Inertia of amoebic cell locomotion as an emergent collective property of the cellular dynamics

Non-Brownian dynamics and strategy of amoeboid cell locomotion

Amoeboid cells such as Dictyostelium discoideum and Madin-Darby canine kidney cells show the non-Brownian dynamics of migration characterized by the superdiffusive increase of mean-squared displacement. In order to elucidate the physical mechanism of this non-Brownian dynamics, a computational model is developed which highlights a group of inhibitory molecules for actin polymerization. Based on this model, we propose a hypothesis that inhibitory molecules are sent backward in the moving cell to accumulate at the rear of cell. The accumulated inhibitory molecules at the rear further promote cell locomotion to form a slow positive feedback loop of the whole-cell scale. The persistent straightforward migration is stabilized with this feedback mechanism, but the fluctuation in the distribution of inhibitory molecules and the cell shape deformation concurrently interrupt the persistent motion to turn the cell into a new direction. A sequence of switching behaviors between persistent motions and random turns gives rise to the superdiffusive migration in the absence of the external guidance signal. In the complex environment with obstacles, this combined process of persistent motions and random turns drives the simulated amoebae to solve the maze problem in a highly efficient way, which suggests the biological advantage for cells to bear the non-Brownian dynamics.

Cortical factor feedback model for cellular locomotion and cytofission

Eukaryotic cells can move spontaneously without being guided by external cues. For such spontaneous movements, a variety of different modes have been observed, including the amoeboid-like locomotion with protrusion of multiple pseudopods, the keratocyte-like locomotion with a widely spread lamellipodium, cell division with two daughter cells crawling in opposite directions, and fragmentations of a cell to multiple pieces. Mutagenesis studies have revealed that cells exhibit these modes depending on which genes are deficient, suggesting that seemingly different modes are the manifestation of a common mechanism to regulate cell motion. In this paper, we propose a hypothesis that the positive feedback mechanism working through the inhomogeneous distribution of regulatory proteins underlies this variety of cell locomotion and cytofission. In this hypothesis, a set of regulatory proteins, which we call cortical factors, suppress actin polymerization. These suppressing factors are diluted at the extending front and accumulated at the retracting rear of cell, which establishes a cellular polarity and enhances the cell motility, leading to the further accumulation of cortical factors at the rear. Stochastic simulation of cell movement shows that the positive feedback mechanism of cortical factors stabilizes or destabilizes modes of movement and determines the cell migration pattern. The model predicts that the pattern is selected by changing the rate of formation of the actin-filament network or the threshold to initiate the network formation.

Nonequilibrium actin polymerization treated by a truncated rate-equation method

Actin polymerization time courses can exhibit rich nonequilibrium dynamics that have not yet been accurately described by simplified rate equations. Sophisticated stochastic simulations and elaborate recursion schemes have been used to model the nonequilibrium dynamics resulting from the hydrolysis and subsequent exchange of the nucleotide bound within the actin molecules. In this work, we use a truncation approach to derive a set of readily accessible deterministic rate equations which are significantly simpler than previous attempts at such modeling. These equations may be incorporated into whole-cell motility models which otherwise quickly become computationally inaccessible if polymerization of individual actin filaments is stochastically simulated within a virtual cell. Our equations accurately predict the relative concentrations of both monomeric and polymerized actin in differing nucleotide hydrolysis states throughout entire polymerization time courses nucleated via seed filaments. We extend our model to include the effects of capping protein. We also detail how our rate-equation method may be used to extract key parameters from experimental data.

Evolution of microorganism locomotion induced by starvation

The search strategies of many organisms play a fundamental role in their competition to survive in a given environment. In this context, the propulsion systems of microorganisms have evolved during life history, to optimize the suitable use of energy they take from nutrients. Starting from a model for the motion of Brownian objects with internal energy depot, we show that the propulsion system of microorganisms has an optimal regimen while searching for new sources of food. Bacteria with a too low or too high energy expenditure in propulsion, moving in a nutrient-depleted environment, do not reach remote distances. In this sense, the mean square displacement has a maximum for a finite value of the propulsion rate. Species using the most efficient locomotion system have a considerable advantage for survival in hostile environments, a common situation in the ocean. Moreover, we found the existence of a lower size limit for useful locomotion. This suggests that, for organisms whose linear dimensions are below a certain threshold, it is advantageous not to use any propulsion mechanism at all, a result that is in agreement with what is observed in nature.

Modulation of the reaction rate of regulating protein induces large morphological and motional change of amoebic cell

Morphologies of moving amoebae are categorized into two types. One is the "neutrophil" type in which the long axis of cell roughly coincides with its moving direction. This type of cell extends a leading edge at the front and retracts a narrow tail at the rear, whose shape has been often drawn as a typical amoeba in textbooks. The other one is the "keratocyte" type with widespread lamellipodia along the front side arc. Short axis of cell in this type roughly coincides with its moving direction. In order to understand what kind of molecular feature causes conversion between two types of morphologies, and how two typical morphologies are maintained, a mathematical model of amoebic cells is developed. This model describes movement of cell and intracellular reactions of activator, inhibitor and actin filaments in a unified way. It is found that the producing rate of activator is a key factor of conversion between two types. This model also explains the observed data that the keratocyte type cells tend to rapidly move along a straight line. The neutrophil type cells move along a straight line when the moving velocity is small, but they show fluctuated motions deviating from a line when they move as fast as the keratocyte type cells. Efficient energy consumption in the neutrophil type cells is predicted.