Hook effect in radioligand assay for Anti Glutamic Acid Decarboxylase (Anti-GAD65). Influence of temperature and physicochemical interpretation

Background: Radioligand assay is one of the principal methods used for analytical determination of the Anti-GAD65 concentration. We studied the influence of temperature on the calibration curves obtained by such a method Matherial and Methods: We used a commercially available RIA kit for Anti-GAD65 and a gamma counter. Data was analyzed using Statistica software. Results and Discusion: Activities bound to the antibody increase with temperature. There was a decrease in activity for high concentrations attributable to the "hook effect". We propose a simple physicochemical model that justifies satisfactorily the results.Objetivo: El análisis por radioligando es uno de los métodos principales utilizados en la determinación analítica del Anti-GAD65. Se ha estudiado la influencia de la temperatura sobre las gráficas de calibración obtenidas por dicha técnica. Material y Métodos: Usamos un kit comercial para Anti-GAD65 y un contador gamma. Los resultados son analizados mediante el programa Statistica. Resultados y Discusión: Las actividades ligadas al anticuerpo aumentan con la temperatura. Se observa una disminución de la actividad para altas concentraciones atribuible al llamado “efecto anzuelo”. Se propone un sencillo modelo fisicoquímico que justifica satisfactoriamente los resultado

Influencia de la temperatura sobre las curvas de calibración en IRMA de IGF I. Interpretación mediante dos modelos no excluyentes

The influence of temperature on the calibration graphs used in the analytical determination of IGF I by IRMA has been studied. The results were analyzed using the equation of the four parameters and a modification of the isotherm BET. Such equations correspond, respectively, to the models of interaction ligand (antigen) - receiver (antibody) and adsorption antigen on the wall of the tube coated antibody. The adjustments to both equations are satisfactory with some advantages for the adsorption model that make it preferable in the interpretation of results. It also determine thermodynamic parameters for the immunocomplex dissociation.Key Words: Four parameters equation, B.E.T. isotherm. Antigen-antibody reaction.Se estudia la influencia de la temperatura sobre las gráficas de calibración utilizadas en la determinación analítica de IGF I mediante IRMA. Los resultados se analizan mediante la ecuación de los cuatro parámetros y una modificación de la isoterma B.E.T. Tales ecuaciones corresponden, respectivamente, a los modelos de interacción ligando (antígeno) – receptor (anticuerpo) y adsorción del antígeno sobre la pared del tubo recubierta de anticuerpo. Los ajustes a ambas ecuaciones son satisfactorios con algunas ventajas para el modelo de adsorción que lo hacen preferible en cuanto a la interpretación de los resultados. Se determinan también los parámetros termodinámicos para la disociación del inmunocomplejo.Palabras clave: Ecuación cuatro parámetros, Isoterma B.E.T. Reacción antígeno-anticuerpo

Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation

[EN] The phenomenon of chaos has been exhibited in mathematical nonlinear models that describe traffic flows, see, for instance (Li and Gao in Modern Phys Lett B 18(26-27):1395-1402, 2004; Li in Phys. D Nonlinear Phenom 207(1-2):41-51, 2005). At microscopic level, Devaney chaos and distributional chaos have been exhibited for some car-following models, such as the quick-thinking-driver model and the forward and backward control model (Barrachina et al. in 2015; Conejero et al. in Semigroup Forum, 2015). We present here the existence of chaos for the macroscopic model given by the Lighthill Whitham Richards equation.The authors are supported by MEC Project MTM2013-47093-P. The second and third authors are supported by GVA, Project PROMETEOII/2013/013Conejero, JA.; Martínez Jiménez, F.; Peris Manguillot, A.; Ródenas Escribá, FDA. (2016). Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation. Nonlinear Dynamics. 84(1):127-133. https://doi.org/10.1007/s11071-015-2245-4S127133841Albanese, A.A., Barrachina, X., Mangino, E.M., Peris, A.: Distributional chaos for strongly continuous semigroups of operators. Commun. Pure Appl. Anal. 12(5), 2069–2082 (2013)Aroza, J., Peris, A.: Chaotic behaviour of birth-and-death models with proliferation. J. Differ. Equ. Appl. 18(4), 647–655 (2012)Banasiak, J., Lachowicz, M.: Chaos for a class of linear kinetic models. C. R. Acad. Sci. Paris Sér. II 329, 439–444 (2001)Banasiak, J., Lachowicz, M.: Topological chaos for birth-and-death-type models with proliferation. Math. Models Methods Appl. Sci. 12(6), 755–775 (2002)Banasiak, J., Moszyński, M.: A generalization of Desch–Schappacher–Webb criteria for chaos. Discrete Contin. Dyn. Syst. 12(5), 959–972 (2005)Banasiak, J., Moszyński, M.: Dynamics of birth-and-death processes with proliferation—stability and chaos. Discrete Contin. Dyn. Syst. 29(1), 67–79 (2011)Barrachina, X., Conejero, J.A.: Devaney chaos and distributional chaos in the solution of certain partial differential equations. Abstr. Appl. Anal. Art. ID 457019, 11 (2012)Barrachina, X., Conejero, J.A., Murillo-Arcila, M., Seoane-Sepúlveda, J.B.: Distributional chaos for the forward and backward control traffic model (2015, preprint)Bayart, F., Matheron, É.: Dynamics of Linear Operators, Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bayart, F., Matheron, É.: Mixing operators and small subsets of the circle. J Reine Angew. Math. (2015, to appear)Bermúdez, T., Bonilla, A., Conejero, J.A., Peris, A.: Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces. Stud. Math. 170(1), 57–75 (2005)Bermúdez, T., Bonilla, A., Martínez-Giménez, F., Peris, A.: Li-Yorke and distributionally chaotic operators. J. Math. Anal. Appl. 373(1), 83–93 (2011)Bernardes Jr, N.C., Bonilla, A., Müller, V., Peris, A.: Distributional chaos for linear operators. J. Funct. Anal. 265(9), 2143–2163 (2013)Brackstone, M., McDonald, M.: Car-following: a historical review. Transp. Res. Part F Traffic Psychol. Behav. 2(4), 181–196 (1999)Conejero, J.A., Lizama, C., Rodenas, F.: Chaotic behaviour of the solutions of the Moore–Gibson–Thompson equation. Appl. Math. Inf. Sci. 9(5), 1–6 (2015)Conejero, J.A., Mangino, E.M.: Hypercyclic semigroups generated by Ornstein-Uhlenbeck operators. Mediterr. J. Math. 7(1), 101–109 (2010)Conejero, J.A., Müller, V., Peris, A.: Hypercyclic behaviour of operators in a hypercyclic $$C_0$$ C 0 -semigroup. J. Funct. Anal. 244, 342–348 (2007)Conejero, J.A., Murillo-Arcila, M., Seoane-Sepúlveda, J.B.: Linear chaos for the quick-thinking-driver model. Semigroup Forum (2015). doi: 10.1007/s00233-015-9704-6Conejero, J.A., Peris, A., Trujillo, M.: Chaotic asymptotic behavior of the hyperbolic heat transfer equation solutions. Int. J. Bifur. Chaos Appl. Sci. Eng. 20(9), 2943–2947 (2010)Conejero, J.A., Rodenas, F., Trujillo, M.: Chaos for the hyperbolic bioheat equation. Discrete Contin. Dyn. Syst. 35(2), 653–668 (2015)Desch, W., Schappacher, W., Webb, G.F.: Hypercyclic and chaotic semigroups of linear operators. Ergod. Theory Dyn. Syst. 17(4), 793–819 (1997)Engel, K.-J., Nagel, R.: One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, vol. 194. Springer, New York (2000). With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. SchnaubeltGrosse-Erdmann, K.-G., Peris Manguillot, A.: Linear Chaos. Universitext. Springer, London (2011)Herzog, G.: On a universality of the heat equation. Math. Nachr. 188, 169–171 (1997)Li, K., Gao, Z.: Nonlinear dynamics analysis of traffic time series. Modern Phys. Lett. B 18(26–27), 1395–1402 (2004)Li, T.: Nonlinear dynamics of traffic jams. Phys. D Nonlinear Phenom. 207(1–2), 41–51 (2005)Lustri, C.: Continuum Modelling of Traffic Flow. Special Topic Report. Oxford University, Oxford (2010)Lighthill, M.J., Whitham, G.B.: On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A. 229, 317–345 (1955)Maerivoet, S., De Moor, B.: Cellular automata models of road traffic. Phys. Rep. 419(1), 1–64 (2005)Mangino, E.M., Peris, A.: Frequently hypercyclic semigroups. Stud. Math. 202(3), 227–242 (2011)Murillo-Arcila, M., Peris, A.: Strong mixing measures for linear operators and frequent hypercyclicity. J. Math. Anal. Appl. 398, 462–465 (2013)Murillo-Arcila, M., Peris, A.: Strong mixing measures for $$C_0$$ C 0 -semigroups. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 109(1), 101–115 (2015)Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol. 44. Springer, New York (1983)Protopopescu, V., Azmy, Y.Y.: Topological chaos for a class of linear models. Math. Models Methods Appl. Sci. 2(1), 79–90 (1992)Richards, P.I.: Shock waves on the highway. Oper. Res. 4, 42–51 (1956

Efecto de gancho en el ensayo de radioligando para Anti-descarboxilasa del ácido glutámico (anti-GAD65). Influencia de la temperatura y la interpretación fisicoquímica

Background: Radioligand assay is one of the principal methods used for analyticaldetermination of the Anti-GAD65 concentration. We studied the influence of temperature onthe calibration curves obtained by such a methodMatherial and Methods: We used a commercially available RIA kit for Anti-GAD65 and agamma counter. Data was analyzed using Statistica software.Results and Discusion: Activities bound to the antibody increase with temperature. Therewas a decrease in activity for high concentrations attributable to the "hook effect". Wepropose a simple physicochemical model that justifies satisfactorily the resultsObjetivo: El análisis por radioligando es uno de los métodos principales utilizados en ladeterminación analítica del Anti-GAD65. Se ha estudiado la influencia de la temperaturasobre las gráficas de calibración obtenidas por dicha técnica.Material y Métodos: Usamos un kit comercial para Anti-GAD65 y un contador gamma. Losresultados son analizados mediante el programa Statistica.Resultados y Discusión: Las actividades ligadas al anticuerpo aumentan con la temperatura.Se observa una disminución de la actividad para altas concentraciones atribuible al llamado“efecto anzuelo”. Se propone un sencillo modelo fisicoquímico que justificasatisfactoriamente los resultado

Distributional chaos for strongly continuous semigroups of operators

Distributional chaos for strongly continuous semigroups is studied and characterized. It is shown to be equivalent to the existence of a distributionally irregular vector. Finally, a sufficient condition for distributional chaos on the point spectrum of the generator of the semigroup is presented. An application to the semigroup generated in L-2 (R) by a translation of the Ornstein-Uhlenbeck operator is also given.This work is supported in part by MEC and FEDER, Project MTM2010-14909, by Generalitat Valenciana, Projects PROMETEO/2008/101 and GV/2010/091, and by Universitat Politecnica de Valencia, Project PAID-06-0-92932. The second author also wants to acknowledge the support of the Project PAID-00-10 and of the grant FPI-UPV2009-04 from Programa de Ayudas de Investigacion y Desarrollo de la Universitat Politecnica de Valencia.Albanese, AA.; Barrachina Civera, X.; Mangino, EM.; Peris Manguillot, A. (2013). Distributional chaos for strongly continuous semigroups of operators. Communications on Pure and Applied Analysis. 12(5):2069-2082. https://doi.org/10.3934/cpaa.2013.12.2069S2069208212