harmful because of the high traffic abrasiveness and loading impact. Furthermore, IAFuR can be used to consider other qualitative and quantitative parameters and to provide recommendations on material properties and the design of any surface, so as to move towards a more grass-like feel. We also suggest the implementation of a decision-making pathway to facilitate the interpretation of movement data in a more comprehensive way, in order to promote consistent, adaptable, timely, and adequate management decisions.

A predictive model and a field study on heterogeneous slug distribution in arable fields arising from density dependent movement

Factors and processes determining heterogeneous (‘patchy’) population distributions in natural environments have long been a major focus in ecology. Existing theoretical approaches proved to be successful in explaining vegetation patterns. In the case of animal populations, existing theories are at most conceptual: they may suggest a qualitative explanation but largely fail to explain patchiness quantitatively. We aim to bridge this knowledge gap. We present a new mechanism of self-organized formation of a patchy spatial population distribution. A factor that was under-appreciated by pattern formation theories is animal sociability, which may result in density dependent movement behaviour. Our approach was inspired by a recent project on movement and distribution of slugs in arable fields. The project discovered a strongly heterogeneous slug distribution and a specific density dependent individual movement. In this paper, we bring these two findings together. We develop a model of density dependent animal movement to account for the switch in the movement behaviour when the local population density exceeds a certain threshold. The model is fully parameterized using the field data. We then show that the model produces spatial patterns with properties closely resembling those observed in the field, in particular to exhibit similar values of the aggregation index.

The role of food odor in invertebrate foraging

Foraging for food is an integral part of animal survival. In small insects and invertebrates, multisensory information and optimized locomotion strategies are used to effectively forage in patchy and complex environments. Here, the importance of olfactory cues for effective invertebrate foraging is discussed in detail. We review how odors are used by foragers to move toward a likely food source and the recent models that describe this sensory-driven behavior. We argue that smell serves a second function by priming an organism for the efficient exploitation of food. By appraising food odors, invertebrates can establish preferences and better adapt to their ecological niches, thereby promoting survival. The smell of food pre-prepares the gastrointestinal system and primes feeding motor programs for more effective ingestion as well. Optimizing resource utilization affects longevity and reproduction as a result, leading to drastic changes in survival. We propose that models of foraging behavior should include odor priming, and illustrate this with a simple toy model based on the marginal value theorem. Lastly, we discuss the novel techniques and assays in invertebrate research that could investigate the interactions between odor sensing and food intake. Overall, the sense of smell is indispensable for efficient foraging and influences not only locomotion, but also organismal physiology, which should be reflected in behavioral modeling.

Tracking of Endothelial Cell Migration and Stiffness Measurements Reveal the Role of Cytoskeletal Dynamics

Cell migration is a complex, tightly regulated multistep process in which cytoskeletal reorganization and focal adhesion redistribution play a central role. Core to both individual and collective migration is the persistent random walk, which is characterized by random force generation and resistance to directional change. We first discuss a model that describes the stochastic movement of ECs and characterizes EC persistence in wound healing. To that end, we pharmacologically disrupted cytoskeletal dynamics, cytochalasin D for actin and nocodazole for tubulin, to understand its contributions to cell morphology, stiffness, and motility. As such, the use of Atomic Force Microscopy (AFM) enabled us to probe the topography and stiffness of ECs, while time lapse microscopy provided observations in wound healing models. Our results suggest that actin and tubulin dynamics contribute to EC shape, compressive moduli, and directional organization in collective migration. Insights from the model and time lapse experiment suggest that EC speed and persistence are directionally organized in wound healing. Pharmacological disruptions suggest that actin and tubulin dynamics play a role in collective migration. Current insights from both the model and experiment represent an important step in understanding the biomechanics of EC migration as a therapeutic target.

Effective Cancer Subtype and Stage Prediction via Dropfeature-DNNs

Precise cancer subtype and/or stage prediction is instrumental for cancer diagnosis, treatment and management. However, most of the existing methods based on genomic profiles suffer from issues such as overfitting, high computational complexity and selected features (i.e., genes) not directly related to forecast precision. These deficiencies are largely due to the nature of "high dimensionality and small sample size" inherent in molecular data, and such a nature is often deemed as an obstacle to the application of deep learning, e.g., deep neural networks (DNNs), to biomedicine and cancer research. In this paper, we propose a DNN-based algorithm coupled with a new embedded feature selection technique, named Dropfeature-DNNs, to address these issues. Dropfeature-DNNs can discard some irrelevant features (i.e., genes) when training DNNs, and we formulate Dropfeature-DNNs as an iterative AUC optimization problem. As such, an "optimal" feature subset that contains meaningful genes for accurate tumor subtype and/or stage prediction can be obtained when the AUC optimization converges in the training stage. Since the feature subset and AUC optimizations are synchronous with the training phase of DNNs, model complexity and computational cost are simultaneously reduced. Rigorous feature subset convergence analysis and error bound inference provide a solid theoretical foundation for the proposed method. Extensive empirical comparisons to benchmark methods further demonstrate the efficacy of Dropfeature-DNNs in cancer subtype and/or stage prediction using HDSS gene expression data from multiple cancer types.

Mean square displacement for a discrete centroid model of cell motion

The mean square displacement (MSD) is an important statistical measure on a stochastic process or a trajectory. In this paper we find an approximation to the mean square displacement for a model of cell motion. The model is a discrete-time jump process which approximates a force-based model for cell motion. In cell motion, the mean square displacement not only gives a measure of overall drift, but it is also an indicator of mode of transport. The key to finding the approximation is to find the mean square displacement for a subset of the state space and use it as an approximation for the entire state space. We give some intuition as to why this is an unexpectedly good approximation. A lower bound and upper bound for the mean square displacement are also given. We show that, although the upper bound is far from the computed mean square displacement, in rare cases the large displacements are approached.

De novo individualized disease modules reveal the synthetic penetrance of genes and inform personalized treatment regimens

Current understandings of individual disease etiology and therapeutics are limited despite great need. To fill the gap, we propose a novel computational pipeline that collects potent disease gene cooperative pathways to envision individualized disease etiology and therapies. Our algorithm constructs individualized disease modules de novo, which enables us to elucidate the importance of mutated genes in specific patients and to understand the synthetic penetrance of these genes across patients. We reveal that importance of the notorious cancer drivers TP53 and PIK3CA fluctuate widely across breast cancers and peak in tumors with distinct numbers of mutations and that rarely mutated genes such as XPO1 and PLEKHA1 have high disease module importance in specific individuals. Furthermore, individualized module disruption enables us to devise customized singular and combinatorial target therapies that were highly varied across patients, showing the need for precision therapeutics pipelines. As the first analysis of de novo individualized disease modules, we illustrate the power of individualized disease modules for precision medicine by providing deep novel insights on the activity of diseased genes in individuals.

Decomposition of cell activities revealing the role of the cell cycle in driving biofunctional heterogeneity

Heterogeneity of cell phenotypes remains a barrier in progressing cell research and a challenge in conquering cancer-related drug resistance. Cell morphology, the most direct property of cell phenotype, evolves along the progression of the cell cycle; meanwhile, cell motility, the dynamic property of cell phenotype, also alters over the cell cycle. However, a quantifiable research understanding the relationship between the cell cycle and cell migration is missing. Herein, we coordinate the migratory behaviours of NIH 3T3 fibroblasts to their corresponding phases of the cell cycle, the G1, the S, and the G2 phases, and explain the relationship through the spatiotemporal arrangements between the Rho GTPases’ signals and cyclin-dependent kinase inhibitors, p21^Cip1, and p27^Kip1. Taken together, we demonstrate that both cell morphology and the dynamic subcellular behaviour are homogenous within each stage of the cell cycle phases but heterogenous between phases through quantitative cell analyses and an interactive molecular mechanism between the cell cycle and cell migration, posing potential implications in countering drug resistance.

Single-cell tracking reveals super-spreading brain cancer cells with high persistence

Cell migration is a fundamental characteristic of vital processes such as tissue morphogenesis, wound healing and immune cell homing to lymph nodes and inflamed or infected sites. Therefore, various brain defect diseases, chronic inflammatory diseases as well as tumor formation and metastasis are associated with aberrant or absent cell migration. We embedded multicellular brain cancer spheroids in Matrigel™ and utilized single-particle tracking to extract the paths of cells migrating away from the spheroids. We found that - in contrast to local invasion - single cell migration is independent of Matrigel™ concentration and is characterized by high directionality and persistence. Furthermore, we identified a subpopulation of super-spreading cells with >200-fold longer persistence times than the majority of cells. These results highlight yet another aspect of cell heterogeneity in tumors.

Odd Diffusivity of Chiral Random Motion

Diffusive transport is characterized by a diffusivity tensor which may, in general, contain both a symmetric and an antisymmetric component. Although the latter is often neglected, we derive Green-Kubo relations showing it to be a general characteristic of random motion breaking time-reversal and parity symmetries, as encountered in chiral active matter. In analogy with the odd viscosity appearing in chiral active fluids, we term this component the odd diffusivity. We show how odd diffusivity emerges in a chiral random walk model, and demonstrate the applicability of the Green-Kubo relations through molecular dynamics simulations of a passive tracer particle diffusing in a chiral active bath.

Mechanistic modelling of COVID-19 and the impact of lockdowns on a short-time scale

BACKGROUND

To mitigate the spread of the COVID-19 coronavirus, some countries have adopted more stringent non-pharmaceutical interventions in contrast to those widely used. In addition to standard practices such as enforcing curfews, social distancing, and closure of non-essential service industries, other non-conventional policies also have been implemented, such as the total lockdown of fragmented regions, which are composed of sparsely and highly populated areas.

METHODS

In this paper, we model the movement of a host population using a mechanistic approach based on random walks, which are either diffusive or super-diffusive. Infections are realised through a contact process, whereby a susceptible host is infected if in close spatial proximity of the infectious host with an assigned transmission probability. Our focus is on a short-time scale (∼ 3 days), which is the average time lag time before an infected individual becomes infectious.

RESULTS

We find that the level of infection remains approximately constant with an increase in population diffusion, and also in the case of faster population dispersal (super-diffusion). Moreover, we demonstrate how the efficacy of imposing a lockdown depends heavily on how susceptible and infectious individuals are distributed over space.

CONCLUSION

Our results indicate that on a short-time scale, the type of movement behaviour does not play an important role in rising infection levels. Also, lock-down restrictions are ineffective if the population distribution is homogeneous. However, in the case of a heterogeneous population, lockdowns are effective if a large proportion of infectious carriers are distributed in sparsely populated sub-regions.

A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators

Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect. Their well-balanced spatiotemporal dynamics are beneficial for healthy sustainability. Therefore, calibrating both anomalous frequency and amplitude of biorhythm prevents physiological dysfunctions or diseases. However, many works were devoted to modulate frequency exclusively whereas amplitude is usually ignored, although both quantities are equally significant for coordinating biological functions and outputs. Especially, a feasible method coordinating the two quantities concurrently and precisely is still lacking. Here, for the first time, we propose a universal approach to design a frequency-amplitude coordinator rigorously via dynamical systems tools. We consider both spatial and temporal information. With a single well-designed coordinator, they can be calibrated to desired levels simultaneously and precisely. The practical usefulness and efficacy of our method are demonstrated in representative neuronal and gene regulatory models. We further reveal its fundamental mechanism and optimal energy consumption providing inspiration for biorhythm regulation in future.

Bayesian uncertainty quantification for data-driven equation learning

Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with relatively small amounts of noise, the relationship between observation noise and uncertainty in the learned differential equation models remains unexplored. We demonstrate that for noisy datasets there exists great variation in both the structure of the learned differential equation models and their parameter values. We explore how to exploit multiple datasets to quantify uncertainty in the learned models, and at the same time draw mechanistic conclusions about the target differential equations. We showcase our results using simulation data from a relatively straightforward agent-based model (ABM) which has a well-characterized partial differential equation description that provides highly accurate predictions of averaged ABM behaviours in relevant regions of parameter space. Our approach combines equation learning methods with Bayesian inference approaches so that a quantification of uncertainty can be given by the posterior parameter distribution of the learned model.

Modelling collective navigation via non-local communication

Collective migration occurs throughout the animal kingdom, and demands both the interpretation of navigational cues and the perception of other individuals within the group. Navigational cues orient individuals towards a destination, while it has been demonstrated that communication between individuals enhances navigation through a reduction in orientation error. We develop a mathematical model of collective navigation that synthesizes navigational cues and perception of other individuals. Crucially, this approach incorporates uncertainty inherent to cue interpretation and perception in the decision making process, which can arise due to noisy environments. We demonstrate that collective navigation is more efficient than individual navigation, provided a threshold number of other individuals are perceptible. This benefit is even more pronounced in low navigation information environments. In navigation ‘blindspots’, where no information is available, navigation is enhanced through a relay that connects individuals in information-poor regions to individuals in information-rich regions. As an expository case study, we apply our framework to minke whale migration in the northeast Atlantic Ocean, and quantify the decrease in navigation ability due to anthropogenic noise pollution.

Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation

We develop a parameter estimation method based on approximate Bayesian computation (ABC) for a stochastic cell invasion model using fluorescent cell cycle labelling with proliferation, migration and crowding effects. Previously, inference has been performed on a deterministic version of the model fitted to cell density data, and not all parameters were identifiable. Considering the stochastic model allows us to harness more features of experimental data, including cell trajectories and cell count data, which we show overcomes the parameter identifiability problem. We demonstrate that, while difficult to collect, cell trajectory data can provide more information about the parameters of the cell invasion model. To handle the intractability of the likelihood function of the stochastic model, we use an efficient ABC algorithm based on sequential Monte Carlo. Rcpp and MATLAB implementations of the simulation model and ABC algorithm used in this study are available at https://github.com/michaelcarr-stats/FUCCI.

Effects of substrate stiffness on mast cell migration

Mast cells (MCs) play important roles in multiple pathologies, including fibrosis; however, their behaviors in different extracellular matrix (ECM) environments have not been fully elucidated. Accordingly, in this study, the migration of MCs on substrates with different stiffnesses was investigated using time-lapse video microscopy. Our results showed that MCs could appear in round, spindle, and star-like shapes; spindle-shaped cells accounted for 80-90 % of the total observed cells. The migration speed of round cells was significantly lower than that of cells with other shapes. Interestingly, spindle-shaped MCs migrated in a jiggling and wiggling motion between protrusions. The persistence index of MC migration was slightly higher on stiffer substrates. Moreover, we found that there was an intermediate optimal stiffness at which the migration efficiency was the highest. These findings may help to improve our understanding of MC-induced pathologies and the roles of MC migration in the immune system.

The Approximate and Analytic Solutions of the Time-Fractional Intermediate Diffusion Wave Equation Associated with the Fokker–Planck Operator and Applications

In this paper, the time-fractional wave equation associated with the space-fractional Fokker–Planck operator and with the time-fractional-damped term is studied. The concept of the Green function is implemented to drive the analytic solution of the three-term time-fractional equation. The explicit expressions for the Green function G3(t) of the three-term time-fractional wave equation with constant coefficients is also studied for two physical and biological models. The explicit analytic solutions, for the two studied models, are expressed in terms of the Weber, hypergeometric, exponential, and Mittag–Leffler functions. The relation to the diffusion equation is given. The asymptotic behaviors of the Mittag–Leffler function, the hypergeometric function 1F1, and the exponential functions are compared numerically. The Grünwald–Letnikov scheme is used to derive the approximate difference schemes of the Caputo time-fractional operator and the Feller–Riesz space-fractional operator. The explicit difference scheme is numerically studied, and the simulations of the approximate solutions are plotted for different values of the fractional orders.

Potential-driven random walks on interconnected systems

Interconnected systems have to route information to function properly: At the lowest scale neural cells exchange electrochemical signals to communicate, while at larger scales animals and humans move between distinct spatial patches and machines exchange information via the Internet through communication protocols. Nontrivial patterns emerge from the analysis of information flows, which are not captured either by broadcasting, such as in random walks, or by geodesic routing, such as shortest paths. In fact, alternative models between those extreme protocols are still eluding us. Here we propose a class of stochastic processes, based on biased random walks, where agents are driven by a physical potential pervading the underlying network topology. By considering a generalized Coulomb dependence on the distance on destination(s), we show that it is possible to interpolate between random walk and geodesic routing in a simple and effective way. We demonstrate that it is not possible to find a one-size-fit-all solution to efficient navigation and that network heterogeneity or modularity has measurable effects. We illustrate how our framework can describe the movements of animals and humans, capturing with a stylized model some measurable features of the latter. From a methodological perspective, our potential-driven random walks open the doors to a broad spectrum of analytical tools, ranging from random-walk centralities to geometry induced by potential-driven network processes.