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Spermatogenesis involves a complex process of cellular differentiation maintained by spermatogonial stem cells (SSCs). Being critical to male reproduction, it is generally assumed that spermatogenesis starts and ends in equivalent transcriptional states in related species. Based on single-cell gene expression profiling, it has been proposed that undifferentiated human spermatogonia can be subclassified into four heterogenous subtypes, termed states 0, 0A, 0B, and 1. To increase the resolution of the undifferentiated compartment and trace the origin of the spermatogenic trajectory, we re-analysed the single-cell (sc) RNA-sequencing libraries of 34 post-pubescent human testes to generate an integrated atlas of germ cell differentiation. We then used this atlas to perform comparative analyses of the putative SSC transcriptome both across human development (using 28 foetal and pre-pubertal scRNA-seq libraries) and across species (including data from sheep, pig, buffalo, rhesus and cynomolgus macaque, rat, and mouse). Alongside its detailed characterisation, we show that the transcriptional heterogeneity of the undifferentiated spermatogonial cell compartment varies not only between species but across development. Our findings associate 'state 0B' with a suppressive transcriptomic programme that, in adult humans, acts to functionally oppose proliferation and maintain cells in a ready-to-react state. Consistent with this conclusion, we show that human foetal germ cells-which are mitotically arrested-can be characterised solely as state 0B. While germ cells with a state 0B signature are also present in foetal mice (and are likely conserved at this stage throughout mammals), they are not maintained into adulthood. We conjecture that in rodents, the foetal-like state 0B differentiates at birth into the renewing SSC population, whereas in humans it is maintained as a reserve population, supporting testicular homeostasis over a longer reproductive lifespan while reducing mutagenic load. Together, these results suggest that SSCs adopt differing evolutionary strategies across species to ensure fertility and genome integrity over vastly differing life histories and reproductive timeframes., Competing Interests: The authors declare that there are no conflicts of interest.

We present an exact dimensionality reduction for dynamics of an arbitrary array of globally coupled complex-valued Riccati equations. It generalizes the Watanabe-Strogatz theory [Integrability of a globally coupled oscillator array, Phys. Rev. Lett. 70, 2391 (1993).PRLTAO0031-900710.1103/PhysRevLett.70.2391] for sinusoidally coupled phase oscillators and seamlessly includes quadratic integrate-and-fire neurons as the real-valued special case. This simple formulation reshapes our understanding of a broad class of coupled systems-including a particular class of phase-amplitude oscillators-which newly fall under the category of integrable systems. Precise and rigorous analysis of complex Riccati arrays is now within reach, paving a way to a deeper understanding of emergent behavior of collective dynamics in coupled systems.

Cerebral oedema develops after anoxic brain injury. In two models of asphyxial and asystolic cardiac arrest without resuscitation, we found that oedema develops shortly after anoxia secondary to terminal depolarizations and the abnormal entry of CSF. Oedema severity correlated with the availability of CSF with the age-dependent increase in CSF volume worsening the severity of oedema. Oedema was identified primarily in brain regions bordering CSF compartments in mice and humans. The degree of ex vivo tissue swelling was predicted by an osmotic model suggesting that anoxic brain tissue possesses a high intrinsic osmotic potential. This osmotic process was temperature-dependent, proposing an additional mechanism for the beneficial effect of therapeutic hypothermia. These observations show that CSF is a primary source of oedema fluid in anoxic brain. This novel insight offers a mechanistic basis for the future development of alternative strategies to prevent cerebral oedema formation after cardiac arrest., (© The Author(s) (2021). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved. For permissions, please email: journals.permissions@oup.com.)

While the acquisition of cellular plasticity in adult stem cells is essential for rapid regeneration after tissue injury, little is known about the underlying mechanisms governing this process. Our data reveal the coordination of airway progenitor differentiation plasticity by inflammatory signals during alveolar regeneration. Following damage, interleukin-1β (IL-1β) signalling-dependent modulation of Jag1 and Jag2 expression in ciliated cells results in the inhibition of Notch signalling in secretory cells, which drives the reprogramming and acquisition of differentiation plasticity. We identify the transcription factor Fosl2 (also known as Fra2) for secretory cell fate conversion to alveolar type 2 cells that retain the distinct genetic and epigenetic signatures of secretory lineages. We also reveal that human secretory cells positive for KDR (also known as FLK-1) display a conserved capacity to generate alveolar type 2 cells via Notch inhibition. Our results demonstrate the functional role of an IL-1β-Notch-Fosl2 axis in the fate decision of secretory cells during injury repair, proposing a potential therapeutic target for human lung alveolar regeneration., (© 2021. The Author(s), under exclusive licence to Springer Nature Limited.)

We derive the AdS_{5}×S^{5} Green-Schwarz superstring from four-dimensional Beltrami-Chern-Simons theory reduced on a manifold with singular boundary conditions. In this construction, the Lax connection and spectral parameter of the integrable superstring have a simple geometric origin in four dimensions as gauge connection and reduction coordinate. κ symmetry arises as a certain class of singular gauge transformations, while the world-sheet metric comes from complex-structure-changing Beltrami differentials. Our approach offers the possibility of investigating integrable holography using traditional field theory methods.

Resistance to anti-cancer drugs is a major cause of treatment failure. While several intracellular mechanisms of resistance have been postulated, the role of extrinsic factors in the development of resistance in individual tumor cells is still not fully understood. Here we used a hybrid agent-based model to investigate how sensitive tumor cells develop drug resistance in the heterogeneous tumor microenvironment. We characterized the spatio-temporal evolution of lineages of the resistant cells and examined how resistance at the single-cell level contributes to the overall tumor resistance. We also developed new methods to track tumor cell adaptation, to trace cell viability trajectories and to examine the three-dimensional spatio-temporal lineage trees. Our findings indicate that drug-induced resistance can result from cells adaptation to the changes in drug distribution. Two modes of cell adaptation were identified that coincide with microenvironmental niches-areas sheltered by cell micro-communities (protectorates) or regions with limited drug penetration (refuga or sanctuaries). We also recognized that certain cells gave rise to lineages of resistant cells (precursors of resistance) and pinpointed three temporal periods and spatial locations at which such cells emerged. This supports the hypothesis that tumor micrometastases do not need to harbor cell populations with pre-existing resistance, but that individual tumor cells can adapt and develop resistance induced by the drug during the treatment., (Copyright © 2020 Pérez-Velázquez and Rejniak.)

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore "master" regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges.

A tumor vasculature that is functionally abnormal results in irregular gradients of metabolites and drugs within the tumor tissue. Recently, significant efforts have been committed to experimentally examine how cellular response to anti-cancer treatments varies based on the environment in which the cells are grown. In vitro studies point to specific conditions in which tumor cells can remain dormant and survive the treatment. In vivo results suggest that cells can escape the effects of drug therapy in tissue regions that are poorly penetrated by the drugs. Better understanding how the tumor microenvironments influence the emergence of drug resistance in both primary and metastatic tumors may improve drug development and the design of more effective therapeutic protocols. This chapter presents a hybrid agent-based model of the growth of tumor micrometastases and explores how microenvironmental factors can contribute to the development of acquired resistance in response to a DNA damaging drug. The specific microenvironments of interest in this work are tumor hypoxic niches and tumor normoxic sanctuaries with poor drug penetration. We aim to quantify how spatial constraints of limited drug transport and quiescent cell survival contribute to the development of drug resistant tumors.

We obtain the all-loop worldsheet S matrix for fundamental excitations on AdS₃×S³×T⁴ by studying the off-shell symmetry algebra of the superspace action in light cone gauge. The massless modes, unaccounted for in earlier works, are automatically included in our treatment. Their exact dispersion relation is found to be nonrelativistic, of giant-magnon form, and their scattering is naturally well defined. This opens the way to a complete investigation of AdS₃/CFT₂ integrability.

Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and operator product expansion coefficients of conformal field theories in diverse space-time dimensions. It appears that the calculations can be done only for theories lying at the boundary of the allowed parameter space. Here it is pointed out that a similar method can be applied to a larger class of conformal field theories, whether unitary or not, and no free parameter remains, provided we know the fusion algebra of the low lying primary operators. As an example we calculate using first principles, with no phenomenological input, the lowest scaling dimensions of the local operators associated with the Yang-Lee edge singularity in three and four space dimensions. The edge exponents compare favorably with the latest numerical estimates. A consistency check of this approach on the 3D critical Ising model is also made.

We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero-Moser-Sutherland type and nonlinear integrable field equations of Korteweg-de Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero-Moser-Sutherland models, we provide three alternative deformations: a complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real-valued field equations of nonlinear integrable systems; and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of Korteweg-de Vries type are studied with regard to different kinds of PT-symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.

There has been previous theoretical explorations of the stability of signals by prey that they have detected a stalking or ambush predator, where such perceptual advertisement dissuades the predator from attacking. Here we use a game theoretical model to extend the theory to consider some empirically-motivated complexities: (i) many perceptual advertisement signals appear to have the potential to vary in intensity, (ii) higher intensity signals are likely to be most costly to produce, and (iii) some high-cost signals (such as staring directly at the predator) can only be utilised if the prey is very confident of the existence of a nearby predator (that is, there are reserved or unfakable signals). We demonstrate that these complexities still allow for stable signalling. However, we do not find solutions where prey use a range of signal intensities to signal different degrees of confidence in the proximity of a predator; with prey simply adopting a binary response of not signalling or always signalling at the same fixed level. However this fixed level will not always be the cheapest possible signal, and we predict that prey that require more certainty about proximity of a predator will use higher-cost signals. The availability of reserved signals does not prohibit the stability of signalling based on lower-cost signals, but we also find circumstances where only the reserved signal is used. We discuss the potential to empirically test our model predictions, and to develop theory further to allow perceptual advertisement to be combined with other signalling functions., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Evolutionary dynamics have been traditionally studied on homogeneously mixed and infinitely large populations. However, real populations are finite and characterised by complex interactions among individuals. Recent studies have shown that the outcome of the evolutionary process might be significantly affected by the population structure. Although an analytic investigation of the process is possible when the contact structure of the population has a simple form, this is usually infeasible on complex structures and the use of various assumptions and approximations is necessary. In this paper, we adopt an approximation method which has been recently used for the modelling of infectious disease transmission to model evolutionary game dynamics on complex networks. Comparisons of the predictions of the model constructed with the results of computer simulations reveal the effectiveness of the method and the improved accuracy that it provides when, for example, compared to well-known pair approximation methods. This modelling framework offers a flexible way to carry out a systematic analysis of evolutionary game dynamics on graphs and to establish the link between network topology and potential system behaviours. As an example, we investigate how the Hawk and Dove strategies in a Hawk-Dove game spread in a population represented by a random regular graph, a random graph and a scale-free network, and we examine the features of the graph which affect the evolution of the population in this particular game.

Factors influencing allocation of resources to male and female offspring continue to be of great interest to evolutionary biologists. A simultaneous hermaphrodite is capable of functioning in both male and female mode at the same time, and such a life-history strategy is adopted by most flowering plants and by many sessile aquatic animals. In this paper, we focus on hermaphrodites that nourish post-zygotic stages, e.g. flowering plants and internally fertilising invertebrates, and consider how their sex allocation should respond to an environmental stress that reduces prospects of survival but does not affect all individuals equally, rather acting only on a subset of the population. Whereas dissemination of pollen and sperm can begin at sexual maturation, release of seeds and larvae is delayed by embryonic development. We find that the evolutionarily stable strategy for allocation between male and female functions will be critically dependent on the effect of stress on the trade-off between the costs of male and female reproduction, (i.e. of sperm and embryos). Thus, we identify evaluation of this factor as an important challenge to empiricists interested in the effects of stress on sex allocation. When only a small fraction of the population is stressed, we predict that stressed individuals will allocate their resources entirely to male function and unstressed individuals will increase their allocation to female function. Conversely, when the fraction of stress-affected individuals is high, stressed individuals should respond to this stressor by increasing investment in sperm and unstressed individuals should invest solely in embryos. A further prediction of the model is that we would not expect to find populations in the natural world where both stressed and unstressed individuals are both hermaphrodite., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Recently, models of evolution have begun to incorporate structured populations, including spatial structure, through the modelling of evolutionary processes on graphs (evolutionary graph theory). One limitation of this otherwise quite general framework is that interactions are restricted to pairwise ones, through the edges connecting pairs of individuals. Yet, many animal interactions can involve many players, and theoretical models also describe such multiplayer interactions. We shall discuss a more general modelling framework of interactions of structured populations with the focus on competition between territorial animals, where each animal or animal group has a "home range" which overlaps with a number of others, and interactions between various group sizes are possible. Depending upon the behaviour concerned we can embed the results of different evolutionary games within our structure, as occurs for pairwise games such as the Prisoner's Dilemma or the Hawk-Dove game on graphs. We discuss some examples together with some important differences between this approach and evolutionary graph theory., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Effective population size is a key parameter in population ecology because it allows prediction of the dynamics of genetic variation and the rate of genetic drift and inbreeding. It is important for the definition of "nearly neutral" mutations and, hence, has consequences for the fixation or extinction probabilities of advantageous and deleterious mutations. As graph-based population models become increasingly popular for studying evolution in spatially or socially structured populations, a neutral theory for evolution on graphs is called for. Here, we derive formulae for two alternative measures of effective population size, the variance effective and inbreeding effective size of general unweighted and undirected graphs. We show how these two quantities relate to each other and we derive effective sizes for the complete graph the cycle and bipartite graphs. For one-dimensional lattices and small-world graphs, we estimate the inbreeding effective size using simulations. The presented method is suitable for any structured population of haploid individuals with overlapping generations., (© 2012 The Author(s). Evolution© 2012 The Society for the Study of Evolution.)

We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a natural geometrical structure. For instance, the spins of a spin-1/2 representation, pointing in various directions, form a sphere. We show that for subsystems with a large number m of local degrees of freedom, the entanglement entropy diverges as d/2 logm, where d is the fractal dimension of the subset of basis elements with nonzero coefficients. We interpret this result by seeing d as the (not necessarily integer) number of zero-energy Goldstone bosons describing the ground state. We suggest that this result holds quite generally for largely degenerate ground states, with potential applications to spin glasses and quenched disorder.

We consider the problem of decomposing a video sequence into a superposition of (a given number of) moving layers. For this problem, we propose an energy minimization approach based on the coding cost. Our contributions affect both the model (what is minimized) and the algorithmic side (how it is minimized). The novelty of the coding-cost model is the inclusion of a refined model of the image formation process, known as super resolution. This accounts for camera blur and area averaging arising in a physically plausible image formation process. It allows us to extract sharp high-resolution layers from the video sequence. The algorithmic framework is based on an alternating minimization scheme and includes the following innovations. 1) A video labeling, we optimize the layer domains. This allows to regularize the shapes of the layers and a very elegant handling of occlusions. 2) We present an efficient parallel algorithm for extracting super-resolved layers based on TV filtering.

Many models of honest signaling, based on Zahavi's handicap principle, predict that if receivers are interested in a quality that shows continuous variation across the population of signalers, then the distribution of signal intensities will also be continuous. However, it has previously been noted that this prediction does not agree with empirical observation in many signaling systems, where signals are limited to a small number of levels despite continuous variation in the trait being signaled. Typically, there is a critical value of the trait, with all individuals with trait values on one side of the threshold using the same cheap signal, and all those with trait values on the other side of the threshold using the same expensive signal. It has already been demonstrated that these classical models naturally predict such "all-or-nothing signaling" if it is additionally assumed that receivers suffer from perceptual error in evaluating signal strength. We show that such all-or-nothing signaling is also predicted if receivers are limited to responding to the signals in one of two ways. We suggest that many ecological situations (such as the decision to attack the signaler or not, or mate with the signaler or not) involve such binary choices., (© 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.)

Kleptoparasitism, the stealing of food items from other animals, is a common behaviour observed across a huge variety of species, and has been subjected to significant modelling effort. Most such modelling has been deterministic, effectively assuming an infinite population, although recently some important stochastic models have been developed. In particular the model of Yates and Broom (Stochastic models of kleptoparasitism. J. Theor. Biol. 248 (2007), 480-489) introduced a stochastic version following the original model of Ruxton and Moody (The ideal free distribution with kleptoparasitism. J. Theor. Biol. 186 (1997), 449-458), and whilst they generated results of interest, they did not solve the model explicitly. In this paper, building on methods used already by van der Meer and Smallegange (A stochastic version of the Beddington-DeAngelis functional response: Modelling interference for a finite number of predators. J. Animal Ecol. 78 (2009) 134-142) we give an exact solution to the distribution of the population over the states for the Yates and Broom model and investigate the effects of some key biological parameters, especially for small populations where stochastic models can be expected to differ most from their deterministic equivalents., (Copyright (c) 2010 Elsevier Ltd. All rights reserved.)

We present a simple model of investment across a suite of different anti-predatory defences. Defences can incur an initial construction cost and and/or may be costly each time they are utilised. Our aim is to use a simple, but general, mathematical model to explore when prey that face a single predatory threat where each attack is of the same nature should invest only in a single defence, and when they should spread their investment across more than one defence. This should help to explain the observed variety of defences that a single prey individual may employ during repeated attacks of a similar nature or even at different stages during one attack. Previous verbal reasoning suggested that prey should specialise in investment in defences that can be utilised early in the predation sequence. Our quantitative model predicts that (depending of the relatively properties of different defences), there may be concentrated investment in early acting, or in late-acting defences, or a spread of investment across both defence types. This variety of predictions is in agreement with the variation in defences shown by natural organisms subjected to repeated predatory attack., ((c) 2010 Elsevier Ltd. All rights reserved.)

Stationary flow- and diffusion-distributed structures (FDS) patterns appear in a reaction-diffusion-advection system when a constant forcing is applied at the inlet of the reactor. We show that if the forcing is subject to noise, the FDS can be destroyed via the noise-induced Hopf instability. However, the FDS patterns are restored if the flow rate is sufficiently high. We demonstrate that the critical flow rate which is required for the stabilization of FDS has a power-law dependence on the noise amplitude.

A novel approach for the description of the protein stoichiometry of viral capsids, that is the protein shells protecting the viral genome, is introduced based on tiling theory. This approach generalizes Caspar-Klug theory of quasi-equivalence to account also for non-quasi-equivalent subunit arrangements in icosahedral virus capsids that have been observed experimentally but are not covered by the Caspar-Klug approach. In particular, the new approach is used to explain the structure of polyoma virus, Simian Virus 40 and L-A virus capsids, which are considered structural puzzles in view of Caspar-Klug theory.