Chromosome Translocation Inflates Bacillus Forespores and Impacts Cellular Morphology.

The means by which the physicochemical properties of different cellular components together determine bacterial cell shape remain poorly understood. Here, we investigate a programmed cell-shape change during Bacillus subtilis sporulation, when a rod-shaped vegetative cell is transformed to an ovoid spore. Asymmetric cell division generates a bigger mother cell and a smaller, hemispherical forespore. The septum traps the forespore chromosome, which is translocated to the forespore by SpoIIIE. Simultaneously, forespore size increases as it is reshaped into an ovoid. Using genetics, timelapse microscopy, cryo-electron tomography, and mathematical modeling, we demonstrate that forespore growth relies on membrane synthesis and SpoIIIE-mediated chromosome translocation, but not on peptidoglycan or protein synthesis. Our data suggest that the hydrated nucleoid swells and inflates the forespore, displacing ribosomes to the cell periphery, stretching septal peptidoglycan, and reshaping the forespore. Our results illustrate how simple biophysical interactions between core cellular components contribute to cellular morphology.

Effectiveness of Pseudomonas aeruginosa type VI secretion system relies on toxin potency and type IV pili-dependent interaction.

The type VI secretion system (T6SS) is an antibacterial weapon that is used by numerous Gram-negative bacteria to gain competitive advantage by injecting toxins into adjacent prey cells. Predicting the outcome of a T6SS-dependent competition is not only reliant on presence-absence of the system but instead involves a multiplicity of factors. Pseudomonas aeruginosa possesses 3 distinct T6SSs and a set of more than 20 toxic effectors with diverse functions including disruption of cell wall integrity, degradation of nucleic acids or metabolic impairment. We generated a comprehensive collection of mutants with various degrees of T6SS activity and/or sensitivity to each individual T6SS toxin. By imaging whole mixed bacterial macrocolonies, we then investigated how these P. aeruginosa strains gain a competitive edge in multiple attacker/prey combinations. We observed that the potency of single T6SS toxin varies significantly from one another as measured by monitoring the community structure, with some toxins acting better in synergy or requiring a higher payload. Remarkably the degree of intermixing between preys and attackers is also key to the competition outcome and is driven by the frequency of contact as well as the ability of the prey to move away from the attacker using type IV pili-dependent twitching motility. Finally, we implemented a computational model to better understand how changes in T6SS firing behaviours or cell-cell contacts lead to population level competitive advantages, thus providing conceptual insight applicable to all types of contact-based competition.

Growth-rate dependent resource investment in bacterial motile behavior quantitatively follows potential benefit of chemotaxis.

Microorganisms possess diverse mechanisms to regulate investment into individual cellular processes according to their environment. How these regulatory strategies reflect the inherent trade-off between the benefit and cost of resource investment remains largely unknown, particularly for many cellular functions that are not immediately related to growth. Here, we investigate regulation of motility and chemotaxis, one of the most complex and costly bacterial behaviors, as a function of bacterial growth rate. We show with experiment and theory that in poor nutritional conditions, Escherichia coli increases its investment in motility in proportion to the reproductive fitness advantage provided by the ability to follow nutrient gradients. Since this growth-rate dependent regulation of motility genes occurs even when nutrient gradients are absent, we hypothesize that it reflects an anticipatory preallocation of cellular resources. Notably, relative fitness benefit of chemotaxis could be observed not only in the presence of imposed gradients of secondary nutrients but also in initially homogeneous bacterial cultures, suggesting that bacteria can generate local gradients of carbon sources and excreted metabolites, and subsequently use chemotaxis to enhance the utilization of these compounds. This interplay between metabolite excretion and their chemotaxis-dependent reutilization is likely to play an important general role in microbial communities.

Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium.

Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. However, most of this interest has focused on developing coarse ecosystem-level maximisation principles, providing little insight into underlying mechanisms that lead to such emergent constraints. Microbial communities are a natural system to decipher this mechanistic basis because their interactions in the form of substrate consumption, metabolite production, and cross-feeding can be described explicitly in thermodynamic terms. Previous work has considered how thermodynamic constraints impact competition between pairs of species, but restrained from analysing how this manifests in complex dynamical systems. To address this gap, we develop a thermodynamic microbial community model with fully reversible reaction kinetics, which allows direct consideration of free-energy dissipation. This also allows species to interact via products rather than just substrates, increasing the dynamical complexity, and allowing a more nuanced classification of interaction types to emerge. Using this model, we find that community diversity increases with substrate lability, because greater free-energy availability allows for faster generation of niches. Thus, more niches are generated in the time frame of community establishment, leading to higher final species diversity. We also find that allowing species to make use of near-to-equilibrium reactions increases diversity in a low free-energy regime. In such a regime, two new thermodynamic interaction types that we identify here reach comparable strengths to the conventional (competition and facilitation) types, emphasising the key role that thermodynamics plays in community dynamics. Our results suggest that accounting for realistic thermodynamic constraints is vital for understanding the dynamics of real-world microbial communities.

A critical-like collective state leads to long-range cell communication in Dictyostelium discoideum aggregation.

The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosphate (cAMP). However, how exactly do transient, short-range chemical gradients lead to coherent collective movement at a macroscopic scale? Here, we developed a multiscale model verified by quantitative microscopy to describe behaviors ranging widely from chemotaxis and excitability of individual cells to aggregation of thousands of cells. To better understand the mechanism of long-range cell-cell communication and hence aggregation, we analyzed cell-cell correlations, showing evidence of self-organization at the onset of aggregation (as opposed to following a leader cell). Surprisingly, cell collectives, despite their finite size, show features of criticality known from phase transitions in physical systems. By comparing wild-type and mutant cells with impaired aggregation, we found the longest cell-cell communication distance in wild-type cells, suggesting that criticality provides an adaptive advantage and optimally sized aggregates for the dispersal of spores.

Thermodynamics of switching in multistable non-equilibrium systems.

Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback, but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and entropy production. Here, we will link fluctuation theorems for the entropy production along trajectories with the action obtainable from the Freidlin-Wentzell theorem to elucidate the thermodynamics of switching between states in the large volume limit of multistable systems. We find that the entropy production at steady state plays no role, but the entropy production during switching is key. Steady-state entropy and diffusive noise strength can be neglected in this limit. The relevance to biological, ecological, and climate models is apparent.

Target shape dependence in a simple model of receptor-mediated endocytosis and phagocytosis.

Phagocytosis and receptor-mediated endocytosis are vitally important particle uptake mechanisms in many cell types, ranging from single-cell organisms to immune cells. In both processes, engulfment by the cell depends critically on both particle shape and orientation. However, most previous theoretical work has focused only on spherical particles and hence disregards the wide-ranging particle shapes occurring in nature, such as those of bacteria. Here, by implementing a simple model in one and two dimensions, we compare and contrast receptor-mediated endocytosis and phagocytosis for a range of biologically relevant shapes, including spheres, ellipsoids, capped cylinders, and hourglasses. We find a whole range of different engulfment behaviors with some ellipsoids engulfing faster than spheres, and that phagocytosis is able to engulf a greater range of target shapes than other types of endocytosis. Further, the 2D model can explain why some nonspherical particles engulf fastest (not at all) when presented to the membrane tip-first (lying flat). Our work reveals how some bacteria may avoid being internalized simply because of their shape, and suggests shapes for optimal drug delivery.

Drift and Behavior of E. coli Cells.

Chemotaxis of the bacterium Escherichia coli is well understood in shallow chemical gradients, but its swimming behavior remains difficult to interpret in steep gradients. By focusing on single-cell trajectories from simulations, we investigated the dependence of the chemotactic drift velocity on attractant concentration in an exponential gradient. Whereas maxima of the average drift velocity can be interpreted within analytical linear-response theory of chemotaxis in shallow gradients, limits in drift due to steep gradients and finite number of receptor-methylation sites for adaptation go beyond perturbation theory. For instance, we found a surprising pinning of the cells to the concentration in the gradient at which cells run out of methylation sites. To validate the positions of maximal drift, we recorded single-cell trajectories in carefully designed chemical gradients using microfluidics.

How cells engulf: a review of theoretical approaches to phagocytosis.

Phagocytosis is a fascinating process whereby a cell surrounds and engulfs particles such as bacteria and dead cells. This is crucial both for single-cell organisms (as a way of acquiring nutrients) and as part of the immune system (to destroy foreign invaders). This whole process is hugely complex and involves multiple coordinated events such as membrane remodelling, receptor motion, cytoskeleton reorganisation and intracellular signalling. Because of this, phagocytosis is an excellent system for theoretical study, benefiting from biophysical approaches combined with mathematical modelling. Here, we review these theoretical approaches and discuss the recent mathematical and computational models, including models based on receptors, models focusing on the forces involved, and models employing energetic considerations. Along the way, we highlight a beautiful connection to the physics of phase transitions, consider the role of stochasticity, and examine links between phagocytosis and other types of endocytosis. We cover the recently discovered multistage nature of phagocytosis, showing that the size of the phagocytic cup grows in distinct stages, with an initial slow stage followed by a much quicker second stage starting around half engulfment. We also address the issue of target shape dependence, which is relevant to both pathogen infection and drug delivery, covering both one-dimensional and two-dimensional results. Throughout, we pay particular attention to recent experimental techniques that continue to inform the theoretical studies and provide a means to test model predictions. Finally, we discuss population models, connections to other biological processes, and how physics and modelling will continue to play a key role in future work in this area.

A model of cell-wall dynamics during sporulation in Bacillus subtilis.

To survive starvation, Bacillus subtilis forms durable spores. After asymmetric cell division, the septum grows around the forespore in a process called engulfment, but the mechanism of force generation is unknown. Here, we derived a novel biophysical model for the dynamics of cell-wall remodeling during engulfment based on a balancing of dissipative, active, and mechanical forces. By plotting phase diagrams, we predict that sporulation is promoted by a line tension from the attachment of the septum to the outer cell wall, as well as by an imbalance in turgor pressures in the mother-cell and forespore compartments. We also predict that significant mother-cell growth hinders engulfment. Hence, relatively simple physical principles may guide this complex biological process.

Protein Connectivity in Chemotaxis Receptor Complexes.

The chemotaxis sensory system allows bacteria such as Escherichia coli to swim towards nutrients and away from repellents. The underlying pathway is remarkably sensitive in detecting chemical gradients over a wide range of ambient concentrations. Interactions among receptors, which are predominantly clustered at the cell poles, are crucial to this sensitivity. Although it has been suggested that the kinase CheA and the adapter protein CheW are integral for receptor connectivity, the exact coupling mechanism remains unclear. Here, we present a statistical-mechanics approach to model the receptor linkage mechanism itself, building on nanodisc and electron cryotomography experiments. Specifically, we investigate how the sensing behavior of mixed receptor clusters is affected by variations in the expression levels of CheA and CheW at a constant receptor density in the membrane. Our model compares favorably with dose-response curves from in vivo Förster resonance energy transfer (FRET) measurements, demonstrating that the receptor-methylation level has only minor effects on receptor cooperativity. Importantly, our model provides an explanation for the non-intuitive conclusion that the receptor cooperativity decreases with increasing levels of CheA, a core signaling protein associated with the receptors, whereas the receptor cooperativity increases with increasing levels of CheW, a key adapter protein. Finally, we propose an evolutionary advantage as explanation for the recently suggested CheW-only linker structures.

Accurate encoding and decoding by single cells: amplitude versus frequency modulation.

Cells sense external concentrations and, via biochemical signaling, respond by regulating the expression of target proteins. Both in signaling networks and gene regulation there are two main mechanisms by which the concentration can be encoded internally: amplitude modulation (AM), where the absolute concentration of an internal signaling molecule encodes the stimulus, and frequency modulation (FM), where the period between successive bursts represents the stimulus. Although both mechanisms have been observed in biological systems, the question of when it is beneficial for cells to use either AM or FM is largely unanswered. Here, we first consider a simple model for a single receptor (or ion channel), which can either signal continuously whenever a ligand is bound, or produce a burst in signaling molecule upon receptor binding. We find that bursty signaling is more accurate than continuous signaling only for sufficiently fast dynamics. This suggests that modulation based on bursts may be more common in signaling networks than in gene regulation. We then extend our model to multiple receptors, where continuous and bursty signaling are equivalent to AM and FM respectively, finding that AM is always more accurate. This implies that the reason some cells use FM is related to factors other than accuracy, such as the ability to coordinate expression of multiple genes or to implement threshold crossing mechanisms.

Bistable forespore engulfment in Bacillus subtilis by a zipper mechanism in absence of the cell wall.

To survive starvation, the bacterium Bacillus subtilis forms durable spores. The initial step of sporulation is asymmetric cell division, leading to a large mother-cell and a small forespore compartment. After division is completed and the dividing septum is thinned, the mother cell engulfs the forespore in a slow process based on cell-wall degradation and synthesis. However, recently a new cell-wall independent mechanism was shown to significantly contribute, which can even lead to fast engulfment in [Formula: see text] 60 [Formula: see text] of the cases when the cell wall is completely removed. In this backup mechanism, strong ligand-receptor binding between mother-cell protein SpoIIIAH and forespore-protein SpoIIQ leads to zipper-like engulfment, but quantitative understanding is missing. In our work, we combined fluorescence image analysis and stochastic Langevin simulations of the fluctuating membrane to investigate the origin of fast bistable engulfment in absence of the cell wall. Our cell morphologies compare favorably with experimental time-lapse microscopy, with engulfment sensitive to the number of SpoIIQ-SpoIIIAH bonds in a threshold-like manner. By systematic exploration of model parameters, we predict regions of osmotic pressure and membrane-surface tension that produce successful engulfment. Indeed, decreasing the medium osmolarity in experiments prevents engulfment in line with our predictions. Forespore engulfment may thus not only be an ideal model system to study decision-making in single cells, but its biophysical principles are likely applicable to engulfment in other cell types, e.g. during phagocytosis in eukaryotes.

Predicting chemical environments of bacteria from receptor signaling.

Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber's law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine.

The mechanism of phagocytosis: two stages of engulfment.

Despite being of vital importance to the immune system, the mechanism by which cells engulf relatively large solid particles during phagocytosis is still poorly understood. From movies of neutrophil phagocytosis of polystyrene beads, we measure the fractional engulfment as a function of time and demonstrate that phagocytosis occurs in two distinct stages. During the first stage, engulfment is relatively slow and progressively slows down as phagocytosis proceeds. However, at approximately half-engulfment, the rate of engulfment increases dramatically, with complete engulfment attained soon afterwards. By studying simple mathematical models of phagocytosis, we suggest that the first stage is due to a passive mechanism, determined by receptor diffusion and capture, whereas the second stage is more actively controlled, perhaps with receptors being driven toward the site of engulfment. We then consider a more advanced model that includes signaling and captures both stages of engulfment. This model predicts that there is an optimum ligand density for quick engulfment. Further, we show how this model explains why nonspherical particles engulf quickest when presented tip-first. Our findings suggest that active regulation may be a later evolutionary innovation, allowing fast and robust engulfment even for large particles.

The motor protein myosin 1G functions in FcγR-mediated phagocytosis.

Phagocytosis is the force-dependent complex cellular process by which immune cells engulf particles. Although there has been considerable progress in understanding ligand-receptor-induced actin polymerisation in pushing the membrane around the particle, significantly less is known about how localised contractile activities regulate cup closure in coordination with the actin cytoskeleton. Herein, we show that the unconventional class-I myosin, myosin 1G (Myo1G) is localised at phagocytic cups following Fcγ-receptor (FcγR) ligation in macrophages. This progressive recruitment is dependent on the activity of phosphoinositide 3-kinase and is particularly important for engulfment of large particles. Furthermore, point mutations in the conserved pleckstrin homology-like domain of Myo1G abolishes the localisation of the motor protein at phagocytic cups and inhibits engulfment downstream of FcγR. Binding of Myo1G to both F-actin and phospholipids might enable cells to transport phospholipids towards the leading edge of cups and to facilitate localised contraction for cup closure.

Unraveling adaptation in eukaryotic pathways: lessons from protocells.

Eukaryotic adaptation pathways operate within wide-ranging environmental conditions without stimulus saturation. Despite numerous differences in the adaptation mechanisms employed by bacteria and eukaryotes, all require energy consumption. Here, we present two minimal models showing that expenditure of energy by the cell is not essential for adaptation. Both models share important features with large eukaryotic cells: they employ small diffusible molecules and involve receptor subunits resembling highly conserved G-protein cascades. Analyzing the drawbacks of these models helps us understand the benefits of energy consumption, in terms of adjustability of response and adaptation times as well as separation of cell-external sensing and cell-internal signaling. Our work thus sheds new light on the evolution of adaptation mechanisms in complex systems.

Unraveling biochemical spatial patterns: Machine learning approaches to the inverse problem of stationary Turing patterns.

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is challenging. To address this, we aim to solve the inverse problem in artificial and experimental Turing patterns. This task is challenging since patterns are often corrupted by noise and slight changes in initial conditions can lead to different patterns. We used both least squares to explore the problem and physics-informed neural networks to build a noise-robust method. We elucidate the functionality of our network in scenarios mimicking biological noise levels and showcase its application using an experimentally obtained chemical pattern. The findings reveal the significant promise of machine learning in steering the creation of synthetic patterns in bioengineering, thereby advancing our grasp of morphological intricacies within biological systems while acknowledging existing limitations.

Dynamics of natural killer cell receptor revealed by quantitative analysis of photoswitchable protein.

Natural Killer (NK) cell activation is dynamically regulated by numerous activating and inhibitory surface receptors that accumulate at the immune synapse. Quantitative analysis of receptor dynamics has been limited by methodologies that rely on indirect measurements such as fluorescence recovery after photobleaching. Here, we report an apparently novel approach to study how proteins traffic to and from the immune synapse using NK cell receptors tagged with the photoswitchable fluorescent protein tdEosFP, which can be irreversibly photoswitched from a green to red fluorescent state by ultraviolet light. Thus, after a localized switching event, the movement of the photoswitched molecules can be temporally and spatially resolved by monitoring fluorescence in two regions of interest. By comparing images with mathematical models, we evaluated the diffusion coefficient of the receptor KIR2DL1 (0.23 ± 0.06 µm(2) s(-1)) and assessed how synapse formation affects receptor dynamics. Our data conclude that the inhibitory NK cell receptor KIR2DL1 is continually trafficked into the synapse, and remains surprisingly stable there. Unexpectedly, however, in NK cells forming synapses with multiple target cells simultaneously, KIR2DL1 at one synapse can relocate to another synapse. Thus, our results reveal a previously undetected intersynaptic exchange of protein.

ROCK1 and ROCK2 regulate epithelial polarisation and geometric cell shape.

BACKGROUND INFORMATION: Cell-cell adhesion and contraction play an essential role in the maintenance of geometric shape and polarisation of epithelial cells. However, the molecular regulation of contraction during cell elongation leading to epithelial polarisation and acquisition of geometric cell shape is not clear. RESULTS: Upon induction of cell-cell adhesion, we find that human keratinocytes acquire specific geometric shapes favouring hexagons, by re-modelling junction length/orientation and thus neighbour allocation. Acquisition of geometric shape correlates temporally with epithelial polarisation, as shown by an increase in lateral height. ROCK1 and ROCK2 are important regulators of myosin II contraction, but their specific role in epithelial cell shape has not been addressed. Depletion of ROCK proteins interferes with the correct proportion of hexagonal cell shapes and full elongation of lateral domain. Interestingly, ROCK proteins are not essential for maintenance of circumferential thin bundles, the main contractile epithelial F-actin pool. Instead, ROCK1 or ROCK2 regulates thin bundle contraction and positioning along the lateral domain, an important event for the stabilisation of the elongating lateral domain. Mechanistically, E-cadherin clustering specifically leads to ROCK1/ROCK2-dependent inactivation of myosin phosphatase and phosphorylation of myosin regulatory light chain. These events correlate temporally with the increase in lateral height and thin bundle compaction towards junctions. CONCLUSION: We conclude that ROCK proteins are necessary for acquisition of elongated and geometric cell shape, two key events for epithelial differentiation.