Simple models for quorum sensing: nonlinear dynamical analysis

Regulatory feedback effects on tissue growth dynamics in a two-stage cell lineage model

Identifying the mechanism of intercellular feedback regulation is critical for the basic understanding of tissue growth control in organisms. In this paper, we analyze a tissue growth model consisting of a single lineage of two cell types regulated by negative feedback signaling molecules that undergo spatial diffusion. By deriving the fixed points for the uniform steady states and carrying out linear stability analysis, phase diagrams are obtained analytically for arbitrary parameters of the model. Two different generic growth modes are found: blow-up growth and final-state controlled growth which are governed by the nontrivial fixed point and the trivial fixed point, respectively, and can be sensitively switched by varying the negative feedback regulation on the proliferation of the stem cells. Analytic expressions for the characteristic timescales for these two growth modes are also derived. Remarkably, the trivial and nontrivial uniform steady states can coexist and a sharp transition occurs in the bistable regime as the relevant parameters are varied. Furthermore, the bistable growth properties allows for the external control to switch between these two growth modes. In addition, the condition for an early accelerated growth followed by a retarded growth can be derived. These analytical results are further verified by numerical simulations and provide insights on the growth behavior of the tissue. Our results are also discussed in the light of possible realistic biological experiments and tissue growth control strategy. Furthermore, by external feedback control of the concentration of regulatory molecules, it is possible to achieve a desired growth mode, as demonstrated with an analysis of boosted growth, catch-up growth and the design for the target of a linear growth dynamic.

Achieving criticality for reservoir computing using environment-induced explosive death

The network of oscillators coupled via a common environment has been widely studied due to its great abundance in nature. We exploit the occurrence of explosive oscillation quenching in a network of non-identical oscillators coupled to each other indirectly via an environment for efficient reservoir computing. At the very edge of explosive transition, the reservoir achieves criticality maximizing its information processing capacity. The efficiency of the reservoir at different configurations is determined by the computational accuracy for different tasks performed by it. We analyze the dependence of accuracy on the dynamical behavior of the reservoir in terms of an order parameter symbolizing the desynchronization of the system. We found that the reservoir achieves the criticality in the steady-state region right at the edge of the hysteresis area. By computing the entropy of the reservoir for different tasks, we confirm that maximum accuracy corresponds to the edge of chaos or the edge of stability for this reservoir.

Ultrasensitivity and noise amplification in a model of V. harveyi quorum sensing

We analyze ultrasensitivity in a model of Vibrio harveyi quorum sensing. We consider a feedforward model consisting of two biochemical networks per cell. The first represents the interchange of a signaling molecule (autoinducer) between the cell cytoplasm and an extracellular domain and the binding of intracellular autoinducer to cognate receptors. The unbound and bound receptors within each cell act as kinases and phosphotases, respectively, which then drive a second biochemical network consisting of a phosphorylation-dephosphorylation cycle. We ignore subsequent signaling pathways associated with gene regulation and the possible modification in the production rate of an autoinducer (positive feedback). We show how the resulting quorum sensing system exhibits ultrasensitivity with respect to changes in cell density. We also demonstrate how quorum sensing can protect against the noise amplification of fast environmental fluctuations in comparison to a single isolated cell.

Regulatory effects on the population dynamics and wave propagation in a cell lineage model

We consider the interplay of cell proliferation, cell differentiation (and de-differentiation), cell movement, and the effect of feedback regulations on the population and propagation dynamics of different cell types in a cell lineage model. Cells are assumed to secrete and respond to negative feedback molecules which act as a control on the cell lineage. The cell densities are described by coupled reaction-diffusion partial differential equations, and the propagating wave front solutions in one dimension are investigated analytically and by numerical solutions. In particular, wavefront propagation speeds are obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effects of the feedback regulations on different stages in the cell lineage. It is found that when the progenitor cell is negatively regulated, the populations of the cell lineage are strongly down-regulated with the steady growth rate of the progenitor cell being driven to zero beyond a critical regulatory strength. An analytic expression for the critical regulation strength in terms of the model parameters is derived and verified by numerical solutions. On the other hand, if the inhibition is acting on the differentiated cells, the change in the population dynamics and wave propagation speed is small. In addition, it is found that only the propagating speed of the progenitor cells is affected by the regulation when the diffusion of the differentiated cells is large. In the presence of de-differentiation, the effect on down-regulating the progenitor population is weakened and there is no effect on the propagation speed due to regulation, suggesting that the effect of regulatory control is diminished by de-differentiation pathways.

Oscillation suppression in indirectly coupled limit cycle oscillators

We study the phenomena of oscillation quenching in a system of limit cycle oscillators which are coupled indirectly via a dynamic environment. The dynamics of the environment is assumed to decay exponentially with some decay parameter. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). The critical curves for the regions of oscillation quenching as a function of coupling strength and decay parameter of the environment are obtained analytically using linear stability analysis and are found to be consistent with the numerics.

Physics of microswimmers--single particle motion and collective behavior: a review

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.

Intrinsic fluctuations of cell migration under different cellular densities

The motility of the Dictyostelium discoideum (DD) cell is studied by video microscopy when the cells are plated on top of an agar plate at different densities, n. It is found that the fluctuating kinetics of the cells can be divided into two normal directions: the cell's forward-moving direction and its normal direction. Along the forward-moving direction, the slope of the amplitude of fluctuation vs. velocity (R||(v)) increases with n, while along the normal direction the slope of R⊥ is independent of n. Both R|| and R⊥ are functions of the cell speed v. The observed linearity in R⊥(v) indicated that the amplitude of orientational fluctuation (κ) of DD cells is a constant independent of v. The independence of the slope of R⊥(v) on n indicated that κ is also not affected by cellular interactions. The independence of κ on both v and n suggests that orientational fluctuation originates from the intrinsic property of motion fluctuations in DD.

Model on cell movement, growth, differentiation and de-differentiation: reaction-diffusion equation and wave propagation

We construct a model for cell proliferation with differentiation into different cell types, allowing backward de-differentiation and cell movement. With different cell types labeled by state variables, the model can be formulated in terms of the associated transition probabilities between various states. The cell population densities can be described by coupled reaction-diffusion partial differential equations, allowing steady wavefront propagation solutions. The wavefront profile is calculated analytically for the simple pure growth case (2-states), and analytic expressions for the steady wavefront propagating speeds and population growth rates are obtained for the simpler cases of 2-, 3- and 4-states systems. These analytic results are verified by direct numerical solutions of the reaction-diffusion PDEs. Furthermore, in the absence of de-differentiation, it is found that, as the mobility and/or self-proliferation rate of the down-lineage descendant cells become sufficiently large, the propagation dynamics can switch from a steady propagating wavefront to the interesting situation of propagation of a faster wavefront with a slower waveback. For the case of a non-vanishing de-differentiation probability, the cell growth rate and wavefront propagation speed are both enhanced, and the wavefront speeds can be obtained analytically and confirmed by numerical solution of the reaction-diffusion equations.

Synchronization and quorum sensing in an ensemble of indirectly coupled chaotic oscillators

The fact that the elements in some realistic systems are influenced by each other indirectly through a common environment has stimulated a new surge of studies on the collective behavior of coupled oscillators. Most of the previous studies, however, consider only the case of coupled periodic oscillators, and it remains unknown whether and to what extent the findings can be applied to the case of coupled chaotic oscillators. Here, using the population density and coupling strength as the tuning parameters, we explore the synchronization and quorum sensing behaviors in an ensemble of chaotic oscillators coupled through a common medium, in which some interesting phenomena are observed, including the appearance of the phase synchronization in the process of progressive synchronization, the various periodic oscillations close to the quorum sensing transition, and the crossover of the critical population density at the transition. These phenomena, which have not been reported for indirectly coupled periodic oscillators, reveal a corner of the rich dynamics inherent in indirectly coupled chaotic oscillators, and are believed to have important implications to the performance and functionality of some realistic systems.