Anomalous dynamics of cell migration

Mechanistic insights from a quantitative analysis of pollen tube guidance

BACKGROUND

Plant biologists have long speculated about the mechanisms that guide pollen tubes to ovules. Although there is now evidence that ovules emit a diffusible attractant, little is known about how this attractant mediates interactions between the pollen tube and the ovules.

RESULTS

We employ a semi-in vitro assay, in which ovules dissected from Arabidopsis thaliana are arranged around a cut style on artificial medium, to elucidate how ovules release the attractant and how pollen tubes respond to it. Analysis of microscopy images of the semi-in vitro system shows that pollen tubes are more attracted to ovules that are incubated on the medium for longer times before pollen tubes emerge from the cut style. The responses of tubes are consistent with their sensing a gradient of an attractant at 100-150 mum, farther than previously reported. Our microscopy images also show that pollen tubes slow their growth near the micropyles of functional ovules with a spatial range that depends on ovule incubation time.

CONCLUSIONS

We propose a stochastic model that captures these dynamics. In the model, a pollen tube senses a difference in the fraction of receptors bound to an attractant and changes its direction of growth in response; the attractant is continuously released from ovules and spreads isotropically on the medium. The model suggests that the observed slowing greatly enhances the ability of pollen tubes to successfully target ovules. The relation of the results to guidance in vivo is discussed.

Physical model of the dynamic instability in an expanding cell culture

Collective cell migration is of great significance in many biological processes. The goal of this work is to give a physical model for the dynamics of cell migration during the wound healing response. Experiments demonstrate that an initially uniform cell-culture monolayer expands in a nonuniform manner, developing fingerlike shapes. These fingerlike shapes of the cell culture front are composed of columns of cells that move collectively. We propose a physical model to explain this phenomenon, based on the notion of dynamic instability. In this model, we treat the first layers of cells at the front of the moving cell culture as a continuous one-dimensional membrane (contour), with the usual elasticity of a membrane: curvature and surface-tension. This membrane is active, due to the forces of cellular motility of the cells, and we propose that this motility is related to the local curvature of the culture interface; larger convex curvature correlates with a stronger cellular motility force. This shape-force relation gives rise to a dynamic instability, which we then compare to the patterns observed in the wound healing experiments.

Directional cell migration and chemotaxis in wound healing response to PDGF-AA are coordinated by the primary cilium in fibroblasts

Cell motility and migration play pivotal roles in numerous physiological and pathophysiological processes including development and tissue repair. Cell migration is regulated through external stimuli such as platelet-derived growth factor-AA (PDGF-AA), a key regulator in directional cell migration during embryonic development and a chemoattractant during postnatal migratory responses including wound healing. We previously showed that PDGFRalpha signaling is coordinated by the primary cilium in quiescent cells. However, little is known about the function of the primary cilium in cell migration. Here we used micropipette analysis to show that a normal chemosensory response to PDGF-AA in fibroblasts requires the primary cilium. In vitro and in vivo wound healing assays revealed that in ORPK mouse (IFT88(Tg737Rpw)) fibroblasts, where ciliary assembly is defective, chemotaxis towards PDGF-AA is absent, leading to unregulated high speed and uncontrolled directional cell displacement during wound closure, with subsequent defects in wound healing. These data suggest that in coordination with cytoskeletal reorganization, the fibroblast primary cilium functions via ciliary PDGFRalpha signaling to monitor directional movement during wound healing.

A bird's eye view tracking slow nanometer-scale movements of single molecular nano-assemblies

Recent improvements in methods of single-particle fluorescence tracking have permitted detailed studies of molecular motion on the nanometer scale. In a quest to introduce these tools to the burgeoning field of DNA nanotechnology, we have exploited fluorescence imaging with one-nanometer accuracy (FIONA) and single-molecule high-resolution colocalization (SHREC) to monitor the diffusive behavior of synthetic molecular walkers, dubbed "spiders," at the single-molecule level. Here we discuss the imaging methods used, results from tracking individual spiders on pseudo-one-dimensional surfaces, and some of the unique experimental challenges presented by the low velocities (approximately 3 nm/min) of these nanowalkers. These experiments demonstrate the promise of fluorescent particle tracking as a tool for the detailed characterization of synthetic molecular nanosystems at the single-molecule level.

Anomalous dynamics of melanosomes driven by myosin-V in Xenopus laevis melanophores

The organization of the cytoplasm is regulated by molecular motors, which transport organelles and other cargoes along cytoskeleton tracks. In this work, we use single particle tracking to study the in vivo regulation of the transport driven by myosin-V along actin filaments in Xenopus laevis melanophores. Melanophores have pigment organelles or melanosomes, which, in response to hormones, disperse in the cytoplasm or aggregate in the perinuclear region. We followed the motion of melanosomes in cells treated to depolymerize microtubules during aggregation and dispersion, focusing the analysis on the dynamics of these organelles in a time window not explored before to our knowledge. These data could not be explained by previous models that only consider active transport. We proposed a transport-diffusion model in which melanosomes may detach from actin tracks and reattach to nearby filaments to resume the active motion after a given time of diffusion. This model predicts that organelles spend approximately 70% and 10% of the total time in active transport during dispersion and aggregation, respectively. Our results suggest that the transport along actin filaments and the switching from actin to microtubule networks are regulated by changes in the diffusion time between periods of active motion driven by myosin-V.

The stochastic search dynamics of interneuron migration

Migration is a dynamic process in which a cell searches the environment and translates acquired information into somal advancement. In particular, interneuron migration during development is accomplished by two distinct processes: the extension of neurites tipped with growth cones; and nucleus translocation, termed nucleokinesis. The primary purpose of our study is to investigate neurite branching and nucleokinesis using high-resolution time-lapse confocal microscopy and computational modeling. We demonstrate that nucleokinesis is accurately modeled by a spring-dashpot system and that neurite branching is independent of the nucleokinesis event, and displays the dynamics of a stochastic birth-death process. This is in contrast to traditional biological descriptions, which suggest a closer relationship between the two migratory mechanisms. Our models are validated on independent data sets acquired using two different imaging protocols, and are shown to be robust to alterations in guidance cues and cellular migratory mechanisms, through treatment with brain-derived neurotrophic factor, neurotrophin-4, and blebbistatin. We postulate that the stochastic branch dynamics exhibited by interneurons undergoing guidance-directed migration permit efficient exploration of the environment.

Substrate topography induces a crossover from 2D to 3D behavior in fibroblast migration

In a three-dimensional environment, cells migrate through complex topographical features. Using microstructured substrates, we investigate the role of substrate topography in cell adhesion and migration. To do so, fibroblasts are plated on chemically identical substrates composed of microfabricated pillars. When the dimensions of the pillars (i.e., the diameter, length, and spacing) are varied, migrating cells encounter alternating flat and rough surfaces that depend on the spacing between the pillars. Consequently, we show that substrate topography affects cell shape and migration by modifying cell-to-substrate interactions. Cells on micropillar substrates exhibit more elongated and branched shapes with fewer actin stress fibers compared with cells on flat surfaces. By analyzing the migration paths in various environments, we observe different mechanisms of cell migration, including a persistent type of migration, that depend on the organization of the topographical features. These responses can be attributed to a spatial reorganization of the actin cytoskeleton due to physical constraints and a preferential formation of focal adhesions on the micropillars, with an increased lifetime compared to that observed on flat surfaces. By changing myosin II activity, we show that actomyosin contractility is essential in the cellular response to micron-scale topographic signals. Finally, the analysis of cell movements at the frontier between flat and micropillar substrates shows that cell transmigration through the micropillar substrates depends on the spacing between the pillars.

Transition to superdiffusive behavior in intracellular actin-based transport mediated by molecular motors

Intracellular transport of large cargoes, such as organelles, vesicles, or large proteins, is a complex dynamical process that involves the interplay of adenosine triphosphate-consuming molecular motors, cytoskeleton filaments, and the viscoelastic cytoplasm. In this work we investigate the motion of pigment organelles (melanosomes) driven by myosin-V motors in Xenopus laevis melanocytes using a high-spatio-temporal resolution tracking technique. By analyzing the obtained trajectories, we show that the melanosomes mean-square displacement undergoes a transition from a subdiffusive to a superdiffusive behavior. A stochastic theoretical model, which explicitly considers the collective action of the molecular motors, is introduced to generalize the interpretation of our data. Starting from a generalized Langevin equation, we derive an analytical expression for the mean square displacement, which also takes into account the experimental noise. By fitting theoretical expressions to experimental data we were able to discriminate the exponents that characterize the passive and active contributions to the dynamics and to estimate the "global" motor forces correctly. Then, our model gives a quantitative description of active transport in living cells with a reduced number of parameters.

Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise

The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using the Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.

The Na+/H+ exchanger NHE1 is required for directional migration stimulated via PDGFR-alpha in the primary cilium

We previously demonstrated that the primary cilium coordinates platelet-derived growth factor (PDGF) receptor (PDGFR) α–mediated migration in growth-arrested fibroblasts. In this study, we investigate the functional relationship between ciliary PDGFR-α and the Na⁺/H⁺ exchanger NHE1 in directional cell migration. NHE1 messenger RNA and protein levels are up-regulated in NIH3T3 cells and mouse embryonic fibroblasts (MEFs) during growth arrest, which is concomitant with cilium formation. NHE1 up-regulation is unaffected in Tg737^orpk MEFs, which have no or very short primary cilia. In growth-arrested NIH3T3 cells, NHE1 is activated by the specific PDGFR-α ligand PDGF-AA. In wound-healing assays on growth-arrested NIH3T3 cells and wild-type MEFs, NHE1 inhibition by 5′-(N-ethyl-N-isopropyl) amiloride potently reduces PDGF-AA–mediated directional migration. These effects are strongly attenuated in interphase NIH3T3 cells, which are devoid of primary cilia, and in Tg737^orpk MEFs. PDGF-AA failed to stimulate migration in NHE1-null fibroblasts. In conclusion, stimulation of directional migration in response to ciliary PDGFR-α signals is specifically dependent on NHE1 activity, indicating that NHE1 activation is a critical event in the physiological response to PDGFR-α stimulation.

Protons make tumor cells move like clockwork

Cancer accounts for 13% of the yearly total mortality worldwide. Most cancer deaths are the sequel of metastatic diseases rather than of primary tumor growth. Thus, the major challenge in tumor therapy is the tumor cells' ability to metastasize. The extent to which a tumor metastasizes correlates with the tumor cells' migratory activity. Tumor cell migration requires a coordinated formation and release of cell adhesion contacts, a controlled cytoskeletal dynamics, the digestion and reorganization of the extracellular matrix, and local ion and water transport across the plasma membrane. All of these operations depend on intracellular pH (pH(i)) and extracellular pH (pH(e)). Numerous H(+), HCO (3) (-) , and monocarboxylate transporters as well as different carbonic anhydrase isozymes have considerable impact on pH(i) and pH(e) which spotlights them as possible, potential targets for anticancer therapeutics. Especially in solid tumors whose vascularization is often not sufficient, tumor cells cope with hypoxia and the resulting glycolysis by overexpressing the Na(+)/H(+) exchanger NHE1, monocarboxylate transporters MCT1 and/or MCT4, and the carbonic anhydrase CA IX. NHE1, MCT, and CA IX activity lead to an acidification of the extracellular space in order to maintain the cytosolic pH homeostasis stable. The present article gives a review on how this characteristic, acidic tumor micro- and nanoenvironment controls tumor cell migration.

Deformable self-propelled particles

A theory of self-propelled particles is developed in such a way that the particles can be deformed from a circular shape when the propagating velocity is finite. A coupled set of equations in terms of the velocity and a tensor variable is introduced to represent the motion of a deformed particle. It is shown that there is a bifurcation from a straight motion to a circular motion by increasing the propagating velocity. The dynamics of assembly of the particles is studied numerically in two dimensions imposing a global interaction such that the elongated particles tend to undergo an orientational order.

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.

Random time-scale invariant diffusion and transport coefficients

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement delta2[over ] of individual particles remains a random variable while indicating that the particle motion is subdiffusive. We investigate this type of ergodicity breaking within the continuous time random walk model and show that delta2[over ] differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable delta2[over ]. Similarly we quantify the response to a constant external field, revealing a generalization of the Einstein relation. Consequences for the interpretation of single molecule tracking data are discussed.

Calculation of superdiffusion for the Chirikov-Taylor model

It is widely known that the paradigmatic Chirikov-Taylor model presents enhanced diffusion for specific intervals of its stochasticity parameter due to islands of stability, which are elliptic orbits surrounding accelerator mode fixed points. In contrast with normal diffusion, its effect has never been analytically calculated. Here, we introduce a differential form for the Perron-Frobenius evolution operator in which normal diffusion and superdiffusion are treated separately through phases formed by angular wave numbers. The superdiffusion coefficient is then calculated analytically resulting in a Schloemilch series with an exponent beta=3/2 for the divergences. Numerical simulations support our results.

Potassium Channels Keep Mobile Cells on the Go

Cell motility is a prerequisite for the creation of new life, and it is required for maintaining the integrity of an organism. Under pathological conditions, “too much” motility may cause premature death. Studies over the past few years have revealed that ion channels are essential for cell motility. This review highlights the importance of K+ channels in regulating cell motility.

KIBRA modulates directional migration of podocytes

Asymmetric delivery and distribution of macromolecules are essential for cell polarity and for cellular functions such as differentiation, division, and signaling. Injury of podocytes, which are polarized epithelial cells, changes the dynamics of the actin meshwork, resulting in foot process retraction and proteinuria. Although the spatiotemporal control of specific protein-protein interactions is crucial for the establishment of cell polarity, the mechanisms controlling polarity-dependent differentiation and division are incompletely understood. In this study, yeast two-hybrid screens were performed using a podocyte cDNA library and the polarity protein PATJ as bait. The protein KIBRA was identified as an interaction partner of PATJ and was localized to podocytes, tubular structures, and collecting ducts. The last four amino acids of KIBRA mediated binding to the eighth PDZ domain of PATJ. In addition, KIBRA directly bound to synaptopodin, an essential organizer of the podocyte cytoskeleton. Stable knockdown of KIBRA in immortalized podocytes impaired directed cell migration, suggesting that KIBRA modulates the motility of podocytes by linking polarity proteins and cytoskeleton-associated protein complexes.

Random walks with random velocities

We consider a random walk model that takes into account the velocity distribution of random walkers. Random motion with alternating velocities is inherent to various physical and biological systems. Moreover, the velocity distribution is often the first characteristic that is experimentally accessible. Here, we derive transport equations describing the dispersal process in the model and solve them analytically. The asymptotic properties of solutions are presented in the form of a phase diagram that shows all possible scaling regimes, including superdiffusive, ballistic, and superballistic motion. The theoretical results of this work are in excellent agreement with accompanying numerical simulations.

TRPC1 channels regulate directionality of migrating cells

Cell migration depends on the generation of structural asymmetry and on different steps: protrusion and adhesion at the front and traction and detachment at the rear part of the cell. The activity of Ca(2+) channels coordinate these steps by arranging intracellular Ca(2+) signals along the axis of movement. Here, we investigated the role of the putative mechanosensitive canonical transient receptor potential channel 1 (TRPC1) in cell migration. We analyzed its function in transformed renal epithelial (Madin-Darby canine kidney-focus) cells with variation of TRPC1 expression. As shown by time lapse video microscopy, TRPC1 knockdown cells have partially lost their polarity and the ability to persistently migrate into a given direction. This failure is linked to the suppression of a local Ca(2+) gradient at the front of migrating TRPC1 knockdown cells, whereas TRPC1 overexpression leads to steeper Ca(2+) gradients. We propose that the Ca(2+) signaling events regulated by TRPC1 within the lamellipodium determine polarity and directed cell migration.

Dynamics of single potassium channel proteins in the plasma membrane of migrating cells

Cell migration is an important physiological process among others controlled by ion channel activity. Calcium-activated potassium channels (K(Ca)3.1) are required for optimal cell migration. Previously, we identified single human (h)K(Ca)3.1 channel proteins in the plasma membrane by means of quantum dot (QD) labeling. In the present study, we tracked single-channel proteins during migration to classify their dynamics in the plasma membrane of MDCK-F cells. Single hK(Ca)3.1 channels were visualized with QD- or Alexa488-conjugated antibodies and tracked at the basal cell membrane using time-lapse total internal reflection fluorescence (TIRF) microscopy. Analysis of the trajectories allowed the classification of channel dynamics. Channel tracks were compared with those of free QD-conjugated antibodies. The size of the label has a pronounced effect on hK(Ca)3.1 channel diffusion. QD-labeled channels have a (sub)diffusion coefficient D(QDbound) = 0.067 microm(2)/s(alpha), whereas that of Alexa488-labeled channels is D(Alexa) = 0.139 microm(2)/s. Free QD-conjugated antibodies move much faster: D(QDfree) = 2.163 microm(2)/s(alpha). Plotting the mean squared distances (msd) covered by hK(Ca)3.1 channels as a function of time points to the mode of diffusion. Alexa488-labeled channels diffuse normally, whereas the QD-label renders hK(Ca)3.1 channel diffusion anomalous. Free QD-labeled antibodies also diffuse anomalously. Hence, QDs slow down diffusion of hK(Ca)3.1 channels and change the mode of diffusion. These results, referring to the role of label size and properties of the extracellular environment, suggest that the pericellular glycocalyx has an important impact on labels used for single molecule tracking. Thus tracking fluorescent particles within the glycocalyx opens up a possibility to characterize the pericellular nanoenvironment.