Chemosensory responses of Acanthamoeba castellanii: visual analysis of random movement and responses to chemical signals

Unravelling mechanisms of bacterial recognition by Acanthamoeba: insights into microbial ecology and immune responses

Acanthamoeba, are ubiquitous eukaryotic microorganisms, that play a pivotal role in recognizing and engulfing various microbes during predation, offering insights into microbial dynamics and immune responses. An intriguing observation lies in the apparent preference of Acanthamoeba for Gram-negative over Gram-positive bacteria, suggesting potential differences in the recognition and response mechanisms to bacterial prey. Here, we comprehensively review pattern recognition receptors (PRRs) and microbe associated molecular patterns (MAMPs) that influence Acanthamoeba interactions with bacteria. We analyze the molecular mechanisms underlying these interactions, and the key finding of this review is that Acanthamoeba exhibits an affinity for bacterial cell surface appendages that are decorated with carbohydrates. Notably, this parallels warm-blooded immune cells, underscoring a conserved evolutionary strategy in microbial recognition. This review aims to serve as a foundation for exploring PRRs and MAMPs. These insights enhance our understanding of ecological and evolutionary dynamics in microbial interactions and shed light on fundamental principles governing immune responses. Leveraging Acanthamoeba as a model organism, provides a bridge between ecological interactions and immunology, offering valuable perspectives for future research.

Taurine, a Component of the Tear Film, Exacerbates the Pathogenic Mechanisms of Acanthamoeba castellanii in the Ex Vivo Amoebic Keratitis Model

Acanthamoeba spp. is the etiological agent of amoebic keratitis. In this study, the effect of taurine in physiological concentrations in tears (195 μM) on trophozoites of Acanthamoeba castellanii through the ex vivo amoebic keratitis model was evaluated. Trophozoites were coincubated with the Syrian golden hamster cornea (Mesocricetus auratus) for 3 and 6 h. Group 1: Control (-). Corneas coincubated with amoebic culture medium and taurine. Group 2: Control (+). Corneas coincubated with trophozoites without taurine. Group 3: Corneas coincubated with taurine 15 min before adding trophozoites. Group 4: Trophozoites coincubated 15 min with taurine before placing them on the cornea. Group 5: Corneas coincubated for 15 min with trophozoites; subsequently, taurine was added. Results are similar for both times, as evaluated by scanning electron microscopy. As expected, in the corneas of Group 1, no alterations were observed in the corneal epithelium. In the corneas of Group 2, few adhered trophozoites were observed on the corneal surface initiating migrations through cell junctions as previously described; however, in corneas of Groups 3, 4 and 5, abundant trophozoites were observed, penetrating through different corneal cell areas, emitting food cups and destabilizing corneal surface in areas far from cell junctions. Significant differences were confirmed in trophozoites adherence coincubated with taurine (p < 0.05). Taurine does not prevent the adhesion and invasion of the amoebae, nor does it favor its detachment once these have adhered to the cornea, suggesting that taurine in the physiological concentrations found in tears stimulates pathogenic mechanisms of A. castellanii.

On the origin of the functional versatility of macrophages

Macrophages represent the most functionally versatile cells in the animal body. In addition to recognizing and destroying pathogens, macrophages remove senescent and exhausted cells, promote wound healing, and govern tissue and metabolic homeostasis. In addition, many specialized populations of tissue-resident macrophages exhibit highly specialized functions essential for the function of specific organs. Sometimes, however, macrophages cease to perform their protective function and their seemingly incomprehensible response to certain stimuli leads to pathology. In this study, we address the question of the origin of the functional versatility of macrophages. To this end, we have searched for the evolutionary origin of macrophages themselves and for the emergence of their characteristic properties. We hypothesize that many of the characteristic features of proinflammatory macrophages evolved in the unicellular ancestors of animals, and that the functional repertoire of macrophage-like amoebocytes further expanded with the evolution of multicellularity and the increasing complexity of tissues and organ systems. We suggest that the entire repertoire of macrophage functions evolved by repurposing and diversification of basic functions that evolved early in the evolution of metazoans under conditions barely comparable to that in tissues of multicellular organisms. We believe that by applying this perspective, we may find an explanation for the otherwise counterintuitive behavior of macrophages in many human pathologies.

Variables Affecting the Recovery of Acanthamoeba Trophozoites

While the results of Acanthamoeba testing have been extensively published, laboratories conducting such testing are left to develop their own methods in the absence of a standardized methodology. The wide disparity of methods has resulted in equally inconsistent reported results for contact lens care (CLC) products. This study's objective was to determine the source of these discrepancies by evaluating basic Acanthamoeba biology and their impact on antimicrobial efficacy testing, including the ability of a recovery method to stimulate a single trophozoite to proliferate. Antimicrobial efficacy testing was conducted using well-published Acanthamoeba strains, storage conditions, and growth-based recovery methods. To identify variables that influence results, test solutions with low Acanthamoeba disinfection rates were utilized to prevent differences from being masked by high log reductions. In addition, single-cell proliferation assays were executed to understand the growth requirements to stimulate trophozoite propagation in two recovery methods. These studies indicated that both nutrient density (>106 CFU) and the length of plate incubation (at least 14 days) could significantly influence the accurate recovery of trophozoites. Together, this study emphasizes the need to understand how Acanthamoeba trophozoites biology can impact test methods to create divergent results.

Novel insights into the potential role of ion transport in sensory perception in Acanthamoeba

Background

Acanthamoeba is well known to produce a blinding keratitis and serious brain infection known as encephalitis. Effective treatment is problematic, and can continue up to a year, and even then, recurrence can ensue. Partly, this is due to the capability of vegetative amoebae to convert into resistant cysts. Cysts can persist in an inactive form for decades while retaining their pathogenicity. It is not clear how Acanthamoeba cysts monitor environmental changes, and determine favourable conditions leading to their emergence as viable trophozoites.

Methods

The role of ion transporters in the encystation and excystation of Acanthamoeba remains unclear. Here, we investigated the role of sodium, potassium and calcium ion transporters as well as proton pump inhibitors on A. castellanii encystation and excystation and their effects on trophozoites.

Results

Remarkably 3′,4′-dichlorobenzamil hydrochloride a sodium–calcium exchange inhibitor, completely abolished excystation of Acanthamoeba. Furthermore, lanthanum oxide and stevioside hydrate, both potassium transport inhibitors, resulted in the partial inhibition of Acanthamoeba excystation. Conversely, none of the ion transport inhibitors affected encystation or had any effects on Acanthamoeba trophozoites viability.

Conclusions

The present study indicates that ion transporters are involved in sensory perception of A. castellanii suggesting their value as potential therapeutic targets to block cellular differentiation that presents a significant challenge in the successful prognosis of Acanthamoeba infections.

3D Hydrogels Containing Interconnected Microchannels of Subcellular Size for Capturing Human Pathogenic Acanthamoeba Castellanii

Porous hydrogel scaffolds are ideal candidates for mimicking cellular microenvironments, regarding both structural and mechanical aspects. We present a novel strategy to use uniquely designed ceramic networks as templates for generating hydrogels with a network of interconnected pores in the form of microchannels. The advantages of this new approach are the high and guaranteed interconnectivity of the microchannels, as well as the possibility to produce channels with diameters smaller than 7 μm. Neither of these assets can be ensured with other established techniques. Experiments using the polyacrylamide substrates produced with our approach have shown that the migration of human pathogenic Acanthamoeba castellanii trophozoites is manipulated by the microchannel structure in the hydrogels. The parasites can even be captured inside the microchannel network and removed from their incubation medium by the porous polyacrylamide, indicating the huge potential of our new technique for medical, pharmaceutical, and tissue engineering applications.

A bacteriophages journey through the human body

The human body is colonized by a diverse collective of microorganisms, including bacteria, fungi, protozoa and viruses. The smallest entity of this microbial conglomerate are the bacterial viruses. Bacteriophages, or phages for short, exert significant selective pressure on their bacterial hosts, undoubtedly influencing the human microbiome and its impact on our health and well-being. Phages colonize all niches of the body, including the skin, oral cavity, lungs, gut, and urinary tract. As such our bodies are frequently and continuously exposed to diverse collections of phages. Despite the prevalence of phages throughout our bodies, the extent of their interactions with human cells, organs, and immune system is still largely unknown. Phages physically interact with our mucosal surfaces, are capable of bypassing epithelial cell layers, disseminate throughout the body and may manipulate our immune system. Here, I establish the novel concept of an "intra-body phageome," which encompasses the collection of phages residing within the classically "sterile" regions of the body. This review will take a phage-centric view of the microbiota, human body, and immune system with the ultimate goal of inspiring a greater appreciation for both the indirect and direct interactions between bacteriophages and their mammalian hosts.

Acanthamoeba and Dictyostelium as Cellular Models for Legionella Infection

Environmental bacteria of the genus Legionella naturally parasitize free-living amoebae. Upon inhalation of bacteria-laden aerosols, the opportunistic pathogens grow intracellularly in alveolar macrophages and can cause a life-threatening pneumonia termed Legionnaires' disease. Intracellular replication in amoebae and macrophages takes place in a unique membrane-bound compartment, the Legionella-containing vacuole (LCV). LCV formation requires the bacterial Icm/Dot type IV secretion system, which translocates literally hundreds of "effector" proteins into host cells, where they modulate crucial cellular processes for the pathogen's benefit. The mechanism of LCV formation appears to be evolutionarily conserved, and therefore, amoebae are not only ecologically significant niches for Legionella spp., but also useful cellular models for eukaryotic phagocytes. In particular, Acanthamoeba castellanii and Dictyostelium discoideum emerged over the last years as versatile and powerful models. Using genetic, biochemical and cell biological approaches, molecular interactions between amoebae and Legionella pneumophila have recently been investigated in detail with a focus on the role of phosphoinositide lipids, small and large GTPases, autophagy components and the retromer complex, as well as on bacterial effectors targeting these host factors.

The many lives of nontuberculous mycobacteria

Nontuberculous mycobacteria (NTM) include species that colonize human epithelia, as well as species that are ubiquitous in soil and aquatic environments. NTM that primarily inhabit soil and aquatic environments include the Mycobacterium avium complex (MAC, M. avium and Mycobacterium intracellulare) and the Mycobacterium abscessus complex (MABSC, M. abscessus subspecies abscessus, massiliense, and bolletii), and can be free-living, biofilm-associated, or amoeba-associated. Although NTM are rarely pathogenic in immunocompetent individuals, those who are immunocompromised - due to either an inherited or acquired immunodeficiency - are highly susceptible to NTM infection (NTMI). Several characteristics such as biofilm formation and the ability of select NTM species to form distinct colony morphotypes all may play a role in pathogenesis not observed in the related, well-characterized pathogen Mycobacterium tuberculosis The recognition of different morphotypes of NTM has been established and characterized since the 1950s, but the mechanisms that underlie colony phenotype change and subsequent differences in pathogenicity are just beginning to be explored. Advances in genomic analysis have led to progress in identifying genes important to the pathogenesis and persistence of MAC disease as well as illuminating genetic aspects of different colony morphotypes. Here we review recent literature regarding NTM ecology and transmission, as well as the factors which regulate colony morphotype and pathogenicity.

Acanthamoeba and Dictyostelium Use Different Foraging Strategies

Amoeba often use cell movement as a mechanism to find food, such as bacteria, in their environment. The chemotactic movement of the soil amoeba Dictyostelium to folate or other pterin compounds released by bacteria is a well-documented foraging mechanism. Acanthamoeba can also feed on bacteria but relatively little is known about the mechanism(s) by which this amoeba locates bacteria. Acanthamoeba movement in the presence of folate or bacteria was analyzed in above agar assays and compared to that observed for Dictyostelium. The overall mobility of Acanthamoeba was robust like that of Dictyostelium but Acanthamoeba did not display a chemotactic response to folate. In the presence of bacteria, Acanthamoeba only showed a marginal bias in directed movement whereas Dictyostelium displayed a strong chemotactic response. A comparison of genomes revealed that Acanthamoeba and Dictyostelium share some similarities in G protein signaling components but that specific G proteins used in Dictyostelium chemotactic responses were not present in current Acanthamoeba genome sequence data. The results of this study suggest that Acanthamoeba does not use chemotaxis as the primary mechanism to find bacterial food sources and that the chemotactic responses of Dictyostelium to bacteria may have co-evolved with chemotactic responses that facilitate multicellular development.

Impact of climate change on larch budmoth cyclic outbreaks

Periodic outbreaks of the larch budmoth Zeiraphera diniana population (and the massive forest defoliation they engender) have been recorded in the Alps over the centuries and are known for their remarkable regularity. But these have been conspicuously absent since 1981. On the other hand, budmoth outbreaks have been historically unknown in the larches of the Carpathian Tatra mountains. To resolve this puzzle, we propose here a model which includes the influence of climate and explains both the 8–9 year periodicity in the budmoth cycle and the variations from this, as well as the absence of cycles. We successfully capture the observed trend of relative frequencies of outbreaks, reproducing the dominant periodicities seen. We contend that the apparent collapse of the cycle in 1981 is due to changing climatic conditions following a tipping point and propose the recurrence of the cycle with a changed periodicity of 40 years – the next outbreak could occur in 2021. Our model also predicts longer cycles.

Subdiffusive motion of bacteriophage in mucosal surfaces increases the frequency of bacterial encounters

Bacteriophages (phages) defend mucosal surfaces against bacterial infections. However, their complex interactions with their bacterial hosts and with the mucus-covered epithelium remain mostly unexplored. Our previous work demonstrated that T4 phage with Hoc proteins exposed on their capsid adhered to mucin glycoproteins and protected mucus-producing tissue culture cells in vitro. On this basis, we proposed our bacteriophage adherence to mucus (BAM) model of immunity. Here, to test this model, we developed a microfluidic device (chip) that emulates a mucosal surface experiencing constant fluid flow and mucin secretion dynamics. Using mucus-producing human cells and Escherichia coli in the chip, we observed similar accumulation and persistence of mucus-adherent T4 phage and nonadherent T4∆hoc phage in the mucus. Nevertheless, T4 phage reduced bacterial colonization of the epithelium >4,000-fold compared with T4∆hoc phage. This suggests that phage adherence to mucus increases encounters with bacterial hosts by some other mechanism. Phages are traditionally thought to be completely dependent on normal diffusion, driven by random Brownian motion, for host contact. We demonstrated that T4 phage particles displayed subdiffusive motion in mucus, whereas T4∆hoc particles displayed normal diffusion. Experiments and modeling indicate that subdiffusive motion increases phage-host encounters when bacterial concentration is low. By concentrating phages in an optimal mucus zone, subdiffusion increases their host encounters and antimicrobial action. Our revised BAM model proposes that the fundamental mechanism of mucosal immunity is subdiffusion resulting from adherence to mucus. These findings suggest intriguing possibilities for engineering phages to manipulate and personalize the mucosal microbiome.

First-passage times in multiscale random walks: The impact of movement scales on search efficiency

An efficient searcher needs to balance properly the trade-off between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free Lévy search strategies. Here we study multiscale random walks as an approximation to the scale-free case and derive the exact expressions for their mean-first-passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the situation in which both nearby and faraway targets are available to the searcher, so the exploration-exploitation trade-off does not have a trivial solution. For this situation, we prove that the combination of only two movement scales is able to outperform both ballistic and Lévy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about target distances or distributions. Furthermore, we found that the incorporation of additional (three, four, …) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies arise through the informed combination of only two walk scales (related to the exploitative and the explorative scales, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through Lévy paths (or, equivalently, through a hierarchical combination of multiple scales).

An update on Acanthamoeba keratitis: diagnosis, pathogenesis and treatment

Free-living amoebae of the genus Acanthamoeba are causal agents of a severe sight-threatening infection of the cornea known as Acanthamoeba keratitis. Moreover, the number of reported cases worldwide is increasing year after year, mostly in contact lens wearers, although cases have also been reported in non-contact lens wearers. Interestingly, Acanthamoeba keratitis has remained significant, despite our advances in antimicrobial chemotherapy and supportive care. In part, this is due to an incomplete understanding of the pathogenesis and pathophysiology of the disease, diagnostic delays and problems associated with chemotherapeutic interventions. In view of the devastating nature of this disease, here we present our current understanding of Acanthamoeba keratitis and molecular mechanisms associated with the disease, as well as virulence traits of Acanthamoeba that may be potential targets for improved diagnosis, therapeutic interventions and/or for the development of preventative measures. Novel molecular approaches such as proteomics, RNAi and a consensus in the diagnostic approaches for a suspected case of Acanthamoeba keratitis are proposed and reviewed based on data which have been compiled after years of working on this amoebic organism using many different techniques and listening to many experts in this field at conferences, workshops and international meetings. Altogether, this review may serve as the milestone for developing an effective solution for the prevention, control and treatment of Acanthamoeba infections.

Optimal cooperative searching using purely repulsive interactions

Foraging, either solitarily or collectively, is a necessary behavior for survival that is demonstrated by many organisms. Foraging can be collectively optimized by utilizing communication between the organisms. Examples of such communication range from high level strategic foraging by animal groups to rudimentary signaling among unicellular organisms. Here we systematically study the simplest form of communication via long range repulsive interactions between multiple diffusing Brownian searchers on a one-dimensional lattice. We show that the mean first passage time for any one of them to reach a fixed target depends non-monotonically on the range of the interaction and can be optimized for a repulsive range that is comparable to the average spacing between searchers. Our results suggest that even the most rudimentary form of collective searching does in fact lower the search time for the foragers suggesting robust mechanisms for search optimization in cellular communities.

Temperature limitation may explain the containment of the trophozoites in the cornea during Acanthamoeba castellanii keratitis

Acanthamoeba keratitis is a serious sight-threatening disease. The relatively low temperature of the cornea may explain why amoebic infections usually are localized in this tissue and rarely spread to other parts of the eye. In this study, the growth rate of the amoeba Acanthamoeba castellanii was examined at different temperatures. The aim was to establish the optimal growth temperature for A. castellanii and to examine the growth within the vicinity of the core body temperature. The growth rates of four clinical and two environmental strains of A. castellanii were estimated at different temperatures, and temperature limitations for the trophozoite stage was established. Movements influenced by temperature gradients were monitored for two clinical strains of A. castellanii. The highest growth rate for each of the six amoebic strains tested was found to be close to 32 °C. The growth of the trophozoites of all examined strains was greatly reduced or completely halted at temperatures above 36 °C and encysted at the elevated temperature. Thus, the optimal growth temperature for the four strains of A. castellanii is close to the surface temperature of the human cornea, while the higher body core-temperature induced encysting of the amoebae. This may explain why most amoebic eye infections are confined to the cornea.

On Relationships Between Fixation Identification Algorithms and Fractal Box Counting Methods

Fixation identification algorithms facilitate data comprehension and provide analytical convenience in eye-tracking analysis. However, current fixation algorithms for eye-tracking analysis are heavily dependent on parameter choices, leading to instabilities in results and incompleteness in reporting. This work examines the nature of human scanning patterns during complex scene viewing. We show that standard implementations of the commonly used distance-dispersion algorithm for fixation identification are functionally equivalent to greedy spatiotemporal tiling. We show that modeling the number of fixations as a function of tiling size leads to a measure of fractal dimensionality through box counting. We apply this technique to examine scale-free gaze behaviors in toddlers and adults looking at images of faces and blocks, as well as large number of adults looking at movies or static images. The distributional aspects of the number of fixations may suggest a fractal structure to gaze patterns in free scanning and imply that the incompleteness of standard algorithms may be due to the scale-free behaviors of the underlying scanning distributions. We discuss the nature of this hypothesis, its limitations, and offer directions for future work.

ON THE ENSEMBLE AVERAGE OF GENERALIZED TRUNCATED RANDOM WALK

A new analytical solution is developed for the one- and two- dimensional generalized discrete time random walk with discrete and finite length of jumping. It is shown that the ensemble average of the mean square displacement has a linear relation with time. This result is general and independent of mathematical form of distribution function but magnitude of diffusion coefficient depends on the distribution function. This result confirms our previous numerical work. The truncated Levy flight is studied as a special case and the diffusion coefficient for different maximum length of jump is calculated numerically. The obtained results are in good agreement with the analytical solution.

Optimization of random searches on defective lattice networks

We study the general problem of how to search efficiently for targets randomly located on defective lattice networks--i.e., regular lattices which have some fraction of its nodes randomly removed. We consider large but finite triangular lattices and assume for the search dynamics that the walker chooses steps lengths lj from the power-law distribution P(lj) approximately lj(-mu) , with the exponent mu regulating the strategy of the search process. At each step lj, the searcher moves in straight lines and constantly looks within a detection radius of vision rv for the targets along the way. If there is contact with a defect, the movement stops and a new step length is chosen. Hence, the presence of defects decreases the efficiency of the overall process. We study numerically how three different aspects of the lattice influence the optimization of the search efficiency: (i) the type of boundary conditions, (ii) the concentration of targets and defects, and (iii) the category or class of search--destructive, nondestructive, or regenerative. Motivated by the results, we develop a type of mean-field model for the problem and obtain an analytical approximation for the search efficiency function. Finally we discuss, in the context of searches, how defective lattices compare with perfect lattices and with continuous environments.

Scaling laws of marine predator search behaviour

Many free-ranging predators have to make foraging decisions with little, if any, knowledge of present resource distribution and availability. The optimal search strategy they should use to maximize encounter rates with prey in heterogeneous natural environments remains a largely unresolved issue in ecology. Lévy walks are specialized random walks giving rise to fractal movement trajectories that may represent an optimal solution for searching complex landscapes. However, the adaptive significance of this putative strategy in response to natural prey distributions remains untested. Here we analyse over a million movement displacements recorded from animal-attached electronic tags to show that diverse marine predators-sharks, bony fishes, sea turtles and penguins-exhibit Lévy-walk-like behaviour close to a theoretical optimum. Prey density distributions also display Lévy-like fractal patterns, suggesting response movements by predators to prey distributions. Simulations show that predators have higher encounter rates when adopting Lévy-type foraging in natural-like prey fields compared with purely random landscapes. This is consistent with the hypothesis that observed search patterns are adapted to observed statistical patterns of the landscape. This may explain why Lévy-like behaviour seems to be widespread among diverse organisms, from microbes to humans, as a 'rule' that evolved in response to patchy resource distributions.

Minimizing errors in identifying Lévy flight behaviour of organisms

1. Lévy flights are specialized random walks with fundamental properties such as superdiffusivity and scale invariance that have recently been applied in optimal foraging theory. Lévy flights have movement lengths chosen from a probability distribution with a power-law tail, which theoretically increases the chances of a forager encountering new prey patches and may represent an optimal solution for foraging across complex, natural habitats. 2. An increasing number of studies are detecting Lévy behaviour in diverse organisms such as microbes, insects, birds, and mammals including humans. A principal method for detecting Lévy flight is whether the exponent (micro) of the power-law distribution of movement lengths falls within the range 1 < micro < or = 3. The exponent can be determined from the histogram of frequency vs. movement (step) lengths, but different plotting methods have been used to derive the Lévy exponent across different studies. 3. Here we investigate using simulations how different plotting methods influence the micro-value and show that the power-law plotting method based on 2(k) (logarithmic) binning with normalization prior to log transformation of both axes yields low error (1.4%) in identifying Lévy flights. Furthermore, increasing sample size reduced variation about the recovered values of micro, for example by 83% as sample number increased from n = 50 up to 5000. 4. Simple log transformation of the axes of the histogram of frequency vs. step length underestimated micro by c.40%, whereas two other methods, 2(k) (logarithmic) binning without normalization and calculation of a cumulative distribution function for the data, both estimate the regression slope as 1-micro. Correction of the slope therefore yields an accurate Lévy exponent with estimation errors of 1.4 and 4.5%, respectively. 5. Empirical reanalysis of data in published studies indicates that simple log transformation results in significant errors in estimating micro, which in turn affects reliability of the biological interpretation. The potential for detecting Lévy flight motion when it is not present is minimized by the approach described. We also show that using a large number of steps in movement analysis such as this will also increase the accuracy with which optimal Lévy flight behaviour can be detected.

Scale-free movement patterns arising from olfactory-driven foraging

The scale-free movement patterns of some foragers has aroused considerable excitement because they are known to optimize the success of random searches when target sites are randomly and sparsely distributed. Here it is shown that scale-free movement patterns can arise from a naive response of foragers to scent concentrations within turbulent plume structures.

Optimization of random searches on regular lattices

We investigate random searches on isotropic and topologically regular square and triangular lattices with periodic boundary conditions and study the efficiency of search strategies based on a power-law distribution P() approximately (-mu) of step lengths . We consider both destructive searches, in which a target can be visited only once, and nondestructive searches, when a target site is always available for future visits. We discuss (i) the dependence of the search efficiency on the choice of the lattice topology, (ii) the relevance of the periodic boundary conditions, (iii) the behavior of the optimal power-law exponent mu(opt) as a function of target site density, (iv) the differences between destructive and nondestructive environments, and finally (v) how the results for the discrete searches differ from the continuous cases previously studied.

Dynamical robustness of Lévy search strategies

We study the role of dynamical constraints in the general problem of finding the best statistical strategy for random searching when the targets can be detected only in the limited vicinity of the searcher. We find that the optimal search strategy depends strongly on the delay time tau during which a previously visited site becomes unavailable. We also find that the optimal search strategy is always described for large step lengths l by a power-law distribution P(l) approximately l(-mu), with 1<mu(tau)</=2. Our findings appear to remain valid even if arbitrary energy costs of locomotion are considered.

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.

Optimizing the success of random searches

We address the general question of what is the best statistical strategy to adapt in order to search efficiently for randomly located objects ('target sites'). It is often assumed in foraging theory that the flight lengths of a forager have a characteristic scale: from this assumption gaussian, Rayleigh and other classical distributions with well-defined variances have arisen. However, such theories cannot explain the long-tailed power-law distributions of flight lengths or flight times that are observed experimentally. Here we study how the search efficiency depends on the probability distribution of flight lengths taken by a forager that can detect target sites only in its limited vicinity. We show that, when the target sites are sparse and can be visited any number of times, an inverse square power-law distribution of flight lengths, corresponding to Lévy flight motion, is an optimal strategy. We test the theory by analysing experimental foraging data on selected insect, mammal and bird species, and find that they are consistent with the predicted inverse square power-law distributions.