Stochastic journeys of cell progenies through compartments and the role of self-renewal, symmetric and asymmetric division.

Division and differentiation events by which cell populations with specific functions are generated often take place as part of a developmental programme, which can be represented by a sequence of compartments. A compartment is the set of cells with common characteristics; sharing, for instance, a spatial location or a phenotype. Differentiation events are transitions from one compartment to the next. Cells may also die or divide. We consider three different types of division events: (i) where both daughter cells inherit the mother's phenotype (self-renewal), (ii) where only one of the daughters changes phenotype (asymmetric division), and (iii) where both daughters change phenotype (symmetric division). The self-renewal probability in each compartment determines whether the progeny of a single cell, moving through the sequence of compartments, is finite or grows without bound. We analyse the progeny stochastic dynamics with probability generating functions. In the case of self-renewal, by following one of the daughters after any division event, we may construct lifelines containing only one cell at any time. We analyse the number of divisions along such lines, and the compartment where lines terminate with a death event. Analysis and numerical simulations are applied to a five-compartment model of the gradual differentiation of hematopoietic stem cells and to a model of thymocyte development: from pre-double positive to single positive (SP) cells with a bifurcation to either SP4 or SP8 in the last compartment of the sequence.

A 17-month longitudinal surface sampling study carried out on public transport vehicles operating in England during the COVID-19 pandemic identified low levels of SARS-CoV-2 RNA contamination.

AIMS: To monitor severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) RNA contamination in vehicles operating in England during the pandemic, to better understand transmission risk of SARS-CoV-2 on public transport. METHODS AND RESULTS: We collected 1314 surface samples between December 2020 and April 2022 on trains and buses managed by five different transport operators. The presence of SARS-CoV-2 RNA was investigated through reverse transcription polymerase chain reaction (RT-PCR). SARS-CoV-2 RNA was found on 197 (15%) of the 1314 surfaces sampled, including seat head rests, handholds, and air extract grilles, but the levels of RNA recovered on those samples (median value of 23.4, interquartile range: 14.3-35.4, N gene copies per extraction) made the presence of infectious virus at the time of sampling extremely unlikely. However, detection rates varied over time with peaks broadly coinciding with times of high community transmission, when it was more likely that people infected with SARS-CoV-2 were travelling on public transport. CONCLUSION: During the pandemic, and as in other public spaces, low levels of SARS-CoV-2 RNA were found on surfaces associated with public transport.

A story of viral co-infection, co-transmission and co-feeding in ticks: how to compute an invasion reproduction number.

With a single circulating vector-borne virus, the basic reproduction number incorporates contributions from tick-to-tick (co-feeding), tick-to-host and host-to-tick transmission routes. With two different circulating vector-borne viral strains, resident and invasive, and under the assumption that co-feeding is the only transmission route in a tick population, the invasion reproduction number depends on whether the model system of ordinary differential equations possesses the property of neutrality. We show that a simple model, with two populations of ticks infected with one strain, resident or invasive, and one population of co-infected ticks, does not have Alizon's neutrality property. We present model alternatives that are capable of representing the invasion potential of a novel strain by including populations of ticks dually infected with the same strain. The invasion reproduction number is analysed with the next-generation method and via numerical simulations.

The Wells-Riley model revisited: Randomness, heterogeneity, and transient behaviours.

The Wells-Riley model has been widely used to estimate airborne infection risk, typically from a deterministic point of view (i.e., focusing on the average number of infections) or in terms of a per capita probability of infection. Some of its main limitations relate to considering well-mixed air, steady-state concentration of pathogen in the air, a particular amount of time for the indoor interaction, and that all individuals are homogeneous and behave equally. Here, we revisit the Wells-Riley model, providing a mathematical formalism for its stochastic version, where the number of infected individuals follows a Binomial distribution. Then, we extend the Wells-Riley methodology to consider transient behaviours, randomness, and population heterogeneity. In particular, we provide analytical solutions for the number of infections and the per capita probability of infection when: (i) susceptible individuals remain in the room after the infector leaves, (ii) the duration of the indoor interaction is random/unknown, and (iii) infectors have heterogeneous quanta production rates (or the quanta production rate of the infector is random/unknown). We illustrate the applicability of our new formulations through two case studies: infection risk due to an infectious healthcare worker (HCW) visiting a patient, and exposure during lunch for uncertain meal times in different dining settings. Our results highlight that infection risk to a susceptible who remains in the space after the infector leaves can be nonnegligible, and highlight the importance of incorporating uncertainty in the duration of the indoor interaction and the infectivity of the infector when estimating risk.

Living jewels: iterative evolution of iridescent blue leaves from helicoidal cell walls.

BACKGROUND AND AIMS: Structural colour is responsible for the remarkable metallic blue colour seen in the leaves of several plants. Species belonging to only ten genera have been investigated to date, revealing four photonic structures responsible for structurally coloured leaves. One of these is the helicoidal cell wall, known to create structural colour in the leaf cells of five taxa. Here we investigate a broad selection of land plants to understand the phylogenetic distribution of this photonic structure in leaves. METHODS: We identified helicoidal structures in the leaf epidermal cells of 19 species using transmission electron microscopy. Pitch measurements of the helicoids were compared with the reflectance spectra of circularly polarized light from the cells to confirm the structure-colour relationship. RESULTS: By incorporating species examined with a polarizing filter, our results increase the number of taxa with photonic helicoidal cell walls to species belonging to at least 35 genera. These include 19 monocot genera, from the orders Asparagales (Orchidaceae) and Poales (Cyperaceae, Eriocaulaceae, Rapateaceae) and 16 fern genera, from the orders Marattiales (Marattiaceae), Schizaeales (Anemiaceae) and Polypodiales (Blechnaceae, Dryopteridaceae, Lomariopsidaceae, Polypodiaceae, Pteridaceae, Tectariaceae). CONCLUSIONS: Our investigation adds considerably to the recorded diversity of plants with structurally coloured leaves. The iterative evolution of photonic helicoidal walls has resulted in a broad phylogenetic distribution, centred on ferns and monocots. We speculate that the primary function of the helicoidal wall is to provide strength and support, so structural colour could have evolved as a potentially beneficial chance function of this structure.

Quantifying in vitro B. anthracis growth and PA production and decay: a mathematical modelling approach.

Protective antigen (PA) is a protein produced by Bacillus anthracis. It forms part of the anthrax toxin and is a key immunogen in US and UK anthrax vaccines. In this study, we have conducted experiments to quantify PA in the supernatants of cultures of B. anthracis Sterne strain, which is the strain used in the manufacture of the UK anthrax vaccine. Then, for the first time, we quantify PA production and degradation via mathematical modelling and Bayesian statistical techniques, making use of this new experimental data as well as two other independent published data sets. We propose a single mathematical model, in terms of delay differential equations (DDEs), which can explain the in vitro dynamics of all three data sets. Since we did not heat activate the B. anthracis spores prior to inoculation, germination occurred much slower in our experiments, allowing us to calibrate two additional parameters with respect to the other data sets. Our model is able to distinguish between natural PA decay and that triggered by bacteria via proteases. There is promising consistency between the different independent data sets for most of the parameter estimates. The quantitative characterisation of B. anthracis PA production and degradation obtained here will contribute towards the ambition to include a realistic description of toxin dynamics, the host immune response, and anti-toxin treatments in future mechanistic models of anthrax infection.

The reproduction number and its probability distribution for stochastic viral dynamics.

We consider stochastic models of individual infected cells. The reproduction number, R, is understood as a random variable representing the number of new cells infected by one initial infected cell in an otherwise susceptible (target cell) population. Variability in R results partly from heterogeneity in the viral burst size (the number of viral progeny generated from an infected cell during its lifetime), which depends on the distribution of cellular lifetimes and on the mechanism of virion release. We analyse viral dynamics models with an eclipse phase: the period of time after a cell is infected but before it is capable of releasing virions. The duration of the eclipse, or the subsequent infectious, phase is non-exponential, but composed of stages. We derive the probability distribution of the reproduction number for these viral dynamics models, and show it is a negative binomial distribution in the case of constant viral release from infectious cells, and under the assumption of an excess of target cells. In a deterministic model, the ultimate in-host establishment or extinction of the viral infection depends entirely on whether the mean reproduction number is greater than, or less than, one, respectively. Here, the probability of extinction is determined by the probability distribution of R, not simply its mean value. In particular, we show that in some cases the probability of infection is not an increasing function of the mean reproduction number.

Multi-variate model of T cell clonotype competition and homeostasis.

Diversity of the naive T cell repertoire is maintained by competition for stimuli provided by self-peptides bound to major histocompatibility complexes (self-pMHCs). We extend an existing bi-variate competition model to a multi-variate model of the dynamics of multiple T cell clonotypes which share stimuli. In order to understand the late-time behaviour of the system, we analyse: (i) the dynamics until the extinction of the first clonotype, (ii) the time to the first extinction event, (iii) the probability of extinction of each clonotype, and (iv) the size of the surviving clonotypes when the first extinction event takes place. We also find the probability distribution of the number of cell divisions per clonotype before its extinction. The mean size of a new clonotype at quasi-steady state is an increasing function of the stimulus available to it, and a decreasing function of the fraction of stimuli it shares with other clonotypes. Thus, the probability of, and time to, extinction of a new clonotype entering the pool of T cell clonotypes is determined by the extent of competition for stimuli it experiences and by its initial number of cells.

Social Distance Approximation on Public Transport Using Stereo Depth Camera and Passenger Pose Estimation.

In order to effectively balance enforced guidance/regulation during a pandemic and limit infection transmission, with the necessity for public transportation services to remain safe and operational, it is imperative to understand and monitor environmental conditions and typical behavioural patterns within such spaces. Social distancing ability on public transport as well as the use of advanced computer vision techniques to accurately measure this are explored in this paper. A low-cost depth-sensing system is deployed on a public bus as a means to approximate social distancing measures and study passenger habits in relation to social distancing. The results indicate that social distancing on this form of public transport is unlikely for an individual beyond a 28% occupancy threshold, with an 89% chance of being within 1-2 m from at least one other passenger and a 57% chance of being within less than one metre from another passenger at any one point in time. Passenger preference for seating is also analysed, which clearly demonstrates that for typical passengers, ease of access and comfort, as well as seats having a view, are preferred over maximising social-distancing measures. With a highly detailed and comprehensive set of acquired data and accurate measurement capability, the employed equipment and processing methodology also prove to be a robust approach for the application.

Why are cell populations maintained via multiple compartments?

We consider the maintenance of 'product' cell populations from 'progenitor' cells via a sequence of one or more cell types, or compartments, where each cell's fate is chosen stochastically. If there is only one compartment then large amplification, that is, a large ratio of product cells to progenitors comes with disadvantages. The product cell population is dominated by large families (cells descended from the same progenitor) and many generations separate, on average, product cells from progenitors. These disadvantages are avoided using suitably constructed sequences of compartments: the amplification factor of a sequence is the product of the amplification factors of each compartment, while the average number of generations is a sum over contributions from each compartment. Passing through multiple compartments is, in fact, an efficient way to maintain a product cell population from a small flux of progenitors, avoiding excessive clonality and minimizing the number of rounds of division en route. We use division, exit and death rates, estimated from measurements of single-positive thymocytes, to choose illustrative parameter values in the single-compartment case. We also consider a five-compartment model of thymocyte differentiation, from double-negative precursors to single-positive product cells.

Measuring Photonics in Photosynthesis: Combined Micro-Fourier Image Spectroscopy and Pulse Amplitude Modulated Chlorophyll Fluorimetry at the Micrometre-Scale.

Natural photonic structures are common across the biological kingdoms, serving a diversity of functionalities. The study of implications of photonic structures in plants and other phototrophic organisms is still hampered by missing methodologies for determining in situ photonic properties, particularly in the context of constantly adapting photosynthetic systems controlled by acclimation mechanisms on the cellular scale. We describe an innovative approach to determining spatial and spectral photonic properties and photosynthesis activity, employing micro-Fourier Image Spectroscopy and Pulse Amplitude Modulated Chlorophyll Fluorimetry in a combined microscope setup. Using two examples from the photosynthetic realm, the dynamic Bragg-stack-like thylakoid structures of Begonia sp. and complex 2.5 D photonic crystal slabs from the diatom Coscinodiscus granii, we demonstrate how the setup can be used for measuring self-adapting photonic-photosynthetic systems and photonic properties on single-cell scales. We suggest that the setup is well-suited for the determination of photonic-photosynthetic systems in a diversity of organisms, facilitating the cellular, temporal, spectral and angular resolution of both light distribution and combined chlorophyll fluorescence determination. As the catalogue of photonic structure from photosynthetic organisms is rich and diverse in examples, a deepened study could inspire the design of novel optical- and light-harvesting technologies.

Counting generations in birth and death processes with competing Erlang and exponential waiting times.

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not divide at all. If individual cells behave independently, then each cell can be imagined as sampling from a probability density of times to division and death. The exponential density is the most mathematically and computationally convenient choice. It has the advantage of satisfying the memoryless property, consistent with a Markov process, but it overestimates the probability of short division times. With the aim of preserving the advantages of a Markovian framework while improving the representation of experimentally-observed division times, we consider a multi-stage model of cellular division and death. We use Erlang-distributed (or, more generally, phase-type distributed) times to division, and exponentially distributed times to death. We classify cells into generations, using the rule that the daughters of cells in generation n are in generation [Formula: see text]. In some circumstances, our representation is equivalent to established models of lymphocyte dynamics. We find the growth rate of the cell population by calculating the proportions of cells by stage and generation. The exponent describing the late-time cell population growth, and the criterion for extinction of the population, differs from what would be expected if N steps with rate [Formula: see text] were equivalent to a single step of rate [Formula: see text]. We link with a published experimental dataset, where cell counts were reported after T cells were transferred to lymphopenic mice, using Approximate Bayesian Computation. In the comparison, the death rate is assumed to be proportional to the generation and the Erlang time to division for generation 0 is allowed to differ from that of subsequent generations. The multi-stage representation is preferred to a simple exponential in posterior distributions, and the mean time to first division is estimated to be longer than the mean time to subsequent divisions.

Effect of Relative Humidity on Transfer of Aerosol-Deposited Artificial and Human Saliva from Surfaces to Artificial Finger-Pads.

Surface to hand transfer of viruses represents a potential mechanism for human exposure. An experimental process for evaluating the touch transfer of aerosol-deposited material is described based on controlling surface, tribological, and soft matter components of the transfer process. A range of high-touch surfaces were evaluated. Under standardized touch parameters (15 N, 1 s), relative humidity (RH) of the atmosphere around the contact transfer event significantly influenced transfer of material to the finger-pad. At RH < 40%, transfer from all surfaces was <10%. Transfer efficiency increased markedly as RH increased, reaching a maximum of approximately 50%. The quantity of material transferred at specific RHs above 40% was also dependent on roughness of the surface material and the properties of the aerosol-deposited material. Smooth surfaces, such as melamine and stainless steel, generated higher transfer efficiencies compared to those with textured roughness, such as ABS pinseal and KYDEX® plastics. Pooled human saliva was transferred at a lower rate compared to artificial saliva, indicating the role of rheological properties. The artificial saliva data were modeled by non-linear regression and the impact of environmental humidity and temperature were evaluated within a Quantitative Microbial Risk Assessment model using SARS-CoV-2 as an example. This illustrated that the trade-off between transfer efficiency and virus survival may lead to the highest risks of fomite transmissions in indoor environments with higher humidity.

Versatile chip-based nanoscopy becomes ready for histopathology assessment.

Nanoscopy is a mature technology used routinely in life science to obtain images well below the optical diffraction limit. But the use of nanoscopy in histopathology assessment is very limited mostly due to the low throughput of traditional nanoscopic techniques. So far, Chip-nanoscopy, nanoscopy in which sample illumination is performed by an integrated photonic chip instead of bulk optics, has been shown to provide an enhanced field of view and throughput for cell biology. Now, a new development shows that chip-nanoscopy also offers interesting progress for the study of histological samples offering a complementary technique to electron microscopy for histopathology assessment.

Modeling the factors that influence exposure to SARS-CoV-2 on a subway train carriage.

We propose the Transmission of Virus in Carriages (TVC) model, a computational model which simulates the potential exposure to SARS-CoV-2 for passengers traveling in a subway rail system train. This model considers exposure through three different routes: fomites via contact with contaminated surfaces; close-range exposure, which accounts for aerosol and droplet transmission within 2 m of the infectious source; and airborne exposure via small aerosols which does not rely on being within 2 m distance from the infectious source. Simulations are based on typical subway parameters and the aim of the study is to consider the relative effect of environmental and behavioral factors including prevalence of the virus in the population, number of people traveling, ventilation rate, and mask wearing as well as the effect of model assumptions such as emission rates. Results simulate generally low exposures in most of the scenarios considered, especially under low virus prevalence. Social distancing through reduced loading and high mask-wearing adherence is predicted to have a noticeable effect on reducing exposure through all routes. The highest predicted doses happen through close-range exposure, while the fomite route cannot be neglected; exposure through both routes relies on infrequent events involving relatively few individuals. Simulated exposure through the airborne route is more homogeneous across passengers, but is generally lower due to the typically short duration of the trips, mask wearing, and the high ventilation rate within the carriage. The infection risk resulting from exposure is challenging to estimate as it will be influenced by factors such as virus variant and vaccination rates.

Modeling fomite-mediated SARS-CoV-2 exposure through personal protective equipment doffing in a hospital environment.

Self-contamination during doffing of personal protective equipment (PPE) is a concern for healthcare workers (HCW) following SARS-CoV-2-positive patient care. Staff may subconsciously become contaminated through improper glove removal; so, quantifying this exposure is critical for safe working procedures. HCW surface contact sequences on a respiratory ward were modeled using a discrete-time Markov chain for: IV-drip care, blood pressure monitoring, and doctors' rounds. Accretion of viral RNA on gloves during care was modeled using a stochastic recurrence relation. In the simulation, the HCW then doffed PPE and contaminated themselves in a fraction of cases based on increasing caseload. A parametric study was conducted to analyze the effect of: (1a) increasing patient numbers on the ward, (1b) the proportion of COVID-19 cases, (2) the length of a shift, and (3) the probability of touching contaminated PPE. The driving factors for the exposure were surface contamination and the number of surface contacts. The results simulate generally low viral exposures in most of the scenarios considered including on 100% COVID-19 positive wards, although this is where the highest self-inoculated dose is likely to occur with median 0.0305 viruses (95% CI =0-0.6 viruses). Dose correlates highly with surface contamination showing that this can be a determining factor for the exposure. The infection risk resulting from the exposure is challenging to estimate, as it will be influenced by the factors such as virus variant and vaccination rates.

Quantification of Type I Interferon Inhibition by Viral Proteins: Ebola Virus as a Case Study.

Type I interferons (IFNs) are cytokines with both antiviral properties and protective roles in innate immune responses to viral infection. They induce an antiviral cellular state and link innate and adaptive immune responses. Yet, viruses have evolved different strategies to inhibit such host responses. One of them is the existence of viral proteins which subvert type I IFN responses to allow quick and successful viral replication, thus, sustaining the infection within a host. We propose mathematical models to characterise the intra-cellular mechanisms involved in viral protein antagonism of type I IFN responses, and compare three different molecular inhibition strategies. We study the Ebola viral protein, VP35, with this mathematical approach. Approximate Bayesian computation sequential Monte Carlo, together with experimental data and the mathematical models proposed, are used to perform model calibration, as well as model selection of the different hypotheses considered. Finally, we assess if model parameters are identifiable and discuss how such identifiability can be improved with new experimental data.

A Stochastic Intracellular Model of Anthrax Infection With Spore Germination Heterogeneity.

We present a stochastic mathematical model of the intracellular infection dynamics of Bacillus anthracis in macrophages. Following inhalation of B. anthracis spores, these are ingested by alveolar phagocytes. Ingested spores then begin to germinate and divide intracellularly. This can lead to the eventual death of the host cell and the extracellular release of bacterial progeny. Some macrophages successfully eliminate the intracellular bacteria and will recover. Here, a stochastic birth-and-death process with catastrophe is proposed, which includes the mechanism of spore germination and maturation of B. anthracis. The resulting model is used to explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. We make use of approximate Bayesian computation to calibrate our model using experimental measurements from in vitro infection of murine peritoneal macrophages with spores of the Sterne 34F2 strain of B. anthracis. The calibrated stochastic model allows us to compute the probability of rupture, mean time to rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate, with a subset of spores expected to germinate much later than the majority. Furthermore, in agreement with experimental evidence, our results suggest that most of the spores taken up by macrophages are likely to be eliminated by the host cell, but a few germinated spores may survive phagocytosis and lead to the death of the infected cell. Finally, we discuss how this stochastic modelling approach, together with dose-response data, allows us to quantify and predict individual infection risk following exposure.

Competitive binding of STATs to receptor phospho-Tyr motifs accounts for altered cytokine responses.

Cytokines elicit pleiotropic and non-redundant activities despite strong overlap in their usage of receptors, JAKs and STATs molecules. We use IL-6 and IL-27 to ask how two cytokines activating the same signaling pathway have different biological roles. We found that IL-27 induces more sustained STAT1 phosphorylation than IL-6, with the two cytokines inducing comparable levels of STAT3 phosphorylation. Mathematical and statistical modeling of IL-6 and IL-27 signaling identified STAT3 binding to GP130, and STAT1 binding to IL-27Rα, as the main dynamical processes contributing to sustained pSTAT1 levels by IL-27. Mutation of Tyr613 on IL-27Rα decreased IL-27-induced STAT1 phosphorylation by 80% but had limited effect on STAT3 phosphorgylation. Strong receptor/STAT coupling by IL-27 initiated a unique gene expression program, which required sustained STAT1 phosphorylation and IRF1 expression and was enriched in classical Interferon Stimulated Genes. Interestingly, the STAT/receptor coupling exhibited by IL-6/IL-27 was altered in patients with systemic lupus erythematosus (SLE). IL-6/IL-27 induced a more potent STAT1 activation in SLE patients than in healthy controls, which correlated with higher STAT1 expression in these patients. Partial inhibition of JAK activation by sub-saturating doses of Tofacitinib specifically lowered the levels of STAT1 activation by IL-6. Our data show that receptor and STATs concentrations critically contribute to shape cytokine responses and generate functional pleiotropy in health and disease.

Effects of patient room layout on viral accruement on healthcare professionals' hands.

Healthcare professionals (HCPs) are exposed to highly infectious viruses, such as norovirus, through multiple exposure routes. Understanding exposure mechanisms will inform exposure mitigation interventions. The study objective was to evaluate the influences of hospital patient room layout on differences in HCPs' predicted hand contamination from deposited norovirus particles. Computational fluid dynamic (CFD) simulations of a hospital patient room were investigated to find differences in spatial deposition patterns of bioaerosols for right-facing and left-facing bed layouts under different ventilation conditions. A microbial transfer model underpinned by observed mock care for three care types (intravenous therapy (IV) care, observational care, and doctors' rounds) was applied to estimate HCP hand contamination. Viral accruement was contrasted between room orientation, care type, and by assumptions about whether bioaerosol deposition was the same or variable by room orientation. Differences in sequences of surface contacts were observed for care type and room orientation. Simulated viral accruement differences between room types were influenced by mostly by differences in bioaerosol deposition and by behavior sequences when deposition patterns for the room orientations were similar. Differences between care types were likely driven by differences in hand-to-patient contact frequency, with doctors' rounds resulting in the greatest predicted viral accruement on hands.