Mathematical models of infectious disease transmission typically neglect within-host dynamics. Yet within-host dynamics - including pathogen replication, host immune responses, and interactions with microbiota - are crucial not only for determining the progression of disease at the individual level, but also for driving within-host evolution and onwards transmission, and therefore shape dynamics at the population level. Various approaches have been proposed to model both within- and between-host dynamics, but these typically require considerable simplifying assumptions to couple processes at contrasting scales (e.g., the within-host dynamics quickly reach a steady state) or are computationally intensive. Here we propose a novel, readily adaptable and broadly applicable method for modelling both within- and between-host processes which can fully couple dynamics across scales and is both realistic and computationally efficient. By individually tracking the deterministic within-host dynamics of infected individuals, and stochastically coupling these to continuous host state variables at the population-level, we take advantage of fast numerical methods at both scales while still capturing individual transient within-host dynamics and stochasticity in transmission between hosts. Our approach closely agrees with full stochastic individual-based simulations and is especially useful when the within-host dynamics do not rapidly reach a steady state or over longer timescales to track pathogen evolution. By applying our method to different pathogen growth scenarios we show how common simplifying assumptions fundamentally change epidemiological and evolutionary dynamics.

In biology, stochastic branching processes with a two-stage, hierarchical structure arise in the study of population dynamics, gene expression, and phylogenetic inference. These models have been commonly analyzed using generating functions, the method of characteristics and various perturbative approximations. Here we describe a general method for analyzing hierarchic first-order reaction networks using Lie theory. Crucially, we identify the fact that the Lie group associated to hierarchic reaction networks decomposes as a wreath product of the groups associated to the subnetworks of the independent and dependent types. After explaining the general method, we illustrate it on a model of population dynamics and the so-called two-state or telegraph model of single-gene transcription. Solutions to such processes provide essential input to downstream methods designed to attempt to infer parameters of these and related models.

Defensive symbionts in the host microbiome can confer protection from infection or reduce the harms of being infected by a parasite. Defensive symbionts are therefore promising agents of biocontrol that could be used to control or ameliorate the impact of infectious diseases. Previous theory has shown how symbionts can evolve along the parasitism-mutualism continuum to confer greater or lesser protection to their hosts and in turn how hosts may coevolve with their symbionts to potentially form a mutualistic relationship. However, the consequences of introducing a defensive symbiont for parasite evolution and how the symbiont may coevolve with the parasite have received relatively little theoretical attention. Here, we investigate the ecological and evolutionary implications of introducing a tolerance-conferring defensive symbiont into an established host-parasite system. We show that while the defensive symbiont may initially have a positive impact on the host population, parasite and symbiont evolution tend to have a net negative effect on the host population in the long term. This is because the introduction of the defensive symbiont always selects for an increase in parasite virulence and may cause diversification into high- and low-virulence strains. Even if the symbiont experiences selection for greater host protection, this simply increases selection for virulence in the parasite, resulting in a net negative effect on the host population. Our results therefore suggest that tolerance-conferring defensive symbionts may be poor biocontrol agents for population-level infectious disease control.

OBJECTIVES/AIMS:Prolonged infections of immunocompromised individuals have been proposed as a crucial source of new variants of SARS-CoV-2 during the COVID-19 pandemic. In principle, sustained within-host antigenic evolution in immunocompromised hosts could allow novel immune escape variants to emerge more rapidly, but little is known about how and when immunocompromised hosts play a critical role in pathogen evolution. MATERIALS AND METHODS:Here, we use a simple mathematical model to understand the effects of immunocompromised hosts on the emergence of immune escape variants in the presence and absence of epistasis. CONCLUSIONS:We show that when the pathogen does not have to cross a fitness valley for immune escape to occur (no epistasis), immunocompromised individuals have no qualitative effect on antigenic evolution (although they may accelerate immune escape if within-host evolutionary dynamics are faster in immunocompromised individuals). But if a fitness valley exists between immune escape variants at the between-host level (epistasis), then persistent infections of immunocompromised individuals allow mutations to accumulate, therefore, facilitating rather than simply speeding up antigenic evolution. Our results suggest that better genomic surveillance of infected immunocompromised individuals and better global health equality, including improving access to vaccines and treatments for individuals who are immunocompromised (especially in lower- and middle-income countries), may be crucial to preventing the emergence of future immune escape variants of SARS-CoV-2.

Non-pharmaceutical interventions (NPIs), such as social distancing and contact tracing, are important public health measures that can reduce pathogen transmission. In addition to playing a crucial role in suppressing transmission, NPIs influence pathogen evolution by mediating mutation supply, restricting the availability of susceptible hosts, and altering the strength of selection for novel variants. Yet it is unclear how NPIs might affect the emergence of novel variants that are able to escape pre-existing immunity (partially or fully), are more transmissible or cause greater mortality. We analyse a stochastic two-strain epidemiological model to determine how the strength and timing of NPIs affect the emergence of variants with similar or contrasting life-history characteristics to the wild type. We show that, while stronger and timelier NPIs generally reduce the likelihood of variant emergence, it is possible for more transmissible variants with high cross-immunity to have a greater probability of emerging at intermediate levels of NPIs. This is because intermediate levels of NPIs allow an epidemic of the wild type that is neither too small (facilitating high mutation supply), nor too large (leaving a large pool of susceptible hosts), to prevent a novel variant from becoming established in the host population. However, since one cannot predict the characteristics of a variant, the best strategy to prevent emergence is likely to be an implementation of strong, timely NPIs.

The COVID-19 pandemic, caused by the coronavirus SARS-CoV-2, has led to a wide range of non-pharmaceutical interventions being implemented around the world to curb transmission. However, the economic and social costs of some of these measures, especially lockdowns, has been high. An alternative and widely discussed public health strategy for the COVID-19 pandemic would have been to ‘shield’ those most vulnerable to COVID-19 (minimising their contacts with others), while allowing infection to spread among lower risk individuals with the aim of reaching herd immunity. Here we retrospectively explore the effectiveness of this strategy using a stochastic SEIR framework, showing that even under the unrealistic assumption of perfect shielding, hospitals would have been rapidly overwhelmed with many avoidable deaths among lower risk individuals. Crucially, even a small (20%) reduction in the effectiveness of shielding would have likely led to a large increase (>150%) in the number of deaths compared to perfect shielding. Our findings demonstrate that shielding the vulnerable while allowing infections to spread among the wider population would not have been a viable public health strategy for COVID-19 and is unlikely to be effective for future pandemics.

Reaction-diffusion mechanisms are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns formed by vegetation in semi-arid landscapes. Moreover, domain growth is an important process for embryonic growth and wound healing. There are many numerical modelling frameworks capable of simulating such systems on growing domains; however, each of these may be well suited to different spatial scales and particle numbers. Recently, spatially extended hybrid methods on static domains have been produced to bridge the gap between these different modelling paradigms in order to represent multi-scale phenomena. However, such methods have not been developed with domain growth in mind. In this paper, we develop three hybrid methods on growing domains, extending three of the prominent static-domain hybrid methods. We also provide detailed algorithms to allow others to employ them. We demonstrate that the methods are able to accurately model three representative reaction-diffusion systems accurately and without bias.

The simulation of stochastic reaction-diffusion systems using fine-grained representations can become computationally prohibitive when particle numbers become large. If particle numbers are sufficiently high then it may be possible to ignore stochastic fluctuations and use a more efficient coarse-grained simulation approach. Nevertheless, for multiscale systems which exhibit significant spatial variation in concentration, a coarse-grained approach may not be appropriate throughout the simulation domain. Such scenarios suggest a hybrid paradigm in which a computationally cheap, coarse-grained model is coupled to a more expensive, but more detailed fine-grained model, enabling the accurate simulation of the fine-scale dynamics at a reasonable computational cost. In this paper, in order to couple two representations of reaction-diffusion at distinct spatial scales, we allow them to overlap in a 'blending region'. Both modelling paradigms provide a valid representation of the particle density in this region. From one end of the blending region to the other, control of the implementation of diffusion is passed from one modelling paradigm to another through the use of complementary 'blending functions' which scale up or down the contribution of each model to the overall diffusion. We establish the reliability of our novel hybrid paradigm by demonstrating its simulation on four exemplar reaction-diffusion scenarios.

Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and proliferation are of great importance. A previously well-used method to incorporate domain growth into on-lattice reaction-diffusion models causes a buildup of particles on the boundaries of the domain, which is particularly evident when diffusion is low in comparison to the rate of domain growth. Here we present an alternative method which addresses this unphysical buildup of particles at the boundaries and demonstrate that it is accurate for scenarios in which the previous method fails. Further, we discuss for which parameter regimes it is feasible to continue using the original method due to diffusion dominating the domain growth mechanism.

During meiosis, induction of DNA double strand breaks (DSB) leads to recombination between homologous chromosomes, resulting in crossovers (CO) and non-crossovers (NCO). In the mouse, only 10% of DSBs resolve as COs, mostly through a class I pathway dependent on MutSγ (MSH4/ MSH5) and MutLγ (MLH1/MLH3), the latter representing the ultimate marker of these CO events. A second Class II CO pathway accounts for only a few COs, but is not thought to involve MutSγ/ MutLγ, and is instead dependent on MUS81-EME1. For class I events, loading of MutLγ is thought to be dependent on MutSγ, however MutSγ loads very early in prophase I at a frequency that far exceeds the final number of class I COs. Moreover, loss of MutSγ in mouse results in apoptosis before CO formation, preventing the analysis of its CO function. We generated a mutation in the ATP binding domain of Msh5 (Msh5GA). While this mutation was not expected to affect MutSγ complex formation, MutSγ foci do not accumulate during prophase I. However, most spermatocytes from Msh5GA/GA mice progress to late pachynema and beyond, considerably further than meiosis in Msh5−/− animals. At pachynema, Msh5GA/GA spermatocytes show persistent DSBs, incomplete homolog pairing, and fail to accumulate MutLγ. Unexpectedly, Msh5GA/GA diakinesis-staged spermatocytes have no chiasmata at all from any CO pathway, indicating that a functional MutSγ complex is critical for all CO events regardless of their mechanism of generation.

Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as partial differential equations are typically fast to simulate, they lack the individual-level detail that may be required in regions of low concentration or small spatial scale. However, to simulate at such an individual level throughout a domain and in regions where concentrations are high can be computationally expensive. Spatially coupled hybrid methods provide a bridge, allowing for multiple representations of the same species in one spatial domain by partitioning space into distinct modelling subdomains. Over the past 20 years, such hybrid methods have risen to prominence, leading to what is now a very active research area across multiple disciplines including chemistry, physics and mathematics. There are three main motivations for undertaking this review. Firstly, we have collated a large number of spatially extended hybrid methods and presented them in a single coherent document, while comparing and contrasting them, so that anyone who requires a multiscale hybrid method will be able to find the most appropriate one for their need. Secondly, we have provided canonical examples with algorithms and accompanying code, serving to demonstrate how these types of methods work in practice. Finally, we have presented papers that employ these methods on real biological and physical problems, demonstrating their utility. We also consider some open research questions in the area of hybrid method development and the future directions for the field.

Reaction–diffusion systems are used to represent many biological and physical phenomena. They model the random motion of particles (diffusion) and interactions between them (reactions). Such systems can be modelled at multiple scales with varying degrees of accuracy and computational efficiency. When representing genuinely multiscale phenomena, fine-scale models can be prohibitively expensive, whereas coarser models, although cheaper, often lack sufficient detail to accurately represent the phenomenon at hand. Spatial hybrid methods couple two or more of these representations in order to improve efficiency without compromising accuracy. In this paper, we present a novel spatial hybrid method, which we call the auxiliary region method (ARM), which couples PDE- and Brownian-based representations of reaction–diffusion systems. Numerical PDE solutions on one side of an interface are coupled to Brownian-based dynamics on the other side using compartment-based ‘auxiliary regions’. We demonstrate that the hybrid method is able to simulate reaction–diffusion dynamics for a number of different test problems with high accuracy. Furthermore, we undertake error analysis on the ARM which demonstrates that it is robust to changes in the free parameters in the model, where previous coupling algorithms are not. In particular, we envisage that the method will be applicable for a wide range of spatial multi-scales problems including filopodial dynamics, intracellular signalling, embryogenesis and travelling wave phenomena.

BACKGROUND:While NGS allows rapid global detection of transcripts, it remains difficult to distinguish ncRNAs from short mRNAs. To detect potentially translated RNAs, we developed an improved protocol for bacterial ribosomal footprinting (RIBOseq). This allowed distinguishing ncRNA from mRNA in EHEC. A high ratio of ribosomal footprints per transcript (ribosomal coverage value, RCV) is expected to indicate a translated RNA, while a low RCV should point to a non-translated RNA.RESULTS:Based on their low RCV, 150 novel non-translated EHEC transcripts were identified as putative ncRNAs, representing both antisense and intergenic transcripts, 74 of which had expressed homologs in E. coli MG1655. Bioinformatics analysis predicted statistically significant target regulons for 15 of the intergenic transcripts; experimental analysis revealed 4-fold or higher differential expression of 46 novel ncRNA in different growth media. Out of 329 annotated EHEC ncRNAs, 52 showed an RCV similar to protein-coding genes, of those, 16 had RIBOseq patterns matching annotated genes in other enterobacteriaceae, and 11 seem to possess a Shine-Dalgarno sequence, suggesting that such ncRNAs may encode small proteins instead of being solely non-coding. To support that the RIBOseq signals are reflecting translation, we tested the ribosomal-footprint covered ORF of ryhB and found a phenotype for the encoded peptide in iron-limiting condition.CONCLUSION:Determination of the RCV is a useful approach for a rapid first-step differentiation between bacterial ncRNAs and small mRNAs. Further, many known ncRNAs may encode proteins as well.

This paper focuses on the mapping of natural language sentences in written stories to a structured knowledge representation. This process yields an exponential explosion of instance combinations since each sentence may contain a set of ambiguous terms, each one giving place to a set of instance candidates. The selection of the best combination of instances is a structured classification problem that yields a high-demanding combinatorial optimization problemwhich, in this paper, is approached by a novel and efficient formulation of a genetic algorithm, which is able to exploit the conditional independence among variables, while improving the parallel scalability. The automatic rating of the resulting set of instance combinations, i.e., possible text interpretations, demands an exhaustive exploitation of the state-of-the-art resources in natural language processing to feed the system with pieces of evidence to be fused by the proposed framework. In this sense, a mapping framework able to reason with uncertainty, to integrate supervision and evidence from external sources, was adopted. To improve the generalization capacity while learning from a limited amount of annotated data, a new constrained learning algorithm for Bayesian networks is introduced. This algorithm bounds the search space through a set of constraints which encode information on mutually exclusive values. Themapping of natural language utterances to a structured knowledge representation is important in the context of game construction, e.g., in an RPG setting, as it alleviates the manual knowledge acquisition bottleneck. The effectiveness of the proposed algorithm is evaluated on a set of three stories, yielding nine experiments. Our mapping framework yields performance gains in predicting the most likely structured representations of sentences when compared with a baseline algorithm.

Interactive Narratives are systems that use automated narrative generation techniques to create multiple story variants which can be shown to an audience, as virtual narratives, using cinematic staging techniques. The focus of previous research has included aspects such as the quality of automatically generated narratives and the way in which audiences respond to them. However in this work we have developed a mechanism for control of interactive narratives that supports their use in experiments to assess story understanding. This is implemented in our demonstration system, which features two parts: an interface that allows high-level specification of criteria for story understanding experiments; and a participant interface in which virtual narratives, conforming to the experimental design, are presented as 3D visualizations. The virtual narrative is based on a pre-existing children's story, and features a cast of virtual characters.

Interactive Narratives are systems that use automated narrative generation techniques to create multiple story variants which can be shown to an audience, as virtual narratives, using cinematic staging techniques. Previous research in this area has focused on assessment of aspects such as the quality of the automatically generated narratives and their acceptance by the audience. However in our work we deviate from this to explore the use of interactive narratives to support cognitive psychology experiments in story understanding. We hypothesized that the use of virtual narratives would enable narrative comprehension to be studied independently of linguistic phenomena. To assess this we developed a demonstration interactive narrative featuring a virtual environment (Unity3D engine) based on a pre-existing children's story which allows for the generation of variants of the original story that can be told via visualization in the 3D world. In the paper we introduce a narrative generation mechanism that provides control over insertion of cues facilitating story understanding, whilst also ensuring that the plot itself is unaffected. An intuitive user interface allows experimenters to insert and order cues and specific events while the narrative generation techniques ensure these requests are effected in a consistent fashion. We also report the results of a field experiment with children (age 9-10) that demonstrates the potential for the use of virtual narratives in story understanding experiments. Our results demonstrated acceptance of virtual narratives, the usability of the system and the impact of cue insertion on inference and story understanding.

Universal Semantic Communication (USC) is a theory that models communication among agents without the assumption of a fixed protocol. We demonstrate a connection, via a concept we refer to as process information, between a special case of USC and evolutionary processes. In this context, one agent attempts to interpret a potentially arbitrary signal produced within its environment. Sources of this effective signal can be modeled as a single alternative agent. Given a set of common underlying concepts that may be symbolized differently by different sources in the environment, any given entity must be able to correlate intrinsic information with input it receives from the environment in order to accurately interpret the ambient signal and ultimately coordinate its own actions. This scenario encapsulates a class of USC problems that provides insight into the semantic aspect of a model of evolution proposed by Rivoire and Leibler. Through this connection, we show that evolution corresponds to a means of solving a special class of USC problems, can be viewed as a special case of the Multiplicative Weights Updates algorithm, and that infinite population selection with no mutation and no recombination conforms to the Rivoire-Leibler model. Finally, using process information we show that evolving populations implicitly internalize semantic information about their respective environments.