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Abstract Proteins fold in 3-dimensional conformations which are important for their function. Characterizing the global conformation of proteins rigorously and separating secondary structure effects from topological effects is a challenge. New developments in applied knot theory allow to characterize the topological characteristics of proteins (knotted or not). By analyzing a small set of two-state and multi-state proteins with no knots or slipknots, our results show that 95.4% of the analyzed proteins have non-trivial topological characteristics, as reflected by the second Vassiliev measure, and that the logarithm of the experimental protein folding rate depends on both the local geometry and the topology of the protein’s native state. 

Estimating the transmission fitness of SARS‐CoV‐2 variants and understanding their evolutionary fitness trends are important for epidemiological forecasting. Existing methods are often constrained by their parametric natures and do not satisfactorily align with the observations during COVID‐19. Here, we introduce a sliding‐window data‐driven pairwise comparison method, the differential population growth rate (DPGR) that uses viral strains as internal controls to mitigate sampling biases. DPGR is applicable in time windows in which the logarithmic ratio of two variant subpopulations is approximately linear. We apply DPGR to genomic surveillance data and focus on variants of concern (VOCs) in multiple countries and regions. We found that the log‐linear assumption of DPGR can be reliably found within appropriate time windows in many areas. We show that DPGR estimates of VOCs align well with regional empirical observations in different countries. We show that DPGR estimates agree with another method for estimating pathogenic transmission. Furthermore, DPGR allowed us to construct viral relative fitness landscapes that capture the shifting trends of SARS‐CoV‐2 evolution, reflecting the relative changes of transmission traits for key genotypic changes represented by major variants. The straightforward log‐linear regression approach of DPGR may also facilitate its easy adoption. This study shows that DPGR is a promising new tool in our repertoire for addressing future pandemics. 

Tandem mass spectrometry (MS/MS) is a widely used technology for identifying metabolites. De novo metabolite identification is an identification strategy that does not refer to any spectral or metabolite database. However, this strategy is time-consuming and cannot meet the need for high-throughput metabolite identification. Böcker et al. converted the de novo identification problem into the maximum colorful subtree (MCS) problem. Unfortunately, the MCS problem is NPhard, which indicates there are no existing efficient exact algorithms. To address this issue, we propose to apply quantum computing to accelerate metabolite identification. Quantum computing performs computations on quantum computers. The recent progress in this area has brought the hope of making some computationally intractable areas trackable, although there are still no general approaches to converting regular computer algorithms into quantum algorithms. Specifically, there is no efficient quantum algorithm for the MCS problem. The MCS problem can be considered as the combination of many maximum spanning tree problems that can be converted into minimum spanning tree problems. This work applies a quantum algorithm designed for the minimum spanning problem to speed up de novo metabolite identification. The possible strategy for further improving the performance is also briefly discussed. 

The novel coronavirus SARS-CoV-2 infects human cells using a mechanism that involves binding and structural rearrangement of its Spike protein. Understanding protein rearrangement and identifying specific amino acids where mutations affect protein rearrangement has attracted much attention for drug development. In this manuscript, we use a mathematical method to characterize the local topology/geometry of the SARS-CoV-2 Spike protein backbone. Our results show that local conformational changes in the FP, HR1, and CH domains are associated with global conformational changes in the RBD domain. The SARS-CoV-2 variants analyzed in this manuscript (alpha, beta, gamma, delta Mink, G614, N501) show differences in the local conformations of the FP, HR1, and CH domains as well. Finally, most mutations of concern are either in or in the vicinity of high local topological free energy conformations, suggesting that high local topological free energy conformations could be targets for mutations with significant impact of protein function. Namely, the residues 484, 570, 614, 796, and 969, which are present in variants of concern and are targeted as important in protein function, are predicted as such from our model. 

Parental care has been gained and lost evolutionarily multiple times. While many studies have focused on the origin of care, few have explored the evolutionary loss of care. Understanding the loss of parental care is important as the conditions that favour its loss will not necessarily be the opposite of those that favour the evolution of care. Evolutionary hysteresis (the case in which evolution depends on the history of a system) could create a situation in which it is relatively challenging to lose care once it has evolved. Here, using a mathematical approach, we explore the evolutionary loss of parental care in relation to basic life-history conditions. Our results suggest that parental care is most likely to be lost when egg and adult death rates are low, eggs mature quickly, and the level of care provided is high. We also predict evolutionary hysteresis with respect to egg maturation rate: as egg maturation rate decreases, it becomes increasingly more costly to lose care than to gain it. This suggests that once care is present, it will be particularly challenging for it to be lost if eggs develop slowly.