Journal of Theoretical Biology

Antiviral therapies are among the most effective pharmaceutical interventions in treatment of a variety of viral pathogens. To optimize the antiviral effectiveness it is crucial to characterize the relationship between multiple cellular modes of antiviral action and the complex response of the hosts innate immune system relative to the within host dynamics of a proliferating virus. Since their introduction in 1968 and 2019, Influenza A virus (IAV) H3N2 and Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2), respectively, have caused unprecedented damage on the public health infrastructure globally. In addition to the substantial burden of morbidity and mortality around the world, both viruses have the potential of undergoing evolution leading to antigenic escape from the prevailing interventions. These biological characteristics advocate for urgent development of effective antivirals for the treatment of IAV and SARS-CoV-2. In this multi-stage study, we develop a suite of within-host models encompassing a number of hypotheses regarding virus-specific innate host functional responses and their impacts on the proliferation of IAV H3N2 and SARS-CoV-2 viruses. We use likelihood-based statistical inference to confront these hypotheses with infection data on IAV H3N2 and SARS-CoV-2 from infection experiments in ferrets. Upon identifying the best-fitting model of within-host dynamics, we can quantify the potential impact of antiviral drug therapy as a function of effectiveness and timing of initiation. We find significant mechanistic differences between the infection dynamics of H3N2 IAV and SARS-CoV-2 and associated model parameters. The treatment consequences of these differences are that SARS-CoV-2 is harder to control with antivirals, requiring earlier initiation and a more effective drug. Author summaryAntiviral drugs are prophylactic chemical agents that are used to contain several viral infections. Influenza A H3N2 virus (H3N2) and Severe Acute Respiratory Syndrome Corona Virus-2 (SARS-CoV-2) are very important viral pathogens that have caused unprecedented, global public health damage in the recent times. This makes development of antiviral drugs crucial along with other pharmaceutical prophylactics like vaccination. To optimize the pathogen specific effectiveness, however, it is necessary to simultaneously explore the relationship among the intra-host viral kinetics, immune dynamics and modes of antiviral action. In this article we theoretically analyze antiviral action of a drug in union with effect of the hosts innate immune system in containing infections of SARS-CoV-2 and H3N2 in infection experiments with ferrets. We find fundamental differences in the requisite antiviral effectiveness which, we posit, is due to substantially different inter-cellular proliferation potential between the two viruses.

The proliferation of mitochondrial DNA (mtDNA) with deletion mutations has been linked to aging, and age related neurodegenerative conditions. In this study we model effect of mtDNA half-life on mtDNA competition and selection. Individual cells effectively form a closed ecosystem containing a large population of independently replicating mtDNA. We would expect competition and selection to occur between wild type mtDNA and various mutant variants. There is a symbiotic relationship between the cell and the mitochondria, and unrestricted mtDNA replication would be detrimental to the host cell. Deletion mutations of mtDNA are relatively common and give a replication advantage to the shorter sequence, as this could be lethal to the host cell, we would expect to see differences in mtDNA replication in short and long lived cells. In this paper, we use a computer simulation of mtDNA replication, where mtDNA sequences may undergo deletion errors and give rise to mutant species that can compete with the wild type. This study focuses on longer lived cells where the wild type mtDNA is expected to be more susceptible to displacement by mutants. Our simulations confirm that deletion mutations have a replication advantage over the wild type due to decreased replication time. Wild type survival times diminished with increased mutation probabilities. The relationship between survival time and mutation rate was non-linear; a ten-fold increase in mutation probability resulted in a halving in wild type survival time. In contrast a modest increase in the mtDNA half-life had a profound affect on the wild type survival time in the presence of deletion mutants, thereby, mitigating the replicative advantage of shorter sequence mutations. Given the relevance of mitochondrial dysfunction to various neurodegenerative conditions, we propose that therapies to increase mtDNA half-life could be a therapeutic strategy.

Advances in genetic engineering have made it possible to reprogram an individuals immune cells to express receptors that recognize markers on tumor cell surfaces. The process of re-engineering T cell lymphocytes to express Chimeric Antigen Receptors (CARs) and reinfusing the CAR-modified T cells into patients to treat various cancers is being explored in clinical trials. While the majority of patients with some cancers (e.g., B cell acute lymphocytic leukemia) respond to CAR-T cell therapy, this success is not evidenced in all cancers. For example, only 26% of Chronic Lymphocytic Leukemia (CLL) patients respond to CAR T cell therapy. Understanding of the factors associated with an individual patients response is important for patient selection and could help develop more effective CAR T cell therapies. Here we present a mechanistic mathematical model to identify factors associated with responses to CAR T cell therapeutic interventions. The proposed model is a system of coupled ordinary differential equations designed based on known immunological principles and prevailing hypotheses on the mechanism of CAR T cell kinetics, Interleukin 6 (IL-6) secretion, and tumor killing in CAR T cell therapy. The model reports in silico disease outcomes using B cell concentration as a surrogate biomarker. Our results are consistent with the in vitro experimental observations that CAR T cell fitness in terms of its tumor cell killing capacity and proliferation plays an important role in the patient response. We demonstrate the utility of mathematical modelling in understanding the factors that play an important role in patient response to CAR T cell therapy.

The evolution and spread of antibiotic resistance poses a major threat to human health. The high level of antibiotic use in the rearing of livestock is contributing to the origin and persistence of antibiotic resistance amongst humans. Understanding how resistance genes spread from livestock to humans and investigating the impact of managing antibiotic use in livestock will be important for guiding strategies to reduce the risk to humans. We have developed a mathematical model of the transmission of resistance genes from livestock to humans and their spread amongst the human population. Using this framework we demonstrate that although resistant zoonotic foodborne infections do not contribute significantly to the annual burden of death, they could be a source of resistance amongst other pathogens, including those that exclusively spread between humans. Amongst these pathogens, only livestock-derived resistant strains that are associated with a net fitness cost would be expected to decline in prevalence following control strategies aimed at reducing the impact on humans of antibiotic use in livestock. Author SummaryAntibiotics are an essential component of human health care. They are also used in the rearing of livestock for human consumption, which contributes to the development of antibiotic resistant pathogens. Although humans are known to be at risk from antibiotic resistance that evolves amongst livestock, the number of human lives that are at stake remains unclear. Furthermore, the number of lives that could be saved through interventions to reduce antibiotic use in livestock has not been evaluated. Here, we have developed a mathematical framework to explore these questions. Using this framework we explicitly demonstrate that there are too many uncertainties to calculate the number of preventable human deaths. Nevertheless, the importance of reserving new and currently effective antibiotics for human use is clear. Once resistance genes that do not have a fitness disadvantage have spread from livestock to humans, it is too late for interventions targeted at livestock to affect their prevalence in humans in the long term.

The pace of aging varies considerably in nature. Historically, scientists focused mostly on why and how has aging evolved, while only a few studies explored mechanisms driving evolution of specific rates of aging. Here we develop an agent-based model simulating evolution of aging in prey subject to predation. Our results suggest that predation affects the pace of aging in prey only if young, vivid animals are not much more likely to escape predators than the old ones. However, even this effect slowly vanishes when the predator diet composition evolves, too. Furthermore, evolution of a specific aging rate, in our model, is driven mainly by a single parameter, the strength of a trade-off between aging and fecundity. Indeed, in absence of this trade-off the evolutionary impacts of predation on the prey aging rate appear random. Our model produces several testable predictions which may be useful for other areas of aging research.

Mitochondria are highly dynamic structures that undergo constant remodeling by the process of fission and fusion. Using simulation methods we study the effects of neuron loss in humans due to the proliferation of deletion mutations. We implement two models of an organelle, namely, closed cristae (CC) and open mitochondrion (OM). With CC, mtDNA are confined to a cristae unless mixed by the process of fission and fusion. Conversely, mtDNA can diffuse freely throughout the organelle in the OM model. We also implement selective mitophagy in the CC model. Higher rates of mixing mtDNA increase the rate of neuron loss which, in turn, increases the prevalence of dementia. Selective mitophagy mitigates against the effect of high rate mixing. However, this mitigation is all or nothing. Even at nominal rates compared to mixing, neuron loss is almost completely eliminated resulting in minimal cognitive decline. These results do not fit the observations of normal aging and dementia prevalence in the elderly human population. This study brings into question the role that fission and fusion is believed play in the removal of defective mtDNA.

Retinal detachment (RD) is the separation of the neural layer from the retinal pigmented epithelium thereby preventing the supply of nutrients to the cells within the neural layer of the retina. In vertebrates, primary photoreceptor cells consisting of rods and cones undergo daily renewal of their outer segment through the addition of disc-like structures and shedding of these discs at their distal end. When the retina detaches, the outer segment of these cells begins to degenerate and, if surgical procedures for reattachment are not done promptly, the cells can die and lead to blindness. The precise effect of RD on the renewal process is not well understood. Additionally, a time frame within which reattachment of the retina can restore proper photoreceptor cell function is not known. Focusing on rod cells, we propose a mathematical model to clarify the influence of retinal detachment on the renewal process. Our model simulation and analysis suggest that RD stops or significantly reduces the formation of new discs and that an alternative removal mechanism is needed to explain the observed degeneration during RD. Sensitivity analysis of our model parameters points to the disc removal rate as the key regulator of the critical time within which retinal reattachment can restore proper photoreceptor cell function.

Global populations are ageing at an unprecedented rate. For many diseases, age is a strong indicator of susceptibility, morbidity, or mortality. Principles of evolutionary biology can be leveraged to understand how pathogens may optimally exploit new populations, and the impact of this on the global burden of infectious-disease-induced mortality. We parameterised an age-specific R0 model with 2017 epidemiological data on Measles, Tuberculosis, Meningitis, and Ebola, and age-specific demographic estimates for 2017 and 2050, for the seven Global Burden of Disease super-regions. We explored the theoretical trade-offs between pathogen virulence & transmission, and virulence & host recovery, parameterising trade-off parameters using Latin Hypercube Sampling. Population ageing between 2017-2050 saw an increase in virulence induced mortality in four settings: 1) Ebola in sub-Saharan Africa, 2) Measles in central/eastern Europe & central Asia region, 3) Measles in North Africa & the Middle East and 4) Tuberculosis in the central/eastern Europe & central Asia region. The decrease in infection duration due to an increase of elderly people drives pathogen virulence down for diseases in the remaining settings. Understanding the mechanisms that shape pathogen dynamics and leveraging this to predict future challenges is key to endemic disease management in a rapidly changing world. Author SummaryKey aspects of disease transmission including susceptibility to infection, the severity of infection, and the probability of dying from that infection, are affected by host age. Global populations are rapidly ageing, so that the mean age of most populations is generally higher than it used to be and is set to continue on this trajectory. This suggests that the dynamics of infectious diseases are also likely to change, although infectious disease dynamics tend to be non-linear as these key parameters interact. We have developed a dynamic modelling framework to explore how changes in population age structure might impact the optimal level of pathogen virulence in a population. We have chosen four infectious diseases as case studies, that differentially impact certain age classes to illustrate these dynamics. We have parameterised this framework with open access data for each of the seven Global Burden of Disease super-regions and show that population ageing can increase virulence for several diseases in differing global regions, whilst increased background rates of mortality can drive virulence down in others.

A recent study (Louca and Pennell, 2020) spotlighted the issue of model congruence, or asymptotic unidentifiability, in time-dependent birth-death models used for reconstructing species diversification histories on phylogenetic trees. The present work investigates this issue in state-dependent speciation and extinction (SSE) models, commonly used to study trait-dependent diversification. We found that model unidentifiability is universal due to hidden states, with every SSE belonging to an infinite congruence class. Notably, any trait-independent model is congruent with trait-dependent models, raising concerns for hypothesis testing. To address this, we propose an analytical solution that resolves model selection within a congruence class. Our findings show that this type of congruence is the only one possible, and with our solution in place, model unidentifiability in SSEs becomes absolutely harmless for inference. However, model selection across congruence classes remains challenging due to extremely high false positive rates. The discovered congruence offers a clear explanation of this issue and suggests potential ways forward.

Cell degeneration, including that resulting in retinal diseases, is linked to metabolic issues. In the retina, photoreceptor degeneration can result from imbalance in lactate production and consumption as well as disturbances to pyruvate and glucose levels. To identify the key mechanisms in metabolism that may be culprits of this degeneration, we use a nonlinear system of differential equations to mathematically model the metabolic pathway of aerobic glycolysis in a healthy cone photoreceptor. This model allows us to analyze the levels of lactate, glucose, and pyruvate within a single cone cell. We perform numerical simulations, use available metabolic data to estimate parameters and fit the model to this data, and conduct a sensitivity analysis using two different methods (LHS/PRCC and eFAST) to identify pathways that have the largest impact on the system. Using bifurcation techniques, we find that the system has a bistable regime, biologically corresponding to a healthy versus a pathological state. The system exhibits a saddle node bifurcation and hysteresis. This work confirms the necessity for the external glucose concentration to sustain the cell even at low initial internal glucose levels. It also validates the role of {beta}-oxidation of fatty acids which fuel oxidative phosphorylation under glucose- and lactate-depleted conditions, by showing that the rate of {beta}-oxidation of ingested outer segment fatty acids in a healthy cone cell must be low. Model simulations reveal the modulating effect of external lactate in bringing the system to steady state; the bigger the difference between external lactate and initial internal lactate concentrations, the longer the system takes to achieve steady state. Parameter estimation for metabolic data demonstrates the importance of rerouting glucose and other intermediate metabolites to produce glycerol 3-phosphate (G3P), thus increasing lipid synthesis (a precursor to fatty acid production) to support their high growth rate. While a number of parameters are found to be significant by one or both of the methods for sensitivity analysis, the rate of {beta}-oxidation of ingested outer segment fatty acids is shown to consistently play an important role in the concentration of glucose, G3P, and pyruvate, whereas the extracellular lactate level is shown to consistently play an important role in the concentration of lactate and acetyl coenzyme A. The ability of these mechanisms to affect key metabolites variability and levels (as revealed in our analyses) signifies the importance of inter-dependent and inter-connected feedback processes modulated by and affecting both the RPEs and cones metabolism.

The exact mechanism controlling cell growth remains a grand challenge in developmental biology and regenerative medicine. The Drosophila wing disc tissue serves as an ideal biological model to study growth regulation due to similar features observed in other developmental systems. The mechanism of growth regulation in the wing disc remains a subject of intense debate. Most existing models to study tissue growth focus on either chemical signals or mechanical forces only. Here we developed a multiscale chemical-mechanical coupled model to test a growth regulation mechanism depending on the spatial range of the morphogen gradient. By comparing the spatial distribution of cell division and the overall shape of tissue obtained in the coupled model with experimental data, our results show that the distribution of the Dpp morphogen can be critical in resulting tissue size and shape. A larger tissue size with a faster growth rate and more symmetric shape can be achieved if the Dpp gradient spreads in a larger domain. Together with the absorbing boundary conditions, the feedback regulation that downregulates Dpp receptors on the cell membrane allows the further spread of the morphogen away from its source region, resulting in prolonged tissue growth at a more spatially homogeneous growth rate. Summary StatementA multiscale chemical-mechanical model was developed by coupling submodels representing dynamics of a morphogen gradient at the tissue level, intracellular chemical signals, and mechanical properties at the subcellular level. By applying this model to study the Drosophila wing disc, it was found that the spatial range of the morphogen gradient affected tissue growth in terms of the growth rate and the overall shape.

Here we argue that quasi-static analyses are insufficient to predict the speed of an organism from its skeletal mechanics alone (i.e. lever arm mechanics). Using a musculoskeletal numerical model we specifically demonstrate that 1) a single lever morphology can produce a range of output velocities, and 2) a single output velocity can be produced by a drastically different set of lever morphologies. These two sets of simulations quantitatively demonstrate that it is incorrect to assume a one-to-one relationship between lever arm morphology and organism maximum velocity. We then use a statistical analysis to quantify what parameters are determining output velocity, and find that muscle physiology, geometry, and limb mass are all extremely important. Lastly we argue that the functional output of a simple lever is dependent on the dynamic interaction of two opposing factors: those decreasing velocity at low mechanical advantage (low torque and muscle work) and those decreasing velocity at high mechanical advantage (muscle force-velocity effects). These dynamic effects are not accounted for in static analyses and are inconsistent with a force-velocity tradeoff in lever systems. Therefore, we advocate for a dynamic, integrative approach that takes these factors into account when analyzing changes in skeletal levers.

Trees accumulate somatic mutations throughout their long lifespan, resulting in genetic mosaicism among branches. While recent genomic studies quantified these mutations, they were largely limited to describing static patterns of variation. In this study, we developed a mathematical model to infer the dynamic processes of somatic mutation accumulation from snapshot genomic data obtained from four tropical trees (Dipterocarpaceae), which dominate tropical rain forests in Southeast Asia. Our model focus on genetic differences between shoot apical meristems (SAMs) at branch tips and explicitly incorporate stem cell dynamics within SAMs during shoot elongation and branching, enabling us to quantify somatic genetic drift arising from stem cell lineage replacement. By comparing model predictions with empirical data from Dipterocarpaceae trees, we estimated key parameters governing stem cell dynamics and somatic mutation rates. Our results indicate that both shoot elongation and branching involve replacement of stem cell lineages, leading to a moderate degree of somatic genetic drift. Accounting for stem cell dynamics resulted in slightly lower mutation rate estimates than previous approaches that ignored these processes. Using the estimated parameters, we further performed stochastic simulations to predict patterns of somatic mutations, including features not directly observed in the sampled trees, such as occasional deviations of somatic mutation phylogenies from physical architecture. Together, our modeling framework provides insights into how genetic mosaicism is shaped within tropical trees and reveals the stem cell dynamics underlying their long-term growth and accumulation of somatic mutations. (236 words) Highlights- We built mathematical models to predict the genetic differences between branch tips by somatic mutations. - The model considers the varying dynamics of stem cells in shoot meristem during shoot elongation and branching. - We compared the model prediction with empirical data from tropical trees, Dipterocarpaceae, and estimated the dynamics of stem cells and mutation rate. - Somatic mutation dynamics were shaped by somatic genetic drift arising from stem cell lineage replacement during shoot elongation and branching. - Accounting for stem cell dynamics led to slightly smaller estimates of mutation rates compared with previous estimates that ignored the dynamics. - Our models offer insights into how genetic variability is shaped in the tropical trees and the stem cell dynamics underlying their long-term growth.

Mitochondrial dynamics play a critical role in the development of aging-related diseases such as type 2 diabetes mellitus. To investigate how mitochondrial dynamics influence cellular behavior in pancreatic beta-cells, we developed a rule-based, multi-level simulation model of insulin secretion. The pancreatic beta cell model encompasses metabolic pathways (glycolysis and oxidative phosphorylation), compartmental processes (mitochondrial fusion and fission), and cellular processes (insulin secretion), allowing for the investigation of their interplay. The rule-based simulation model captures the high plasticity of these organelles and integrates and builds upon insights from various experimental studies and previous simulation models. Its rule-based specification facilitates the exploration of new hypotheses, the integration of new knowledge and data, and the successive extension of the model. The results of our simulation experiments underscore the importance of peripheral, sorted mitochondrial fission in maintaining mitochondrial health. Downregulation of the fission-associated anchor proteins Fis1 and MFF impacts mitochondrial structure and function differently, highlighting their distinct roles in maintaining mitochondrial health and cellular biogenesis, respectively. With respect to insulin secretion, Drp1 suppression shows that beta cells become unresponsive to glucose, whereas Fis1 downregulation only attenuates the cellular response. The simulation model and simulation results corroborates experimental findings and contribute to a deeper understanding of the mechanisms involved in mitochondrial dynamics of pancreatic beta cells and their relation to metabolic dysregulation in type 2 diabetes mellitus. Author summaryMitochondria, often described as the powerhouses of the cell, undergo constant changes through fusion and fission processes. These dynamics are essential for maintaining cell health and proper functioning. In type 2 diabetes mellitus, this balance can be disrupted. In this work, we developed a multi-level, rule-based simulation model to analyze processes of mitochondrial dynamics and their impact on insulin secretion within pancreatic beta cells. Our model captures diverse biological processes that operate at different but interconnected organizational levels, including energy metabolism, mitochondrial dynamics, and insulin secretion. We found that peripheral fission plays a crucial role in determining whether cells secrete insulin properly. In addition, downregulation of the fission-associated proteins MFF and Fis1 reveals a distinct impact on the structure and function of the mitochondrial network, as well as on insulin secretion in pancreatic beta cells. The simulation model and results provide insights into how mitochondrial dynamics affect beta cell metabolism and insulin release. It enables the study of dynamics at different organizational levels, and its rule-based approach facilitates the integration of new knowledge (e.g., by updating or adding specific rules) and experimental data.

O_LIIn addition to allometric biomass partitioning theory, optimal partitioning theory is one of the most important theoretical frame-works in predicting plant biomass allocation patterns. However, focus-ing on the equilibrium state leads to a mismatch between some empirical observations and estimations from optimal hypotheses. C_LIO_LITo address this issue, I developed a heuristic approach with a quantitative metric to study the transient patterns of plants allocating photosynthetic products to various combinations among plant organ parts. Moreover, the approach also discovers the mech-anisms under which various factors drive the transient patterns. C_LIO_LIWith this approach, I provide a case study and find that the per-turbations of the transient patterns of plant leaf and stem biomass periodically decrease and increase in response to plant height, crown diameter, and projected crown area. Predictions with the approach are well demonstrated by empirical data consisting of global forest plants. C_LIO_LISynthesis. The approach here complements the limitations of optimal partitioning theory by revealing the variations of plant photosynthetic partitioning in short time scales. Given the central role of plant biomass allocation pattern in both empirical applica-tions and theoretical foundations, there is a large scope for using this approach to investigate the directions in estimations of carbon stock, stabilized yields in agriculture as well as forest management. C_LI

AO_SCPLOWBSTRACTC_SCPLOWLife is based on energy conversion. In particular, in the nervous system significant amounts of energy are needed to maintain synaptic transmission and homeostasis. To a large extent, neurons depend on oxidative phosphorylation in mitochondria to meet their high energy demand (Pekkurnaz and Wang, 2022). For a comprehensive understanding of the metabolic demands in neuronal signaling, accurate models of ATP production in mitochondria are required. Here, we present a thermodynamically consistent model of ATP production in mitochondria based on previous work (Pietrobon and Caplan, 1985; Magnus and Keizer, 1997; Metelkin et al., 2006; Garcia et al., 2019). The significant improvement of the model is that the reaction rate constants are set such that detailed balance is satisfied. Moreover, using thermodynamic considerations, the dependence of the reaction rate constants on membrane potential, pH, and substrate concentrations are explicitly provided. These constraints assure the model is physically plausible. Furthermore, we explore different parameter regimes to understand in which conditions ATP production or its export are the limiting steps in making ATP available in the cytosol. The outcomes reveal that, under the conditions used in our simulations, ATP production is the limiting step and not its export. Finally, we performed spatial simulations with nine 3D realistic mitochondrial reconstructions and linked the ATP production rate in the cytosol with morphological features of the organelles. 1. SO_SCPLOWUMMARYC_SCPLOWIn this work, Garcia et al present a thermodynamically consistent model for ATP production in mitochondria, in which reaction rate constants are set such that detailed balance is satisfied. Simulations revealed that ATP production, but not its export, is the limiting step, and simulations with 3D mitochondrial reconstructions linked the ATP production rate in the cytosol with the morphological features of the organelles.

Photoreceptors (PRs) are metabolically demanding and packed at high density, which presents a challenge for nutrient exchange between the associated vascular beds and the tissue. Motivated by the ambition to understand the constraints under which PRs function, in this study we have drawn together diverse physiological and anatomical data in order to generate estimates of the rates of ATP production per mm2 of retinal surface area. With the predictions of metabolic demand in the companion paper, we seek to develop an integrated energy budget for the outer retina. It is known that rod PR number and the extent of the choriocapillaris (CC) vascular network that supports PRs both decline with age. To set the outer retina energy budget in the context of aging we demonstrate how, at different eccentricities, decline CC density is more than matched by rod loss in a way that tends to preserve nutrient exchange per rod. Together these finds provide an integrated framework for the study of outer retinal metabolism and how it might change with age.

The study of hematopoietic stem cell (HSCs) maintenance and differentiation to supply the hematopoietic system presents unique challenges, given the complex regulation of the process and the difficulty in observing cellular interactions in the stem cell niche. Quantitative methods and tools have emerged as valuable mechanisms to address this issue; however, the stochasticity of HSCs presents significant challenges for mathematical modeling, especially when bridging the gap between theoretical models and experimental validation. In this work, we have built a flexible and user-friendly stochastic dynamical and spatial model for long-term HSCs (LT-HSCs) and short-term HSCs (ST-HSCs) that captures experimentally observed cellular variability and heterogeneity. Our model implements the behavior of LT-HSCs and ST-HSCs and predicts their homeostatic dynamics. Furthermore, our model can be modified to explore various biological scenarios, such as stress-induced perturbations mediated by apoptosis, and successfully implement these conditions. Finally, the model incorporates spatial dynamics, simulating cell behavior in a 2D environment by combining Brownian motion with spatially graded parameters. *Summary StatementThis study addresses the challenge of characterizing hematopoietic stem cell (HSC) dynamics by developing a flexible, user-friendly stochastic spatial model of long-term and short-term HSCs. The model captures observed cellular variability and heterogeneity, predicts homeostatic dynamics, can be adapted to simulate stress-induced perturbations like apoptosis, and incorporates a spatial component to analyze HSC movement within a bone marrow niche.

A phylogenetic tree has three types of attributes: size, shape (topology), and branch lengths. Phylody-namic studies are often motivated by questions regarding the size of clades, nevertheless, nearly all of the inference methods only make use of the other two attributes. In this paper, we ask whether there is additional information if we consider tree size more explicitly in phylodynamic inference methods. To address this question, we first needed to be able to compute the expected tree size distribution under a specified phylodynamic model; perhaps surprisingly, there is not a general method for doing so -- it is known what this is under a Yule or constant rate birth-death model but not for the more complicated scenarios researchers are often interested in. We present three different solutions to this problem: using i) the deterministic limit; ii) master equations; and iii) an ensemble moment approximation. Using simulations, we evaluate the accuracy of these three approaches under a variety of scenarios and alternative measures of tree size (i.e., sampling through time or only at the present; sampling ancestors or not). We then use the most accurate measures for the situation, to investigate the added informational content of tree size. We find that for two critical phylodynamic questions -- i) is diversification diversity dependent? and, ii) can we distinguish between alternative diversification scenarios? -- knowing the expected tree size distribution under the specified scenario provides insights that could not be gleaned from considering the expected shape and branch lengths alone. The contribution of this paper is both a novel set of methods for computing tree size distributions and a path forward for richer phylodynamic inference into the evolutionary and epidemiological processes that shape lineage trees.

Generation intervals are distributions that describe the time between infection and onward transmission. They are a key epidemiological quantity because, together with the reproduction number R, they determine the population-level growth rate of a pathogen and its doubling time. Conversely, when fitting epidemiological models to data, assumed generation intervals impact R inference. This is well-known from studies that have used case data for R inference, with many studies emphasizing the importance of choosing an accurate distribution for the generation interval. In phylodynamic inference of R, the generation interval distribution is often not explicitly mentioned, and the impact of generation interval misspecification has been studied less. Here, we explore the impact of a commonly assumed (but rarely empirically accurate) exponential generation interval distribution on the estimation of R in phylodynamic inference. Using simulations and inference on these simulated datasets, we find that during the early exponential growth of an epidemic, if the generation interval is assumed to be exponentially distributed when it actually has a lower variance, then estimates of R will be biased low. Furthermore, uncertainty in the biased R estimates will be small. Our work highlights the importance of acknowledging implicit generation interval assumptions in phylodynamic inference and points to the need for methodological developments in phylodynamic inference to provide greater flexibility in the specification of accurate generation intervals.