Network theoretic analysis of JAK/STAT pathway and extrapolation to drugs and viruses including COVID-19

Whenever some phenomenon can be represented as a graph or a network it seems pertinent to explore how much the mathematical properties of that network impact the phenomenon. In this study we explore the same philosophy in the context of immunology. Our objective was to assess the correlation of “size” (number of edges and minimum vertex cover) of the JAK/STAT network with treatment effect in rheumatoid arthritis (RA), phenotype of viral infection and effect of immunosuppressive agents on a system infected with the coronavirus. We extracted the JAK/STAT pathway from Kyoto Encyclopedia of Genes and Genomes (KEGG, hsa04630). The effects of the following drugs, and their combinations, commonly used in RA were tested: methotrexate, prednisolone, rituximab, tocilizumab, tofacitinib and baricitinib. Following viral systems were also tested for their ability to evade the JAK/STAT pathway: Measles, Influenza A, West Nile virus, Japanese B virus, Yellow Fever virus, respiratory syncytial virus, Kaposi’s sarcoma virus, Hepatitis B and C virus, cytomegalovirus, Hendra and Nipah virus and Coronavirus. Good correlation of edges and minimum vertex cover with clinical efficacy were observed (for edge, rho = − 0.815, R2 = 0.676, p = 0.007, for vertex cover rho = − 0.793, R2 = 0.635, p = 0.011). In the viral systems both edges and vertex cover were associated with acuteness of viral infections. In the JAK/STAT system already infected with coronavirus, maximum reduction in size was achieved with baricitinib. To conclude, algebraic and combinatorial invariant of a network may explain its biological behaviour. At least theoretically, baricitinib may be an attractive target for treatment of coronavirus infection.

Network theoretic analysis of JAK/STAT pathway and extrapolation to drugs and viruses including COVID-19

Whenever some phenomenon can be represented as a graph or a network it seems pertinent to explore how much the mathematical properties of that network impact the phenomenon. In this study we explore the same philosophy in the context of immunology. Our objective was to assess the correlation of “size” (number of edges and minimum vertex cover) of the JAK/STAT network with treatment effect in rheumatoid arthritis (RA), phenotype of viral infection and effect of immunosuppressive agents on a system infected with the coronavirus. We extracted the JAK/STAT pathway from Kyoto Encyclopedia of Genes and Genomes (KEGG, hsa04630). The effects of the following drugs, and their combinations, commonly used in RA were tested: methotrexate, prednisolone, rituximab, tocilizumab, tofacitinib and baricitinib. Following viral systems were also tested for their ability to evade the JAK/STAT pathway: Measles, Influenza A, West Nile virus, Japanese B virus, Yellow Fever virus, respiratory syncytial virus, Kaposi’s sarcoma virus, Hepatitis B and C virus, cytomegalovirus, Hendra and Nipah virus and Coronavirus. Good correlation of edges and minimum vertex cover with clinical efficacy were observed (for edge, rho= -0.815, R2= 0.676, p=0.007, for vertex cover rho= -0.793, R2= 0.635, p=0.011). In the viral systems both edges and vertex cover were associated with acuteness of viral infections. In the JAK/STAT system already infected with coronavirus, maximum reduction in size was achieved with baricitinib. To conclude, algebraic and combinatorial invariant of a network may explain its biological behaviour. At least theoretically, baricitinib may be an attractive target for treatment of coronavirus infection.

Combinatorial invariant of Morse-Smale diffeomorphisms on surfaces with orientable heteroclinic

In this paper we consider class of orientation-preserving Morse-Smale diffeomorphisms f, given on orientable surface M2. In their articles A.A.~Bezdenezhnich and V. Z. Grines has shown, that such diffeomorfisms contain finite number of heteroclinic orbits. Moreover, the problem of classification for such diffeomorphisms is reduced to the problem of distinguishing orientable graphs with substitutions describing the geometry of heteroclinic intersections. Howewer, these graphs generally do not allow polynomial distinguishing algorithms. In this paper, we propose a new approach to the classification of such cascades. To this end, each considered diffeomorphism f is associated with a graph whose embeddablility in the ambient surface makes it possible to construct an effective algoritm for distinguishing such graphs.

Systolic geometry and simplicial complexity for groups

Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called simplicial complexity that allows to obtain a quite satisfactory answer to his question. Using this new complexity, we also derive new results on systolic area for groups that specify its topological behaviour.

Nearly free curves and arrangements: a vector bundle point of view

Over the past forty years many papers have studied logarithmic sheaves associated to reduced divisors, in particular logarithmic bundles associated to plane curves. An interesting family of these curves are the so-called free ones for which the associated logarithmic sheaf is the direct sum of two line bundles. Terao conjectured thirty years ago that when a curve is a finite set of distinct lines (i.e. a line arrangement) its freeness depends solely on its combinatorics, but this has only been proved for sets of up to 12 lines. In looking for a counter-example to Terao’s conjecture, the nearly free curves introduced by Dimca and Sticlaru arise naturally. We prove here that the logarithmic bundle associated to a nearly free curve possesses a minimal non-zero section that vanishes on one single point, P say, called the jumping point, and that this characterises the bundle. We then give a precise description of the behaviour of P. Based on detailed examples we then show that the position of P relative to its corresponding nearly free arrangement of lines may or may not be a combinatorial invariant, depending on the chosen combinatorics.

D-SPECTRUM AND RELIABILITY OF A BINARY SYSTEM WITH TERNARY COMPONENTS

We consider a monotone binary system with ternary components. “Ternary” means that each component can be in one of three states: up, middle (mid) and down. Handling such systems is a hard task, even if a part of the components have no mid state. Nevertheless, the permutation Monte Carlo methods, that proved very useful for dealing with binary components, can be efficiently used also for ternary monotone systems. It turns out that for “ternary” system there also exists a combinatorial invariant by means of which it becomes possible to count the number C(r;x) of system failure sets which have a given number r and x of components in up and down states, respectively. This invariant is called ternary D-spectrum and it is an analogue of the D-spectrum (or signature) of a system with binary components. Its value is the knowledge of system failure or path set properties which do not depend on stochastic mechanism governing component failures. In case of independent and identical components, knowing D-spectrum makes it easy to calculate system UP or DOWN probability for a variety of UP/DOWN definitions suitable for systems of many types, like communication networks, flow and supply networks, etc.