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    Polyconvex double well functions

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    This version fixes a flaw in the main theorem of the previous version.We investigate polyconvexity of the double well function f(X):=XX12XX22f(X) := |X-X_1|^2|X-X_2|^2 for given matrices X1,X2Rn×nX_1, X_2 \in \R^{n \times n}. Such functions are fundamental in the modeling of phase transitions in materials, but their non-convex nature presents challenges for the analysis of variational problems. Polyconvexity of ff is related to the singular values of the matrix difference X1X2X_1 - X_2. We prove that ff is polyconvex if and only if the square of the largest singular value does not exceed the sum of the squares of the other singular values. This condition allows the function to be decomposed into the sum of a strictly convex part and a null Lagrangean. As a direct application of this result, we prove an existence and uniqueness theorem for the corresponding Dirichlet minimization problem of the integral functional

    Exploring Natural Diversity of Limonene Synthases and Molecular Determinants Involved in Substrate Specificity in Escherichia coli

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    International audienceLimonene is a chiral, high-demand monoterpene that has wide applications in therapeutics, cosmetics, biofuels, agri-food, biomaterials, and solvent industries. However, its biosynthesis by microbial cell factories is often limited by the poor activity of limonene synthase (LS). Optimization of the rate-limiting enzyme is thus crucial for boosting limonene production. Here, we report the identification of ten LS homologues from sequence data mining and their testing in cells accumulating geranyl pyrophosphate (GPP) or neryl pyrophosphate (NPP) for limonene production. The selectivity of these enzymes toward GPP or NPP was investigated, leading to the identification of a limonene synthase from Agastache rugosa that displays a clear substrate preference for NPP over GPP in vivo. This enzyme was selected as a template for engineering. Using in silico analyses and mutagenesis, several mutants were engineered that revealed differences in substrate specificity. Among them, a combination of mutations (S8K/I265V/E276P/P277R/A281K/N282T/I285Q/I286L) improved limonene production by 4.8- and 1.9-fold with the GPP and NPP pathways, respectively. The mutant predominantly produced (+)-limonene from GPP and a mixture of limonene from NPP, with ∼85-90% of (+)-limonene. This decreased the selectivity for NPP by 2.4-fold. This supports the improved biological production of limonene enantiomers from renewable carbon sources

    Synchronization of Multi-Agent Hybrid Systems With Synchronous State-Dependent Jumps

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    International audienceIn this letter, we investigate the problem of synchronization of multi-agent systems described by hybrid non-linear input affine dynamics. We consider networks described by undirected connected graphs without leader. We present a set of sufficient conditions based on an LMI approach in order to design a state-feedback distributed control law. Then, by exploiting the properties of the graph incidence matrix we provide an optimization of the tuning parameters. The incidence matrix properties also allow us to construct a Lyapunov function to establish synchronization of the hybrid network

    The role of selection for function in aging and chronic diseases: a novel evolutionary perspective

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    International audienceAging, and by extension age‐related diseases, has traditionally been understood through classical evolutionary genetic models, such as the mutation accumulation and antagonistic pleiotropy theories. However, these frameworks primarily focus on the declining efficacy of organismal‐level selection against mutations with deleterious effects in late life. Here, we propose a novel hypothesis: many chronic diseases associated with aging may emerge, at least in part, as a result of selection acting at lower organizational levels, including non‐replicative biological entities, enabled by the relaxation of selective pressures that constrained within‐organism evolutionary processes in early life. This hypothesis is built on the recently proposed concept of selection for function that extends the evolutionary process to non‐replicative entities. While Darwinian selection acting at the organismal level strongly constrains within‐organism evolution during an organism's reproductive lifespan, these constraints weaken with age. As a consequence, lower‐level non‐replicative entities, such as benign and malignant tumors, atherosclerotic plaques, and neurodegenerative aggregates, may experience a form of selection that favors those with increased stability, organization, and long‐term persistence, sometimes at the cost to host fitness. These entities do not evolve via long‐term differential reproduction, but rather certain configurations of their structure persist preferentially over others due to environmental constraints, microenvironmental selection, and internal stabilization mechanisms. Understanding aging through the lens of selection for function at the level of internal non‐replicative entities provides new insights into the evolution of chronic diseases and opens novel therapeutic avenues aimed at disrupting internal functional organization, rather than merely targeting cellular proliferation/abnormalities or disease symptoms

    Room temperature dinitrogen cleavage and hydrogenation with organometallic complexes of uranium

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    International audienceAn organometallic uranium complex enables dinitrogen activation, cleavage, and hydrogenation at ambient temperature and pressure. The ligand's steric hindrance plays an essential role in this rare reactivity

    Solvatochromism and Redox Multi‐Switch in a Trinuclear Cobalt(II) Complex

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    International audienceA trinuclear cobalt(II) complex incorporating the redox‐active hexahydroxytriphenylene (H6HHTP) ligand was prepared and isolated in two different redox states: [CoII3(sq‐sq‐sq)]3+ ( 1 ) and [CoII3(cat‐sq‐sq)]2+ ( 2 ) (sq = semiquinone; cat = catecholate), enabled by its remarkable solvatochromic behavior. The ligand field tuning of the Co(II) centers through the ancillary ligand Me 3 TPA (tris(6‐methyl‐2‐pyridylmethyl)amine) allowed accessing six reversible one‐electron processes instead of only three with the parent TPA ligand, therefore increasing the range of redox‐coupled magnetic and optical switching in this system. Upon reduction, the three redox processes are ligand‐centered and involve the three sq•−/cat2− couples of hexahydroxytriphenylene (HHTP), while we hypothesize that some of the oxidation processes may involve the Co(II) metallic species

    Leveraging selection for function in tumor evolution: System-level cancer therapies

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    International audienceCurrent cancer therapies often fail due to tumor heterogeneity and rapid resistance evolution. A new evolutionary framework, ‘selection for function,’ proposes that tumor progression is driven by group phenotypic composition (GPC) and its interaction with the microenvironment, not by individual cell traits. This perspective opens new therapeutic avenues: targeting the tumor’s functional networks rather than individual cells. Real-time tracking of GPC changes could inform adaptive treatments, delaying progression and resistance. By integrating evolutionary and ecological principles with conventional therapies, this strategy aims to transform cancer from a fatal to a manageable chronic disease. Crucially, it does not necessarily require new drugs but offers a way to repurpose existing therapies to impair a tumor’s evolutionary potential. By steering tumor evolution toward less aggressive states, this approach could improve prognosis and long-term patient survival compared to current methods. We argue that leveraging GPC dynamics represents a critical, yet underexplored, opportunity in oncology

    Towards site-specific information on PET degrading enzymes using NMR near operational temperature

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    International audiencePETases are enzymes that can break down the poly-ethylene terephthalate (PET) polymer in its constituent building blocks. This enzymatic recycling process offers a sustainable solution for producing new, high-quality plastics from previously used materials. NMR spectroscopy can help in understanding and ultimately improving these enzymes but is always confronted with the lengthy step of acquisition and interpretation of triple resonance spectra for the spectral assignment. Here, we explore whether this step can be made more efficient by recording the spectra directly at high temperature, which simultaneously corresponds to more realistic working conditions for the enzyme. Taking the inactive variant of LCCICCG as an example, we compare spectral quality at 30°C and 50°C, and find that the latter condition greatly improves the Signal-to-Noise (S/N) ratio of the standard triple resonance spectra. Going up to 60°C, we show that pulse sequences mainly used for the assignment of intrinsically disordered proteins (IDPs) also become feasible. As a result, we present a methodology enabling exhaustive backbone assignment based on a minimal set of triple resonance spectra acquired and analysed in less than two weeks. The assignment process hence can be completed on a time scale comparable to crystallography, bringing NMR in a favourable position to contribute to bio-structural studies on this family of highly thermostable PETases

    Tailoring Co 2 P Shell of Co@Co 2 P Nanorods through the P-Source and Influence on Their Stability in Water

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    International audienceCobalt nanorods (NRs) with a diameter below 20 nm exhibiting both high magnetization and high magnetic coercivity are interesting building blocks for different applications ranging from permanent magnets to biosensors. One of the challenges is to develop simple methods of protecting such NRs to make them resistant to oxidation without degrading their magnetic properties, thus, opening the way to a wider field of uses. This study presents the reactivity of Co NRs prepared by the polyol process with two different P-sources, tris(diethylamino)phosphine (DEAP) and the tris(trimethylsilyl) phosphine (PTMS). We show that depending on P-source, temperature and P: Co molar ratio, Co NRs can be progressively transformed into core-shell Co@Co2P NRs of increasing shell-thickness and then to Co2P@CoP NRs. All these transformations retain the anisotropic shape of the particles showing that the phosphidation proceeds at least partially through a topotactic reaction. Complementary to the electron microscope and x-ray diffraction analyses, the magnetic properties of the NRs at different stages of the phosphidation allows following precisely the transformation of the NRs. When the phosphide shell is very thin, the disappearance of exchange bias shows that the native cobalt oxide shell of the raw Co NRs is transformed first. Thanks to the optimal diameter of the bare Co nanorods, the formation of a thick phosphide shell is possible, without degradation of the ferromagnetic properties of the Co core for thicker Co2P shells, as the high coercive field of the Co@Co2P NRs shows that both the shape and the magnetocrystalline anisotropy of the cobalt core are preserved. It is only when the transformation of the metallic Co to Co2P/CoP is complete that the NRs are no more magnetic. The core-shell Co@Co2P NRs present a very good resistance toward oxidation in water which is not so common with ferromagnetic nanoparticles of such size.</div

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