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1. A Numerical Integrator for Kinetostatic Folding of Protein Molecules Modeled as Robots with Hyper Degrees of Freedom

   https://doi.org/10.3390/robotics13100150  

   Kacem, Amal; Zbiss, Khalil; Mohammadi, Alireza (October 2024, Robotics (Special Issue Bioinspired Robotics: Toward Softer, Smarter and Safer))

   The kinetostatic compliance method (KCM) models protein molecules as nanomechanisms consisting of numerous rigid peptide plane linkages. These linkages articulate with respect to each other through changes in the molecule dihedral angles, resulting in a kinematic mechanism with hyper degrees of freedom. Within the KCM framework, nonlinear interatomic forces drive protein folding by guiding the molecule’s dihedral angle vector towards its lowest energy state in a kinetostatic manner. This paper proposes a numerical integrator that is well suited to KCM-based protein folding and overcomes the limitations of traditional explicit Euler methods with fixed step size. Our proposed integration scheme is based on pseudo-transient continuation with an adaptive step size updating rule that can efficiently compute protein folding pathways, namely, the transient three-dimensional configurations of protein molecules during folding. Numerical simulations utilizing the KCM approach on protein backbones confirm the effectiveness of the proposed integrator. 

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2. Thermal Transport in Poly(p-phenylene): Anomalous Dimensionality Dependence and Role of π–π Stacking

   https://doi.org/10.1021/acs.jpcb.3c02947  

   Yang, Cong; Raza, Saqlain; Li, Xiaobo; Liu, Jun (August 2023, The Journal of Physical Chemistry B)

   For heat conduction along polymer chains, a decrease in the axial thermal conductivity often occurs when the polymer structure changes from one-dimensional (1D) to three-dimensional (3D). For example, a single extended aliphatic chain (e.g., polyethylene or poly(dimethylsiloxane)) usually has a higher axial thermal conductivity than its double-chain or crystal counterparts because coupling between chains induces strong interchain anharmonic scatterings. Intuitively, for chains with an aromatic backbone, the even stronger π–π stacking, once formed between chains, should enhance thermal transport across chains and suppress the thermal conductivity along the chains. However, we show that this trend is the opposite in poly(p-phenylene) (PPP), a typical chain with an aromatic backbone. Using molecular dynamics simulations, we found that the axial thermal conductivity of PPP chains shows an anomalous dimensionality dependence where the thermal conductivity of double-chain and 3D crystal structures is higher than that of a 1D single chain. We analyzed the probability distribution of dihedral angles and found that π–π stacking between phenyl rings restricts the free rotation of phenyl rings and forms a long-range order along the chain, thus enhancing thermal transport along the chain direction. Though possessing a stronger bonding strength and stabilizing the multiple-chain structure, π–π stacking does not lead to a higher interchain thermal conductance between phenyl rings compared with that between aliphatic chains. Our simulation results on the effects of π–π stacking provide insights to engineer thermal transport in polymers at the molecular level. 

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3. On superintegral Kleinian sphere packings, bugs, and arithmetic groups

   https://doi.org/10.1515/crelle-2023-0004  

   Kapovich, Michael; Kontorovich, Alex (March 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   We develop the notion of a Kleinian Sphere Packing, a generalization of“crystallographic” (Apollonian-like) sphere packings defined in [A. Kontorovich and K. Nakamura,Geometry and arithmetic of crystallographic sphere packings,Proc. Natl. Acad. Sci. USA 116 2019, 2, 436–441].Unlike crystallographic packings, Kleinian packings exist in all dimensions, as do “superintegral” such.We extend the Arithmeticity Theorem to Kleinian packings, that is, the superintegral ones come from ℚ-arithmetic lattices of simplest type.The same holds for more general objects we call Kleinian Bugs, in which the spheres need not be disjoint but can meet with dihedral angles π/m for finitely many m. We settle two questions from Kontorovich and Nakamura (2019): (i) that the Arithmeticity Theorem is in general false over number fields, and (ii)that integral packings only arise from non-uniform lattices. 

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4. Repurposing DNA-binding agents as H-bonded organic semiconductors

   https://doi.org/10.1038/s41467-019-12248-9  

   Zhang, Fengjiao; Lemaur, Vincent; Choi, Wookjin; Kafle, Prapti; Seki, Shu; Cornil, Jérôme; Beljonne, David; Diao, Ying (September 2019, Nature Communications)

   Abstract Organic semiconductors are usually polycyclic aromatic hydrocarbons and their analogs containing heteroatom substitution. Bioinspired materials chemistry of organic electronics promises new charge transport mechanism and specific molecular recognition with biomolecules. We discover organic semiconductors from deoxyribonucleic acid topoisomerase inhibitors, featuring conjugated backbone decorated with hydrogen-bonding moieties distinct from common organic semiconductors. Using ellipticine as a model compound, we find that hydrogen bonds not only guide polymorph assembly, but are also critical to forming efficient charge transport pathways along π−conjugated planes when at a low dihedral angle by shortening the end-to-end distance of adjacent π planes. In the π−π stacking and hydrogen-bonding directions, the intrinsic, short-range hole mobilities reach as high as 6.5 cm²V⁻¹s⁻¹and 4.2 cm²V⁻¹s⁻¹measured by microwave conductivity, and the long-range apparent hole mobilities are up to 1.3 × 10^–3cm²V⁻¹s⁻¹and 0.4 × 10^–3cm²V⁻¹s⁻¹measured in field-effect transistors. We further demonstrate printed transistor devices and chemical sensors as potential applications. 

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5. Chiral and Achiral Crystal Structures of Au ₂₅ (PET) ₁₈ ⁰ Reveal Effects of Ligand Rotational Isomerization on Optoelectronic Properties

   https://doi.org/10.1002/chem.202202760  

   Kuda‐Singappulige, Gowri_Udayangani; Window, Phillip_S; Hosier, Christopher_A; Anderson, Ian_D; Aikens, Christine_M; Ackerson, Christopher_J (November 2023, Chemistry – A European Journal)

   Abstract The crystal structures of 4 ligand‐rotational isomers of Au₂₅(PET)₁₈are presented. Two new ligand‐rotational isomers are revealed, and two higher‐quality structures (allowing complete solution of the ligand shell) of previously solved Au₂₅(PET)₁₈clusters are also presented. One of the structures lacks an inversion center, making it the first chiral Au₂₅(SR)₁₈structure solved. These structures combined with previously published Au₂₅(SR)₁₈structures enable an analysis of the empirical ligand conformation landscape for Au₂₅(SR)₁₈clusters. This analysis shows that the dihedral angles within the PET ligand are restricted to certain observable values, and also that the dihedral angle values are interdependent, in a manner reminiscent of biomolecule dihedral angles such as those in proteins and DNA. The influence of ligand conformational isomerism on optical and electronic properties was calculated, revealing that the ligand conformations affect the nanocluster absorption spectrum, which potentially provides a way to distinguish between isomers at low temperature. 

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