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1. Syntheses of Families of Enantiopure and DiastereopureCobalt Catalysts Derived from Trications of the Formula [Co(NH2CHArCHArNH2)3]3+

   https://doi.org/10.1021/acs.inorgchem.6b03042  

   Ghosh, Subrata K; Lewis, Kyle G; Kumar, Anil; Gladysz, John A (February 2017, Inorganic Chemistry)

   Abstract Aerobic reactions of CoX2 (X = OAc, Cl) or Co(ClO4)2 with (S,S)-1,2-diphenylethylenediamine [(S,S)-dpen] in CH3OH, followed by HCl or HClO4 additions, give the diastereomeric lipophobic salts Λ-[Co((S,S)-dpen)3]3+3Cl– [Λ-(S,S)-13+3Cl–] or Δ-(S,S)-13+3ClO4– (60–65%) with high degrees of selectivity. Anion metatheses (room temperature) and equilibrations (charcoal, CH3OH, 70 °C) show that the former is more stable than Δ-(S,S)-13+3Cl–, and the latter is more stable than Λ-(S,S)-13+3ClO4–. Additional anion metatheses lead to large families of lipophilic salts Λ- and Δ-(S,S)-13+2X–X′– [X/X′ = Cl/BArf [BArf = B(3,5-C6H3(CF3)2)4], PF6/BArf, BF4/BArf, PhBF3/BArf, Cl/BArf20 [BArf20 = B(C6F5)4], BArf/BArf, BArf20/BArf20, BF4/BF4, PF6/PF6]. Mixed salts of the formula Λ- and Δ-[Co((S,S)-NH2CHArCHArNH2)3]3+2Cl–BArf– are similarly prepared (Ar = 4-C6H4n-Bu, 4-C6H4Cl, 4-C6H4CF3, 4-C6H4OCH3, α-naphthyl, β-naphthyl, 2-C6H4OBn). The diastereotopic NHH′ protons exhibit different 1H NMR signals; one shifts far downfield when X/X′ = Cl/BArf (δ ca. 8.0 vs 4.0 ppm). This is believed to arise from hydrogen bonding between the two Cl– anions and the two C3 faces of the D3-symmetric trication, each of which feature three synperiplanar NH groups. When all of the anions are poor hydrogen-bond acceptors (e.g., BArf–, BF4–, ClO4–), equilibria favor Δ diastereomers. 

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2. Screening of Wild Potatoes Identifies New Sources of Late Blight Resistance

   https://doi.org/10.1094/pdis-06-20-1367-re  

   Karki, Hari S.; Jansky, Shelly H.; Halterman, Dennis A. (February 2021, Plant Disease)

   Late blight (LB) of potato is considered one of the most devastating plant diseases in the world. Most cultivated potatoes are susceptible to this disease. However, wild relatives of potatoes are an excellent source of LB resistance. We screened 384 accessions of 72 different wild potato species available from the U.S. Potato GeneBank against the LB pathogen Phytophthora infestans in a detached leaf assay (DLA). P. infestans isolates US-23 and NL13316 were used in the DLA to screen the accessions. Although all plants in 273 accessions were susceptible, all screened plants in 39 accessions were resistant. Resistant and susceptible plants were found in 33 accessions. All tested plants showed a partial resistance phenotype in two accessions, segregation of resistant and partial resistant plants in nine accessions, segregation of partially resistant and susceptible plants in four accessions, and segregation of resistant, partially resistant, and susceptible individuals in 24 accessions. We found several species that were never before reported to be resistant to LB: Solanum albornozii, S. agrimoniifolium, S. chomatophilum, S. ehrenbergii, S. hypacrarthrum, S. iopetalum, S. palustre, S. piurae, S. morelliforme, S. neocardenasii, S. trifidum, and S. stipuloideum. These new species could provide novel sources of LB resistance. P. infestans clonal lineage-specific screening of selected species was conducted to identify the presence of RB resistance. We found LB resistant accessions in Solanum verrucosum, Solanum stoloniferum, and S. morelliforme that were susceptible to the RB overcoming isolate NL13316, indicating the presence of RB-like resistance in these species. 

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3. Symmetry and asymmetry between positive and negative square energies of graphs

   https://doi.org/10.13001/ela.2024.8447  

   Elphick, Clive; Linz, William (January 2024, The Electronic Journal of Linear Algebra)

   The positive and negative square energies of a graph, $s^+(G)$ and $s^-(G)$, are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively. The first results on square energies revealed symmetry between $s^+(G)$ and $s^-(G)$. This paper reviews examples of asymmetry between these parameters, for example using large random graphs and the ratios $s^+/s^-$ and $s^-/s^+$, as well as new examples of symmetry. Some questions previously asked about $$s^{+}$$ and $$s^{-}$$ are answered and several further avenues of research are suggested. 

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4. In-silico investigation of systematic missense mutations of middle east respiratory coronavirus spike protein

   https://doi.org/10.3389/fmolb.2022.933553  

   Rhoades, Raina; Sobitan, Adebiyi; Mahase, Vidhyanand; Gebremedhin, Brhan; Tang, Qiyi; Rawat, Danda; Cao, Hongbao; Teng, Shaolei (September 2022, Frontiers in Molecular Biosciences)

   Middle East Respiratory Syndrome Coronavirus (MERS-CoV) causes severe pneumonia-like symptoms and is still pose a significant threat to global public health. A key component in the virulence of MERS-CoV is the Spike (S) protein, which binds with the host membrane receptor dipeptidyl peptidase 4 (DPP4). The goal of the present investigation is to examine the effects of missense mutations in the MERS-CoV S protein on protein stability and binding affinity with DPP4 to provide insight that is useful in developing vaccines to prevent coronavirus infection. We utilized a saturation mutagenesis approach to simulate all possible mutations in the MERS-CoV full-length S, S Receptor Binding Domain (RBD) and DPP4. We found the mutations in MERS-CoV S protein residues, G552, C503, C526, N468, G570, S532, S451, S419, S465, and S435, affect protein stability. We identified key residues, G538, E513, V555, S557, L506, L507, R511, M452, D537, and S454 in the S protein RBD region are important in the binding of MERS-CoV S protein to the DPP4 receptor. We investigated the effects of MERS-CoV S protein viral mutations on protein stability and binding affinity. In addition, we studied all DPP4 mutations and found the functional substitution R336T weakens both DPP4 protein stability and S-DPP4 binding affinity. We compared the S protein structures of MERS-CoV, SARS-CoV, and SARS-CoV-2 viruses and identified the residues like C526, C383, and N468 located in equivalent positions of these viruses have effects on S protein structure. These findings provide further information on how mutations in coronavirus S proteins effect protein function. 

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5. Sums of proper divisors follow the Erdős–Kac law

   https://doi.org/10.1090/proc/16167  

   Pollack, Paul; Troupe, Lee (March 2023, Proceedings of the American Mathematical Society)

   Let s ( n ) = ∑ d ∣ n ,   d > n d s(n)=\sum _{d\mid n,~d>n} d denote the sum of the proper divisors of n n . The second-named author proved that ω ( s ( n ) ) \omega (s(n)) has normal order log ⁡ log ⁡ n \log \log {n} , the analogue for s s -values of a classical result of Hardy and Ramanujan [ The normal number of prime factors of a number n [Quart. J. Math. 48 (1917), 76–92], AMS Chelsea Publ., Providence, RI, 2000, pp. 262–275]. We establish the corresponding Erdős–Kac theorem: ω ( s ( n ) ) \omega (s(n)) is asymptotically normally distributed with mean and variance log ⁡ log ⁡ n \log \log {n} . The same method applies with s ( n ) s(n) replaced by any of several other unconventional arithmetic functions, such as β ( n ) ≔ ∑ p ∣ n p \beta (n)≔\sum _{p\mid n} p , n − φ ( n ) n-\varphi (n) , and n + τ ( n ) n+\tau (n) ( τ \tau being the divisor function). 

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