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We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in…
This work presents a mathematical model which describes both the genesis and growth of oxygenic photogranules (OPGs) and the related treatment process. The photogranule has been modelled as a free boundary domain with radial symmetry, which…
Selective energy transport throughout a quantum network connected to more than one reaction center can play an important role in many natural and technological considerations in photo-systems. In this work, we propose a method in which an…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the…
Inferring parameters of macro-kinetic growth models, typically represented by Ordinary Differential Equations (ODE), from the experimental data is a crucial step in bioprocess engineering. Conventionally, estimates of the parameters are…
Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal non-standard behaviors and mark the boundary where…
In this paper we study, at different levels of generality, certain systems of delay differential equations (DDE). One focus and motivation is a system with state-dependent delay (SD-DDE) that has been formulated to describe the maturation…
A general scheme for construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the…
Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens in a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under…
In this paper, we derive a new chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migration process for its early and late stages. Different from the…
Autocatalytic sets are sets of entities that mutually catalyse each other's production through chemical reactions from a basic food source. Recently, the reflexively autocatalytic and food generated theory has introduced a formal definition…
End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of…
Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…
Living cells display a remarkable capacity to compartmentalize their functional biochemistry. A particularly fascinating example is the cell nucleus. Exchange of macromolecules between the nucleus and the surrounding cytoplasm does not…
In this paper we introduce a formalism that allows to describe the response of a part of a biochemical system in terms of renewal equations. In particular, we examine under which conditions the interactions between the different parts of a…
We present significantly advanced studies of the previously introduced physical growth mechanism and unite it with biochemical growth factors. Obtained results allowed formulating the general growth law which governs growth and evolutional…
A dissipative particle dynamics (DPD) model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow…
Autophagy is a conserved biological stress response in mammalian cells that is responsible for clearing damaged proteins and organelles from the cytoplasm and recycling their contents via the lysosomal pathway. In cases of mild stress,…