Gradients in the self-organization of the mitotic spindle

Recent evidence points at a role of protein interaction gradients around chromatin in mitotic spindle morphogenesis in large eukaryotic cells. Here, we explain how gradients can arise over distances of tens of microns around supramolecular structures from mixtures of soluble molecules. We discuss how coupled sets of such reaction diffusion processes generate the spatial information that determines the local dynamics of microtubules required to form a bipolar spindle. We argue that such reaction diffusion processes are involved in the self-organization of supramolecular structures in the cell.     

Cell-to-cell variability in deformations across compressed myoblasts

Many biological consequences of external mechanical loads applied to cells depend on localized cell deformations rather than on average whole-cell-body deformations. Such localized intracellular deformations are likely to depend, in turn, on the individual geometrical features of each cell, e.g., the local surface curvatures or the size of the nucleus, which always vary from one cell to another, even within the same culture. Our goal here was to characterize cell-to-cell variabilities in magnitudes and distribution patterns of localized tensile strains that develop in the plasma membrane (PM) and nuclear surface area (NSA) of compressed myoblasts, in order to identify resemblance or differences in mechanical performances across the cells. For this purpose, we utilized our previously developed confocal microscopy-based three-dimensional cell-specific finite element modeling methodology. Five different C2C12 undifferentiated cells belonging to the same culture were scanned confocally and modeled, and were then subjected to compression in the simulation setting. We calculated the average and peak tensile strains in the PM and NSA, the percentage of PM area subjected to tensile strains above certain thresholds and the coefficient of variation (COV) in average and peak strains. We found considerable COV values in tensile strains developing at the PM and NSA (up to ~35%) but small external compressive deformations induced greater variabilities in intracellular strains across cells compared to large deformations. Interestingly, the external deformations needed to cause localized PM or NSA strains exceeding each threshold were very close across the different cells. Better understanding of variabilities in mechanical performances of cells-either of the same type or of different types-is important for interpreting experimental data in any experiments involving delivery of mechanical loads to cells.     

Statistical study of rapid mechanodependent cell movements in deformed explants of african clawed frog <Emphasis Type="Italic">Xenopus laevis</Emphasis> embryonic tissues

Computer analysis of artificially deformed (stretched or compressed) double explants (sandwiches) of the blastocoel roof (BRs) and suprablastoporal region (SBRs) of African clawed frog Xenopus laevis early gastrula has been performed using frames of time-lapse microfilming. During the first 14 min after cutting off, the velocities and displacement angles of several hundreds of cells relative to one another, as well as to fixed points and the extension axis, were measured in the control and deformed samples. It has been found that the deformation of samples leads to a rapid reorientation of large cell masses and increase in the velocities of movements along the extension axes or perpendicularly to the compression axes. In addition, an increase in the velocities of mutual cell displacements in the stretched BRs and cell convergence to the extension axes have been observed. Comparison of different angular sectors demonstrates a statistically significant positive correlation between the mean velocities of cell movements and the number of cells moving within an individual sector. This suggests cooperativity of mechanodependent cell movements. In general, these results demonstrate an important role of mechanical factors in regulation of collective cell movements.     

Role of mechano-dependent cell movements in the establishment of spatial organization of axial rudiments in <Emphasis Type="Italic">Xenopus laevis</Emphasis> embryos

Trajectories of individual cell movements and patterns of differentiation in the axial rudiments in suprablastoporal areas (SBA) in whole embryos of Xenopus laevis artificially stretched in the transverse direction up to 120–200% from the initial length at the early gastrula stage were mapped. We observed the impairment of anisotropic cell movements of longitudinal stretching and latero-medial convergence inherent for SBA. Axial rudiments occurred in all cases, but their location was completely impaired and dramatically different from the normal topology for moderate (120–140%) stretching. Stronger stretching caused a partial ordering of the whole axial complex and its reorientation toward stretching. We concluded that induction factors determine short-range order in their arrangement in SBA, whereas anisotropic cell movements in any direction are needed for long-range order. Moderate transverse stretching destroys normally oriented anisotropy, but it is not enough for establishment of the anisotropy oriented perpendicular to the normal. This explains the disorder at light stretching. The main conclusion of this study is that anisotropic tensions of embryonic tissues play role of long-range order parameters of cell differentiation.     

Statistical study of rapid mechanodependent cell movements in deformed explants of African clawed frog Xenopus laevis embryonic tissues

Computer analysis of artificially deformed (stretched or compressed) double explants (sandwiches) of the blastocoel roof (BRs) and suprablastoporal region (SBRs) of African clawed frog Xenopus laevis early gastrula has been performed using frames of time-lapse microfilming. During the first 14 min after cutting off, the velocities and displacement angles of several hundreds of cells relative to one another, as well as to fixed points and the extension axis, were measured in the control and deformed samples. It has been found that the deformation of samples leads to a rapid reorientation of large cell masses and increase in the velocities of movements along the extension axes or perpendicularly to the compression axes. In addition, an increase in the velocities of mutual cell displacements in the stretched BRs and cell convergence to the extension axes have been observed. Comparison of different angular sectors demonstrates a statistically significant positive correlation between the mean velocities of cell movements and the number of cells moving within an individual sector. This suggests cooperativity of mechanodependent cell movements. In general, these results demonstrate an important role of mechanical factors in regulation of collective cell movements.     

Chromosome fiber dynamics and congression oscillations in metaphase PtK2 cells at 23 degrees C

A bioriented chromosome is tethered to opposite spindle poles during congression by bundles of kinetochore microtubules (kMts). At room temperature, kinetochore fibers are a dominant component of mitotic spindles of PtK2 cells. PtK2 cells at room temperature were injected with purified tubulin covalently bound to DTAF and congression movements of individual chromosomes were recorded in time lapse. Congression movements of bioriented chromosomes between the poles occur over distances of 4.5 microns or greater. DTAF-tubulin injection had no effect on either the velocity or extent of these movements. Other cells were lysed, fixed, and the location of DTAF-tubulin incorporation was detected from digitally processed images of indirect immunofluorescence of an antibody to DTAF. Microtubules were labeled with an anti-beta tubulin antibody. At 2-5 minutes after injection, concentrated DTAF-tubulin staining was seen in the kinetochore fibers proximal to the kinetochores; a low concentration of DTAF-tubulin staining occurred at various sites through the remaining length of the fibers toward the pole. Kinetochore fibers in the same cell displayed different lengths (0.2 to 4 microns) of concentrated DTAF-tubulin incorporation proximal to the kinetochore, as did sister kinetochore fibers. Ten minutes after injection, the lengths of DTAF-containing chromosomal fibers were greater than expected if incorporation resulted solely from the lengthening of kinetochore microtubules due to congression movements of the chromosomes. Besides incorporation as a result of chromosome movement, two other mechanisms might explain the length of the DTAF-containing segments: 1) a poleward flux of tubulin subunits (Mitchison, 1989) or 2) capture of DTAF-containing nonkinetochore microtubules.     

A Novel Method to Produce Immobilised Biomolecular Concentration Gradients to Study Cell Activities: Design and Modelling

It is well known that many cell functions are activated by chemical signals with a time and space-dependent profile. To mimic these profiles in vitro, it is necessary to develop a system that is able to generate concentration gradients with a resolution similar to that perceived by cells, which is around nanomolar with a spatial resolution of a few tens of microns. Many devices capable of generating steady-state concentration gradients have been developed using continuous flow micro-fluidic techniques. However, these systems cannot reproduce the immobilised concentration gradients that are present in the extracellular matrix. For this reason, we have developed a new gradient generator to enable precise and reproducible studies on the effects of immobilised concentration gradients on cell behaviour. A well-known gradient of a desired molecule was generated on the bottom surface of a hydrogel, which was then used as a stamp to immobilise the molecule on a functionalised substrate. A concentration gradient was thus obtained using a simple silane-based chemical reaction. To validate the method, image analysis was performed on glass slides printed with fluorescein isothiocyanate (FITC)- collagen and FITC-poly-lysine concentration gradients. Preliminary cell adhesion tests were also carried out by seeding NIH-3T3 and mesencephalic cells on lab-glass slides printed with concentration profiles of collagen and poly-lysine, respectively.     

Micromechanical mapping of live cells by multiple-particle-tracking microrheology

This paper introduces the method of live-cell multiple-particle-tracking microrheology (MPTM), which quantifies the local mechanical properties of living cells by monitoring the Brownian motion of individual microinjected fluorescent particles. Particle tracking of carboxylated microspheres imbedded in the cytoplasm produce spatial distributions of cytoplasmic compliances and frequency-dependent viscoelastic moduli. Swiss 3T3 fibroblasts are found to behave like a stiff elastic material when subjected to high rates of deformations and like a soft liquid at low rates of deformations. By analyzing the relative contributions of the subcellular compliances to the mean compliance, we find that the cytoplasm is much more mechanically heterogeneous than reconstituted actin filament networks. Carboxylated microspheres embedded in cytoplasm through endocytosis and amine-modified polystyrene microspheres, which are microinjected or endocytosed, often show directed motion and strong nonspecific interactions with cytoplasmic proteins, which prevents computation of local moduli from the microsphere displacements. Using MPTM, we investigate the mechanical function of alpha-actinin in non-muscle cells: alpha-actinin-microinjected cells are stiffer and yet mechanically more heterogeneous than control cells, in agreement with models of reconstituted cross-linked actin filament networks. MPTM is a new type of functional microscopy that can test the local, rate-dependent mechanical and ultrastructural properties of living cells.     

Rapid firing rates from mechanosensory neurons in copepod antennules

Small detection distances coupled with rapid movements require copepods to respond to stimuli with behavioral latencies on the order of milliseconds. Receiving adequate sensory information in such a short time necessitates extremely rapid firing rates of the efferent receptors. Here we show that copepod mechanoreceptors can fire at frequencies up to 5 kHz in response to fluid mechanical stimuli. Neural activity at these frequencies enables these animals to code for a range of fluid velocities thus providing important information regarding the nature of different fluid disturbances.     

Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics

This study introduces a new confocal microscopy-based three-dimensional cell-specific finite element (FE) modeling methodology for simulating cellular mechanics experiments involving large cell deformations. Three-dimensional FE models of undifferentiated skeletal muscle cells were developed by scanning C2C12 myoblasts using a confocal microscope, and then building FE model geometries from the z-stack images. Strain magnitudes and distributions in two cells were studied when the cells were subjected to compression and stretching, which are used in pressure ulcer and deep tissue injury research to induce large cell deformations. Localized plasma membrane and nuclear surface area (NSA) stretches were observed for both the cell compression and stretching simulation configurations. It was found that in order to induce large tensile strains (>5%) in the plasma membrane and NSA, one needs to apply more than ～15% of global cell deformation in cell compression tests, or more than ～3% of tensile strains in the elastic plate substrate in cell stretching experiments. Utilization of our modeling can substantially enrich experimental cellular mechanics studies in classic cell loading designs that typically involve large cell deformations, such as static and cyclic stretching, cell compression, micropipette aspiration, shear flow and hydrostatic pressure, by providing magnitudes and distributions of the localized cellular strains specific to each setup and cell type, which could then be associated with the applied stimuli.     

Self-Generated Chemoattractant Gradients: Attractant Depletion Extends the Range and Robustness of Chemotaxis

Chemotaxis is fundamentally important, but the sources of gradients in vivo are rarely well understood. Here, we analyse self-generated chemotaxis, in which cells respond to gradients they have made themselves by breaking down globally available attractants, using both computational simulations and experiments. We show that chemoattractant degradation creates steep local gradients. This leads to surprising results, in particular the existence of a leading population of cells that moves highly directionally, while cells behind this group are undirected. This leading cell population is denser than those following, especially at high attractant concentrations. The local gradient moves with the leading cells as they interact with their surroundings, giving directed movement that is unusually robust and can operate over long distances. Even when gradients are applied from external sources, attractant breakdown greatly changes cells'' responses and increases robustness. We also consider alternative mechanisms for directional decision-making and show that they do not predict the features of population migration we observe experimentally. Our findings provide useful diagnostics to allow identification of self-generated gradients and suggest that self-generated chemotaxis is unexpectedly universal in biology and medicine.     

Possible role of cell cycle-dependent morphology, geometry, and mechanical properties in tumor cell metastasis.

Studies that examine the shear- and abrasion-sensitivity of proliferating cells are important in order to understand the behavior of hybridoma cells in bioreactor culture and metastasizing cancer cells in the bloodstream. Little is known about the link between morphology, structure, and mechanical properties of a given cell line, especially with respect to variations throughout the cell cycle. In our experiments with GAP A3 hybridoma cells, distinct cell morphologies were identified and correlated with phases of the cell cycle by video microscopic observation of synchronized cells, and of individual cells that were followed throughout their cell cycle. Micropipet manipulation was used to measure the geometrical (cell volume) and mechanical (apparent cell viscosity) properties of single cells. As the cell cycle progressed at 37 degrees C, an increase in cell volume from 1400 microns 3 to 5700 microns 3 was accompanied by an increase in apparent cell viscosity from 430 poise to 12,000 poise, consistent with an accumulation of more cytoplasmic material in the "older" cells. Hybridomas are representative of the various leukemias derived from hemopoietic cells, and even though as a whole, they appeared to be rather shear-insensitive, the wide range of property values demonstrates that a given cell line cannot be characterized by a single value for any one property, and that properties must be related to the cell cycle when considering proliferating cells. It is interesting to see if distinct stages in the metastatic sequence of events might correlate with any of these physical features of the cell cycle, irrespective of cell type or cell line. For example, the cytokinetic doublet could represent a fragile structure that may fail and produce cell death under fluid-shear conditions that would not affect the cells at any other stage in the cell cycle. Identifying such cell cycle-dependent features in metastasizing cancer cells could lead to a better understanding of the metastatic process and to possible clinical treatments directed at making cells more shear- and abrasion-sensitive, and therefore, more likely to be killed by the natural hydrodynamic forces of the circulatory system.     

A phase-contrast microscopy-based method for modeling the mechanical behavior of mesenchymal stem cells

We present three-dimensional (3D) finite element (FE) models of single, mesenchymal stem cells (MSCs), generated from images obtained by optical phase-contrast microscopy and used to quantify the structural responses of the studied cells to externally applied mechanical loads. Mechanical loading has been shown to affect cell morphology and structure, phenotype, motility and other biological functions. Cells experience mechanical loads naturally, yet under prolonged or sizable loading, damage and cell death may occur, which motivates research regarding the structural behavior of loaded cells. For example, near the weight-bearing boney prominences of the buttocks of immobile persons, tissues may become highly loaded, eventually leading to massive cell death that manifests as pressure ulcers. Cell-specific computational models have previously been developed by our group, allowing simulations of cell deformations under compressive or stretching loads. These models were obtained by reconstructing specific cell structures from series of 2D fluorescence, confocal image-slices, requiring cell-specific fluorescent-staining protocols and costly (confocal) microscopy equipment. Alternative modeling approaches represent cells simply as half-spheres or half-ellipsoids (i.e. idealized geometries), which neglects the curvature details of the cell surfaces associated with changes in concentrations of strains and stresses. Thus, we introduce here for the first time an optical image-based FE modeling, where loads are simulated on reconstructed 3D geometrical cell models from a single 2D, phase-contrast image. Our novel modeling method eliminates the need for confocal imaging and fluorescent staining preparations (both expensive), and makes cell-specific FE modeling affordable and accessible to the biomechanics community. We demonstrate the utility of this cost-effective modeling method by performing simulations of compression of MSCs embedded in a gel.     

Three dimensional multi-scale modelling and analysis of cell damage in cell-encapsulated alginate constructs

One of the major challenges in scaffold guided regenerative therapies is identifying the essential cues such as mechanical forces that induce cellular responses to form functional tissue. Developing multi-scale modelling methods would facilitate in predicting responses of encapsulated cells for controlling and maintaining the cell phenotype in an engineered tissue construct, when mechanical loads are applied. The objective of this study is to develop a 3D multi-scale numerical model for analyzing the stresses and deformations of the cell when the tissue construct is subjected to macro-scale mechanical loads and to predict load-induced cell damage. Specifically, this methodology characterizes the macro-scale structural behavior of the scaffold, and quantifies 3D stresses and deformations of the cells at the micro-scale and at a cellular level, wherein individual cell components are incorporated. Assuming that cells have inherent ability to sustain a critical load without damage, a damage criterion is established and a stochastic simulation is employed to predict the percentage cell viability within the tissue constructs. Bio-printed cell-alginate tissue constructs were tested with 1%, 5% and 10% compression strain applied and the cell viability were characterized experimentally as 23.2±16.8%, 9.0±5.4% and 4.6±2.1%. Using the developed method, the corresponding micro-environments of the cells were analyzed, the mean critical compressive strain was determined as 0.5%, and the cell viability was predicted as 26.6±7.0, 13.3±4.5, and 10.1±2.8. The predicted results capture the trend of the damage observed from the experimental study.     

Observation and quantification of individual microtubule behavior in vivo: microtubule dynamics are cell-type specific

Recent experiments have demonstrated that the behavior of the interphase microtubule array is cell-type specific: microtubules in epithelial cells are less dynamic than microtubules in fibroblasts (Pepper-kok et al., 1990; Wadsworth and McGrail, 1990). To determine which parameters of microtubule dynamic instability behavior are responsible for this difference, we have examined the behavior of individual microtubules in both cell types after injection with rhodamine-labeled tubulin subunits. Individual microtubules in both cell types were observed to grow, shorten, and pause, as expected. The average amount of time microtubules remained within the lamellae of CHO fibroblasts, measured from images acquired at 10-s intervals, was significantly shorter than the average amount of time microtubules remained within lamellae of PtK1 epithelial cells. Further analysis of individual microtubule behavior from images acquired at 2-s intervals reveals that microtubules in PtK1 cells undergo multiple brief episodes of growth and shortening, resulting in little overall change in the microtubule network. In contrast, microtubules in lamellae of CHO fibroblasts are observed to undergo fewer transitions which are of longer average duration, resulting in substantial changes in the microtubule network over time. A small subset of more stable microtubules was also detected in CHO fibroblasts. Quantification of the various parameters of dynamic instability behavior from these sequences demonstrates that the average rates of both growth and shortening are significantly greater for the majority of microtubules in fibroblasts than for microtubules in epithelial cells (19.8 +/- 10.8 microns/min, 32.2 +/- 17.7 microns/min, 11.9 +/- 6.5 microns/min, and 19.7 +/- 8.1 microns/min, respectively). The frequency of catastrophe events (1/interval between catastrophe events) was similar in both cell types, but the frequency of rescue events (1/time spent shrinking) was significantly higher in PtK1 cells. Thus, individual microtubules in PtK1 lamellae undergo frequent excursions of short duration and extent, whereas most microtubules in CHO lamellae undergo more extensive excursions often resulting in the appearance or disappearance of microtubules within the field of view. These observations provide the first direct demonstration of cell-type specific behavior of individual microtubules in living cells, and indicate that these differences can be brought about by modulation of the frequency of rescue. These results directly support the view that microtubule dynamic instability behavior is regulated in a cell-type specific manner.     

Locomotion of human bone marrow and peripheral blood leukocytes is associated with maturational stage and altered in malignancy.

Using high-resolution phase contrast time-lapse microcinematography, slow movements (0.8-2.0 microns/minute) of human myeloblasts, monoblasts, and megakaryocytes can be recorded. Upon maturation to promyelocytes, motility is lost until cells have reached the stage of metamyelocytes (0.4 microns/minute). Motility increases sharply following maturation into segmented neutrophils (20.4 microns/minute). Monocytes and promonocytes display a mean track velocity of 7.1 microns/minute. The distribution of lymphocyte velocities is not bell-shaped but shows three maxima of 2.1 microns/minute, 7.8 microns/minute, and 18.4 microns/minute. Atypical lymphocytes from patients with infectious mononucleosis belong to the fast group, whereas lymphocytes activated in vitro by mitogens belong to the slow group. Red blood cell precursors from normal human bone marrow do not move actively. In contrast, erythroleukemic blasts show a motility comparable to normal myeloblasts. Similarly, acute promyelocytic leukemia cells move at 6.7 microns/minute, while their normal counterparts are sessile. Increased motility is also observed in blast cells from a variety of acute myelogenous and lymphoblastic leukemias.     

"Stop and go" kinetics of receptor movements induced by anti-Ig or antigen on individual lymphocytes.

Serial observations were conducted on the time course of surface immunoglobulin (Ig) redistribution (capping) on individual mouse spleen lymphocytes. Capping of surface Ig by anti-Ig fluorescein and also antigen-induced capping of receptors on specific sheep erythrocyte antigen-binding cells were observed and the times required for individual cells to clear 90 and 180 ° of their circumference were recorded. There were striking differences between individual cells in both the onset and duration of receptor movements. Although the number of cells achieving complete clearing of first and second quadrants in successive time intervals declined, there was no correlation between the time required by a cell to clear the first quadrant and the time required by the same cell to clear the second quadrant. Thus, instead of observing gradual progressive migration of marker toward one pole of each individual cell at a rate resembling that of the whole population, we observed grossly discontinuous receptor movements, characterized by brief major shifts in receptors followed by a period of relative stability. Capping is thus viewed as a series of discrete contractile events related to the activity of membrane-associated cytoskeletal elements rather than a manifestation of “membrane flow”.     

Advancing Edge Speeds of Epithelial Monolayers Depend on Their Initial Confining Geometry

Collective cell migrations are essential in several physiological processes and are driven by both chemical and mechanical cues. The roles of substrate stiffness and confinement on collective migrations have been investigated in recent years, however few studies have addressed how geometric shapes influence collective cell migrations. Here, we address the hypothesis that the relative position of a cell within the confinement influences its motility. Monolayers of two types of epithelial cells—MCF7, a breast epithelial cancer cell line, and MDCK, a control epithelial cell line—were confined within circular, square, and cross-shaped stencils and their migration velocities were quantified upon release of the constraint using particle image velocimetry. The choice of stencil geometry allowed us to investigate individual cell motility within convex, straight and concave boundaries. Cells located in sharp, convex boundaries migrated at slower rates than those in concave or straight edges in both cell types. The overall cluster migration occurred in three phases: an initial linear increase with time, followed by a plateau region and a subsequent decrease in cluster speeds. An acto-myosin contractile ring, present in the MDCK but absent in MCF7 monolayer, was a prominent feature in the emergence of leader cells from the MDCK clusters which occurred every ~125 μm from the vertex of the cross. Further, coordinated cell movements displayed vorticity patterns in MDCK which were absent in MCF7 clusters. We also used cytoskeletal inhibitors to show the importance of acto-myosin bounding cables in collective migrations through translation of local movements to create long range coordinated movements and the creation of leader cells within ensembles. To our knowledge, this is the first demonstration of how bounding shapes influence long-term migratory behaviours of epithelial cell monolayers. These results are important for tissue engineering and may also enhance our understanding of cell movements during developmental patterning and cancer metastasis.     

A Quantitative Study of Regional and Stage Specific Reaction of Xenopus laevisEmbryonic Tissues on Mechanical Load

Residual deformation of fragments of the embryonic tissues preserved after relaxation of the stretching force serve as a criterion of active redistribution of their cells caused by this stretching. We measured residual deformations of the Xenopus laevis ventral and dorsal ectoderm at the early gastrula and lateral ectoderm at the late gastrula-early neurula after stretching of varying time and force. While the samples responded to moderate (up to 40%) short-term stretching as elastic bodies (residual deformations were absent), residual deformation appeared in the early gastrula tissues after 30–60-min stretching, which were more pronounced in the ventral tissues than in the dorsal ones. On the contrary, a contractile reaction developed in the late gastrula-early neurula tissues in response to 60-min stretching, which almost relaxed residual deformation within 20 min after unloading. A conclusion was drawn that gastrulation and neurulation proceed under the conditions of relaxing and nonrelaxing mechanical tensions, respectively. Mechanical bases and morphogenetic role of the described reactions is discussed.     

Remodeling of Fibrous Extracellular Matrices by Contractile Cells: Predictions from Discrete Fiber Network Simulations

Contractile forces exerted on the surrounding extracellular matrix (ECM) lead to the alignment and stretching of constituent fibers within the vicinity of cells. As a consequence, the matrix reorganizes to form thick bundles of aligned fibers that enable force transmission over distances larger than the size of the cells. Contractile force-mediated remodeling of ECM fibers has bearing on a number of physiologic and pathophysiologic phenomena. In this work, we present a computational model to capture cell-mediated remodeling within fibrous matrices using finite element–based discrete fiber network simulations. The model is shown to accurately capture collagen alignment, heterogeneous deformations, and long-range force transmission observed experimentally. The zone of mechanical influence surrounding a single contractile cell and the interaction between two cells are predicted from the strain-induced alignment of fibers. Through parametric studies, the effect of cell contractility and cell shape anisotropy on matrix remodeling and force transmission are quantified and summarized in a phase diagram. For highly contractile and elongated cells, we find a sensing distance that is ten times the cell size, in agreement with experimental observations.