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Brownian dynamics simulations demonstrating chemotactic performance a–c Simulated trajectories of a non-motile cell, a Haloferax sp. Boulby Mine (HXBM) cell, and an E. coli cell (respectively) in a chemical gradient. d Effects of modulating τrun for chemotactic strategies as indicated. Drift speed increases until τrun ~ 10 s for bipolar and run-lengthening modes. In run-shortening mode, the optimal run duration is around τrun ~ 20 s. Error bars represent s.e.m. (standard error of the mean). e Mean-squared displacements per unit time for simulated cells. Series represent HXBM unless otherwise indicated. Molecular diffusivities are given to the right, for comparison. S.e.m. is <0.02% of the values for all but the purely diffusive case and so have been omitted. f Fractional chemotactic drift speed of HXBM. The fractional drift speed increases at low v0 before saturating at around vx ≈ 0.1v0. Error bars represent s.e.m., and the series are coloured according to the swimming modes as in panel d. g Swimming efficiency (ε) multiplied by the friction coefficient (γ), showing a broad decline in efficiency at higher speeds, consistent with the results in panel f. Error bars represent s.e.m., and the series are coloured according to the swimming modes as in panel d.
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Archaea have evolved to survive in some of the most extreme environments on earth. Life in extreme, nutrient-poor conditions gives the opportunity to probe fundamental energy limitations on movement and response to stimuli, two essential markers of living systems. Here we use three-dimensional holographic microscopy and computer simulations to reve...
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Citations
... Bacterial cells (sizes ∼ 10 −6 m) often swim in a series of relatively straight runs (length ∼ 10 −4 to 10 −5 m) separated by reorientation events. Depending on the species, bacterial reorientations vary from deflections in swimming trajectory (32) through to reversals (33)(34)(35) or complete stops (36), during which time Brownian motion reorients cells. One of the most commonly observed swimming phenotypes is the "run-and-tumble" motility observed in soil bacteria such as Bacillus subtilis and enteric bacteria such as Escherichia coli. ...
... Presence of a Chemoattractant. To test for the presence or absence of a soluble chemoattractant produced by the plant, we initially attempted some holographic particle tracking (33,54) to see whether the swimming patterns of P. multimicronucleaton were modified when swimming close to the rhizophyll. These results were inconclusive so instead we performed a T-maze choice assay of the type used by van Houten et al. (42) (as in Fig. 1E). ...
Carnivory in plants is an unusual trait that has arisen multiple times, independently, throughout evolutionary history. Plants in the genus Genlisea are carnivorous and feed on microorganisms that live in soil using modified subterranean leaf structures (rhizophylls). A surprisingly broad array of microfauna has been observed in the plants’ digestive chambers, including ciliates, amoebae, and soil mites. Here, we show, through experiments and simulations, that Genlisea exploit active matter physics to “rectify” bacterial swimming and establish a local flux of bacteria through the structured environment of the rhizophyll toward the plant’s digestion vesicle. In contrast, macromolecular digestion products are free to diffuse away from the digestion vesicle and establish a concentration gradient of carbon sources to draw larger microorganisms further inside the plant. Our experiments and simulations show that this mechanism is likely to be a localized one and that no large-scale efflux of digested matter is present.
... Many microorganisms employ swimming mechanisms to optimize their survival strategies and explore their diverse habitats, where they are subject to strong confinements, hydrodynamic flows, and various external stimuli [1][2][3][4][5][6]. Environmental cues can steer the orientation of microswimmers and thus generate interesting dynamics emerging from the translational-orientational coupling. ...
... Analytical results have been obtained in some parameter and temporal regimes using perturbative approaches [43], yet a characterization of the full spatiotemporal dynamics has not been elaborated. Establishing a profound understanding of those dynamics is expected to provide fundamental insights for both biological systems, where the interplay of rotational diffusion and directed motion via chemotaxis plays an important role for microbial survival strategies [5,7], and for engineering efficient cargo-carriers at the micro-scale [29,30], where a reset of their swimming direction through external means could allow overcoming diffusion and guiding them towards the desired target. ...
We employ renewal processes to characterize the spatiotemporal dynamics of an active Brownian particle under stochastic orientational resetting. By computing the experimentally accessible intermediate scattering function (ISF) and reconstructing the full time-dependent distribution of the displacements, we study the interplay of rotational diffusion and resetting. The resetting process introduces a new spatiotemporal regime reflecting the directed motion of agents along the resetting direction at large length scales, which becomes apparent in an imaginary part of the ISF. We further derive analytical expressions for the low-order moments of the displacements and find that the variance displays an effective diffusive regime at long times, which decreases for increasing resetting rates. At intermediate times the dynamics are characterized by a negative skewness as well as a non-zero non-Gaussian parameter.
... It was shown that biological cells operate at the informationtheoretic limits of gradient sensing during chemotaxis if concentration gradients are shallow (see Refs. [6,7,22] for SC and Refs. [12,13,23,24] for TC). ...
Biological cells and small organisms navigate in concentration fields of signaling molecules using two fundamental gradient-sensing strategies: spatial comparison of concentrations measured at different positions on their surface and temporal comparison of concentrations measured at different locations visited along their motion path. It is believed that size and speed dictate which gradient-sensing strategy cells choose, yet this has never been formally proven. Using information theory, we investigate the optimal gradient-sensing mechanism for an ideal chemotactic agent that combines spatial and temporal comparisons. We account for the physical limits of chemosensation: molecule counting noise at physiological concentrations and motility noise inevitable at the microscale. Our simulation data collapse onto an empirical power law that predicts an optimal weighting of information as a function of motility and sensing noise, demonstrating how spatial comparison becomes more beneficial for agents that are large, slow, and less persistent. This refines and quantifies the previous heuristic notion. Our idealized model assuming unlimited information processing capabilities serves as a benchmark for the chemotaxis of biological cells.
Published by the American Physical Society 2024
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Quantitative tracking of rapidly moving micron-scale objects remains an elusive challenge in microscopy due to low signal-to-noise. This paper describes a novel method for tracking micron-sized motile organisms in off-axis Digital Holographic Microscope (DHM) raw holograms and/or reconstructions. We begin by processing the microscopic images with the previously reported Holographic Examination for Life-like Motility (HELM) software, which provides a variety of tracking outputs including motion history images (MHIs). MHIs are stills of videos where the frame-to-frame changes are indicated with color time-coding. This exposes tracks of objects that are difficult to identify in individual frames at a low signal-to-noise ratio. The visible tracks in the MHIs are superior to tracks identified by all tested automated tracking algorithms that start from object identification at the frame level, particularly in low signal-to-noise ratio data, but do not provide quantitative track data. In contrast to other tracking methods, like Kalman filter, where the recording is analyzed frame by frame, MHIs show the whole time span of particle movement at once and eliminate the need to identify objects in individual frames. This feature also enables post-tracking identification of low-SNR objects. We use these tracks, rather than object identification in individual frames, as a basis for quantitative tracking of Bacillus subtilis by first generating MHIs from X, Y, and t stacks (raw holograms or a projection over reconstructed planes), then using a region-tracking algorithm to identify and separate swimming pathways. Subsequently, we identify each object's Z plane of best focus at the corresponding X, Y, and t points, yielding ap full description of the swimming pathways in three spatial dimensions plus time. This approach offers an alternative to object-based tracking for processing large, low signal-to-noise datasets containing highly motile organisms.
... Digital Holographic Microscopy (DHM) is a high-throughput tool for imaging microscopic objects in three-dimensional space. It has great utility in biological research as a tool for studying the behaviour of microbes [1][2][3][4][5], and colloidal particles [6,7]. The three-dimensional swimming behaviour of microbes has been suggested as a way to classify species [8][9][10], and the simplicity and scalability of the DHM setup allows for its potential use in finding terrestrial or exobiological microbial life [11,12]. ...
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... Here we present a method of localising cells in three dimensions using YOLOv5 [34], for analysis in tracking routines. We trained the algorithm on a representative database of annotated DHM images of swimming Escherichia coli cells that were produced using previously described techniques [4,27]. We image at relatively low magnification (approximately 1 pixel per micrometer) in order to capture the cells' swimming patterns, which may extend for hundreds of micrometers. ...
The three-dimensional swimming tracks of motile microorganisms can be used to identify their species, which holds promise for the rapid identification of bacterial pathogens. The tracks also provide detailed information on the cells’ responses to external stimuli such as chemical gradients and physical objects. Digital holographic microscopy (DHM) is a well-established, but computationally intensive method for obtaining three-dimensional cell tracks from video microscopy data. We demonstrate that a common neural network (NN) accelerates the analysis of holographic data by an order of magnitude, enabling its use on single-board computers and in real time. We establish a heuristic relationship between the distance of a cell from the focal plane and the size of the bounding box assigned to it by the NN, allowing us to rapidly localise cells in three dimensions as they swim. This technique opens the possibility of providing real-time feedback in experiments, for example by monitoring and adapting the supply of nutrients to a microbial bioreactor in response to changes in the swimming phenotype of microbes, or for rapid identification of bacterial pathogens in drinking water or clinical samples.
... The framework of renewal processes is not limited to the RT motion of bacteria and can be extended to other multimode motility patterns, such as the "run-reverse(-flick)" [6][7][8] or "run-reverse-wrap" [9] motion. In future work, our method may thus allow for a quantitative characterization of a large variety of microorganisms. ...
We introduce a numerical method to extract the parameters of run-and-tumble dynamics from experimental measurements of the intermediate scattering function. We show that proceeding in Laplace space is unpractical and employ instead renewal processes to work directly in real time. We first validate our approach against data produced using agent-based simulations. This allows us to identify the length and time scales required for an accurate measurement of the motility parameters, including tumbling frequency and swim speed. We compare different models for the run-and-tumble dynamics by accounting for speed variability at the single-cell and population level, respectively. Finally, we apply our approach to experimental data on wild-type obtained using differential dynamic microscopy.
Published by the American Physical Society 2024
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We characterize the full spatiotemporal gait of populations of swimming using renewal processes to analyze the measurements of intermediate scattering functions. This allows us to demonstrate quantitatively how the persistence length of an engineered strain can be controlled by a chemical inducer and to report a controlled transition from perpetual tumbling to smooth swimming. For wild-type , we measure simultaneously the microscopic motility parameters and the large-scale effective diffusivity, hence quantitatively bridging for the first time small-scale directed swimming and macroscopic diffusion.
Published by the American Physical Society 2024
... The Berg-Purcell limit was later refined and 36 fundamental sensing limits for either pure SC or TC derived, see [16,17] for SC, and 37 [18][19][20][21] for TC. It was shown that biological cells operate at the information-theoretic 38 limits of gradient sensing during chemotaxis if concentration gradients are shallow, see 39 [6,7,22] for SC, [12,13,23,24] for TC. 40 Yet, the elementary question, which gradient-sensing strategy is optimal in which 41 noise regime and for which cell size remains unanswered. ...
Biological cells and small organisms navigate in concentration fields of signaling molecules using two fundamental gradient-sensing strategies: spatial comparison of concentrations measured at different positions on their surface, or temporal comparison of concentrations measured at different locations visited along their motion path. It is believed that size and speed dictate which gradient-sensing strategy cells choose, yet this has never been formally proven. Using information theory, we investigate the optimal gradient-sensing mechanism from the perspective of an ideal chemotactic agent that combines spatial and temporal comparison. We account for physical limits of chemo-sensation: molecule counting noise at physiological concentrations, and motility noise inevitable at the micro-scale. Our simulation data collapses onto an empirical power-law that predicts an optimal weighting of information as function of motility and sensing noise, demonstrating how spatial comparison becomes more beneficial for agents that are large, slow and less persistent. This refines and quantifies the previous heuristic notion. Our idealized model provides a base-line for biological chemotaxis and may inspire the design of robots guided by scalar fields.
... Digital holographic microscopy (DHM) is an established volumetric, 3D imaging technique particularly useful for particle tracking applications 4,5 . The inline DHM features a simple configuration compared to the off-axis version and has been applied for high-throughput, volumetric, 3D characterization of bacterial swimming behaviors 6,7,8 . However, these applications are limited to bacterial isolates, i.e., only one species/strain is measured in each experimental realization, which differs from more realistic conditions involving multiple species. ...
... Motility improves chances of survival as it enables active movement to sources of nutrients and away from toxins, instead of relying solely on diffusion (Stocker et al., 2008;Taylor and Buckling, 2013;Taylor and Stocker, 2011). The mechanisms of motility in different life-forms vary drastically, from flagella in prokaryotes and flagellates, to cilia in ciliates, to propagating kinks in filamentous bacteria, to polysaccharide pili secretion in filamentous cyanobacteria and pennate diatoms, and many more (Bayless et al., 2019;Bondoc et al., 2016;Khayatan et al., 2015;Merz et al., 2000;Nakamura and Minamino, 2019;Palma et al., 2022;Shaevitz et al., 2005;Thornton et al., 2020). These mechanisms manifest in different forms of motility that are often characterized as swimming, sliding, gliding, twitching, and swarming (Henrichsen, 1972;Wadhwa and Berg, 2022). ...
Motility is widely distributed across the tree of life and can be recognized by microscopy regardless of phylogenetic affiliation, biochemical composition, or mechanism. Microscopy has thus been proposed as a potential tool for detection of biosignatures for extraterrestrial life; however, traditional light microscopy is poorly suited for this purpose, as it requires sample preparation, involves fragile moving parts, and has a limited volume of view. In this study, we deployed a field-portable digital holographic microscope (DHM) to explore microbial motility in Badwater Spring, a saline spring in Death Valley National Park, and complemented DHM imaging with 16S rRNA gene amplicon sequencing and shotgun metagenomics. The DHM identified diverse morphologies and distinguished run-reverse-flick and run-reverse types of flagellar motility. PICRUSt2- and literature-based predictions based on 16S rRNA gene amplicons were used to predict motility genotypes/phenotypes for 36.0-60.1% of identified taxa, with the predicted motile taxa being dominated by members of Burkholderiaceae and Spirochaetota. A shotgun metagenome confirmed the abundance of genes encoding flagellar motility, and a Ralstonia metagenome-assembled genome encoded a full flagellar gene cluster. This study demonstrates the potential of DHM for planetary life detection, presents the first microbial census of Badwater Spring and brine pool, and confirms the abundance of mobile microbial taxa in an extreme environment.
