Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · q-bio/0612035

Network formation of tissue cells via preferential attraction to elongated structures

Andras Szabo·Erica D. Perryn·Andras Czirok
View original source ↗Read source document ↗Export metadata ↓

Abstract

Vascular and non-vascular cells often form an interconnected network in vitro, similar to the early vascular bed of warm blooded embryos. Our time-lapse recordings show that the network forms by extending sprouts, i.e., multicellular linear segments. To explain the emergence of such structures, we propose a simple model of preferential attraction to stretched cells. Numerical simulations reveal that the model evolves into a quasi-stationary pattern containing linear segments, which interconnect above the critical volume fraction of 0.2. In the quasi-stationary state the generation of new branches offset the coarsening driven by surface tension. In agreement with empirical data, the characteristic size of the resulting polygonal pattern is density-independent within a wide range of volume fractions.

Explore related subjects

q-bio.CB

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Andras Szabo, Erica D. Perryn, Andras Czirok. 2006-12-18. Network formation of tissue cells via preferential attraction to elongated structures. https://doi.org/10.1103/physrevlett.98.038102

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Kinetics, Proofreading, and the Lifetime of Multivalent Contacts

Selective recognition is how a cell finds the right partner in a crowd and how a drug carrier finds the right cell, so getting it wrong means a missed target or a toxic one. It must also be reversible: a cell has to hold its target tightly enough to tell it from everything else, then release it to act again, and equilibrium binding, which weighs only how favorable a contact is, cannot do both. What settles recognition is how long a contact lasts. We make lifetime the control variable, passing from a master equation through a Smoluchowski equation to the Kramers lifetime of a multivalent contact. Lifetimes are exponential in free energy, so a tenfold change in receptor number moves a contact from seconds to months, turning a smooth thermodynamic gradient into a switch. Selectivity then depends on the encounter: under flow a nanoparticle is kept only if its contact outlives the vascular dwell time, which sharpens the density threshold beyond equilibrium binding. Receptor-mediated endocytosis is itself a kinetic-proofreading cascade, so uptake inherits the Kramers exponential raised to the number of driven steps, a double amplification that vanishes without metabolism and gives a testable route to phenotype-selective delivery. The same readout, on a single bond, is how a T cell discriminates antigen, with immune memory lowering the activation threshold while leaving the specificity untouched.

q-bio.CB↗
arXiv2026

Stationary Action Principles for Neuronal Growth

Neuronal growth is guided by biochemical, mechanical, and geometrical cues while being influenced by stochastic fluctuations in cytoskeletal dynamics, adhesion, and growth cone sensing. Here, we develop two complementary variational descriptions of mechanically guided axonal growth. First, for neurons growing on periodic parallel micropatterns, we use Langevin and Fokker--Planck models to derive a stochastic path action incorporating deterministic substrate guidance and random fluctuations. The probability of a growth trajectory decreases exponentially with this action, and the most probable trajectories correspond to minimum action paths for fixed boundary conditions. Second, for axons growing on substrates with spatially varying stiffness, we show that stiffness dependent traction generates mechanical guidance and axonal turning at stiffness interfaces. In the quasi-static limit, this response leads to a Fermat-like spatial action with an effective axonal refractive index determined by the traction and substrate stiffness relationship. The resulting framework predicts axonal refraction across stiffness boundaries, including an approximate Snell-like relation and a critical angle condition. Although the stochastic and Fermat-like actions have distinct physical meanings and ranges of validity, both describe how substrate mechanics constrain axonal trajectories. These results connect measurable quantities, including drift, diffusion, stiffness, traction, and growth direction, to global properties of axonal paths and provide a framework for designing biomimetic substrates for controlled neuronal growth and regeneration.

q-bio.CB↗
arXiv2026

Randomness-aware multiscale models of glioma invasion and treatment

In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity and anti-crowding mechanisms, while explicitly addressing treatment-related uncertainties through stochastic processes. Starting from a microscopic description of individual cell dynamics, we derive the corresponding system of macroscopic random reaction-diffusion-taxis equations governing cell density and tissue evolution. Finally, we conduct several numerical experiments to assess the efficacy of different treatment protocols, evaluated with respect to both established and newly proposed clinical criteria and measurable outcomes.

q-bio.CB↗