Semigroup analysis of structured parasite populations

Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then, we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In the case of a separable fertility function, we deduce a characteristic equation, and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.Comment: to appear in Mathematical Modelling of Natural Phenomen

Steady states in a structured epidemic model with Wentzell boundary condition

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we establish global existence of solutions and the Principle of Linearised Stability for our model. Then, in our main result, we formulate simple conditions, which guarantee the existence of non-trivial steady states of the model. Our method utilizes an operator theoretic framework combined with a fixed point approach. Finally, in the last section we establish a sufficient condition for the local asymptotic stability of the positive steady state

A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1

Genomic and immune landscape Of metastatic pheochromocytoma and paraganglioma

Adrenal gland diseases; Cancer genomics; Prognostic markersMalalties de les glàndules suprarenals; Genòmica del càncer; Marcadors pronòsticsEnfermedades de las glándulas suprarrenales; Genómica del cáncer; Marcadores pronósticosThe mechanisms triggering metastasis in pheochromocytoma/paraganglioma are unknown, hindering therapeutic options for patients with metastatic tumors (mPPGL). Herein we show by genomic profiling of a large cohort of mPPGLs that high mutational load, microsatellite instability and somatic copy-number alteration burden are associated with ATRX/TERT alterations and are suitable prognostic markers. Transcriptomic analysis defines the signaling networks involved in the acquisition of metastatic competence and establishes a gene signature related to mPPGLs, highlighting CDK1 as an additional mPPGL marker. Immunogenomics accompanied by immunohistochemistry identifies a heterogeneous ecosystem at the tumor microenvironment level, linked to the genomic subtype and tumor behavior. Specifically, we define a general immunosuppressive microenvironment in mPPGLs, the exception being PD-L1 expressing MAML3-related tumors. Our study reveals canonical markers for risk of metastasis, and suggests the usefulness of including immune parameters in clinical management for PPGL prognostication and identification of patients who might benefit from immunotherapy.This work was supported by Project PI17/01796 and PI20/01169 to M.R. [Instituto de Salud Carlos III (ISCIII), Acción Estratégica en Salud, cofinanciado a través del Fondo Europeo de Desarrollo Regional (FEDER)], Paradifference Foundation [no grant number applicable to M.R.], Pheipas Association [no grant number applicable to M.R.], the Clinical Research Priority Program of the University of Zurich for the CRPP HYRENE to F.B., the Deutsche Forschungsgemeinschaft (DFG) within the CRC/Transregio 205/1 (Project No. 314061271-TRR205 to to F.B., M.F., N.B., and G.E.) and the Instituto de Salud Carlos III (ISCIII), Spanish Ministry of Science and Innovation (Project No. PID2019-111356RA-I00 to G.M.). B.C. was supported by the Rafael del Pino Foundation (Becas de Excelencia Rafael del Pino 2017). A.M.M.-M. was supported by CAM (S2017/BMD-3724; TIRONET2-CM). A.F.-S. and J.L. received the support of a fellowship from La Caixa Foundation (ID 100010434; LCF/BQ/DR21/11880009 and LCF/BQ/DR19/11740015, respectively). M.M., S.M., and M.S. were supported by the Spanish Ministry of Science, Innovation and Universities “Formación del Profesorado Universitario— FPU” fellowship with ID number FPU18/00064, FPU19/04940 and FPU16/05527. A.D.-T. is supported by the Centro de Investigacion Biomédica en Red de Enfermedades Raras (CIBERER). L.J.L.-G. was supported both by the Banco Santander Foundation and La Caixa Postdoctoral Junior Leader Fellowship (LCF/BQ/PI20/11760011). C.M.-C. was supported by a grant from the AECC Foundation (AIO15152858 MONT). We thank the Spanish National Tumor Bank Network (RD09/0076/00047) for the support in obtaining tumorsamples and all patients, physicians and tumor biobanks involved in the study

Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin

Novel DNMT3A Germline Variant in a Patient with Multiple Paragangliomas and Papillary Thyroid Carcinoma

Over the past few years, next generation technologies have been applied to unravel the genetics of rare inherited diseases, facilitating the discovery of new susceptibility genes. We recently found germline DNMT3A gain-of-function variants in two patients with head and neck paragangliomas causing a characteristic hypermethylated DNA profile. Here, whole-exome sequencing identifies a novel germline DNMT3A variant (p.Gly332Arg) in a patient with bilateral carotid paragangliomas, papillary thyroid carcinoma and idiopathic intellectual disability. The variant, located in the Pro-Trp-Trp-Pro (PWWP) domain of the protein involved in chromatin targeting, affects a residue mutated in papillary thyroid tumors and located between the two residues found mutated in microcephalic dwarfism patients. Structural modelling of the variant in the DNMT3A PWWP domain predicts that the interaction with H3K36me3 will be altered. An increased methylation of DNMT3A target genes, compatible with a gain-of-function effect of the alteration, was observed in saliva DNA from the proband and in one independent acute myeloid leukemia sample carrying the same p.Gly332Arg variant. Although further studies are needed to support a causal role of DNMT3A variants in paraganglioma, the description of a new DNMT3A alteration in a patient with multiple clinical features suggests a heterogeneous phenotypic spectrum related to DNMT3A germline variants

Linear stability and positivity results for a generalized size-structured Daphnia model with inflow§

We employ semigroup and spectral methods to analyze the linear stability of positive stationary solutions of a generalized size-structured Daphnia model. Using the regularity properties of the governing semigroup, we are able to formulate a general stability condition which permits an intuitively clear interpretation in a special case of model ingredients. Moreover, we derive a comprehensive instability criterion that reduces to an elegant instability condition for the classical Daphnia population model in terms of the inherent net reproduction rate of Daphnia individuals

Effects of Goat Manure Fertilization on Grain Nutritional Value in Two Contrasting Quinoa (Chenopodium quinoa Willd.) Varieties Cultivated at High Altitudes

In this study, the effects of goat manure fertilization (2, 4, 8, and 12 Tn/ha) on the grain yield, organic compounds, and mineral composition of two quinoa varieties (CICA-17 and Regalona Baer) were evaluated under field conditions in Northwest Argentina. The results indicate that fertilization improved the quinoa grain yield and total protein content. Low manure doses positively affected the fatty acid (FA) profile, and significant changes were determined for the monounsaturated (MUFA) and polyunsaturated (PUFA) fatty acid contents of CICA-17 and on the saturated fatty acid (SFA) contents of R. Baer seeds. The amino acid contents were positively affected in CICA-17 and negatively in R. Baer. Soluble sugars (glucose, fructose, and sucrose), major elements (K, Si, P, Mg, Ca, and Na), minor elements (Fe, Mn, Al, Zn, and Cu), and ultratrace elements (Cr and Li) were detected and discussed in terms of their impact on human nutrition and health. Conclusively, manure addition affected some essential amino acids, the desaturase activity, the n6:n3 and SFA/UFA ratios, the atherogenic index, soluble sugars, and mineral content, and the fatty acid metabolism of each variety was differently affected, especially the C16 and C18 desaturase activity, which responded differently to various manure doses. Manure addition is a promising alternative to improve the nutritional quality and functionality of quinoa grains, but the response is not linear

Effects of Goat Manure Fertilization on Grain Nutritional Value in Two Contrasting Quinoa (Chenopodium quinoa Willd.) Varieties Cultivated at High Altitudes

In this study, the effects of goat manure fertilization (2, 4, 8, and 12 Tn/ha) on the grain yield, organic compounds, and mineral composition of two quinoa varieties (CICA-17 and Regalona Baer) were evaluated under field conditions in Northwest Argentina. The results indicate that fertilization improved the quinoa grain yield and total protein content. Low manure doses positively affected the fatty acid (FA) profile, and significant changes were determined for the monounsaturated (MUFA) and polyunsaturated (PUFA) fatty acid contents of CICA-17 and on the saturated fatty acid (SFA) contents of R. Baer seeds. The amino acid contents were positively affected in CICA-17 and negatively in R. Baer. Soluble sugars (glucose, fructose, and sucrose), major elements (K, Si, P, Mg, Ca, and Na), minor elements (Fe, Mn, Al, Zn, and Cu), and ultratrace elements (Cr and Li) were detected and discussed in terms of their impact on human nutrition and health. Conclusively, manure addition affected some essential amino acids, the desaturase activity, the n6:n3 and SFA/UFA ratios, the atherogenic index, soluble sugars, and mineral content, and the fatty acid metabolism of each variety was differently affected, especially the C16 and C18 desaturase activity, which responded differently to various manure doses. Manure addition is a promising alternative to improve the nutritional quality and functionality of quinoa grains, but the response is not linear.EEA FamailláFil: González, Juan A. Fundación Miguel Lillo. Instituto de Ecología, Comportamiento y Conservación; ArgentinaFil: Yousif, Sawsan K.M. Al-Baha University. College of Arts and Science in Baljurashi. Department of Chemistry; Arabia SauditaFil: Erazzu, Luis Ernesto. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Famaillá; ArgentinaFil: Erazzu, Luis Ernesto. Universidad Nacional de Tucumán. Facultad de Agronomía y Zootecnia; ArgentinaFil: Martinez Calsina, Luciana. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Famaillá; ArgentinaFil: Lizarraga, Emilio. Fundación Miguel Lillo. Instituto de Fisiología Animal; ArgentinaFil: Lizarraga, Emilio. Universidad Nacional de Tucumán. Facultad de Ciencias Naturales e Instituto Miguel Lillo; ArgentinaFil: Omer, Rihab M. Al-Baha University. College of Arts and Science in Baljurashi. Department of Chemistry; Arabia SauditaFil: Bazile, D. CIRAD, UMR SENS; FranciaFil: Bazile, D. University Paul Valery Montpellier 3. CIRAD, IRD; FranciaFil: Fernandez-Turiel, J.L. CSIC. Geosciences Barcelona; EspañaFil: Buedo, Sebastián E. Fundación Miguel Lillo. Instituto de Ecología, Comportamiento y Conservación; ArgentinaFil: Rejas, M. CSIC. Geosciences Barcelona; EspañaFil: Fontana, Paola Daniela. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Famaillá; ArgentinaFil: González, D.A. Universidad Nacional de Tucumán. Facultad de Ciencias Naturales e Instituto Miguel Lillo. Instituto de Bioprospección y Fisiología Vegetal (INBIOFIV); ArgentinaFil: González, D.A. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Bioprospección y Fisiología Vegetal (INBIOFIV); ArgentinaFil:Oviedo, A. Fundación Miguel Lillo. Instituto de Fisiología Animal; ArgentinaFil: Alzuaibr, Fahad Mohammed. University of Tabuk. Faculty of Science. Department of Biology; Arabia SauditaFil: Al-Qahtani, Salem Mesfer. University of Tabuk. University College of Tayma. Biology Department; Arabia SauditaFil: Al-Harbi, Nadi Awad. University of Tabuk. University College of Tayma. Biology Department; Arabia SauditaFil: Ibrahim, Mohamed F.M. Ain Shams University. Faculty of Agriculture. Department of Agricultural Botany; EgiptoFil: Van Nieuwenhove, Carina. Universidad Nacional de Tucumán. Facultad de Ciencias Naturales e Instituto Miguel Lillo; ArgentinaFil: Van Nieuwenhove, Carina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Centro de Referencia para Lactobacilos. Laboratorio de Ecofisiología Tecnológica; Argentin

Direct competition results from strong competiton for limited resource

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already proved, this model, although more complicated than the usual Lotka-Volterra direct competition model, describes competitive interactions leading to concentrated distributions of species in continuous trait space. Here we assume a very fast dynamics for the supply of the resource and a fast dynamics for death and uptake rates. In this regime we show that factors that are independent of the resource competition become as important as the competition efficiency and that the direct competition model is a good approximation of the chemostat. Assuming these two timescales allows us to establish a mathematically rigorous proof showing that our resource-competition model with continuous traits converges to a direct competition model. We also show that the two timescales assumption is required to mathematically justify the corresponding classic result on a model consisting of only finite number of species and resources (MacArthur, R. Theor. Popul. Biol. 1970:1, 1-11). This is performed through asymptotic analysis, introducing different scales for the resource renewal rate and the uptake rate. The mathematical difficulty relies in a possible initial layer for the resource dynamics. The chemostat model comes with a global convex Lyapunov functional. We show that the particular form of the competition kernel derived from the uptake kernel, satisfies a positivity property which is known to be necessary for the direct competition model to enjoy the related Lyapunov functional