A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spatial linkage mechanisms which consist of n-copies of a rigid body joined together by hinges to form a ring. Each hinge joint has its own axis of revolution and rigid bodies joined to it can be freely rotated around the axis. The family includes the famous threefold symmetric Bricard 6R linkage, also known as the Kaleidocycle, which exhibits a characteristic "turning-over" motion. We can model such a linkage as a discrete closed curve in R 3 of constant torsion up to sign. Then, its motion is described as the deformation of the curve preserving torsion and arc length. We describe certain motions of this object that are governed by the semi-discrete mKdV and sine-Gordon equations, where infinitesimally the motion of each vertex is confined in the osculating plane.

Background Mpox virus (MPXV) is a zoonotic orthopoxvirus and caused an outbreak in 2022. Although tecovirimat and brincidofovir are approved as anti-smallpox drugs, their effects in mpox patients have not been well documented. In this study, by a drug repurposing approach, we identified potential drug candidates for treating mpox and predicted their clinical impacts by mathematical modeling. Methods We screened approved 132 drugs using an MPXV infection cell system. We quantified antiviral activities of hit drugs by measuring intracellular viral DNA and analyzed the modes of action by time-of-addition assay and electron microscopic analysis. We further predicted the efficacy of drugs under clinical concentrations by mathematical simulation and examined combination treatment. Results Atovaquone, mefloquine, and molnupiravir exhibited anti-MPXV activity, with 50% inhibitory concentrations of 0.51-5.2 μM, which was more potent than cidofovir. Whereas mefloquine was suggested to inhibit viral entry, atovaquone and molnupiravir targeted post-entry process. Atovaquone was suggested to exert its activity through inhibiting dihydroorotate dehydrogenase. Combining atovaquone with tecovirimat enhanced the anti-MPXV effect of tecovirimat. Quantitative mathematical simulations predicted that atovaquone can promote viral clearance in patients by seven days at clinically relevant drug concentrations. Conclusion These data suggest that atovaquone would be potential candidates for treating mpox.

Monkeypox virus (MPXV) is a zoonotic orthopoxvirus that causes smallpox-like symptoms in humans and caused an outbreak in May 2022 that led the WHO to declare global health emergency. In this study, from a screening of approved-drug libraries using an MPXV infection cell system, atovaquone, mefloquine, and molnupiravir exhibited anti-MPXV activity, with 50% inhibitory concentrations of 0.51-5.2 microM, which is more potent than cidofovir. Whereas mefloquine was suggested to inhibit viral entry, atovaquone and molnupiravir targeted post-entry process to impair intracellular virion accumulation. Inhibitors of dihydroorotate dehydrogenase, a target enzyme of atovaquone, showed conserved anti-MPXV activities. Combining atovaquone with tecovirimat enhanced the anti-MPXV effect of tecovirimat. Quantitative mathematical simulations predicted that atovaquone can promote viral clearance in patients by seven days at clinically relevant drug concentrations. Moreover, atovaquone and molnupiravir exhibited pan-Orthopoxvirus activity against vaccinia and cowpox viruses. These data suggest that atovaquone would be potential candidates for treating monkeypox.

Antibody titers wane after two-dose COVID-19 vaccinations, but individual variation in vaccine-elicited antibody dynamics remains to be explored. Here, we created a personalized antibody score that enables individuals to infer their antibody status by use of a simple calculation. We recently developed a mathematical model of B cell differentiation to accurately interpolate the longitudinal data from a community-based cohort in Fukushima, Japan, which consists of 2,159 individuals who underwent serum sampling two or three times after a two-dose vaccination with either BNT162b2 or mRNA-1273. Using the individually reconstructed time course of the vaccine-elicited antibody response, we first elucidated individual background factors that contributed to the main features of antibody dynamics, i.e., the peak, the duration, and the area under the curve. We found that increasing age was a negative factor and a longer interval between the two doses was a positive factor for individual antibody level. We also found that the presence of underlying disease and the use of medication affected antibody levels negatively, whereas the presence of adverse reactions upon vaccination affected antibody levels positively. We then applied to these factors a recently proposed computational method to optimally fit clinical scores, which resulted in an integer-based score that can be used to evaluate the antibody status of individuals from their basic demographic and health information. This score can be easily calculated by individuals themselves or by medical practitioners. There is a potential usefulness of this score for identifying vulnerable populations and encouraging them to get booster vaccinations.Significance statementDifferent individuals show different antibody titers even after the same COVID-19 vaccinations, making some individuals more prone to breakthrough infections than others. Such variability remains to be clarified. Here we used mathematical modeling to reconstruct individual post-vaccination antibody dynamics from a cohort of 2,159 individuals in Fukushima, Japan. Machine learning identified several positive and negative factors affecting individual antibody titers. Positive factors included adverse reactions after vaccinations and a longer interval between two vaccinations. Negative factors included age, underlying medical conditions, and medications. We combined these factors and developed an “antibody score” to estimate individual antibody dynamics from basic demographic and health information. This score can help to guide individual decision-making about taking further precautions against COVID-19.

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