Table of contents

We present a study of in vitro cell migration in two dimensions as a first step towards understanding the mechanisms governing the motility of glioma cells. Our study is based on a cellular automaton model which aims at reproducing the kinetics of a lump of glioma cells deposited on a substrate of collagen. The dynamical effects of cell attraction and motion inertia are introduced through adequate automaton rules. We compare the density profiles given by the model to those obtained experimentally. The result of the best fit indicates a substantial cell–cell attraction due to cell–cell communication through gap junctions (or chemotaxis) and negligible inertia effects during migration. Tracking of individual migrating cells indicates highly convoluted cell trajectories.

A new mechanism of selective transport and localization of proteins inside any living cell is presented. The mechanism is based on pH-induced protein trapping. It is shown that spontaneous and unique spatial redistribution of different proteins is possible in any aqueous solution with stable non-uniform distribution of H⁺ ions. This phenomenon was observed in artificial systems with fixed non-uniform pH distribution and in living cells.

Morphogens are proteins, often produced in a localized region, whose concentrations spatially demarcate regions of differing gene expression in developing embryos. The boundaries of gene expression are typically sharp and the genes can be viewed as abruptly switching from on to off or vice versa upon crossing the boundary. To ensure the viability of the organism these boundaries must be set at certain fractional positions within the corresponding developing field. Remarkably this can be done with high precision despite the fact that the size of the developing field itself can vary widely from embryo to embryo. How this scaling is accomplished is unknown but it is clear that a single morphogen gradient is insufficient. Here we show how a pair of morphogens A and B, produced at opposite ends of a one-dimensional developing field, can solve the pattern-scaling problem. In the most promising scenario the morphogens interact via an effective annihilation reaction A + B → ∅ and the switch occurs according to the absolute concentration of A or B. We define a scaling criterion and show that morphogens coupled in this way can set embryonic markers across the entire developing field in proportion to the field size. This scaling occurs at developing-field sizes of a few times the morphogen decay length. The scaling criterion is not met if instead the gradients couple combinatorially such that downstream genes are regulated by the ratio A/B of the morphogen concentrations.

Most biological functions, including photosynthetic activity, are mediated by protein interactions. The proteins plastocyanin and cytochrome f are reaction partners in a photosynthetic electron transport chain. We designed a 3D computer simulation model of diffusion and interaction of spinach plastocyanin and turnip cytochrome f in solution. It is the first step in simulating the electron transfer from cytochrome f to photosystem 1 in the lumen of thylakoid. The model is multiparticle and it can describe the interaction of several hundreds of proteins. In our model the interacting proteins are represented as rigid bodies with spatial fixed charges. Translational and rotational motion of proteins is the result of the effect of stochastic Brownian force and electrostatic force. The Poisson–Boltzmann formalism is used to determine the electrostatic potential field generated around the proteins. Using this model we studied the kinetic characteristics of plastocyanin–cytochrome f complex formation for plastocyanin mutants at pH 7 and a variety of ionic strength values.

We present a phenomenological description of cell locomotion on a solid substrate. The material properties of the actin cytoskeleton in the lamellipodium are described by the constitutive equations of a viscous polar gel with intrinsic activity. The polymerization of the gel takes place in a localized region near the leading edge. Using a simple two-dimensional description, we calculate in the steady state the thickness profile of the lamellipodium which at the rear connects to the cell body; we also calculate the flow profiles and the forces exerted on the substrate. The cell velocity is estimated as a function of externally applied forces. Our description is consistent with experimentally observed properties of motile cells such as the existence of a retrograde flow in the lamellipodium and a dipolar force distribution exerted by the cell on the substrate.

Self-organization processes in multicellular aggregates of bacteria and amoebae offer fascinating insights into the evolution of cooperation and differentiation of cells. During myxobacterial development a variety of spatio-temporal patterns emerges such as counterpropagating waves of cell density that are known as rippling. Recently, several models have been introduced that qualitatively reproduce these patterns. All models include active motion and a collision-triggered reversal of individual bacteria. Here, we present a systematic study of a generalized discrete model that is based on similar assumptions as the continuous model by Igoshin et al (2001 Proc. Natl Acad. Sci. USA98 14913). We find counterpropagating as well as unidirectional rippling waves in extended regions of the parameter space. If the interaction strength and the degree of cooperativity are large enough, rippling patterns appear even in the absence of a refractory period. We show for the first time that the experimentally observed double peak in the reversal statistics of bacteria in rippling colonies (Welch and Kaiser 2001 Proc. Natl Acad. Sci. USA98 14907) can be reproduced in simulations of counterpropagating rippling waves which are dominant in experiments. In addition, the reversal statistics in the pre-rippling phase is correctly reproduced.

The nicotinic acetylcholine receptor (nAChR) is the prototypic member of the 'Cys-loop' superfamily of ligand-gated ion channels which mediate synaptic neurotransmission, and whose other members include receptors for glycine, γ-aminobutyric acid and serotonin. Cryo-electron microscopy has yielded a three-dimensional structure of the nAChR in its closed state. However, the exact nature and location of the channel gate remains uncertain. Although the transmembrane pore is constricted close to its center, it is not completely occluded. Rather, the pore has a central hydrophobic zone of radius about 3 Å. Model calculations suggest that such a constriction may form a hydrophobic gate, preventing movement of ions through a channel. We present a detailed and quantitative simulation study of the hydrophobic gating model of the nicotinic receptor, in order to fully evaluate this hypothesis. We demonstrate that the hydrophobic constriction of the nAChR pore indeed forms a closed gate. Potential of mean force (PMF) calculations reveal that the constriction presents a barrier of height about 10 kT to the permeation of sodium ions, placing an upper bound on the closed channel conductance of 0.3 pS. Thus, a 3 Å radius hydrophobic pore can form a functional barrier to the permeation of a 1 Å radius Na⁺ ion. Using a united-atom force field for the protein instead of an all-atom one retains the qualitative features but results in differing conductances, showing that the PMF is sensitive to the detailed molecular interactions.