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Recruited neutrophils are among the first phagocytic cells to interact with the phagosomal pathogen Leishmania following inoculation into the mammalian dermis. Analysis of Leishmania-infected neutrophils has revealed alterations in neutrophil viability, suggesting that the parasite can both induce or inhibit apoptosis. In this study, we demonstrate that entry of Leishmania major into murine neutrophils is dependent on the neutrophil surface receptor CD11b (CR3/Mac-1) and is enhanced by parasite opsonization with C3. Infected neutrophils underwent robust NADPH oxidase isoform 2 (NOX2)–dependent respiratory burst based on detection of reactive oxygen species within the phagolysosome but largely failed to eliminate the metacyclic promastigote life cycle stage of the parasite. Infected neutrophils displayed an “apoptotic” phosphatidylserine (PS)-positive phenotype, which was induced by both live and fixed parasites but not latex beads, suggesting that PS expression was parasite specific but does not require active infection. In addition, neutrophils from parasite/neutrophil coculture had increased viability, decreased caspase 3, 8, and 9 gene expression, and reduced protein levels of both the pro and cleaved forms of the classical apoptosis-inducing executioner caspase, Caspase 3. Our data suggest that CD11b-mediated Leishmania internalization initiates respiratory burst and PS externalization, followed by a reduction in both the production and cleavage of caspase 3, resulting in a phenotypic state of “stalled apoptosis.”

This survey for mathematicians summarizes several works by the author on protein geometry and protein function with applications to viral glycoproteins in general and the spike glycoprotein of the SARS-CoV-2 virus in particular. Background biology and biophysics are sketched. This body of work culminates in a postulate that protein secondary structure regulates mutation, with backbone hydrogen bonds materializing in critical regions to avoid mutation, and disappearing from other regions to enable it., Comment: 18 pages, 4 figures

New tools developed by Moderna, BioNTech/Pfizer, and Oxford/Astrazeneca, among others, provide universal solutions to previously problematic aspects of drug or vaccine delivery, uptake and toxicity, portending new tools across the medical sciences. A novel method is presented based on estimating protein backbone free energy via geometry to predict effective antiviral targets, antigens and vaccine cargos that are resistant to viral mutation. This method, partly described in earlier work of the author, is reviewed and reformulated here in light of the recent proliferation of structural data on the SARS-CoV-2 spike glycoprotein and its latest mutations in the variants of concern and several further variants of interest including all international lineages. Particular attention to structures computed with Cryo Electron Microscopy allows the novel approach of probing the pH dependence of free energy in order to infer function. Key findings include: collections of recurring mutagenic residues occur across strains, presumably through cooperative convergent evolution; the preponderance of mutagenic residues do not participate in backbone hydrogen bonds; metastability of the spike glycoprotein limits the change of free energy from before to after mutation and thereby constrains selective pressure; and there are mRNA or virus-vector cargos which target low free energy peptides proximal to conserved high free energy peptides providing specific recipes for vaccines with greater specificity than the current full-spike approach. These results serve to limit peptides in the spike glycoprotein with high mutagenic potential and thereby provide a priori constraints on viral and attendant vaccine evolution. Scientific and regulatory challenges to nucleic acid therapeutic and vaccine development and deployment are finally discussed.

This short note provides an overview of some theorems and conjectures obtained by the author and his collaborators. It is an extended abstract for the Oberwolfach workshop "New Trends in Teichmuller Theory and Mapping Class Groups", 2 September - 8 September 2018.

Various homotopy lifting properties from topology are subsumed by generalization to abelian categories.

We build a theoretical model of morphogenesis. This model describes cell fate in the developing organism using the notion of epigenetic code of each cell. Namely, given the epigenetic spectra of a cell and its neighboring cells, we can determine the corresponding cell event it will perform. This means that the properties of a group of cells (comprising an embryo or its part) at any time point are also known, and thus, the evolution of an embryo can be described. By this strategy, it is possible to establish the tissue, organ, or embryo shapes at any time, starting from a zygote. As an essential part of the model, the formalization of the notion of cell potency is introduced, and the related properties are discussed.

Fibered and cofibered catgeories are defined, and the Kan formulae are given in this context.

The plus construction is defined, and Quillen’s K-groups are compared to previous definitions in special cases.

The Leray spectral sequence is derived. Quillen’s generalization of the Kan formulae is proved.

The isomorphism \(K_0~A \cong K_0~A[T]\) of Grothendieck groups is proved for a regular noetherian ring A using localization and the Resolution Theorem.

Simplicial complexes are considered as a special case of simplicial sets. The Normalization Theorem for simplicial groups is stated, conical contractibility is defined, and their consequences are explored in examples.

The first cohomology group of a group is explained. Categories are introduced, examples are given, and their nerves are defined.

Theorem B gives another useful sufficient condition for homotopy equivalence, and its application is sketched for the Localization Theorem and the consequent long exact sequence of Kgroups. Example applications include \(K_n A\cong K_n~A[T]\) and \(K_n~A[T, T^{-1}]\cong K_n A\oplus K_{n-1} A\).

Bi-simplicial sets are defined and employed to prove Theorem A giving a useful sufficient condition for homotopy equivalence and applied to the example of the Dold-Thom construction.

Categorical versions of the mapping cone and mapping cylinder constructions from topology are given and their basic properties generalized.

The higher K-groups of an exact category \(\mathcal M\) are defined to be the higher homotopy groups of the classifying space of the category \(Q \mathcal{M}\).

The Hochschild-Serre spectral sequence is derived using the generalized Kan formulae, and its variants for contravariant functors and cohomology are proposed.

Spectral sequences for the canonical filtrations of a complex are applied to compute the homology of a small category.

The Yoneda Lemma is introduced and its consequences explored. Adjoint functors are defined.

Convergence of spectral sequences is considered. The canonical increasing and decreasing (Postnikov) filtrations of a complex are defined.

Short exact sequences of groups are introduced, and their isomorphism classes are identified with the second cohomology group of an appropriate cochain complex.

A natural filtration is given for the category \({\mathcal P}_A\) of finitely generated projective modules over a Dedekind domain A and used to study the graded homology. Tits buildings and Steinberg groups are given as examples.

Grothendieck’s Devissage Theorem is proved and examples given, and his Resolution Theorem is stated with a sketch of its proof.

Exact categories and admissible morphisms are introduced, and the Resolution Theorem is proved.

A range of examples across algebra and topology of fibered and cofibered categories are given.

The transfer map is discussed and its basic identities derived. These tools are then used to prove the theorem of Schur-Zassenhaus.

The homology and cohomology of cyclic groups are computed, and the main theorem on \(\delta \)-functors is proved.

Exact sequences of homotopy classes of maps are explored using mapping cones and cylinders, and the Puppe sequence from topology is proved in the context of additive categories.

The process of morphogenesis is an evolution of shape of an organism together with the differentiation of its parts. This process encompasses numerous biological processes ranging from embryogenesis to regeneration following crisis such as amputation or transplantation. A fundamental theoretical question is where exactly do these instructions for (re-)construction reside and how are they implemented? We have recently proposed a set of concepts, aiming to respond to these questions and to provide an appropriate mathematical formalization of the geometry of morphogenesis [1]. First, we consider a possibility that the evolution of shape is determined by epigenetic information, responsible for realization of different types of cell events. Second, we suggest a set of rules for converting this epigenetic information into instructive signals for cell event for each cell, as well as for transforming it after each cell event. Next we give notions of cell state, determined by its epigenetic array, and cell event, which is a change of cell state, and formalize development as a graph (tree) of cell states connected by 5 types of cell events, corresponding to the processes of cell division, cell growth, cell death, cell movement and cell differentiation. Here we present a Morphogenesis software capable to simulate an evolution of a 3D embryo starting from zygote, following a set of rules, based on our theoretical assumptions, and thus to provide a proof-of-concept of the hypothesis of epigenetic code regulation. The software creates a developing embryo and a corresponding graph of cell events according to the zygotic epigenetic spectrum and chosen parameters of the developmental rules. Variation of rules influencing the resulting shape of an embryo may help elucidating the principal laws underlying pattern formation., SCOPUS: ar.j, info:eu-repo/semantics/published