Pablo A. Iglesias

Models of Eukaryotic Gradient Sensing: Application to Chemotaxis of Amoebae and Neutrophils

Eukaryotic cells can detect shallow gradients of chemoattractants with exquisite precision and respond quickly to changes in the gradient steepness and direction. Here, we describe a set of models explaining both adaptation to uniform increases in chemoattractant and persistent signaling in response to gradients. We demonstrate that one of these models can be mapped directly onto the biochemical signal-transduction pathways underlying gradient sensing in amoebae and neutrophils. According to this scheme, a locally acting activator (PI3-kinase) and a globally acting inactivator (PTEN or a similar phosphatase) are coordinately controlled by the G-protein activation. This signaling system adapts perfectly to spatially homogeneous changes in the chemoattractant. In chemoattractant gradients, an imbalance between the action of the activator and the inactivator results in a spatially oriented persistent signaling, amplified by a substrate supply-based positive feedback acting through small G-proteins. The amplification is activated only in a continuous presence of the external signal gradient, thus providing the mechanism for sensitivity to gradient alterations. Finally, based on this mapping, we make predictions concerning the dynamics of signaling. We propose that the underlying principles of perfect adaptation and substrate supply-based positive feedback will be found in the sensory systems of other chemotactic cell types.

MAPK-mediated bimodal gene expression and adaptive gradient sensing in yeast.

The mating pathway in Saccharomyces cerevisiae has been the focus of considerable research effort, yet many quantitative aspects of its regulation still remain unknown. Using an integrated approach involving experiments in microfluidic chips and computational modelling, we studied gene expression and phenotypic changes associated with the mating response under well-defined pheromone gradients. Here we report a combination of switch-like and graded pathway responses leading to stochastic phenotype determination in a specific range of pheromone concentrations. Furthermore, we show that these responses are critically dependent on mitogen-activated protein kinase (MAPK)-mediated regulation of the activity of the pheromone-response-specific transcription factor, Ste12, as well as on the autoregulatory feedback of Ste12. In particular, both the switch-like characteristics and sensitivity of gene expression in shmooing cells to pheromone concentration were significantly diminished in cells lacking Kss1, one of the MAP kinases activated in the mating pathway. In addition, the dynamic range of gradient sensing of Kss1-deficient cells was reduced compared with wild type. We thus provide unsuspected functional significance for this kinase in regulation of the mating response.

Navigating through models of chemotaxis

Chemotaxis in eukaryotic cells involves the coordination of several related but separable processes: motility, polarization, and gradient sensing. Mathematical models that have been proposed to explain chemotaxis typically focus on only one of these processes. We summarize the strengths and weaknesses of the models and point out the need for an integrated model.

Chromosome Alignment and Segregation Regulated by Ubiquitination of Survivin

Proper chromosome segregation requires the attachment of sister kinetochores to microtubules from opposite spindle poles to form bi-oriented chromosomes on the metaphase spindle. The chromosome passenger complex containing Survivin and the kinase Aurora B regulates this process from the centromeres. We report that a de-ubiquitinating enzyme, hFAM, regulates chromosome alignment and segregation by controlling both the dynamic association of Survivin with centromeres and the proper targeting of Survivin and Aurora B to centromeres. Survivin is ubiquitinated in mitosis through both Lys48 and Lys63 ubiquitin linkages. Lys63 de-ubiquitination mediated by hFAM is required for the dissociation of Survivin from centromeres, whereas Lys63 ubiquitination mediated by the ubiquitin binding protein Ufd1 is required for the association of Survivin with centromeres. Thus, ubiquitinaton regulates dynamic protein-protein interactions and chromosome segregation independently of protein degradation.

State-space approach to discrete-time H∞ control

Abstract State-space solutions to a discrete-time ℋ∞ problem are given. For a given number γ>0we give a characterization of all controllers such that the ℋ ∞ norm of the closed-loop transfer function is less than γ The approach taken is based on the solution of two Riccati equations using the stable deflating subspace of a symplectic pencil. This ensures that no unnecessary assumptions on the ‘A’ matrix on the realization of the transfer function are needed. While the results are the direct analogues of those in the continuous time, the state-space derivation is considerably more difficult.

Cells navigate with a local-excitation, global-inhibition-biased excitable network

Cells have an internal compass that enables them to move along shallow chemical gradients. As amoeboid cells migrate, signaling events such as Ras and PI3K activation occur spontaneously on pseudopodia. Uniform stimuli trigger a symmetric response, whereupon cells stop and round up; then localized patches of activity appear as cells spread. Finally cells adapt and resume random migration. In contrast, chemotactic gradients continuously direct signaling events to the front of the cell. Local-excitation, global-inhibition (LEGI) and reaction–diffusion models have captured some of these features of chemotaxing cells, but no system has explained the complex response kinetics, sensitivity to shallow gradients, or the role of recently observed propagating waves within the actin cytoskeleton. We report here that Ras and PI3K activation move in phase with the cytoskeleton events and, drawing on all of these observations, propose the LEGI-biased excitable network hypothesis. We formulate a model that simulates most of the behaviors of chemotactic cells: In the absence of stimulation, there are spontaneous spots of activity. Stimulus increments trigger an initial burst of patches followed by localized secondary events. After a few minutes, the system adapts, again displaying random activity. In gradients, the activity patches are directed continuously and selectively toward the chemoattractant, providing an extraordinary degree of amplification. Importantly, by perturbing model parameters, we generate distinct behaviors consistent with known classes of mutants. Our study brings together heretofore diverse observations on spontaneous cytoskeletal activity, signaling responses to temporal stimuli, and spatial gradient sensing into a unified scheme.

PIP3-independent activation of TorC2 and PKB at the cell's leading edge mediates chemotaxis.

BACKGROUND Studies show that high phosphotidylinositol 3,4,5-trisphosphate (PIP(3)) promotes cytoskeletal rearrangements and alters cell motility and chemotaxis, possibly through activation of protein kinase Bs (PKBs). However, chemotaxis can still occur in the absence of PIP(3), and the identities of the PIP(3)-independent pathways remain unknown. RESULTS Here, we outline a PIP(3)-independent pathway linking temporal and spatial activation of PKBs by Tor complex 2 (TorC2) to the chemotactic response. Within seconds of stimulating Dictyostelium cells with chemoattractant, two PKB homologs, PKBA and PKBR1, mediate transient phosphorylation of at least eight proteins, including Talin, PI4P 5-kinase, two Ras GEFs, and a RhoGap. Surprisingly, all of the substrates are phosphorylated with normal kinetics in cells lacking PI 3-kinase activity. Cells deficient in TorC2 or PKB activity show reduced phosphorylation of the endogenous substrates and are impaired in chemotaxis. The PKBs are activated through phosphorylation of their hydrophobic motifs via TorC2 and subsequent phosphorylation of their activation loops. These chemoattractant-inducible events are restricted to the cells leading edge even in the absence of PIP(3). Activation of TorC2 depends on heterotrimeric G protein function and intermediate G proteins, including Ras GTPases. CONCLUSIONS The data lead to a model where cytosolic TorC2, encountering locally activated small G protein(s) at the leading edge of the cell, becomes activated and phosphorylates PKBs. These in turn phosphorylate a series of signaling and cytoskeletal proteins, thereby regulating directed migration.

Interactions between Myosin and Actin Crosslinkers Control Cytokinesis Contractility Dynamics and Mechanics

INTRODUCTION Contractile networks are fundamental to many cellular functions, particularly cytokinesis and cell motility. Contractile networks depend on myosin-II mechanochemistry to generate sliding force on the actin polymers. However, to be contractile, the networks must also be crosslinked by crosslinking proteins, and to change the shape of the cell, the network must be linked to the plasma membrane. Discerning how this integrated network operates is essential for understanding cytokinesis contractility and shape control. Here, we analyzed the cytoskeletal network that drives furrow ingression in Dictyostelium. RESULTS We establish that the actin polymers are assembled into a meshwork and that myosin-II does not assemble into a discrete ring in the Dictyostelium cleavage furrow of adherent cells. We show that myosin-II generates regional mechanics by increasing cleavage furrow stiffness and slows furrow ingression during late cytokinesis as compared to myoII nulls. Actin crosslinkers dynacortin and fimbrin similarly slow furrow ingression and contribute to cell mechanics in a myosin-II-dependent manner. By using FRAP, we show that the actin crosslinkers have slower kinetics in the cleavage furrow cortex than in the pole, that their kinetics differ between wild-type and myoII null cells, and that the protein dynamics of each crosslinker correlate with its impact on cortical mechanics. CONCLUSIONS These observations suggest that myosin-II along with actin crosslinkers establish local cortical tension and elasticity, allowing for contractility independent of a circumferential cytoskeletal array. Furthermore, myosin-II and actin crosslinkers may influence each other as they modulate the dynamics and mechanics of cell-shape change.

Quantifying robustness of biochemical network models

BackgroundRobustness of mathematical models of biochemical networks is important for validation purposes and can be used as a means of selecting between different competing models. Tools for quantifying parametric robustness are needed.ResultsTwo techniques for describing quantitatively the robustness of an oscillatory model were presented and contrasted. Single-parameter bifurcation analysis was used to evaluate the stability robustness of the limit cycle oscillation as well as the frequency and amplitude of oscillations. A tool from control engineering – the structural singular value (SSV) – was used to quantify robust stability of the limit cycle. Using SSV analysis, we find very poor robustness when the models parameters are allowed to vary.ConclusionThe results show the usefulness of incorporating SSV analysis to single parameter sensitivity analysis to quantify robustness.

Mechanosensing through Cooperative Interactions between Myosin II and the Actin Crosslinker Cortexillin I

BACKGROUND Mechanosensing governs many processes from molecular to organismal levels, including during cytokinesis where it ensures successful and symmetrical cell division. Although many proteins are now known to be force sensitive, myosin motors with their ATPase activity and force-sensitive mechanical steps are well poised to facilitate cellular mechanosensing. For a myosin motor to experience tension, the actin filament must also be anchored. RESULTS Here, we find a cooperative relationship between myosin II and the actin crosslinker cortexillin I where both proteins are essential for cellular mechanosensory responses. Although many functions of cortexillin I and myosin II are dispensable for cytokinesis, all are required for full mechanosensing. Our analysis demonstrates that this mechanosensor has three critical elements: the myosin motor where the lever arm acts as a force amplifier, a force-sensitive bipolar thick-filament assembly, and a long-lived actin crosslinker, which anchors the actin filament so that the motor may experience tension. We also demonstrate that a Rac small GTPase inhibits this mechanosensory module during interphase, allowing the module to be primarily active during cytokinesis. CONCLUSIONS Overall, myosin II and cortexillin I define a cellular-scale mechanosensor that controls cell shape during cytokinesis. This system is exquisitely tuned through the enzymatic properties of the myosin motor, its lever arm length, and bipolar thick-filament assembly dynamics. The system also requires cortexillin I to stably anchor the actin filament so that the myosin motor can experience tension. Through this cross-talk, myosin II and cortexillin I define a cellular-scale mechanosensor that monitors and corrects shape defects, ensuring symmetrical cell division.