This paper describes the extension of the variable lumping transformation, being a well-known eng... more This paper describes the extension of the variable lumping transformation, being a well-known engineering-type model simplification method, to a special class of nonlinear reaction kinetic systems, to the cascade activation reactions. Two methods of cascade lumping is investigated: (i) variable lumping with changing the stoichiometric coefficients, and (ii) variable lumping with output variable transformation.
The realization problem in reaction kinetics Reaction kinetic systems form a special class of pos... more The realization problem in reaction kinetics Reaction kinetic systems form a special class of positive systems with smooth nonlinearities where advantageous dynamic properties, such as global may be ensured thanks to the special structure of the system model. In the classical case, these systems are described by a set of ordinary differential equations (ODEs) with polynomial right-hand sides . Beside the description of classical chemical reactions, reaction kinetic systems are the main building blocks of highly interconnected biochemical systems with complex behavior such as metabolic or cell signalling pathways .
In this paper a simple one compartment Hodgkin-Huxley type electrophysiological model of GnRH neu... more In this paper a simple one compartment Hodgkin-Huxley type electrophysiological model of GnRH neurons is presented, that is able to reasonably reproduce the most important qualitative features of the firing pattern, such as baseline potential, depolarization amplitudes, sub-baseline hyperpolarization phenomenon and average firing frequency in response to excitatory current. In addition, the same model provides an acceptable numerical fit of voltage clamp (VC) measurement results. The parameters of the model have been estimated using averaged VC traces, and characteristic values of measured current clamp traces originating from GnRH neurons in hypothalamic slices. The resulting parameter values show a good agreement with literature data in most of the cases. Applying parametric changes, which lead to the increase of baseline potential and enhance cell excitability, the model becomes capable of bursting. The effects of various parameters to burst length have been analyzed by simulation.
In this paper the qualitative dynamic behavior of reaction kinetic models of G protein signaling ... more In this paper the qualitative dynamic behavior of reaction kinetic models of G protein signaling is examined. A simplified basic G protein signaling structure is defined, which is extended to be able to take the effect of slow transmission, RGS mediated feedback regulation and ERK-phosphatase mediated feedback regulation into account.
In this paper a modular model of the GnRH neuron is presented. For the aim of simplicity, the cur... more In this paper a modular model of the GnRH neuron is presented. For the aim of simplicity, the currents corresponding to fast time scales and action potential generation are described by an impulsive system, while the slower currents and calcium dynamics are described by usual ordinary differential equations (ODEs). The model is able to reproduce the depolarizing afterpotentials, afterhyperpolarization, periodic bursting behavior and the corresponding calcium transients observed in the case of GnRH neurons.
An electrical transmission network consists of producers, consumers and the power lines connectin... more An electrical transmission network consists of producers, consumers and the power lines connecting them. We build an ideal (lossless) DC load flow model as a cooperative game over a graph with the producers and consumers located at the nodes, each described by a maximum supply or desired demand and the power lines represented by the edges, each with a given power transmission capacity and admittance value describing its ability to transmit electricity. Today's transmission networks are highly interconnected, but organisationally partitioned into several subnetworks, the so-called balancing groups with balanced production and consumption. We study the game of balancing group formation and show that the game contains widespread externalities that can be both negative and positive.
An electrical transmission network consists of producers, consumers and the power lines connectin... more An electrical transmission network consists of producers, consumers and the power lines connecting them. We build an ideal (lossless) DC load ow model as a cooperative game over a graph with the producers and consumers located at the nodes, each described by a maximum supply or desired demand and the power lines represented by the edges, each with a given power transmission capacity and admittance value describing its ability to transmit electricity.
This paper describes the extension of the variable lumping transformation, being a well-known eng... more This paper describes the extension of the variable lumping transformation, being a well-known engineering-type model simplification method, to a special class of nonlinear reaction kinetic systems, to the cascade activation reactions. Two methods of cascade lumping is investigated: (i) variable lumping with changing the stoichiometric coefficients, and (ii) variable lumping with output variable transformation.
The realization problem in reaction kinetics Reaction kinetic systems form a special class of pos... more The realization problem in reaction kinetics Reaction kinetic systems form a special class of positive systems with smooth nonlinearities where advantageous dynamic properties, such as global may be ensured thanks to the special structure of the system model. In the classical case, these systems are described by a set of ordinary differential equations (ODEs) with polynomial right-hand sides . Beside the description of classical chemical reactions, reaction kinetic systems are the main building blocks of highly interconnected biochemical systems with complex behavior such as metabolic or cell signalling pathways .
In this paper a simple one compartment Hodgkin-Huxley type electrophysiological model of GnRH neu... more In this paper a simple one compartment Hodgkin-Huxley type electrophysiological model of GnRH neurons is presented, that is able to reasonably reproduce the most important qualitative features of the firing pattern, such as baseline potential, depolarization amplitudes, sub-baseline hyperpolarization phenomenon and average firing frequency in response to excitatory current. In addition, the same model provides an acceptable numerical fit of voltage clamp (VC) measurement results. The parameters of the model have been estimated using averaged VC traces, and characteristic values of measured current clamp traces originating from GnRH neurons in hypothalamic slices. The resulting parameter values show a good agreement with literature data in most of the cases. Applying parametric changes, which lead to the increase of baseline potential and enhance cell excitability, the model becomes capable of bursting. The effects of various parameters to burst length have been analyzed by simulation.
In this paper the qualitative dynamic behavior of reaction kinetic models of G protein signaling ... more In this paper the qualitative dynamic behavior of reaction kinetic models of G protein signaling is examined. A simplified basic G protein signaling structure is defined, which is extended to be able to take the effect of slow transmission, RGS mediated feedback regulation and ERK-phosphatase mediated feedback regulation into account.
In this paper a modular model of the GnRH neuron is presented. For the aim of simplicity, the cur... more In this paper a modular model of the GnRH neuron is presented. For the aim of simplicity, the currents corresponding to fast time scales and action potential generation are described by an impulsive system, while the slower currents and calcium dynamics are described by usual ordinary differential equations (ODEs). The model is able to reproduce the depolarizing afterpotentials, afterhyperpolarization, periodic bursting behavior and the corresponding calcium transients observed in the case of GnRH neurons.
An electrical transmission network consists of producers, consumers and the power lines connectin... more An electrical transmission network consists of producers, consumers and the power lines connecting them. We build an ideal (lossless) DC load flow model as a cooperative game over a graph with the producers and consumers located at the nodes, each described by a maximum supply or desired demand and the power lines represented by the edges, each with a given power transmission capacity and admittance value describing its ability to transmit electricity. Today's transmission networks are highly interconnected, but organisationally partitioned into several subnetworks, the so-called balancing groups with balanced production and consumption. We study the game of balancing group formation and show that the game contains widespread externalities that can be both negative and positive.
An electrical transmission network consists of producers, consumers and the power lines connectin... more An electrical transmission network consists of producers, consumers and the power lines connecting them. We build an ideal (lossless) DC load ow model as a cooperative game over a graph with the producers and consumers located at the nodes, each described by a maximum supply or desired demand and the power lines represented by the edges, each with a given power transmission capacity and admittance value describing its ability to transmit electricity.
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Papers by David Csercsik