Disrupting microtubule network immobilizes amoeboid chemotactic receptor in the plasma membrane.

Signaling cascades are initiated in the plasma membrane via activation of one molecule by another. The interaction depends on the mutual availability of the molecules to each other and this is determined by their localization and lateral diffusion in the cell membrane. The cytoskeleton plays a very important role in this process by enhancing or restricting the possibility of the signaling partners to meet in the plasma membrane. In this study we explored the mode of diffusion of the cAMP receptor, cAR1, in the plasma membrane of Dictyostelium discoideum cells and how this is regulated by the cytoskeleton. Single-particle tracking of fluorescently labeled cAR1 using Total Internal Reflection Microscopy showed that 70% of the cAR1 molecules were mobile. These receptors showed directed motion and we demonstrate that this is not because of tracking along the actin cytoskeleton. Instead, destabilization of the microtubules abolished cAR1 mobility in the plasma membrane and this was confirmed by Fluorescence Recovery after Photobleaching. As a result of microtubule stabilization, one of the first downstream signaling events, the jump of the PH domain of CRAC, was decreased. These results suggest a role for microtubules in cAR1 dynamics and in the ability of cAR1 molecules to interact with their signaling partners.

Receptor-mediated and intrinsic polarization and their interaction in chemotaxing cells.

Polarization--the clear and persistent localization of different signaling molecules to opposite ends of the cell-is critical for effective chemotaxis in eukaryotic systems. In many systems, polarization can also occur without an externally imposed chemical gradient. We build a modeling framework to study the relationship between the intrinsic capacity for polarization, and that induced by an external gradient. Working within this framework, we analyze different scenarios for the interaction of these pathways. The models are qualitatively simplified, motivated by known properties of the signaling pathways. We also examine the possible role of nonlinear transitions occurring in the polarization pathways. The modeling framework generates testable predictions regarding the relationship between intrinsic polarization and that induced during chemotaxis, and is the first step toward a systematic analysis of the interaction between these pathways.

Robustness analysis of biochemical network models.

Biological systems that have been experimentally verified to be robust to significant changes in their environments require mathematical models that are themselves robust. In this context, a necessary condition for model robustness is that the model dynamics should not be sensitive to small variations in the model's parameters. Robustness analysis problems of this type have been extensively studied in the field of robust control theory and have been found to be very difficult to solve in general. The authors describe how some tools from robust control theory and nonlinear optimisation can be used to analyse the robustness of a recently proposed model of the molecular network underlying adenosine 3',5'-cyclic monophosphate (cAMP) oscillations observed in fields of chemotactic Dictyostelium cells. The network model, which consists of a system of seven coupled nonlinear differential equations, accurately reproduces the spontaneous oscillations in cAMP observed during the early development of D. discoideum. The analysis by the authors reveals, however, that very small variations in the model parameters can effectively destroy the required oscillatory dynamics. A biological interpretation of the analysis results is that correct functioning of a particular positive feedback loop in the proposed model is crucial to maintaining the required oscillatory dynamics.

A modelling framework describing the enzyme regulation of membrane lipids underlying gradient perception in Dictyostelium cells II: input-output analysis.

Spatial sensing in Dictyostelium involves localization of the phosphoinositide lipids PI(3,4,5)P3 and PI(3,4)P2 at the leading edge of the cell in response to an external gradient. We have previously proposed a modelling framework describing the regulation of these lipids by the enzymes PI3K and PTEN. In this paper we analyse this regulation from an input-output perspective. When the inputs are homogeneous, we obtain explicit analytical expressions for the lipid concentrations as a function of enzyme concentrations and model parameters. We also show that the system can be cast as an open-loop bilinear control system, and employ control engineering tools to show that a local three-dimensional region in the four-dimensional phase space can be accessed by temporally varying either or both enzyme concentrations. For spatially graded enzyme profiles, we show that diffusion limits the extent to which lipid profiles can be manipulated by enzymes. However, we also demonstrate that for certain ranges of network parameters, increasing lipid diffusion can lead to an increase in steady-state leading-edge concentrations of PI(3,4,5)P3 or PI(3,4)P2, even though all lipid diffusion coefficients are equal. Finally, in order to determine the extent to which lipid profiles can be regulated by the enzymes, we formulate and solve inverse problems, where we determine the enzyme profiles required to realize particular lipid profiles at steady state.

A modeling framework describing the enzyme regulation of membrane lipids underlying gradient perception in Dictyostelium cells.

Gradient perception describes the process by which information about the chemoattractant concentration field surrounding a cell is transformed into an internal signal which is responsible for directed cell motion. Recently, many important biochemical details in immobilized and mobile Dictyostelium cells have been uncovered regarding the roles of enzymes regulating phosphoinositide lipids on the cell membrane which are responsible for gradient perception. We report on a modeling framework that describes the relationship between the membrane concentration of the primary 3'phosphoinositide lipids and the enzymes which regulate them. The model takes the form of partial differential equations describing the membrane concentration of these lipids. Working within this framework, we describe mechanisms which can be responsible for spatial amplification of these lipids and which do not employ lipid-enzyme feedback. An analysis of a basic module underlying this process is also performed.

Uncovering directional sensing: where are we headed?

We survey aspects of directional sensing, i.e. how a cell interprets differences in the external concentration of a chemoattractant to guide its motion, from the perspective of systems biology. We focus on questions that need to be addressed using a combination of modelling and experimental approaches. After briefly summarising the ideas underlying recent modelling efforts, we discuss a variety of experimental questions which are motivated by these models. Some of these questions focus on basic features of the chemotactic response, without involving much biochemistry, while others focus on filling some of the gaps in the biochemistry, which have been brought to light by the models. The emphasis is on systematic quantitative experiments that will unambiguously resolve many of these issues. Finally, we describe some current challenges for theoretical modelling and survey some of the theoretical tools and approaches employed to model the chemotaxis pathways.

Analysis of the signal transduction properties of a module of spatial sensing in eukaryotic chemotaxis.

The movement of cells in response to a gradient in chemical concentration-known as chemotaxis-is crucial for the proper functioning of uni- and multicellular organisms. How a cell senses the chemical concentration gradient surrounding it, and what signal is transmitted to its motion apparatus is known as gradient sensing. The ability of a cell to sense gradients persists even when the cell is immobilized (i.e., its motion apparatus is deactivated). This suggests that important features of gradient sensing can be studied in isolation, decoupling this phenomenon from the movement of the cell. A mathematical model for gradient sensing in Dictyostelium cells and neutrophils was recently proposed. This consists of an adaptation/spatial sensing module. This spatial sensing module feeds into an amplification module, magnifying the effects of the former. In this paper, we analyze the spatial sensing module in detail and examine its signal transduction properties. We examine the response of this module to several inputs of experimental and biological relevance.