On the calculation of finite-gap solutions of the KdV equation

A simple and general approach for calculating the elliptic finite-gap solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is based on the use of the finite-gap equations and the general representation of these solutions in the form of rational functions of the elliptic Weierstrass function. The calculation of initial elliptic finite-gap solutions is reduced to the solution of the finite-band equations with respect to the parameters of the representation. The time evolution of these solutions is described via the dynamic equations of their poles, integrated with the help of the finite-gap equations. The proposed approach is applied by calculating the elliptic 1-, 2- and 3-gap solutions of the KdV equations

Algebro-geometric approach in the theory of integrable hydrodynamic type systems

The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. This method is significantly simplified for so-called symmetric hydrodynamic type systems. Plenty interesting and physically motivated examples are investigated

A hybrid discrete-continuum model of immune responses to SARS-CoV-2 infection in the lung alveolar region, with a focus on interferon induced innate response

We develop a lattice-based, hybrid discrete-continuum modeling framework for SARS-CoV-2 exposure and infection in the human lung alveolar region, or parenchyma, the massive surface area for gas exchange. COVID-19 pneumonia is alveolar infection by the SARS-CoV-2 virus significant enough to compromise gas exchange. The modeling framework orchestrates the onset and progression of alveolar infection, spatially and temporally, beginning with a pre-immunity baseline, upon which we superimpose multiple mechanisms of immune protection conveyed by interferons and antibodies. The modeling framework is tunable to individual profiles, focusing here on degrees of innate immunity, and to the evolving infection–replication properties of SARS-CoV-2 variant strains. The model employs partial differential equations for virion, interferon, and antibody concentrations governed by diffusion in the thin fluid coating of alveolar cells, species and lattice interactions corresponding to sources and sinks for each species, and multiple immune protections signaled by interferons. The spatial domain is a two-dimensional, rectangular lattice of alveolar type I (non-infectable) and type II (infectable) cells with a stochastic, species-concentration-governed, switching dynamics of type II lattice sites from healthy to infected. Once infected, type II cells evolve through three phases: an eclipse phase during which RNA copies (virions) are assembled; a shedding phase during which virions and interferons are released; and then cell death. Model simulations yield the dynamic spread of, and immune protection against, alveolar infection and viral load from initial sites of exposure. We focus in this paper on model illustrations of the diversity of outcomes possible from alveolar infection, first absent of immune protection, and then with varying degrees of four known mechanisms of interferon-induced innate immune protection. We defer model illustrations of antibody protection to future studies. Results presented reinforce previous recognition that interferons produced solely by infected cells are insufficient to maintain a high efficacy level of immune protection, compelling additional mechanisms to clear alveolar infection, such as interferon production by immune cells and adaptive immunity (e.g., T cells). This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”

A minimal physiologically based pharmacokinetic model that predicts anti-PEG IgG-mediated clearance of PEGylated drugs in human and mouse

Circulating antibodies that specifically bind polyethylene glycol (PEG), a polymer routinely used in protein and nanoparticle therapeutics, have been associated with reduced efficacy and increased adverse reactions to some PEGylated therapeutics. In addition to acute induction of anti-PEG antibodies (APA) by PEGylated drugs, typically low but detectable levels of APA are also found in up to 70% of the general population. Despite the broad implications of APA, the dynamics of APA-mediated clearance of PEGylated drugs, and why many patients continue to respond to PEGylated drugs despite the presence of pre-existing APA, remains not well understood. Here, we developed a minimal physiologically based pharmacokinetic (mPBPK) model that incorporates various properties of APA and PEGylated drugs. Our mPBPK model reproduced clinical PK data of APA-mediated accelerated blood clearance of pegloticase, as well as APA-dependent elimination of PEGyated liposomes in mice. Our model predicts that the prolonged circulation of PEGylated drugs will be compromised only at APA concentrations greater than ~500 ng/mL, providing a quantitative explanation to why the effects of APA on PEGylated treatments appear to be limited in most patients. This mPBPK model is readily adaptable to other PEGylated drugs and particles to predict the precise levels of APA that could render them ineffective, providing a powerful tool to support the development and interpretation of preclinical and clinical studies of various PEGylated therapeutics

Statistical mechanics of chromosomes: In vivo and in silico approaches reveal high-level organization and structure arise exclusively through mechanical feedback between loop extruders and chromatin substrate properties

The revolution in understanding higher order chromosome dynamics and organization derives from treating the chromosome as a chain polymer and adapting appropriate polymer-based physical principles. Using basic principles, such as entropic fluctuations and timescales of relaxation of Rouse polymer chains, one can recapitulate the dominant features of chromatin motion observed in vivo. An emerging challenge is to relate the mechanical properties of chromatin to more nuanced organizational principles such as ubiquitous DNA loops. Toward this goal, we introduce a real-time numerical simulation model of a long chain polymer in the presence of histones and condensin, encoding physical principles of chromosome dynamics with coupled histone and condensin sources of transient loop generation. An exact experimental correlate of the model was obtained through analysis of a model-matching fluorescently labeled circular chromosome in live yeast cells. We show that experimentally observed chromosome compaction and variance in compaction are reproduced only with tandem interactions between histone and condensin, not from either individually. The hierarchical loop structures that emerge upon incorporation of histone and condensin activities significantly impact the dynamic and structural properties of chromatin. Moreover, simulations reveal that tandem condensin-histone activity is responsible for higher order chromosomal structures, including recently observed Z-loops

On universality of critical behavior in the focusing nonlinear Schr\uf6dinger equation, elliptic umbilic catastrophe and the Tritronqu\ue9e solution to the Painlev\ue9-I equation

We argue that the critical behavior near the point of "gradient catastrophe" of the solution to the Cauchy problem for the focusing nonlinear Schrodinger equation i epsilon Psi(t) + epsilon(2)/2 Psi(xx) + vertical bar Psi vertical bar(2)Psi = 0, epsilon << 1, with analytic initial data of the form Psi( x, 0; epsilon) = A(x)e(i/epsilon) (S(x)) is approximately described by a particular solution to the Painleve-I equation

A universal probe set for targeted sequencing of 353 nuclear genes from any flowering plant designed using k-medoids clustering

Sequencing of target-enriched libraries is an efficient and cost-effective method for obtaining DNA sequence data from hundreds of nuclear loci for phylogeny reconstruction. Much of the cost of developing targeted sequencing approaches is associated with the generation of preliminary data needed for the identification of orthologous loci for probe design. In plants, identifying orthologous loci has proven difficult due to a large number of whole-genome duplication events, especially in the angiosperms (flowering plants). We used multiple sequence alignments from over 600 angiosperms for 353 putatively single-copy protein-coding genes identified by the One Thousand Plant Transcriptomes Initiative to design a set of targeted sequencing probes for phylogenetic studies of any angiosperm group. To maximize the phylogenetic potential of the probes, while minimizing the cost of production, we introduce a k-medoids clustering approach to identify the minimum number of sequences necessary to represent each coding sequence in the final probe set. Using this method, 5-15 representative sequences were selected per orthologous locus, representing the sequence diversity of angiosperms more efficiently than if probes were designed using available sequenced genomes alone. To test our approximately 80,000 probes, we hybridized libraries from 42 species spanning all higher-order groups of angiosperms, with a focus on taxa not present in the sequence alignments used to design the probes. Out of a possible 353 coding sequences, we recovered an average of 283 per species and at least 100 in all species. Differences among taxa in sequence recovery could not be explained by relatedness to the representative taxa selected for probe design, suggesting that there is no phylogenetic bias in the probe set. Our probe set, which targeted 260 kbp of coding sequence, achieved a median recovery of 137 kbp per taxon in coding regions, a maximum recovery of 250 kbp, and an additional median of 212 kbp per taxon in flanking non-coding regions across all species. These results suggest that the Angiosperms353 probe set described here is effective for any group of flowering plants and would be useful for phylogenetic studies from the species level to higher-order groups, including the entire angiosperm clade itself

Global change effects on plant communities are magnified by time and the number of global change factors imposed

Global change drivers (GCDs) are expected to alter community structure and consequently, the services that ecosystems provide. Yet, few experimental investigations have examined effects of GCDs on plant community structure across multiple ecosystem types, and those that do exist present conflicting patterns. In an unprecedented global synthesis of over 100 experiments that manipulated factors linked to GCDs, we show that herbaceous plant community responses depend on experimental manipulation length and number of factors manipulated. We found that plant communities are fairly resistant to experimentally manipulated GCDs in the short term (<10 y). In contrast, long-term (≥10 y) experiments show increasing community divergence of treatments from control conditions. Surprisingly, these community responses occurred with similar frequency across the GCD types manipulated in our database. However, community responses were more common when 3 or more GCDs were simultaneously manipulated, suggesting the emergence of additive or synergistic effects of multiple drivers, particularly over long time periods. In half of the cases, GCD manipulations caused a difference in community composition without a corresponding species richness difference, indicating that species reordering or replacement is an important mechanism of community responses to GCDs and should be given greater consideration when examining consequences of GCDs for the biodiversity–ecosystem function relationship. Human activities are currently driving unparalleled global changes worldwide. Our analyses provide the most comprehensive evidence to date that these human activities may have widespread impacts on plant community composition globally, which will increase in frequency over time and be greater in areas where communities face multiple GCDs simultaneously