Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms

We study kinetic models for chemotaxis, incorporating the ability of cells to assess temporal changes of the chemoattractant concentration as well as its spatial variations. For prescribed smooth chemoattractant density, the macroscopic limit is carried out rigorously. It leads to a drift equation with a chemotactic sensitivity depending on the time derivative of the chemoattractant density. As an application it is shown by numerical experiments that the new model can resolve the chemotactic wave paradox. For this purpose, the macroscopic equation is coupled to a simple activation-inhibition model for the chemoattractant which produces the chemoattractant waves typical for the slime mold Dictyostelium discoideum.     

Chemotaxis with directional sensing during Dictyostelium aggregation

We show that the chemotactic movements of colonies of the starving amoeba Dictyostelium discoideum are driven by a force that depends on both the direction of propagation (directional sensing) of reaction-diffusion chemotactic waves and on the gradient of the concentration of the chemoattractant, solving the chemotactic wave paradox. It is shown that the directional sensing of amoebae is due to the sensitivity of the cells to the time variation of the concentration of the chemoattractant combined with its spatial gradient. It is also shown that chemotaxis exclusively driven by local concentration gradient leads to unstable local motion, preventing cells from aggregation. These findings show that the formation of mounds, which initiate multicellularity in Dictyostelium discoideum, is caused by the sensitivity of the amoebae due to three factors, namely, to the direction of propagation of the chemoattractant, to its spatial gradient, and to the emergence of cAMP “emitting centres”, responsible for the local accumulation of the amoebae.     

Pseudopodium activation and inhibition signals in chemotaxis by Dictyostelium discoideum amoebae

The behaviour of Dictyostelium discoideum amoebae has been studied in natural cAMP waves and in controlled spatial and temporal gradients. Chemoattractant gradients induce responses which indicate that amoebae spatially compare concentration increases at different points on the cell surface. This allows them to respond to the relative spatial and temporal gradients in a manner that is little affected by the absolute attractant concentration over several orders of magnitude. The changes in turning behaviour, motility and morphology that are induced by attractant gradients are consistent with transduction of stimuli into two intracellular signals - one activating and the other inhibiting pseudopodium formation. The former measures the present attractant concentration at particular points on the cell surface - the local, current signal. The latter measures the average attractant concentration over the whole cell surface during the recent past - the global, past signal. Both signals may be part of a normal pseudopodium autoactivation and inhibition system responsible for amoeboid morphology and motility. Attractants could modulate this system to generate the complex behavioural responses observed.     

Selection of chemotaxis mutants of Dictyostelium discoideum

A method has been developed for the efficient selection of chemotaxis mutants of Dictyostelium discoideum. Mutants defective in the chemotactic response to folate could be enriched up to 30-fold in one round of selection using a chamber in which a compartment that contained the chemoattractant was separated by a sandwich of four nitrocellulose filters from a compartment that contained buffer. Mutagenized cells were placed in the center of the filter layer and exposed to the attractant gradient built up between the compartments for a period of 3-4 h. While wild-type cells moved through the filters in a wave towards the compartment that contained attractant, mutant cells remained in the filter to which they were applied. After several repetitions of the selection procedure, mutants defective in chemotaxis made up 10% of the total cell population retained in that filter. Mutants exhibiting three types of alterations were collected: motility mutants with either reduced speed of movement, or altered rates of turning; a single mutant defective in production of the attractant-degrading enzyme, folate deaminase; and mutants with normal motility but reduced chemotactic responsiveness. One mutant showed drastically reduced sensitivity in folate-induced cGMP production. Morphogenetic alterations of mutants defective in folate chemotaxis are described.     

A discrete cell model with adaptive signalling for aggregation of Dictyostelium discoideum.

Dictyostelium discoideum (Dd) is a widely studied model system from which fundamental insights into cell movement, chemotaxis, aggregation and pattern formation can be gained. In this system aggregation results from the chemotactic response by dispersed amoebae to a travelling wave of the chemoattractant cAMP. We have developed a model in which the cells are treated as discrete points in a continuum field of the chemoattractant, and transduction of the extracellular cAMP signal into the intracellular signal is based on the G protein model developed by Tang & Othmer. The model reproduces a number of experimental observations and gives further insight into the aggregation process. We investigate different rules for cell movement the factors that influence stream formation the effect on aggregation of noise in the choice of the direction of movement and when spiral waves of chemoattractant and cell density are likely to occur. Our results give new insight into the origin of spiral waves and suggest that streaming is due to a finite amplitude instability.     

Guanylate Cyclase Activity in Dictyostelium discoideum and Its Increase during Cell Development

Following consumption of the food supply, cells of the cellular slime mould Dictyostelium discoideum aggregate and form a multicellular organism. The mechanism for cell aggregation is chemotaxis. The chemotactic signal in D. discoideum is released periodically from aggregation centers and propagated from cell to cell. cAMP mediates cell aggregation by acting as chemotactic attractant and as propagator of the signal. cAMP signals are measured by cell-surface receptors. Recent evidence indicates a role for cGMP during cAMP-mediated cell aggregation in D. discoideum .
During cell differentiation to aggregation competence, cAMP binding sites appear at the cell surface, and the activity of the enzymes adenylate cyclase and phosphodiesterase increases several-fold. In the present work we investigate the synthesis of cGMP in D. discoideum . Conditions for the assay of guanylate cyclase in cell homogenates are described. Guanylate cyclase activity was followed during cell differentiation to aggregation competence and found to increase fourfold. These results indicate that cGMP is involved in cell differentiation of D. discoideum . In contrast to adenylate cyclase, which is activated by cAMP, guanylate cyclase was under our conditions activated neither by cAMP, nor by folic acid.     

Signal emission and signal propagation during early aggregation in Dictyostelium discoideum.

Waves of chemotactic movement during the early phase of aggregation in Dictyostelium discoideum are of 2 kinds, concentric waves produced by cells that emit cyclic AMP signals spontaneously, and spirals generated by excitations relayed continuously around loops of excitable cells. The period of a spiral wave is the time taken for the excitation to make one complete circuit of the pacemaker loop. We have compared signal emission from the 2 types of source in time-lapse films made at a variety of temperatures. Our results show that spiral waves have a characteristic period length throughout most if not all of the early phase of aggregation, and that the period of concentric waves is generally longer and more variable. Temperature has a pronounced effect on period length and a lesser effect on propagation velocity. We find that each individual wave is propagated at constant velocity over distances of 1-2 cm but that the velocity of successive waves declines. This decline probably reflects some cumulative effect of the chemotactic excitations on the excitable properties of the aggregating cells.     

Cells responding to chemoattractant on a structured substrate

Cell migration on an adhesive substrate surface comprises actin-based protrusion at the front and retraction of the tail in combination with coordinated adhesion to, and detachment from, the substrate. To study the effect of cell-to-substrate adhesion on the chemotactic response of Dictyostelium discoideum cells, we exposed the cells to patterned substrate surfaces consisting of adhesive and inert areas, and forced them by a gradient of chemoattractant to enter the border between the two areas. Wild-type as well as myosin II-deficient cells stop at the border of an adhesive area. They do not detach with their rear part, while on the nonadhesive area they protrude pseudopods at their front toward the source of chemoattractant. Avoidance of the nonadhesive area may cause a cell to move in tangential direction relative to the attractant gradient, keeping its tail at the border of the adhesive surface.     

The chemotaxis defect of Shwachman-Diamond Syndrome leukocytes

Shwachman-Diamond Syndrome (SDS) is a rare autosomal recessive, multisystem disorder presenting in childhood with intermittent neutropenia and pancreatic insufficiency. It is characterized by recurrent infections independent of neutropenia, suggesting a functional neutrophil defect. While mutations at a single gene locus (SBDS) appear to be responsible for SDS in a majority of patients, the function of that gene and a specific defect in SDS neutrophil behavior have not been elucidated. Therefore, employing 2D and 3D computer-assisted motion analysis systems, we have analyzed the basic motile behavior and chemotactic responsiveness of individual polymorphonuclear leukocytes (PMNs) of 14 clinically diagnosed SDS patients. It is demonstrated that the basic motile behavior of SDS PMNs is normal in the absence of chemoattractant, that SDS PMNs respond normally to increasing and decreasing temporal gradients of the chemoattractant fMLP, and that SDS PMNs exhibit a normal chemokinetic response to a spatial gradient of fMLP. fMLP receptors were also distributed uniformly through the plasma membrane of SDS PMNs as in control PMNs. SDS PMNs, however, were incapable of orienting in and chemotaxing up a spatial gradient of fMLP. This unique defect in orientation was manifested by the PMNs of every SDS patient tested. The PMNs of an SDS patient who had received an allogenic hematopoietic stem cell transplant, as well as PMNs from a cystic fibrosis patient, oriented normally. These results suggest that the defect in SDS PMNs is in a specific pathway emanating from the fMLP receptor that is involved exclusively in regulating orientation in response to a spatial gradient of fMLP. This pathway must function in parallel with additional pathways, intact in SDS patients, that emanate from the fMLP receptor and regulate responses to temporal rather than spatial changes in receptor occupancy.     

EppA, a putative substrate of DdERK2, regulates cyclic AMP relay and chemotaxis in Dictyostelium discoideum

The mitogen-activated protein kinase DdERK2 is critical for cyclic AMP (cAMP) relay and chemotaxis to cAMP and folate, but the details downstream of DdERK2 are unclear. To search for targets of DdERK2 in Dictyostelium discoideum, 32PO4(3-)-labeled protein samples from wild-type and Dderk2- cells were resolved by 2-dimensional electrophoresis. Mass spectrometry was used to identify a novel 45-kDa protein, named EppA (ERK2-dependent phosphoprotein A), as a substrate of DdERK2 in Dictyostelium. Mutation of potential DdERK2 phosphorylation sites demonstrated that phosphorylation on serine 250 of EppA is DdERK2 dependent. Changing serine 250 to alanine delayed development of Dictyostelium and reduced Dictyostelium chemotaxis to cAMP. Although overexpression of EppA had no significant effect on the development or chemotaxis of Dictyostelium, disruption of the eppA gene led to delayed development and reduced chemotactic responses to both cAMP and folate. Both eppA gene disruption and overexpression of EppA carrying the serine 250-to-alanine mutation led to inhibition of intracellular cAMP accumulation in response to chemoattractant cAMP, a pivotal process in Dictyostelium chemotaxis and development. Our studies indicate that EppA regulates extracellular cAMP-induced signal relay and chemotaxis of Dictyostelium.     

Quantitative elucidation of a distinct spatial gradient-sensing mechanism in fibroblasts

Migration of eukaryotic cells toward a chemoattractant often relies on their ability to distinguish receptor-mediated signaling at different subcellular locations, a phenomenon known as spatial sensing. A prominent example that is seen during wound healing is fibroblast migration in platelet-derived growth factor (PDGF) gradients. As in the well-characterized chemotactic cells Dictyostelium discoideum and neutrophils, signaling to the cytoskeleton via the phosphoinositide 3-kinase pathway in fibroblasts is spatially polarized by a PDGF gradient; however, the sensitivity of this process and how it is regulated are unknown. Through a quantitative analysis of mathematical models and live cell total internal reflection fluorescence microscopy experiments, we demonstrate that PDGF detection is governed by mechanisms that are fundamentally different from those in D. discoideum and neutrophils. Robust PDGF sensing requires steeper gradients and a much narrower range of absolute chemoattractant concentration, which is consistent with a simpler system lacking the feedback loops that yield signal amplification and adaptation in amoeboid cells.     

An information-theoretic characterization of the optimal gradient sensing response of cells

Many cellular systems rely on the ability to interpret spatial heterogeneities in chemoattractant concentration to direct cell migration. The accuracy of this process is limited by stochastic fluctuations in the concentration of the external signal and in the internal signaling components. Here we use information theory to determine the optimal scheme to detect the location of an external chemoattractant source in the presence of noise. We compute the minimum amount of mutual information needed between the chemoattractant gradient and the internal signal to achieve a prespecified chemotactic accuracy. We show that more accurate chemotaxis requires greater mutual information. We also demonstrate that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes with existing experimental measurements and models of eukaryotic gradient sensing. Remarkably, there is good quantitative agreement between the optimal response when no a priori assumption is made about the location of the existing source, and the observed experimental response of unpolarized Dictyostelium discoideum cells. In contrast, the measured response of polarized D. discoideum cells matches closely the optimal scheme, assuming prior knowledge of the external gradient-for example, through prolonged chemotaxis in a given direction. Our results demonstrate that different observed classes of responses in cells (polarized and unpolarized) are optimal under varying information assumptions.     

Suppression of cyclic AMP-induced cell excitation in Dictyostelium discoideum by inhibitors of eicosanoid oxidation

Abstract Receptor-mediated stimulation of Dictyostelium cells by the aggregative chemoattractant cyclic AMP leads to a complex excitatory response resulting in chemotaxis and the synthesis and release of cyclic AMP as the relayed chemotactic signal. However, the mechanism of this stimulus-response coupling is not well understood. In this study, we show that a number of compounds, best known as inhibitors of cyclooxygenase activity in mammalian cells, prevent cyclic AMP receptor-mediated cell excitation and cyclic AMP accumulation in aggregation-competent Dictyostelium cells. These observations suggest that some eicosanoid-like compound(s) may be involved in stimulus-response coupling in this organism, as is the case in higher eukaryotic cells.     

A talin homologue of Dictyostelium rapidly assembles at the leading edge of cells in response to chemoattractant

In an attempt to identify unknown actin-binding proteins in cells of Dictyostelium discoideum that may be involved in the control of cell motility and chemotaxis, monoclonal antibodies were raised against proteins that had been enriched on an F-actin affinity matrix. One antibody recognized a protein distinguished by its strong accumulation at the tips of filopods. These cell-surface extensions containing a core of bundled actin filaments are rapidly protruded and retracted by cells in the growth-phase stage. The protein of 269 kD turned out to resemble mouse fibroblast talin (Rees et al., 1990) in its primary structure. The fit is best among the first 400-amino acid residues of the NH2-terminal region where identity between the two proteins is 44% and the last 200-amino acid residues of the COOH-terminal region with 36% identity. In the elongated cells of the aggregation stage the Dictyostelium talin is accumulated at the entire front where also F- actin is enriched. Since this protein exists in a soluble state in the cytoplasm, mechanisms are predicted that cause accumulation at sites of the cell where a front is established. Evidence for receptor-mediated accumulation was obtained by local stimulation of cells with cAMP. When a new front was induced by the chemoattractant, the talin accumulated there within half a minute, indicating a signal cascade in Dictyostelium responsible for assembly of the talin beneath sites of the plasma membrane where chemoattractant receptors are strongly activated. The ordered assembly of the talin homologue together with actin and a series of other proteins is considered to play a key role in chemotactic orientation.     

Measurement of the chemotaxis coefficient for human neutrophils in the under-agarose migration assay

Clinical and scientific investigations of leukocyte chemotaxis will be greatly aided by an ability to measure quantitative parameters characterizing the intrinsic random motility, chemokinetic, and chemotactic properties of cell populations responding to a given attractant. Quantities typically used at present, such as leading front distances, migrating cell numbers, etc., are unsatisfactory in this regard because their values are affected by many aspects of the assay system unrelated to cell behavioral properties. In this paper we demonstrate the measurement of cell migration parameters that do, in fact, characterize the intrinsic cell chemosensory movement responses using cell density profiles obtained in the linear under-agarose assay. These parameters are the random motility coefficient, mu, and the chemotaxis coefficient, chi, which appear in a theoretical expression for cell population migration. We propose a priori the dependence of chi on attractant concentration, based on an independent experimental correlation of individual cell orientation bias in an attractant gradient with a spatial difference in receptor occupancy. Our under-agarose population migration results are consistent with this proposition, allowing chemotaxis to be reliably characterized by a chemotactic sensitivity constant, chi 0, to which chi is directly proportional. Further, chi 0 has fundamental significance; it represents the reciprocal of the difference in number of bound receptors across cell dimensions required for directional orientation bias. In particular, for the system of human peripheral blood polymorphonuclear neutrophil leukocytes responding to FNLLP, we find that the chemotaxis coefficient is a function of attractant concentration, a following the expression: chi = chi 0NT0 f(a) S(a) Kd/(Kd + a)2 where Kd is the FNLLP-receptor equilibrium dissociation constant and NT0 is the total number of cell surface receptors for FNLLP. f(a) is the fraction of surface receptors remaining after down-regulation, and S(a) is the cell movement speed, both known functions of FNLLP concentration. We find that chi 0NT0 = 0.2 cm; according to a theoretical argument outlined in the Appendix this means that these cells exhibit 75% orientation toward higher attractant concentration when the absolute spatial difference in bound receptors is 0.0025NT0 over 10 micron. (For example, if NT0 = 50,000 this would correspond to a spatial difference of 125 bound receptors over 10 micron.) This result can be compared with estimates obtained from visual studies of individual neutrophils.     

Dual chemotaxis signalling regulates Dictyostelium development: intercellular cyclic AMP pulses and intracellular F-actin disassembly waves induce each other

Aggregating Dictyostelium discoideum amoebae periodically emit and relay cAMP, which regulates their chemotaxis and morphogenesis into a multicellular, differentiated organism. Cyclic AMP also stimulates F-actin assembly and chemotactic pseudopodium extension. We used actin-GFP expression to visualise for the first time intracellular F-actin assembly as a spatio-temporal indicator of cell reactions to cAMP, and thus the kinematics of cell communication, in aggregating streams. Every natural cAMP signal pulse induces an autowave of F-actin disassembly, which propagates from each cell's leading end to its trailing end at a linear rate, much slower than the calculated and measured velocities of cAMP diffusion in aggregating Dictyostelium. A sequence of transient reactions follows behind the wave, including anterior F-actin assembly, chemotactic pseudopodium extension and cell advance at the cell front and, at the back, F-actin assembly, extension of a small retrograde pseudopodium (forcing a brief cell retreat) and chemotactic stimulation of the following cell, yielding a 20s cAMP relay delay. These dynamics indicate that stream cell behaviour is mediated by a dual signalling system: a short-range cAMP pulse directed from one cell tail to an immediately following cell front and a slower, long-range wave of intracellular F-actin disassembly, each inducing the other.     

Morphogenetic cell movement in Dictyostelium

Dictyostelium morphogenesis starts with the chemotactic aggregation of starving individual cells. The cells move in response to propagating waves of the chemoattractant cyclic AMP initiated by cells in the aggregation centre. During aggregation the cells begin to differentiate into several types with different signalling and chemotactic properties. These cell types sort out from each other to form an axial pattern in the slug. There is now good evidence that periodic chemotactic signals not only control aggregation, but also later stages of morphogenesis. These signals take the form of target patterns, spirals, multi-armed spirals and scroll waves. I will discuss their role in the control of cell movement during mound and slug formation and in the formation of the fruiting body.     

Mechanisms of Gradient Sensing and Chemotaxis: Conserved Pathways,Diverse Regulation

Directed cell migration is critical for normal development, immune responses, and wound healing and plays a prominent role in tumor metastasis. In eukaryotes, cell orientation is biased by an external chemoattractant gradient through a spatial contrast in chemoattractant receptor-mediated signal transduction processes that differentially affect cytoskeletal dynamics at the cell front and rear. Mechanisms of spatial gradient sensing and chemotaxis have been studied extensively in the social amoeba Dictyostelium discoideum and mammalian leukocytes (neutrophils), which are similar in their remarkable sensitivity to shallow gradients and robustness of response over a broad range of chemoattractant concentration. Recently, we have quantitatively characterized a different gradient sensing system, that of platelet-derived growth factor-stimulated fibroblasts, an important component of dermal wound healing. The marked differences between this system and the others have led us to speculate on the diversity of gradient sensing mechanisms and their biological implications.     

The role of cytoplasmic microtubules in polymorphonuclear leukocyte chemotaxis : Evidence for the release hypothesis by means of time-lapse analysis of PMN movement relative to dot-like attractants

The present experiments were designed to elucidate the role of cytoplasmic microtubules in the chemotaxis of human polymorphonuclear leukocytes (PMNs) by means of the Boyden chamber technique and by means of analysis of PMN locomotion around a dot-like attractant.Casein induced positive chemotaxis in a small and variable fraction of the PMNs in the Boyden chamber.The movements of individual PMNs in coverslip preparations of clotted autoplasma were analysed as regards velocity of locomotion, locomotive index and net radial dislocation relative to the cell centre, with or without a yeast-phagocytosing leukocyte as a dot-like attractant.PMNs without obvious attractants tended to leave the visual field, i.e. they had a negative net radial dislocation relative to the centre of the visual field. Their locomotive indices suggested that their disappearance from the visual field was due to random movement. In contrast, the locomotive indices of PMNs influenced by attractants suggested the presence of both positive and negative chemotaxis in the population of moving PMNs.Yeast-phagocytosing leukocytes attracted wandering PMNs isolated by the Isopaque-Ficoll method (IF-PMNs) with a force which approximately balanced the basic tendency of the IF-PMNs to leave the visual field. Selective pretreatment of the moving IF-PMNs with podophyllic acid ethylhydrazide (SPI), 0.5 μg/ml (1.05 × 10⁻⁶ M), did not inhibit their attraction towards the central yeast phagocyte. The attraction of wandering IF-PMNs towards the central yeast phagocyte was inhibited by selective pretreatment of the phagocytes with SPI, 0.5 μg/ml. These observations indicate that cytoplasmic microtubules have an essential role in the release of chemotactic substances from phagocytosing leukocytes but not in the direction-finding of attractant-approaching PMNs.From the present observations by means of SPI, it is suggested that antitubulin inhibition of the release of chemotactic substances from phagocytosing leukocytes is the mechanism of inhibition of PMN chemotaxis by sub-antimitotic antitubulin concentrations in vitro. The latter phenomenon is thought to reflect the cellular basis of the anti-inflammatory action of the antitubulins.     

Myosin I phosphorylation is increased by chemotactic stimulation

Directed cell migration occurs in response to extracellular cues. Following stimulation of a cell with chemoattractant, a significant rearrangement of the actin cytoskeleton is mediated by intracellular signaling pathways and results in polarization of the cell and movement via pseudopod extension. Amoeboid myosin Is play a critical role in regulating pseudopod formation in Dictyostelium, and their activity is activated by heavy chain phosphorylation. The effect of chemotactic stimulation on the in vivo phosphorylation level of a Dictyostelium myosin I, myoB, was tested. The myoB heavy chain is phosphorylated in vivo on serine 322 (the myosin TEDS rule phosphorylation site) in chemotactically competent cells. The level of myoB phosphorylation increases following stimulation of starving cells with the chemoattractant cAMP. A 3-fold peak increase in the level of phosphorylation is observed at 60 s following stimulation, a time at which the Dictyostelium cell actively extends pseudopodia. These findings suggest that chemotactic stimulation results in increased myoB activity via heavy chain phosphorylation and contributes to the global extension of pseudopodia that occurs prior to polarization and directed motility.