Diversity and ecotones in a model ecosystems of sessile species.

Sessile species compete for space and accessible light, with directed interactions evident in one species overgrowing another and with multispecies systems characterized by nontransitive relationships. Such patterns are observed in coral reefs or lichens on rock surfaces. Open systems with episodic invasions of such species have been predicted to exhibit a stable high-diversity state when the interaction probability is below a certain critical threshold. Here, we explore this metastable high-diversity state and find that the diversity in the high-diversity state scales with the square root of the system area. When introducing two different environments, we predict a hugely increased diversity along mutual environment border. Further, the presence of spatially segregated environments is predicted to allow for increased robustness of the high-diversity state.

The dynamics of phage predation on a microcolony.

Phage predation is an important factor for controlling the bacterial biomass. At face value, dense microbial habitats are expected to be vulnerable to phage epidemics due to the abundance of fresh hosts immediately next to any infected bacteria. Despite this, the bacterial microcolony is a common habitat for bacteria in nature. Here, we experimentally quantify the fate of microcolonies of Escherichia coli exposed to virulent phage T4. It has been proposed that the outer bacterial layers of the colony will shield the inner layers from the phage invasion and thereby constrain the phage to the colony's surface. We develop a dynamical model that incorporates this shielding mechanism and fit the results with experimental measurements to extract important phage-bacteria interaction parameters. The analysis suggests that, while the shielding mechanism delays phage attack, T4 phage are able to diffuse so deep into the dense bacterial environment that colony-level survival of the bacterial community is challenged.

Epigenetic switching with asymmetric bridging interactions.

Gene expression states are often stably sustained in cis despite massively disruptive events like DNA replication. This is achieved by on-going enzymatic activity that maintains parts of the DNA in either heterochromatic (packed) or euchromatic (free) states, each of which is stabilized by both positive feedback and bridging interactions between individual nucleosomes. In contrast to condensed matter, however, the dynamics is not only governed by equilibrium binding interactions but is also mediated by enzymes that recognize and act on specific amino acid tails of the nucleosomes. The mechanical result is that some nucleosomes can bind to one another and form tightly packed polymer configurations, whereas others remain unbound and form free, noncompact polymer configurations. Here, we study the consequences of such an asymmetric interaction pattern on the dynamics of epigenetic switching. We develop a 3D polymer model and show that traits associated with epigenetic switching, such as bistability and epigenetic memory, are permitted by such a model. We find, however, that the experimentally observed burst-like nature of some epigenetic switches is difficult to reproduce by this biologically motivated interaction. Instead, the behavior seen in experiments can be explained by introducing partial confinement, which particularly affects the euchromatic regions of the chromosome.

Host heterogeneity and epistasis explain punctuated evolution of SARS-CoV-2.

Identifying drivers of viral diversity is key to understanding the evolutionary as well as epidemiological dynamics of the COVID-19 pandemic. Using rich viral genomic data sets, we show that periods of steadily rising diversity have been punctuated by sudden, enormous increases followed by similarly abrupt collapses of diversity. We introduce a mechanistic model of saltational evolution with epistasis and demonstrate that these features parsimoniously account for the observed temporal dynamics of inter-genomic diversity. Our results provide support for recent proposals that saltational evolution may be a signature feature of SARS-CoV-2, allowing the pathogen to more readily evolve highly transmissible variants. These findings lend theoretical support to a heightened awareness of biological contexts where increased diversification may occur. They also underline the power of pathogen genomics and other surveillance streams in clarifying the phylodynamics of emerging and endemic infections. In public health terms, our results further underline the importance of equitable distribution of up-to-date vaccines.

Jag1-Notch cis-interaction determines cell fate segregation in pancreatic development.

The Notch ligands Jag1 and Dll1 guide differentiation of multipotent pancreatic progenitor cells (MPCs) into unipotent pro-acinar cells (PACs) and bipotent duct/endocrine progenitors (BPs). Ligand-mediated trans-activation of Notch receptors induces oscillating expression of the transcription factor Hes1, while ligand-receptor cis-interaction indirectly represses Hes1 activation. Despite Dll1 and Jag1 both displaying cis- and trans-interactions, the two mutants have different phenotypes for reasons not fully understood. Here, we present a mathematical model that recapitulates the spatiotemporal differentiation of MPCs into PACs and BPs. The model correctly captures cell fate changes in Notch pathway knockout mice and small molecule inhibitor studies, and a requirement for oscillatory Hes1 expression to maintain the multipotent state. Crucially, the model entails cell-autonomous attenuation of Notch signaling by Jag1-mediated cis-inhibition in MPC differentiation. The model sheds light on the underlying mechanisms, suggesting that cis-interaction is crucial for exiting the multipotent state, while trans-interaction is required for adopting the bipotent fate.

Emerging diversity in a population of evolving intransitive dice.

Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for coevolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a set of evolving agents that interact competitively in a closed system, in which both the dynamics of mutations and competitive advantage emerge directly from interpreting a genome as the sides of a die. The model demonstrates sympatric speciation where new species evolve from existing ones while in contact with the entire ecosystem. Allowing free mutations both in the genomes and the mutation rates, we find, in contrast to hierarchical models of fitness, the emergence of a metastable state of finite mutation rate and diversity.

Emergence of networks of shared restriction-modification systems in phage-bacteria ecosystems.

Restriction-modification (RM) systems are the most ubiquitous bacterial defence systems against bacteriophages. Using genome sequence data, we showed that RM systems are often shared among bacterial strains in a structured way. Examining the network of interconnections between bacterial strains within genera, we found that many strains share more RM systems than expected compared with a suitable null model. We also found that many genera have a larger than expected number of bacterial strains with unique RM systems. We used population dynamics models of closed and open phage-bacteria ecosystems to qualitatively understand the selection pressures that could lead to such network structures with enhanced overlap or uniqueness. In our models, we found that the phages impose a selection pressure that favours bacteria with greater number of RM systems, and higher overlap of RM systems with other strains, but in bacteria-dominated states, this is opposed by the increased cost-to-growth rate of these bacteria. Similar to what we observed in the genome data, we found that two distinct bacterial strategies emerge - strains either have a greater overlap than expected, or, at the other extreme, have unique RM systems. The former strategy appears to dominate when the repertoire of available RM systems is smaller but the average number of RM systems per strain is larger.

Lockdowns exert selection pressure on overdispersion of SARS-CoV-2 variants.

The SARS-CoV-2 ancestral strain has caused pronounced superspreading events, reflecting a disease characterized by overdispersion, where about 10% of infected people cause 80% of infections. New variants of the disease have different person-to-person variability in viral load, suggesting for example that the Alpha (B.1.1.7) variant is more infectious but relatively less prone to superspreading. Meanwhile, non-pharmaceutical mitigation of the pandemic has focused on limiting social contacts (lockdowns, regulations on gatherings) and decreasing transmission risk through mask wearing and social distancing. Using a mathematical model, we show that the competitive advantage of disease variants may heavily depend on the restrictions imposed. In particular, we find that lockdowns exert an evolutionary pressure which favours variants with lower levels of overdispersion. Our results suggest that overdispersion is an evolutionarily unstable trait, with a tendency for more homogeneously spreading variants to eventually dominate.

From kill the winner to eliminate the winner in open phage-bacteria systems.

Phages and bacteria manage to coexist and sustain ecosystems with a high diversity of strains, despite limited resources and heavy predation. This diversity can be explained by the "kill the winner" model where virulent phages predominantly prey on fast-growing bacteria and thereby suppress the competitive exclusion of slower-growing bacteria. Here we computationally investigate the robustness of these systems against invasions, where new phages or bacteria may interact with more than one of the resident strains. The resulting interaction networks were found to self-organize into a network with strongly interacting specialized predator-prey pairs, resembling that of the "kill the winner" model. Furthermore, the "kill the winner" dynamics is enforced with the occasional elimination of even the fastest-growing bacteria strains due to a phage infecting the fast and slow growers. The frequency of slower-growing strains was increased with the introduction of even a few non-diagonal interactions. Hence, phages capable of infecting multiple hosts play significant roles both in the evolution of the ecosystem by eliminating the winner and in supporting diversity by allowing slow growers to coexist with faster growers.

Immune Heterogeneity and Epistasis Explain Punctuated Evolution of SARS-CoV-2.

Identifying drivers of viral diversity is key to understanding the evolutionary as well as epidemiological dynamics of the COVID-19 pandemic. Using rich viral genomic data sets, we show that periods of steadily rising diversity have been punctuated by sudden, enormous increases followed by similarly abrupt collapses of diversity. We introduce a mechanistic model of saltational evolution with epistasis and demonstrate that these features parsimoniously account for the observed temporal dynamics of inter-genomic diversity. Our results provide support for recent proposals that saltational evolution may be a signature feature of SARS-CoV-2, allowing the pathogen to more readily evolve highly transmissible variants. These findings lend theoretical support to a heightened awareness of biological contexts where increased diversification may occur. They also underline the power of pathogen genomics and other surveillance streams in clarifying the phylodynamics of emerging and endemic infections. In public health terms, our results further underline the importance of equitable distribution of up-to-date vaccines.

The transcription factor Atf1 lowers the transition barrier for nucleosome-mediated establishment of heterochromatin.

Transcription factors can exert opposite effects depending on the chromosomal context. The fission yeast transcription factor Atf1 both activates numerous genes in response to stresses and mediates heterochromatic gene silencing in the mating-type region. Investigating this context dependency, we report here that the establishment of silent heterochromatin in the mating-type region occurs at a reduced rate in the absence of Atf1 binding. Quantitative modeling accounts for the observed establishment profiles by a combinatorial recruitment of histone-modifying enzymes: locally by Atf1 at two binding sites and over the whole region by dynamically appearing heterochromatic nucleosomes, a source of which is the RNAi-dependent cenH element. In the absence of Atf1 binding, the synergy is lost, resulting in a slow rate of heterochromatin formation. The system shows how DNA-binding proteins can influence local nucleosome states and thereby potentiate long-range positive feedback on histone-modification reactions to enable heterochromatin formation over large regions in a context-dependent manner.

Protection of bacteriophage-sensitive Escherichia coli by lysogens.

SignificanceSome viruses that infect bacteria, temperate bacteriophages, can confer immunity to infection by the same virus. Here we report λ-immune bacteria could protect λ-sensitive bacteria from killing by phage λ in mixed culture. The protection depended on the extent to which the immune bacteria were able to adsorb the phage. Reconciling modeling with experiment led to identifying a decline in protection as bacteria stopped growing. Adsorption of λ was compromised by inhibition of bacterial energy metabolism, explaining the loss of protection as bacterial growth ceased.

Spatial model of Ebola outbreaks contained by behavior change.

The West African Ebola (2014-2016) epidemic caused an estimated 11.310 deaths and massive social and economic disruption. The epidemic was comprised of many local outbreaks of varying sizes. However, often local outbreaks recede before the arrival of international aid or susceptible depletion. We modeled Ebola virus transmission under the effect of behavior changes acting as a local inhibitor. A spatial model is used to simulate Ebola epidemics. Our findings suggest that behavior changes can explain why local Ebola outbreaks recede before substantial international aid was mobilized during the 2014-2016 epidemic.

Superspreading quantified from bursty epidemic trajectories.

The quantification of spreading heterogeneity in the COVID-19 epidemic is crucial as it affects the choice of efficient mitigating strategies irrespective of whether its origin is biological or social. We present a method to deduce temporal and individual variations in the basic reproduction number directly from epidemic trajectories at a community level. Using epidemic data from the 98 districts in Denmark we estimate an overdispersion factor k for COVID-19 to be about 0.11 (95% confidence interval 0.08-0.18), implying that 10 % of the infected cause between 70 % and 87 % of all infections.

Differences in social activity increase efficiency of contact tracing.

ABSTRACT: Digital contact tracing has been suggested as an effective strategy for controlling an epidemic without severely limiting personal mobility. Here, we use smartphone proximity data to explore how social structure affects contact tracing of COVID-19. We model the spread of COVID-19 and find that the effectiveness of contact tracing depends strongly on social network structure and heterogeneous social activity. Contact tracing is shown to be remarkably effective in a workplace environment and the effectiveness depends strongly on the minimum duration of contact required to initiate quarantine. In a realistic social network, we find that forward contact tracing with immediate isolation can reduce an epidemic by more than 70%. In perspective, our findings highlight the necessity of incorporating social heterogeneity into models of mitigation strategies. SUPPLEMENTARY INFORMATION: The online version supplementary material available at 10.1140/epjb/s10051-021-00222-8.

Superspreading of airborne pathogens in a heterogeneous world.

Epidemics are regularly associated with reports of superspreading: single individuals infecting many others. How do we determine if such events are due to people inherently being biological superspreaders or simply due to random chance? We present an analytically solvable model for airborne diseases which reveal the spreading statistics of epidemics in socio-spatial heterogeneous spaces and provide a baseline to which data may be compared. In contrast to classical SIR models, we explicitly model social events where airborne pathogen transmission allows a single individual to infect many simultaneously, a key feature that generates distinctive output statistics. We find that diseases that have a short duration of high infectiousness can give extreme statistics such as 20% infecting more than 80%, depending on the socio-spatial heterogeneity. Quantifying this by a distribution over sizes of social gatherings, tracking data of social proximity for university students suggest that this can be a approximated by a power law. Finally, we study mitigation efforts applied to our model. We find that the effect of banning large gatherings works equally well for diseases with any duration of infectiousness, but depends strongly on socio-spatial heterogeneity.

The COVID-19 pandemic: key considerations for the epidemic and its control.

The response to the ongoing COVID-19 pandemic has been characterized by draconian measures and far too many important unknowns, such as the true mortality risk, the role of children as transmitters and the development and duration of immunity in the population. More than a year into the pandemic much has been learned and insights into this novel type of pandemic and options for control are shaping up. Using a historical lens, we review what we know and still do not know about the ongoing COVID-19 pandemic. A pandemic caused by a member of the coronavirus family is a new situation following more than a century of influenza A pandemics. However, recent pandemic threats such as outbreaks of the related and novel deadly coronavirus SARS in 2003 and of MERS since 2012 had put coronaviruses on WHOs blueprint list of priority diseases. Like pandemic influenza, SARS-CoV-2 is highly transmissible (R0 ~ 2.5). Furthermore, it can fly under the radar due to a broad clinical spectrum where asymptomatic and pre-symptomatic infected persons also transmit the virus-including children. COVID-19 is far more deadly than seasonal influenza; initial data from China suggested a case fatality rate of 2.3%-which would have been on par with the deadly 1918 Spanish influenza. But, while the Spanish influenza killed young, otherwise healthy adults, it is the elderly who are at extreme risk of dying of COVID-19. We review available seroepidemiological evidence of infection rates and compute infection fatality rates (IFR) for Denmark (0.5%), Spain (0.85%), and Iceland (0.3%). We also deduce that population age structure is key. SARS-CoV-2 is characterized by superspreading, so that ~10% of infected individuals yield 80% of new infections. This phenomenon turns out to be an Achilles heel of the virus that may explain our ability to effectively mitigate outbreaks so far. How will this pandemic come to an end? Herd immunity has not been achieved in Europe due to intense mitigation by non-pharmaceutical interventions; for example, only ~8% of Danes were infected across the 1st and 2nd wave. Luckily, we now have several safe and effective vaccines. Global vaccine control of the pandemic depends in great measure on our ability to keep up with current and future immune escape variants of the virus. We should thus be prepared for a race between vaccine updates and mutations of the virus. A permanent reopening of society highly depends on winning that race.

COVID-19 Superspreading Suggests Mitigation by Social Network Modulation.

Although COVID-19 has caused severe suffering globally, the efficacy of nonpharmaceutical interventions has been greater than typical models have predicted. Meanwhile, evidence is mounting that the pandemic is characterized by superspreading. Capturing this phenomenon theoretically requires modeling at the scale of individuals. Using a mathematical model, we show that superspreading drastically enhances mitigations which reduce the overall personal contact number and that social clustering increases this effect.

Establishment of heterochromatin in domain-size-dependent bursts.

Methylation of histone H3K9 is a hallmark of epigenetic silencing in eukaryotes. Nucleosome modifications often rely on positive feedback where enzymes are recruited by modified nucleosomes. A combination of local and global feedbacks has been proposed to account for some dynamic properties of heterochromatin, but the range at which the global feedbacks operate and the exact mode of heterochromatin propagation are not known. We investigated these questions in fission yeast. Guided by mathematical modeling, we incrementally increased the size of the mating-type region and profiled heterochromatin establishment over time. We observed exponential decays in the proportion of cells with active reporters, with rates that decreased with domain size. Establishment periods varied from a few generations in wild type to >200 generations in the longest region examined, and highly correlated silencing of two reporters located outside the nucleation center was observed. On a chromatin level, this indicates that individual regions are silenced in sudden bursts. Mathematical modeling accounts for these bursts if heterochromatic nucleosomes facilitate a deacetylation or methylation reaction at long range, in a distance-independent manner. A likely effector of three-dimensional interactions is the evolutionarily conserved Swi6HP1 H3K9me reader, indicating the bursting behavior might be a general mode of heterochromatin propagation.