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Journal articleRichards DM, Endres RG, 2017,
How cells engulf: a review of theoretical approaches to phagocytosis.
, Reports on Progress in Physics, Vol: 80, ISSN: 0034-4885Phagocytosis 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.
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Journal articleYap L, Endres RG, 2017,
A model of cell-wall dynamics during sporulation in Bacillus subtilis
, Soft Matter, Vol: 13, Pages: 8089-8095, ISSN: 1744-683XTo 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.
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Journal articleRotrattanadumrong R, Endres RG, 2017,
Emergence of cooperativity in a model biofilm
, Journal of Physics D: Applied Physics, Vol: 50, ISSN: 0022-3727Evolution to multicellularity from an aggregate of cells involves altruistic cooperation between individual cells, which is in conflict with Darwinian evolution. How cooperation arises and how a cell community resolves such conflicts remains unclear. In this study, we investigated the spontaneous emergence of cell differentiation and the subsequent division of labour in evolving cellular metabolic networks. In spatially extended cell aggregates, our findings reveal that resource limitation can lead to the formation of subpopulations and cooperation of cells, and hence multicellular communities. A specific example of our model can explain the recently observed oscillatory growth in Bacillus subtilis biofilms.
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Journal articleWeber CA, Lee CF, Juelicher F, 2017,
Droplet ripening in concentration gradients
, New Journal of Physics, Vol: 19, ISSN: 1367-2630Living cells use phase separation and concentration gradients to organize chemical compartments inspace. Here, we present a theoretical study of droplet dynamics in gradient systems. We derive thecorresponding growth law of droplets andfind that droplets exhibit a drift velocity and positiondependent growth. As a consequence, the dissolution boundary moves through the system, therebysegregating droplets to one end. We show that for steep enough gradients, the ripening leads to atransient arrest of droplet growth that is induced by a narrowing of the droplet size distribution.
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Journal articleDe Palo G, Yi D, Endres RG, 2017,
A critical-like collective state leads to long-range cell communication in Dictyostelium discoideum aggregation
, PLOS Biology, Vol: 15, ISSN: 1544-9173The 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.
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Journal articleOjkic N, Lopez-Garrido J, Pogliano K, et al., 2016,
Cell-wall remodeling drives engulfment during Bacillus subtiliss porulation
, eLife, Vol: 5, ISSN: 2050-084XWhen starved, the Gram-positive bacterium Bacillus subtilis forms durable spores forsurvival. Sporulation initiates with an asymmetric cell division, creating a large mother cell and asmall forespore. Subsequently, the mother cell membrane engulfs the forespore in a phagocytosislikeprocess. However, the force generation mechanism for forward membrane movement remainsunknown. Here, we show that membrane migration is driven by cell wall remodeling at the leadingedge of the engulfing membrane, with peptidoglycan synthesis and degradation mediated bypenicillin binding proteins in the forespore and a cell wall degradation protein complex in themother cell. We propose a simple model for engulfment in which the junction between the septumand the lateral cell wall moves around the forespore by a mechanism resembling the ‘templatemodel’. Hence, we establish a biophysical mechanism for the creation of a force for engulfmentbased on the coordination between cell wall synthesis and degradation.
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Journal articleKral N, Hanna Ougolnikova A, Sena G, 2016,
Externally imposed electric field enhances plant root tip regeneration
, Regeneration, Vol: 3, Pages: 156-167, ISSN: 2052-4412In plants, shoot and root regeneration can be induced in the distinctive conditions oftissue culture (in vitro), but is also observed in intact individuals (in planta) recoveringfrom tissue damage. Roots, for example, can regenerate their fully excised meristems inplanta, even in mutants with impaired apical stem cell niches. Unfortunately, to date acomprehensive understanding of regeneration in plants is still missing.Here, we provide evidence that an imposed electric field can perturb apical rootregeneration in Arabidopsis. Crucially, we explored both spatial and temporalcompetences of the stump to respond to electrical stimulation, respectively by varyingthe position of the cut and the time interval between excision and stimulation.Our data indicate that a brief pulse of an electric field parallel to the root is sufficient toincrease by up to two-fold the probability of its regeneration, and to perturb the localdistribution of the hormone auxin, as well as cell division regulation. Remarkably, theorientation of the root towards the anode or the cathode is shown to play a role.
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Journal articleJean L, Lee CF, Hodder P, et al., 2016,
Dynamics of the formation of a hydrogel by a pathogenic amyloid peptide: islet amyloid polypeptide
, Scientific Reports, Vol: 6, ISSN: 2045-2322Many chronic degenerative diseases result from aggregation of misfolded polypeptides to form amyloids. Many amyloidogenic polypeptides are surfactants and their assembly can be catalysed by hydrophobic-hydrophilic interfaces (an air-water interface in-vitro or membranes in-vivo). We recently demonstrated the specificity of surface-induced amyloidogenesis but the mechanisms of amyloidogenesis and more specifically of adsorption at hydrophobic-hydrophilic interfaces remain poorly understood. Thus, it is critical to determine how amyloidogenic polypeptides behave at interfaces. Here we used surface tensiometry, rheology and electron microscopy to demonstrate the complex dynamics of gelation by full-length human islet amyloid polypeptide (involved in type II diabetes) both in the bulk solution and at hydrophobic-hydrophilic interfaces (air-water interface and phospholipids). We show that the hydrogel consists of a 3D supramolecular network of fibrils. We also assessed the role of solvation and dissected the evolution over time of the assembly processes. Amyloid gelation could have important pathological consequences for membrane integrity and cellular functions.
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Journal articleRichards D, Endres RG, 2016,
Target-shape dependence in a simple model of receptor-mediated endocytosis and phagocytosis
, Proceedings of the National Academy of Sciences of the United States of America, Vol: 113, Pages: 6113-6118, ISSN: 1091-6490Along with other forms of internalisation, phagocytosis and receptormediatedendocytosis are vitally important for many cell types, rangingfrom single-cell organisms to immune cells. It is known experimentallythat engulfment in both cases depends critically on particleshape and orientation. However, most previous theoretical workhas focused only on spherical particles and hence disregards the widerangingparticle shapes occurring in nature, such as those of bacteria.Here, by implementing a simple model in one- and two-dimensions, wecompare and contrast receptor-mediated endocytosis and phagocytosisfor a range of biologically-relevant shapes, including spheres, ellipsoids,capped-cylinders and hourglasses. We find a whole range of different engulfmentbehaviours with some ellipsoids engulfing quicker than spheres,and that phagocytosis is able to engulf a greater range of target shapesthan other types of endocytosis. Further, the two-dimensional modelcan explain why some non-spherical particles engulf quickest (not at all)when presented to the membrane tip-first (lying flat). Our work revealshow some bacteria may avoid being internalised simply by their shape,and suggests shapes for optimal drug delivery.
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Journal articleLee CF, Pruessner G, 2016,
Percolation mechanism drives actin gels to the critically connected state
, Physical Review E, Vol: 93, ISSN: 1539-3755Cell motility and tissue morphogenesis depend crucially on the dynamic remodelling of actomyosinnetworks. An actomyosin network consists of an actin polymer network connected by crosslinkerproteins and motor protein myosins that generate internal stresses on the network. A recent discoveryshows that for a range of experimental parameters, actomyosin networks contract to clusterswith a power-law size distribution [Alvarado J. et al. (2013) Nature Physics 9 591]. Here, weargue that actomyosin networks can exhibit robust critical signature without fine-tuning becausethe dynamics of the system can be mapped onto a modified version of percolation with trapping(PT), which is known to show critical behaviour belonging to the static percolation universalityclass without the need of fine-tuning of a control parameter. We further employ our PT model togenerate experimentally testable predictions.
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