A theory of measurement error and its implications for spatial and temporal gradient sensing during chemotaxis. II. The effects of non-equilibrated ligand binding

Cells generally chemotax along a direction in which their receptor occupancy gradient--whether spatial or temporal--is maximum. Occupancy differentials are, however, often so small as to be masked by thermal noise; i.e., by fluctuations inherent in the stochastic nature of ligand binding. Such fluctuations therefore impose a fundamental limit on the sensitivity of a cell's ability to detect a chemoattractant gradient. In order to pursue the implications of this limit, fluctuation theories have been developed. The theories assume that the signal is some function of the receptor occupancy gradient, allow an estimate of the standard deviation about the mean signal, and permit an evaluation of, among other things, the extent to which a receptor defect can impair an effective response. Previous theories have assumed an equilibrated ligand-receptor interaction. In this paper we introduce a generalized definition of a signal caused by a receptor occupancy gradient that allows us to develop a non-equilibrium theory of thermal noise. We show that previous formulations are a special case of the current development. More specifically, we find the following. Swimming cells subject to Brownian tumbling must generally average their signals over a very long time period to achieve a signal-to-noise ratio less than or equal to 1. Spatial gradient detection is possible with ligand-receptor equilibrium constants less than 10(3)M-1, but since such ligands are rare, theory predicts that tumbling cells will generally not detect gradients by measuring spatial occupancy differentials. These conclusions hold irrespective of whether chemical equilibrium is achieved. For crawling cells not subject to Brownian tumbling, a range of affinities exists in which spatial or temporal gradient detection is possible. In general a spatial mechanism is more efficient for low affinity ligands (dissociation times less than 0.3 s), whereas a temporal mechanism is more efficient for higher K. In this case the detection of gradients in slowly dissociating ligand will be facilitated if signal processing begins prior to chemical equilibration. An important new parameter is indicated by the theory. The definitions of a temporal gradient signal is based on estimating and comparing average occupancy over two time intervals displaced by a time t1. The theory predicts an optimal t1, of order milliseconds, that leads to the shortest minimum averaging time. For t1 values at and longer than the optimum, and for all averaging times exceeding some minimum, the cell will detect a temporal signal.(ABSTRACT TRUNCATED AT 400 WORDS)     

A theory of measurement error and its implications for spatial and temporal gradient sensing during chemotaxis

Cells generally chemotax along a direction in which their receptor occupancy gradient—whether spatial or temporal—is maximum. Occupancy differentials are, however, often so small as to be masked by thermal noise; i.e., by fluctuations inherent in the stochastic nature of ligand binding. Such fluctuations therefore impose a fundamental limit on the sensitivity of a cell's ability to detect a chemoattractant gradient. In order to pursue the implications of this limit, fluctuation theories have been developed. The theories assume that the signal is some function of the receptor occupancy gradient, allow an estimate of the standard deviation abouts the mean signal, and permit an evaluation of, among other things, the extent to which a receptor defect can impair an effective response. Previous theories have assumed an equilibrated ligand-receptor interaction. In this paper we introduce a generalized definition of a signal caused by a receptor occupancy gradient that allows us to develop a non-equilibrium theory of thermal noise. We show that previous formulations are a special case of the current development. More specifically, we find the following.

1. Swimming cells subject to Brownian tumbling must generally average their signals over a very long time period to achieve a signal-to-noise ratio≤1. Spatial gradient detection is possible with ligand-receptor equilibrium constants<10³ M ^?1, but since such ligands are rare, theory predicts that tumbling cells will generally not detect gradients by measuring spatial occupancy differentials.These conclusions hold irrespective of whether chemical equilibrium is achieved.
2. For crawling cells not subject to Brownian tumbling, a range of affinities exists in which spatial or temporal gradient detection is possible. In general a spatial mechanism is more efficient for low affinity ligands (dissociation times <0.3s), whereas a temporal mechanism is more efficients for higherK. In this case the detection of gradients in slowly dissociating ligand will be facilitated if signal processing begins prior to chemical equilibration.
3. An important new parameter is indicated by the theory. The definitions of a temporal gradient signal is based on estimating and comparing average occupancy over two time intervals displaced by a timet ₁. The theory predicts an optimalt ₁, of order milliseconds, that leads to the shortest minimum averaging time.
4. Fort ₁ values at and longer than the optimum, and for all averaging times exceeding some minimum, the cell will detect a temporal signal.
5. For values oft ₁ at and near the optimum, if the averaging time becomes too long, the cell enters a region of insensitivity in which it can no longer respond.
6. Finally, as the interval between estimates of average occupancy decreases below the optimum, a critical value oft ₁ is reached at which the minimum averaging time undergoes an abrupt transition from a relatively short value to a value five orders of magnitude longer.

The molecular process(es) controllingt ₁ are at present unknown, nor has any attempt been made to identify them since the parameter has not been previously recognized. We speculate that the search for its molecular basis might uncover a highly sensitive control mechanism, with defects in this mechanism predicted to have a far more pronounced effect on the cells behavior than defects in receptor number or affinity.     

Adaptation is not required to explain the long-term response of axons to molecular gradients

It has been suggested that growth cones navigating through the developing nervous system might display adaptation, so that their response to gradient signals is conserved over wide variations in ligand concentration. Recently however, a new chemotaxis assay that allows the effect of gradient parameters on axonal trajectories to be finely varied has revealed a decline in gradient sensitivity on either side of an optimal concentration. We show that this behavior can be quantitatively reproduced with a computational model of axonal chemotaxis that does not employ explicit adaptation. Two crucial components of this model required to reproduce the observed sensitivity are spatial and temporal averaging. These can be interpreted as corresponding, respectively, to the spatial spread of signaling effects downstream from receptor binding, and to the finite time over which these signaling effects decay. For spatial averaging, the model predicts that an effective range of roughly one-third of the extent of the growth cone is optimal for detecting small gradient signals. For temporal decay, a timescale of about 3 minutes is required for the model to reproduce the experimentally observed sensitivity.     

Spatial sensing of stimulus gradients can be superior to temporal sensing for free-swimming bacteria.

Predictions of the minimal size an organism must have to swim along stimulus gradients were used to compare the relative advantages of sensory systems employing spatial (simultaneous) and temporal (sequential) gradient detection mechanisms for small free-swimming bacteria, leading to the following conclusions: 1) there are environmental conditions where spatial detection mechanisms can function for smaller organisms than can temporal mechanisms, 2) temporal mechanisms are superior (have a smaller size limit) for the difficult conditions of low concentration and shallow gradients, but 3) observed bacterial chemotaxis occurs mostly under conditions where spatial mechanisms have a smaller size limit, and 4) relevant conditions in the natural environment favor temporal mechanisms in some cases and spatial mechanisms in others. Thus, sensory ecology considerations do not preclude free-swimming bacteria from employing spatial detection mechanisms, as has been thought, and microbiologists should be on the lookout for them. If spatial mechanisms do not occur, the explanation should be sought elsewhere.     

Chemoattraction and chemotaxis in Dictyostelium discoideum: myxamoeba cannot read spatial gradients of cyclic adenosine monophosphate

Myxamoebae of the morphogenetic cellular slime mold Dictyostelium discoideum are thought to be able to accurately read and respond to directional information in spatial gradients of cyclic AMP. We examined the spatial and temporal mechanisms proposed for chemotaxis by comparing the behavior of spreading or evenly distributed cell populations after exposure to well-defined spatial gradients. The effects of gradient generation on cells were avoided by using predeveloped gradients. Qualitatively different responses were obtained using (a) isotropic, (b) static spatial, or (c) temporal (impulse) gradients in a simple chamber of penetrable micropore filters. We simulated models of chemotaxis and chemokinesis to aid our interpretations. The attractive and locomotory responses of populations were maximally stimulated by 0.05 microM cyclic AMP, provided that cellular phosphodiesterase was inhibited. But a single impulse of cyclic AMP during gradient development caused a greater and qualitatively different attraction. Attraction in spatial gradients was only transient, in that populations eventually developed a random distribution when confined to a narrow territory. Populations never accumulated nor lost their random distribution even in extremely steep spatial gradients. Attraction in spatial gradients was inducible only in spreading populations, not randomly distributed ones. Thus, spatial gradients effect biased-random locomotion: i.e., chemokinesis without adaptation. Cells cannot read gradients; the reaction of the cells is stochastic. Spatial gradients do not cause chemotaxis, which probably requires a sharp stimulant concentration increase (a temporal gradient) as a pulse or impulse. The results also bear on concepts of how embryonic cells might be able to decipher the positional information in a morphogen spatial gradient during development.     

Monte Carlo Simulation of Buffered Diffusion into and out of a Model Synapse

Buffered diffusion occurs when ligands enter or leave a restricted space, such as a chemical synapse, containing a high density of binding sites. This study used Monte Carlo simulations to determine the time and spatial dependences of buffered diffusion without a priori assumptions about kinetics. The synapse was modeled as a box with receptors on one inner face. The exterior was clamped to some ligand concentration and ligands diffused through two sides. Onset and recovery simulations were carried out and the effects of receptor density, ligand properties and synapse geometry were investigated. This study determined equilibration times for binding and the spatial gradient of unliganded receptors. Onset was characterized by a high spatial gradient; equilibration was limited by the time needed for sufficient ligands to enter the synapse. Recovery showed a low spatial gradient with receptor equilibration limited by ligand rebinding. Decreasing ligand association rate or increasing ligand diffusion coefficient reduced the role of buffered diffusion and decreased the spatial gradient. Simulations with irreversible ligands showed larger, persistent spatial gradients. These simulations identify characteristics that can be used to test whether a synaptic process is governed by buffered diffusion. They also indicate that fundamental differences in synapse function may occur with irreversible ligands.     

Dictyostelium Chemotactic Response to Spatial and Temporal Gradients. Theories of the Limits of Chemotactic Sensitivity and of Pseudochemotaxis

Four aspects of ameboid cell chemotaxis are discussed: 1) Ameboid cells (Dictyostelium discoideum, leukocytes) might orient to chemotaxin gradients by sensing a spatial gradient or a temporal change in the concentration. Using a moving micropipette source of cAMP, we show the D discoideum cells can orient toward a gradient in which the concentration is everywhere decreasing with time–implying a spatial mechanism. 2) The number of molecules N that must be released by a source to orient a cell is limited by the natural concentration “noise” due to diffusion. N is shown to be simply related to the cell size and the distance from the source. 3) We show that previous diffusion equations for cell population movement have not taken the speed variations (klinokinesis) into account properly, and we present a new result that does. 4) We briefly discuss reaction-diffusion models of cell orientation.     

Theoretical analysis of gradient detection by growth cones.

Gradients of diffusible and substrate-bound molecules play an important role in guiding axons to appropriate targets in the developing nervous system. Although some of the molecules involved have recently been identified, little is known about the physical mechanisms by which growth cones sense gradients. This article applies the seminal Berg and Purcell (1977) model of gradient sensing to this problem. The model provides estimates for the statistical fluctuations in the measurement of concentration by a small sensing device. By assuming that gradient detection consists of the comparison of concentrations at two spatially or temporally separated points, the model therefore provides an estimate for the steepness of gradient that can be detected as a function of physiological parameters. The model makes the following specific predictions. (a) It is more likely that growth cones use a spatial rather than temporal sensing strategy. (b) Growth cone sensitivity increases with the concentration of ligand, the speed of ligand diffusion, the size of the growth cone, and the time over which it averages the gradient signal. (c) The minimum detectable gradient steepness for growth cones is roughly in the range 1-10%. (d) This value varies depending on whether a bound or freely diffusing ligand is being sensed, and on whether the sensing occurs in three or two dimensions. The model also makes predictions concerning the role of filopodia in gradient detection.     

Theoretical analysis of gradient detection by growth cones

Gradients of diffusible and substrate‐bound molecules play an important role in guiding axons to appropriate targets in the developing nervous system. Although some of the molecules involved have recently been identified, little is known about the physical mechanisms by which growth cones sense gradients. This article applies the seminal Berg and Purcell (1977) model of gradient sensing to this problem. The model provides estimates for the statistical fluctuations in the measurement of concentration by a small sensing device. By assuming that gradient detection consists of the comparison of concentrations at two spatially or temporally separated points, the model therefore provides an estimate for the steepness of gradient that can be detected as a function of physiological parameters. The model makes the following specific predictions. (a) It is more likely that growth cones use a spatial rather than temporal sensing strategy. (b) Growth cone sensitivity increases with the concentration of ligand, the speed of ligand diffusion, the size of the growth cone, and the time over which it averages the gradient signal. (c) The minimum detectable gradient steepness for growth cones is roughly in the range 1–10%. (d) This value varies depending on whether a bound or freely diffusing ligand is being sensed, and on whether the sensing occurs in three or two dimensions. The model also makes predictions concerning the role of filopodia in gradient detection. © 1999 John Wiley & Sons, Inc. J Neurobiol 41: 230–241, 1999     

Construction of a thermotaxis chamber providing spatial or temporal thermal gradients monitored by an infrared video camera system.

A thermotaxis chamber was constructed to quantitatively study thermotaxis in eukaryotic amoeboid cells. The apparatus provided either spatial or temporal temperature gradients in an observation chamber set in an inverted microscope. With an infrared video camera system, spatial thermal gradients were monitored directly and the temperature at the actual location of the cells could be estimated accurately. This enabled a precise determination of the strength of thermal stimuli. With this apparatus, we were able to simultaneously measure temperature and observe cellular behavior directly. This feature permits quantitative studies on stimulus-response relationships. The utility of the apparatus was demonstrated by thermotaxis assay under a spatial thermal gradient in polymorphonuclear leukocytes. Since this apparatus can also provide temporal thermal gradients, it may have several applications in studies of temperature-dependent phenomena in cell biology.     

Stability and nuclear dynamics of the bicoid morphogen gradient

Patterning in multicellular organisms results from spatial gradients in morphogen concentration, but the dynamics of these gradients remain largely unexplored. We characterize, through in vivo optical imaging, the development and stability of the Bicoid morphogen gradient in Drosophila embryos that express a Bicoid-eGFP fusion protein. The gradient is established rapidly (approximately 1 hr after fertilization), with nuclear Bicoid concentration rising and falling during mitosis. Interphase levels result from a rapid equilibrium between Bicoid uptake and removal. Initial interphase concentration in nuclei in successive cycles is constant (+/-10%), demonstrating a form of gradient stability, but it subsequently decays by approximately 30%. Both direct photobleaching measurements and indirect estimates of Bicoid-eGFP diffusion constants (D < or = 1 microm(2)/s) provide a consistent picture of Bicoid transport on short ( approximately min) time scales but challenge traditional models of long-range gradient formation. A new model is presented emphasizing the possible role of nuclear dynamics in shaping and scaling the gradient.     

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.     

Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching

We used single DNA molecule stretching to investigate DNA intercalation by ethidium and three ruthenium complexes. By measuring ligand-induced DNA elongation at different ligand concentrations, we determined the binding constant and site size as a function of force. Both quantities depend strongly on force and, in the limit of zero force, converge to the known bulk solution values, when available. This approach allowed us to distinguish the intercalative mode of ligand binding from other binding modes and allowed characterization of intercalation with binding constants ranging over almost six orders of magnitude, including ligands that do not intercalate under experimentally accessible solution conditions. As ligand concentration increased, the DNA stretching curves saturated at the maximum amount of ligand intercalation. The results showed that the applied force partially relieves normal intercalation constraints. We also characterized the flexibility of intercalator-saturated dsDNA for the first time.     

Spatial and temporal demographic variation drives within-season fluctuations in sexual selection

Our understanding of selection in nature stems mainly from whole-season and cross-sectional estimates of selection gradients. These estimates suggest that selection is relatively constant within, but fluctuates between seasons. However, the strength of selection depends on demographics, and because demographics can vary within seasons, there is a gap in our understanding regarding the extent to which seasonal fluctuations in demographics may cause variation in selection. Here we use two populations of the golden orb-web spider (Nephila plumipes) that differ in density to examine how demographics change within a season and whether there are correlated shifts in selection. We demonstrate that there is within-season variation in sex ratio and density at multiple spatial and temporal scales. This variation led to changes in the competitive challenges that males encountered at different times of the season and was correlated with significant variation in selection gradients on male size and weight between sampling periods. We highlight the importance of understanding the biology of the organism under study to correctly determine the relevant scale in which to examine selection. We also argue that studies may underestimate the true variation in selection by averaging values, leading to misinterpretation of the effect of selection on phenotypic evolution.     

The internal phosphodiesterase RegA is essential for the suppression of lateral pseudopods during Dictyostelium chemotaxis

Dictyostelium strains in which the gene encoding the cytoplasmic cAMP phosphodiesterase RegA is inactivated form small aggregates. This defect was corrected by introducing copies of the wild-type regA gene, indicating that the defect was solely the consequence of the loss of the phosphodiesterase. Using a computer-assisted motion analysis system, regA(-) mutant cells were found to show little sense of direction during aggregation. When labeled wild-type cells were followed in a field of aggregating regA(-) cells, they also failed to move in an orderly direction, indicating that signaling was impaired in mutant cell cultures. However, when labeled regA(-) cells were followed in a field of aggregating wild-type cells, they again failed to move in an orderly manner, primarily in the deduced fronts of waves, indicating that the chemotactic response was also impaired. Since wild-type cells must assess both the increasing spatial gradient and the increasing temporal gradient of cAMP in the front of a natural wave, the behavior of regA(-) cells was motion analyzed first in simulated temporal waves in the absence of spatial gradients and then was analyzed in spatial gradients in the absence of temporal waves. Our results demonstrate that RegA is involved neither in assessing the direction of a spatial gradient of cAMP nor in distinguishing between increasing and decreasing temporal gradients of cAMP. However, RegA is essential for specifically suppressing lateral pseudopod formation during the response to an increasing temporal gradient of cAMP, a necessary component of natural chemotaxis. We discuss the possibility that RegA functions in a network that regulates myosin phosphorylation by controlling internal cAMP levels, and, in support of that hypothesis, we demonstrate that myosin II does not localize in a normal manner to the cortex of regA(-) cells in an increasing temporal gradient of cAMP.     

Ion transport and the vibrating probe.

The theory of ion transport in the vicinity of a vibrating probe is developed. It is shown that the convection loops produced by the probe will not affect the electrical current density, assuming that the action of the probe does not affect the sources of the current in the biological system. However, the convection loops will significantly alter the ion concentration gradients in the unstirred layer near a tissue or cell surface. The concentration gradients within each convection loop will be reduced, while the concentration gradients between the loops and outside of the loops will be increased relative to the gradients existing without the probe. As a consequence, the electrical potential gradients can be changed relative to the potential gradients existing in the absence of the convection caused by the probe. If the mobility of the ion species carrying the electrical current is greater than the average ion mobility in the medium, then a decrease in ion concentration gradient will be accompanied by an increase in electrical potential gradient, while an increase in concentration gradient will be accompanied by a decrease or even a reversal of electrical potential gradient. Thus, the electrical potential gradient measured by the probe will depend on the concentration gradient in the vicinity of the probe, which will depend in turn on the spatial relation of the convection loops to the probe. An example of the effect of the convection loops on ion concentration and electrical potential is obtained from the theory via a numerical computer calculation. Experimental tests of this theory are discussed.     

A stochastic model for chemosensory cell movement: application to neutrophil and macrophage persistence and orientation

Two central features of leukocyte chemosensory movement behavior demand fundamental theoretical understanding. In uniform concentrations of chemoattractant, these cells exhibit a persistent random walk, with a characteristic “persistence time” between significant changes in direction. In chemoattractant concentration gradients, they demonstrate a biased random walk, with an “orientation bias” characterizing the fraction of cells moving up the gradient. A coherent picture of cell-movement responses to chemoattractant requires that both the persistence time and the orientation bias be explained within a unifying framework. In this paper we offer the possibility that “noise” in the cellular signal perception/response mechanism can simultaneously account for these two key phenomena. In particular, we report on a stochastic mathematical model for cell locomotion based on kinetic fluctuations in chemoattractant receptor binding. This model proves to be capable of stimulating cell paths similar to those observed experimentally for two cell types examined to date: neutrophils and alveolar macrophages, under conditions of uniform chemoattractant concentrations as well as chemoattractant concentration gradients. Further, this model can quantitatively predict both cell persistence time and dependence of orientation bias on gradient size. The model also successfully predicts that an increase in persistence time is associated with a decrease in orientation for typical system parameter values, as is observed for alveolar macrophages in comparison to neutrophils. Thus, the concept of signal “noise” can quantitatively unify the major characteristics of leukocyte random motility and chemotaxis. The same level of noise large enough to account for the observed frequency of turning in uniform environments is simultaneously small enough to allow for the observed degree of directional bias in gradients. This suggests that chemosensory cell movement behavior may be based on a “usefully” imperfect integrated signal response system, which allows both random and directed searches under appropriate conditions.     

Northern fowl mite orientation in a thermal gradient and evidence for idiothetic course control

Abstract.  The northern fowl mite, Ornithonyssus sylviarum , is an ectoparasite of birds and a poultry pest. The ability of northern fowl mites to orientate to a heat source is investigated with individual mites video-recorded in two-dimensional arenas and exposed to spatial or temporal heat gradients. Recorded tracks are digitally analysed for variation in linear velocity, mean direction of movement, and patterns in angular displacement. Mean direction of movement in a spatial gradient is significantly associated with the position of the heat source for 24/29 mites tested ( P  < 0.05), whereas most control (no heat) mean bearings are randomly distributed (16/25; P  > 0.1). Angular displacement that orientates a mite towards the heat source is positively correlated with the preceding deviation from that direction ( P  < 0.01). Angular displacement away from the heat source is random. The temporal heat gradient is such that no spatial reference to the heat source exists within the plane of the arena. Mites in an ambient (27 °C) to heated (30 °C) transition have angular displacement distributions similar to control mites (ambient to ambient transition). However, mites in a heated to ambient transition execute angular displacements approximately 25° greater than mites in the other treatments ( P  < 0.03). Mites compare the shift in temperature over time and alter their direction of movement by a programmed (idiothetic) response to a decrease in temperature, rather than through detection of the spatial position of the gradient (allothetic).     

Diverse chemotactic responses of Dictyostelium discoideum amoebae in the developing (temporal) and stationary (spatial) concentration gradients of folic acid,cAMP, Ca(2+) and Mg(2+)

The responses of Dictyostelium discoideum amoebae to developing (temporal) and stationary (spatial) gradients of folic acid, cAMP, Ca(2+), and Mg(2+) were studied using the methods of computer-aided image analysis. The results presented demonstrate that the new type of experimental chambers used for the observation of single cells moving within the investigated gradients of chemoattractants permit time lapse recording of single amoebae and determination of the trajectories of moving cells. It was found that, besides folic acid and cAMP (natural chemoattractants for Dictyostelium discoideum amoebae), also extracellular Ca(2+) and Mg(2+) are potent inducers of these cells' chemotaxis, and the amoebae of D. discoideum can respond to various chemoattractants differently. In the positively developing gradients of folic acid, cAMP, Ca(2+), and Mg(2+) oriented locomotion of amoebae directed towards the higher concentration of the tested chemoattractants was observed. However, in the negatively developing (temporal) and stationary linear (spatial) gradients, the univocal chemotaxis of amoebae was recorded only in the case of the Mg(2+) concentration gradient. This demonstrates that amoebae can respond to both developing and stationary gradients, depending upon the nature of the chemoattractant. We also investigated the effects of chosen inhibitors of signalling pathways upon chemotaxis of D. discoideum amoebae in the positively developing (temporal) gradients of tested chemoattractants. Verapamil was found to abolish the chemotaxis of amoebae only in the Ca(2+) gradients. Pertussis toxin suppressed the chemotactic response of cells in the gradients of folic acid and cAMP but did not prevent chemotaxis in those of Ca(2+) and Mg(2+), while quinacrine inhibited chemotaxis in the gradients of folic acid, cAMP, and Ca(2+) but only slightly affected chemotaxis in the Mg(2+) gradient. None of the tested inhibitors causes inhibition of cell random movement, when applied in isotropic solution. Also EDTA and EGTA up to 50 mM concentration did not inhibit locomotion of amoebae in control isotropic solutions.