In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular those tissues and organs. Our current implementation combines modified discrete model statistical mechanics, Cellular Potts Model, with continuum reaction–diffusion state automaton well-defined conditions for cell differentiation transitions genetic regulation. This environment rapidly compactly create...

This study investigates the regulation of tissue growth through mathematical modeling systemic and local feedback mechanisms. Employing reaction-diffusion equations, models explore dynamics growth, emphasizing endocrine signaling inter-tissue communication. The analysis identifies critical factors influencing emergence spatial structures, bifurcation phenomena, existence stability stationary pulse wave solutions. It also elucidates mechanisms for achieving coordinated growth. In particular,...

Atherosclerosis begins as an inflammation in blood vessel walls (intima). The inflammatory response of the organism leads to recruitment monocytes. Trapped intima, they differentiate into macrophages and foam cells leading production cytokines further white cells. This self-accelerating process, strongly influenced by low-density lipoproteins (cholesterol), results a dramatic increase width walls, formation atherosclerotic plaque and, possibly, its rupture. We suggest 2D mathematical model...

A new model of viral infection spreading in cell cultures is proposed taking into account virus mutation. This represents a reaction-diffusion system equations with time delay for the concentrations uninfected cells, infected cells and load. Infection progression characterized by replication number Rv, which determines total Analytical formulas speed propagation load are obtained confirmed numerical simulations. It shown that mutation leads to emergence variant. Conditions coexistence two...

Infection spreading in cell culture occurs due to virus replication infected cells and its random motion the extracellular space. Multiplicity of infection experiments cultures are conventionally used for characterization viral by number plaques rate their growth. We describe this process with a delay reaction-diffusion system equations concentrations uninfected cells, virus, interferon. Time corresponds duration inside cells. show that propagates as wave, we determine wave speed prove...

Atherosclerosis is an inflammatory disease. The atherosclerosis process starts when low-density lipoproteins (LDLs) enter the intima of blood vessel, where they are oxidized (ox-LDLs). anti-inflammatory response triggers recruitment monocytes. Once in intima, monocytes transformed into macrophages and foam cells, leading to production cytokines further This auto-amplified leads formation atherosclerotic plaque and, possibly, its rupture. In this paper we develop two mathematical models based...

We proposed a spatially extended model of early events B cell receptors (BCR) activation, which is based on mutual kinase-receptor interactions that are characteristic for the immune and Src family kinases. These lead to positive feedback which, together with two nonlinearities resulting from double phosphorylation Michaelis-Menten dephosphorylation kinetics, responsible system bistability. demonstrated can be activated by formation tiny cluster or displacement nucleus. The kinases...

Mitochondria not only govern energy production, but are also involved in crucial cellular signalling processes. They one of the most important organelles determining Ca2+ regulatory pathway cell. Several mathematical models explaining these mechanisms were constructed, few them describe interplay between calcium concentrations endoplasmic reticulum (ER), cytoplasm and mitochondria. Experiments measuring mitochondria ER suggested existence cytosolic microdomains with locally elevated...

The NF-κB pathway is known to transmit merely 1 bit of information about stimulus level. We combined experimentation with mathematical modeling elucidate how TNF concentration turned into a binary decision. Using Kolmogorov-Smirnov distance, we quantified the cell's ability discern 8 concentrations at each step pathway, find that input discernibility decreases as signal propagates along pathway. Discernibility low restricted by noise receptor level, whereas high it saturation/depletion...

The paper is devoted to solvability conditions for linear elliptic problems with non-Fredholm operators. We show that the operator becomes normally solvable a finite-dimensional kernel on properly chosen subspaces. In particular case of scalar

The stability of Turing patterns in an n-dimensional cube (0, π)n is studied, where n ≥ 2. It shown by using a generalization classical result Ermentrout concerning spots and stripes two dimensions that under appropriate assumptions only sheet-like or nodule-like structures can be stable cube. Other also regions comprising products lower-dimensional cubes intervals length. Stability results are applied to new model skeletal pattern formation the vertebrate limb.

Viral infection in cell culture and tissue is modeled with delay reaction‐diffusion equations. It shown that progression of viral can be characterized by the replication number, time‐dependent load, speed spreading. These three characteristics are determined through original model parameters including rates virus production infected cells. The clinical manifestations infection, depending on damage, correlate spreading, while infectivity a respiratory depends load upper tract. Parameter...

We consider the problem of existence and properties pulse solutions to a system equations modeling fast calcium waves in long cells. These have speed up 1000 m/s. They propagate via inflow ions from extracellular space through mechanically stimulated membrane channels. The channels open due mechano‐chemical interaction, which stretching cell's at point opens neighboring points forces exerted by actomyosin network. homoclinic is based on celebrated exchange lemma, cannot be applied...

We study the existence and properties of calcium waves in presence buffers. The model represents a reaction–diffusion system equations with some diffusion coefficients equal to zero. They correspond immobile proof travelling is carried out by passing zero coefficients.

The spatiotemporal kinetics of proteins and other substrates regulate cell fate signaling. In this study, we consider a reaction–diffusion model interaction membrane receptors with two-step kinase cascade. activate the 'up-stream' kinase, which may diffuse over volume 'down-stream' is also diffusing. Both species are inactivated by uniformly distributed phosphatases. positive feedback, key to considered dynamics, arises since up-stream activates receptors. Such mutual characteristic for...

We consider a class of biological models represented by system composed reactiondiffusion PDE coupled with difference equations (renewal equations) in n -dimensional space, nonlocal dispersal terms and implicit time delays. The equation generally arises, means the method characteristics, from an age-structured partial differential system. Using upper lower solutions, we study existence monotonic planar traveling wave fronts connecting extinction state to uniform positive state. corresponding...

The existence and structural stability of travelling waves systems the free cytosolic calcium concentration in presence immobile buffers are studied. proof is carried out by passing to zero with diffusion coefficients buffers. Thus, its method different from Ref. 13 where proved straightforwardly.

We prove an averaging principle which asserts convergence of diffusion processes on domains separated by semi-permeable membranes, when coefficients tend to infinity while the flux through membranes remains constant. In limit, points in each domain are lumped into a single state limit Markov chain. The chain’s intensities proportional membranes’ permeability and inversely domains’ sizes. Analytically, is example singular perturbation boundary transmission conditions play crucial role. This...