Gábor Szederkényi

Distributed delays play an important role in biological modeling, and are often inevitable to obtain a sufficiently precise quantitative description of certain important processes. It is known from previous studies that mass-action type complex balanced chemical reaction networks (CRNs) containing distributed delays are stable. In this paper, we consider complex balanced biochemical reaction networks with distributed delays, containing a general class of reaction rates including Michaelis–Menten and Hill-type kinetics. We show that for integrable delay distributions defined on a finite time interval, there exists precisely one equilibrium in each stoichiometric compatibility class. The local stability of the equilibria is shown using a logarithmic Lyapunov–Krasovski functional. The theoretical results are demonstrated through two illustrative examples.

In this paper a computationally efficient solution is proposed for the reachable sequence computation problem in the context of sub and superconservative discrete state Chemical Reaction Network (CRN) subclasses. It is shown that a minimal-length reachable state transition sequence and reaction vector sequence can be determined in polynomial time, assuming that the reachability relation holds. A constructive proof is provided in which a computational procedure is composed to find a reachable state transition sequence, provided a pair of initial and target states. In the studied subclasses of discrete state CRNs it is known that the reachability problem - as a decision problem - can be decided in polynomial time by solving a Linear Program formulated by means of the CRN state equation. Leveraging the LP relaxation, the constructed procedure formulates the computational problem of feasible sequence calculation by iteratively solving Linear Programs related to the decision problem of CRN reachability.

It has been clearly demonstrated over the past years that control theory can provide an efficient framework for the solution of several complex tasks in epidemiology. In this paper, we present a computational approach for the state estimation based reference tracking control and historical data reconstruction using nonlinear compartmental epidemic models. The control model is given in nonlinear input-affine form, where the manipulable input is the disease transmission rate influenced by possible measures and restrictions, while the observed or computed output is the number of infected people. The control design is built around a simple SEIR model and relies on a feedback linearization technique. We examine and compare different control setups distinguished by the availability of state information, complementing the directly measurable data with an extended Kalman filter used for state estimation. To illustrate the capabilities and robustness of the proposed method, we carry out multiple case studies for output tracking and data reconstruction on Swedish and Hungarian data, all in the presence of serious model and parameter mismatch. Computation results show that a well-designed feedback, even in the presence of significant observation uncertainties, can sufficiently reduce the effect of modeling errors.

In this work, a family of finite volume discretization schemes for LWR-type first order traffic flow models (with possible on- and off-ramps) is proposed: the Traffic Reaction Model (TRM). These schemes yield systems of ODEs that are formally equivalent to the kinetic systems used to model chemical reaction networks. An in-depth numerical analysis of the TRM is performed. On the one hand, the analytical properties of the scheme (nonnegative, conservative, capacity-preserving, monotone) and its relation to more traditional schemes for traffic flow models (Godunov, CTM) are presented. Finally, the link between the TRM and kinetic systems is exploited to offer a novel compartmental interpretation of traffic models. In particular, kinetic theory is used to derive dynamical properties (namely persistence and Lyapunov stability) of the TRM for a specific road configuration. Two extensions of the proposed model, to networks and changing driving conditions, are also described.

Autophagy-dependent cellular survival is tightly regulated by both kinases and phosphatases. While mTORC1 inhibits autophagy by phosphorylating ULK1, PP2A is able to remove this phosphate group from ULK1 and promotes the key inducer of autophagosome formation. However, ULK1 inhibits mTORC1, mTORC1 is able to down-regulate PP2A. In addition, the active ULK1 promotes PP2A via phosphorylation. We claim that these double-negative (mTORC1 –| PP2A –| mTORC1, mTORC1 –| ULK1 –| mTORC1) and positive (ULK1 -> PP2A -> ULK1) feedback loops are all necessary for the robust, irreversible decision making process between the autophagy and non-autophagy states. We approach our scientific analysis from a systems biological perspective by applying both theoretical and molecular biological techniques. For molecular biological experiments, HEK293T cell line is used, meanwhile the dynamical features of the regulatory network are described by mathematical modelling. In our study, we explore the dynamical characteristic of mTORC1-ULK1-PP2A regulatory triangle in detail supposing that the positive feedback loops are essential to manage a robust cellular answer upon various cellular stress events (such as mTORC1 inhibition, starvation, PP2A inhibition or ULK1 silencing). We confirm that active ULK1 can up-regulate PP2A when mTORC1 is inactivated. By using theoretical analysis, we explain the importance of cellular PP2A level in stress response mechanism. We proved both experimentally and theoretically that PP2A down-regulation (via addition of okadaic acid) might generate a periodic repeat of autophagy induction. Understanding how the regulation of the cell survival occurs with the precise molecular balance of ULK1-mTORC1-PP2A in autophagy, is highly relevant in several cellular stress-related diseases (such as neurodegenerative diseases or diabetes) and might help to promote advanced therapies in the near future, too.

In this paper we show that the dynamics of a class of kinetic compartmental models with bounded capacities, monotone reaction rates and a strongly connected interconnection structure is persistent. The result is based on the chemical reaction network (CRN) and the corresponding Petri net representation of the system. For the persistence analysis, it is shown that all siphons in the Petri net of the studied model class can be characterized efficiently. Additionally, the existence and stability of equilibria are also analyzed building on the persistence and the theory of general compartmental systems. The obtained results can be applied in the analysis of general kinetic models based on the simple exclusion principle.