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  • Journal article
    Plesa T, Dack A, Ouldridge T, 2023,

    Integral feedback in synthetic biology: negative-equilibrium catastrophe

    , Journal of Mathematical Chemistry, Vol: 61, Pages: 1980-2018, ISSN: 0259-9791

    A central goal of synthetic biology is the design of molecular controllers that can manipulate the dynamics of intracellular networks in a stable and accurate manner. To address the factthat detailed knowledge about intracellular networks is unavailable, integral-feedback controllers(IFCs) have been put forward for controlling molecular abundances. These controllers can maintainaccuracy in spite of the uncertainties in the controlled networks. However, this desirable feature isachieved only if stability is also maintained. In this paper, we show that molecular IFCs can sufferfrom a hazardous instability called negative-equilibrium catastrophe (NEC), whereby all nonnegative equilibria vanish under the action of the controllers, and some of the molecular abundancesblow up. We show that unimolecular IFCs do not exist due to a NEC. We then derive a familyof bimolecular IFCs that are safeguarded against NECs when uncertain unimolecular networks,with any number of molecular species, are controlled. However, when IFCs are applied on uncertain bimolecular (and hence most intracellular) networks, we show that preventing NECs generallybecomes an intractable problem as the number of interacting molecular species increases. NECstherefore place a fundamental limit to design and control of molecular networks.

  • Journal article
    Qureshi BJ, Juritz J, Poulton JM, Beersing-Vasquez A, Ouldridge TEet al., 2023,

    A universal method for analyzing copolymer growth

    , Journal of Chemical Physics, Vol: 158, Pages: 1-22, ISSN: 0021-9606

    Polymers consisting of more than one type of monomer, known as copolymers,are vital to both living and synthetic systems. Copolymerisation has beenstudied theoretically in a number of contexts, often by considering a Markovprocess in which monomers are added or removed from the growing tip of a longcopolymer. To date, the analysis of the most general models of this class hasnecessitated simulation. We present a general method for analysing suchprocesses without resorting to simulation. Our method can be applied to modelswith an arbitrary network of sub-steps prior to addition or removal of amonomer, including non-equilibrium kinetic proofreading cycles. Moreover, theapproach allows for a dependency of addition and removal reactions on theneighbouring site in the copolymer, and thermodynamically self-consistentmodels in which all steps are assumed to be microscopically reversible. Usingour approach, thermodynamic quantities such as chemical work; kineticquantities such as time taken to grow; and statistical quantities such as thedistribution of monomer types in the growing copolymer can be derived eitheranalytically or numerically directly from the model definition.

  • Journal article
    Ouldridge T, Hertel S, Spinney R, Xu S, Morris R, Lee Let al., 2022,

    The stability and number of nucleating interactions determine DNA hybridisation rates in the absence of secondary structure

    , Nucleic Acids Research, Vol: 50, Pages: 7829-7841, ISSN: 0305-1048

    The kinetics of DNA hybridisation are fundamental to biological processes and DNA-based technologies.However, the precise physical mechanisms that determine why different DNA sequences hybridise at differentrates are not well understood. Secondary structure is one predictable factor that influences hybridisation ratesbut is not sufficient on its own to fully explain the observed sequence-dependent variance. In this context, wemeasured hybridisation rates of 43 different DNA sequences that are not predicted to form secondarystructure and present a parsimonious physically justified model to quantify our observations. Accounting onlyfor the combinatorics of complementary nucleating interactions and their sequence-dependent stability, themodel achieves good correlation with experiment with only two free parameters. Our results indicate thatgreater repetition of Watson-Crick pairs increases the number of initial states able to proceed to fullhybridisation, with the stability of those pairings dictating the likelihood of such progression, thus providingnew insight into the physical factors underpinning DNA hybridisation rates.

  • Book chapter
    Ouldridge T, Doye J, Louis A, Schreck J, Romano F, Harrison R, Mosayebi M, Engel Met al., 2022,

    Free energy landscapes of DNA and its assemblies: perspectives from coarse-grained modelling

    , Energy Landscapes of Nanoscale Systems, Publisher: Elsevier, Pages: 195-210, ISBN: 9780128244067

    This chapter will provide an overview of how characterising free energy landscapes can provide insights into the biophysical properties of DNA, as well as into the behaviour of the DNA assemblies used in the field of DNA nanotechnology. The landscapes for these complex systems are accessible through the use of accurate coarse-grained descriptions of DNA. Particular foci will be the landscapes associated with DNA self-assembly and mechanical deformation, where the latter can arise from either externally imposed forces or internal stresses.

  • Journal article
    Juritz J, Poulton JM, Ouldridge TE, 2022,

    Minimal mechanism for cyclic templating of length-controlled copolymers under isothermal conditions

    , Journal of Chemical Physics, Vol: 156, ISSN: 0021-9606

    The production of sequence-specific copolymers using copolymer templates is fundamental to the synthesis of complex biological molecules and is a promising framework for the synthesis of synthetic chemical complexes. Unlike the superficially similar process of self-assembly, however, the development of synthetic systems that implement templated copying of copolymers under constant environmental conditions has been challenging. The main difficulty has been overcoming product inhibition or the tendency of products to adhere strongly to their templates—an effect that gets exponentially stronger with the template length. We develop coarse-grained models of copolymerization on a finite-length template and analyze them through stochastic simulation. We use these models first to demonstrate that product inhibition prevents reliable template copying and then ask how this problem can be overcome to achieve cyclic production of polymer copies of the right length and sequence in an autonomous and chemically driven context. We find that a simple addition to the model is sufficient to generate far longer polymer products that initially form on, and then separate from, the template. In this approach, some of the free energy of polymerization is diverted into disrupting copy–template bonds behind the leading edge of the growing copy copolymer. By additionally weakening the final copy–template bond at the end of the template, the model predicts that reliable copying with a high yield of full-length, sequence-matched products is possible over large ranges of parameter space, opening the way to the engineering of synthetic copying systems that operate autonomously.

  • Journal article
    Poulton JM, Ouldridge TE, 2021,

    Edge-effects dominate copying thermodynamics for finite-length molecular oligomers

    , New Journal of Physics, Vol: 23, Pages: 1-14, ISSN: 1367-2630

    A signature feature of living systems is their ability to produce copies ofinformation-carrying molecular templates such as DNA. These copies are madeby assembling a set of monomer molecules into a linear macromolecule with a sequence determined by the template. The copies produced have a finite length –they are often “oligomers”, or short polymers – and must eventually detach fromtheir template. We explore the role of the resultant initiation and termination ofthe copy process in the thermodynamics of copying. By splitting the free-energychange of copy formation into informational and chemical terms, we show that,surprisingly, copy accuracy plays no direct role in the overall thermodynamics. Instead, finite-length templates function as highly-selective engines that interconvertchemical and information-based free energy stored in the environment; it is thermodynamically costly to produce outputs that are more similar to the oligomersin the environment than sequences obtained by randomly sampling monomers. Incontrast to previous work that neglects separation, any excess free energy stored incorrelations between copy and template sequences is lost when the copy fully detaches and mixes with the environment; these correlations therefore do not featurein the overall thermodynamics. Previously-derived constraints on copy accuracytherefore only manifest as kinetic barriers experienced while the copy is templateattached; these barriers are easily surmounted by shorter oligomers.

  • Journal article
    Sengar A, Ouldridge TE, Henrich O, Rovigatti L, Sulc Pet al., 2021,

    A primer on the oxDNA model of DNA: When to use it, how to simulate it and how to interpret the results

    , Frontiers in Molecular Biosciences, Vol: 8, Pages: 1-22, ISSN: 2296-889X

    The oxDNA model of DNA has been applied widely to systems in biology,biophysics and nanotechnology. It is currently available via two independentopen source packages. Here we present a set of clearly-documented exemplarsimulations that simultaneously provide both an introduction to simulating themodel, and a review of the model's fundamental properties. We outline howsimulation results can be interpreted in terms of -- and feed into ourunderstanding of -- less detailed models that operate at larger length scales,and provide guidance on whether simulating a system with oxDNA is worthwhile.

  • Journal article
    Cabello-Garcia J, Bae W, Stan G-BV, Ouldridge TEet al., 2021,

    Handhold-mediated strand displacement: a nucleic acid based mechanism for generating far-from-equilibrium assemblies through templated reactions.

    , ACS Nano, Vol: 15, Pages: 3272-3283, ISSN: 1936-0851

    The use of templates is a well-established method for the production of sequence-controlled assemblies, particularly long polymers. Templating is canonically envisioned as akin to a self-assembly process, wherein sequence-specific recognition interactions between a template and a pool of monomers favor the assembly of a particular polymer sequence at equilibrium. However, during the biogenesis of sequence-controlled polymers, template recognition interactions are transient; RNA and proteins detach spontaneously from their templates to perform their biological functions and allow template reuse. Breaking template recognition interactions puts the product sequence distribution far from equilibrium, since specific product formation can no longer rely on an equilibrium dominated by selective copy-template bonds. The rewards of engineering artificial polymer systems capable of spontaneously exhibiting nonequilibrium templating are large, but fields like DNA nanotechnology lack the requisite tools; the specificity and drive of conventional DNA reactions rely on product stability at equilibrium, sequestering any recognition interaction in products. The proposed alternative is handhold-mediated strand displacement (HMSD), a DNA-based reaction mechanism suited to producing out-of-equilibrium products. HMSD decouples the drive and specificity of the reaction by introducing a transient recognition interaction, the handhold. We measure the kinetics of 98 different HMSD systems to prove that handholds can accelerate displacement by 4 orders of magnitude without being sequestered in the final product. We then use HMSD to template the selective assembly of any one product DNA duplex from an ensemble of equally stable alternatives, generating a far-from-equilibrium output. HMSD thus brings DNA nanotechnology closer to the complexity of out-of-equilibrium biological systems.

  • Journal article
    Berengut J, Kui Wong C, Berengut J, Doye J, Ouldridge T, Lee Let al., 2020,

    Self-limiting polymerization of DNA origami subunits with strain accumulation

    , ACS Nano, Vol: 14, Pages: 17428-17441, ISSN: 1936-0851

    Biology demonstrates how a near infinite array of complex systems and structures at many scales can originate from the self-assembly of component parts on the nanoscale. But to fully exploit the benefits of self-assembly for nanotechnology, a crucial challenge remains: How do we rationally encode well-defined global architectures in subunits that are much smaller than their assemblies? Strain accumulation via geometric frustration is one mechanism that has been used to explain the self-assembly of global architectures in diverse and complex systems a posteriori. Here we take the next step and use strain accumulation as a rational design principle to control the length distributions of self-assembling polymers. We use the DNA origami method to design and synthesize a molecular subunit known as the PolyBrick, which perturbs its shape in response to local interactions via flexible allosteric blocking domains. These perturbations accumulate at the ends of polymers during growth, until the deformation becomes incompatible with further extension. We demonstrate that the key thermodynamic factors for controlling length distributions are the intersubunit binding free energy and the fundamental strain free energy, both which can be rationally encoded in a PolyBrick subunit. While passive polymerization yields geometrical distributions, which have the highest statistical length uncertainty for a given mean, the PolyBrick yields polymers that approach Gaussian length distributions whose variance is entirely determined by the strain free energy. We also show how strain accumulation can in principle yield length distributions that become tighter with increasing subunit affinity and approach distributions with uniform polymer lengths. Finally, coarse-grained molecular dynamics and Monte Carlo simulations delineate and quantify the dominant forces influencing strain accumulation in a molecular system. This study constitutes a fundamental investigation of the use of strain accumula

  • Journal article
    Deshpande A, Ouldridge T, 2020,

    Optimizing enzymatic catalysts for rapid turnover of substrates with low enzyme sequestration

    , Biological Cybernetics: communication and control in organisms and automata, Vol: 114, Pages: 653-668, ISSN: 0340-1200

    Enzymes are central to both metabolism and information processing in cells. In both cases, an enzyme’s ability to accelerate a reaction without being consumed in the reaction is crucial. Nevertheless, enzymes are transiently sequestered when they bind to their substrates; this sequestration limits activity and potentially compromises information processing and signal transduction. In this article, we analyse the mechanism of enzyme–substrate catalysis from the perspective of minimizing the load on the enzymes through sequestration, while maintaining at least a minimum reaction flux. In particular, we ask: which binding free energies of the enzyme–substrate and enzyme–product reaction intermediates minimize the fraction of enzymes sequestered in complexes, while sustaining a certain minimal flux? Under reasonable biophysical assumptions, we find that the optimal design will saturate the bound on the minimal flux and reflects a basic trade-off in catalytic operation. If both binding free energies are too high, there is low sequestration, but the effective progress of the reaction is hampered. If both binding free energies are too low, there is high sequestration, and the reaction flux may also be suppressed in extreme cases. The optimal binding free energies are therefore neither too high nor too low, but in fact moderate. Moreover, the optimal difference in substrate and product binding free energies, which contributes to the thermodynamic driving force of the reaction, is in general strongly constrained by the intrinsic free-energy difference between products and reactants. Both the strategies of using a negative binding free-energy difference to drive the catalyst-bound reaction forward and of using a positive binding free-energy difference to enhance detachment of the product are limited in their efficacy.

  • Journal article
    Irmisch P, Ouldridge TE, Seidel R, 2020,

    Modelling DNA-strand displacement reactions in the presence of base-pair mismatches

    , Journal of the American Chemical Society, Vol: 142, Pages: 11451-11463, ISSN: 0002-7863

    Toehold-mediated strand displacement is the most abundantly used method to achieve dynamic switching in DNA-based nanotechnology. An ‘invader’ strand binds to the ‘toehold’ overhang of a target strand and replaces a target-bound ’incumbent’ strand. Hereby, complementarity of the invader to the single-stranded toehold provides the energetic bias of the reaction. Despite the widespread use of strand displacement reactions for realizing dynamic DNA nanostructures, variants on the basic motif have not been completely characterized. Here we introduce a simple thermodynamic model, which is capable of quantitatively describing the kinetics of strand displacement reactions in the presence of mismatches, using a minimal set of parameters. Furthermore, our model highlights that base pair fraying and internal loop formation are important mechanisms when involving mismatches in the displacement process. Our model should provide a helpful tool for the rational design of strand-displacement reaction networks.

  • Journal article
    Ouldridge T, Turberfield A, Mullor Ruiz I, Louis A, Bath J, Haley N, Geraldini Aet al., 2020,

    Design of hidden thermodynamic driving for non-equilibrium systems via mismatch elimination during DNA strand displacement

    , Nature Communications, Vol: 11, ISSN: 2041-1723

    Recent years have seen great advances in the development of synthetic self-assembling molecular systems. Designing out-of-equilibrium architectures, however, requires a more subtle control over the thermodynamics and kinetics of reactions. We propose a mechanism for enhancing the thermodynamic drive of DNA strand-displacement reactions whilst barely perturbing forward reaction rates: the introduction of mismatches within the initial duplex. Through a combination of experiment and simulation, we demonstrate that displacement rates are strongly sensitive to mismatch location and can be tuned by rational design. By placing mismatches away from duplex ends, the thermodynamic drive for a strand-displacement reaction can be varied without significantly affecting the forward reaction rate. This hidden thermodynamic driving motif is ideal for the engineering of non-equilibrium systems that rely on catalytic control and must be robust to leak reactions.

  • Journal article
    Brittain R, Jones N, Ouldridge T, 2019,

    Biochemical Szilard engines for memory-limited inference

    , New Journal of Physics, Vol: 21, ISSN: 1367-2630

    By designing and leveraging an explicit molecular realisation of a measurement-and-feedback-powered Szilard engine, we investigate the extraction of work from complex environments by minimal machines with finite capacity for memory and decision-making. Living systems perform inference to exploit complex structure, or correlations, in their environment, but the physical limits and underlying cost/benefit trade-offs involved in doing so remain unclear. To probe these questions, we consider a minimal model for a structured environment—a correlated sequence of molecules—and explore mechanisms based on extended Szilard engines for extracting the work stored in these non-equilibrium correlations. We consider systems limited to a single bit of memory making binary 'choices' at each step. We demonstrate that increasingly complex environments allow increasingly sophisticated inference strategies to extract more free energy than simpler alternatives, and argue that optimal design of such machines should also consider the free energy reserves required to ensure robustness against fluctuations due to mistakes.

  • Journal article
    Weber C, Zwicker D, Juelicher F, Lee CFet al., 2019,

    Physics of active emulsions

    , Reports on Progress in Physics, Vol: 82, Pages: 1-40, ISSN: 0034-4885

    Phase separating systems that are maintained away from thermodynamic equilibrium 
 via molecular processes represent a class of active systems, which we call \textit{ active emulsions}.
 These systems are driven by external energy input for example provided by an external fuel reservoir. 
 The external energy input gives rise to novel phenomena that are not present in passive systems.
 For instance, concentration gradients can spatially organise emulsions and cause novel droplet size distributions.
 Another example are active droplets that are subject to chemical reactions such that their nucleation and size can be controlled and they can spontaneously divide. 
 In this review we discuss the physics of phase separation and emulsions 
 and show how the concepts that governs such phenomena can be extended to capture the physics of active emulsions. 
 This physics is relevant to the spatial organisation of the biochemistry in living cells, for the development novel applications in chemical engineering and models for the origin of life.

  • Journal article
    Reijne A-M, Bordeu I, Pruessner G, Sena Get al., 2018,

    Linear stability analysis of morphodynamics during tissue regeneration in plants

    , Journal of Physics D: Applied Physics, Vol: 52, Pages: 1-9, ISSN: 0022-3727

    One of the key characteristics of multicellular organisms is the ability to establish and maintain shapes, or morphologies, under a variety of physical and chemical perturbations. A quantitative description of the underlying morphological dynamics is a critical step to fully understand the self-organising properties of multicellular systems. Although many powerful mathematical tools have been developed to analyse stochastic dynamics, rarely these are applied to experimental developmental biology.Here, we take root tip regeneration in the plant model system Arabidopsis thaliana as an example of robust morphogenesis in living tissue, and present a novel approach to quantify and model the relaxation of the system to its unperturbed morphology. By generating and analysing time-lapse series of regenerating root tips captured with confocal microscopy, we are able to extract and model the dynamics of key morphological traits at cellular resolution. We present a linear stability analysis of its Markovian dynamics, with the stationary state representing the intact root in the space of morphological traits. This analysis suggests the intriguing co-existence of two distinct temporal scales during the process of root regeneration in Arabidopsis.We discuss the possible biological implications of our specific results, and suggest future experiments to further probe the self-organising properties of living tissue.

  • Journal article
    Lee C, Wurtz JD, 2018,

    Novel physics arising from phase transitions in biology

    , Journal of Physics D: Applied Physics, Vol: 52, ISSN: 0022-3727

    Phase transitions, such as the freezing of water and the magnetisation of a ferromagnet upon lowering the ambient temperature, are familiar physical phenomena. Interestingly, such a collective change of behaviour at a phase transition is also of importance to living systems. From cytoplasmic organisation inside a cell to the collective migration of cell tissue during organismal development and wound healing, phase transitions have emerged as key mechanisms underlying many crucial biological processes. However, a living system is fundamentally different from a thermal system, with driven chemical reactions (e.g. metabolism) and motility being two hallmarks of its non-equilibrium nature. In this review, we will discuss how driven chemical reactions can arrest universal coarsening kinetics expected from thermal phase separation, and how motility leads to the emergence of a novel universality class when the rotational symmetry is spontaneously broken in an incompressible fluid.

  • Journal article
    Lee C, 2018,

    Equilibrium kinetics of self-assembling, semi-flexible polymers

    , Journal of Physics: Condensed Matter, Vol: 30, ISSN: 0953-8984

    Self-assembling, semi-flexible polymers are ubiquitous in biology and technology. However, conflicting accounts of the equilibrium kinetics remain for such an important system. Here, by focusing on a dynamical description of a minimal model in an overdamped environment, I identify the correct kinetic scheme that describes the system at equilibrium in the limits of high bonding energy and dilute concentration.

  • Journal article
    Lee C, Leanne M, Liu L-N, Madine J, Davies Het al., 2018,

    Insights into the origin of distinct medin fibril morphologies induced by incubation conditions and seeding.

    , International Journal of Molecular Sciences, Vol: 19, ISSN: 1661-6596

    Incubation conditions are an important factor to consider when studying protein aggregation in vitro. Here, we employed biophysical methods and atomic force microscopy to show that agitation dramatically alters the morphology of medin, an amyloid protein deposited in the aorta. Agitation reduces the lag time for fibrillation by ~18-fold, suggesting that the rate of fibril formation plays a key role in directing the protein packing arrangement within fibrils. Utilising preformed sonicated fibrils as seeds, we probed the role of seeding on medin fibrillation and revealed three distinct fibril morphologies, with biophysical modelling explaining the salient features of experimental observations. We showed that nucleation pathways to distinct fibril morphologies may be switched on and off depending on the properties of the seeding fibrils and growth conditions. These findings may impact on the development of amyloid-based biomaterials and enhance understanding of seeding as a pathological mechanism.

  • Journal article
    Wurtz J, Lee C, 2018,

    Stress granule formation via ATP depletion-triggered phase separation

    , New Journal of Physics, Vol: 20, Pages: 1-20, ISSN: 1367-2630

    Stress granules (SG) are droplets of proteins and RNA that formin the cell cytoplasm during stress conditions. We consider minimal models ofstress granule formation based on the mechanism of phase separation regulatedby ATP-driven chemical reactions. Motivated by experimental observations, weidentify a minimal model of SG formation triggered by ATP depletion. Ouranalysis indicates that ATP is continuously hydrolysed to deter SG formationunder normal conditions, and we provide specific predictions that can be testedexperimentally.

  • Journal article
    Wurtz JD, Lee C, 2018,

    Chemical reaction-controlled phase separated drops: Formation, size selection, and coarsening

    , Physical Review Letters, Vol: 120, Pages: 1-5, ISSN: 0031-9007

    Phase separation under nonequilibrium conditions is exploited by biological cells to organize their cytoplasm but remains poorly understood as a physical phenomenon. Here, we study a ternary fluid model in which phase-separating molecules can be converted into soluble molecules, and vice versa, via chemical reactions. We elucidate using analytical and simulation methods how drop size, formation, and coarsening can be controlled by the chemical reaction rates, and categorize the qualitative behavior of the system into distinct regimes. Ostwald ripening arrest occurs above critical reaction rates, demonstrating that this transition belongs entirely to the nonequilibrium regime. Our model is a minimal representation of the cell cytoplasm.

  • Journal article
    Lopez-Garrido J, Ojkic N, Khanna K, Wagner FR, Villa E, Endres RG, Pogliano Ket al., 2018,

    Chromosome translocation inflates bacillus forespores and impacts cellular morphology

    , Cell, Vol: 172, Pages: 758-770.e14, ISSN: 0092-8674

    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.

  • Book chapter
    Baesso P, Randall RS, Sena G, 2018,

    Light Sheet Fluorescence Microscopy Optimized for Long-Term Imaging of Arabidopsis Root Development.

    , Pages: 145-163

    Light sheet fluorescence microscopy (LSFM) allows sustained and repeated optical sectioning of living specimens at high spatial and temporal resolution, with minimal photodamage. Here, we describe in detail both the hardware and the software elements of a live imaging method based on LSFM and optimized for tracking and 3D scanning of Arabidopsis root tips grown vertically in physiological conditions. The system is relatively inexpensive and with minimal footprint; hence it is well suited for laboratories of any size.

  • Journal article
    Endres RG, 2017,

    Entropy production selects nonequilibrium states in multistable systems

    , Scientific Reports, Vol: 7, ISSN: 2045-2322

    Far-from-equilibrium thermodynamics underpins the emergence of life, but how has been a long-outstanding puzzle. Best candidate theories based on the maximum entropy production principle could not be unequivocally proven, in part due to complicated physics, unintuitive stochastic thermodynamics, and the existence of alternative theories such as the minimum entropy production principle. Here, we use a simple, analytically solvable, one-dimensional bistable chemical system to demonstrate the validity of the maximum entropy production principle. To generalize to multistable stochastic system, we use the stochastic least-action principle to derive the entropy production and its role in the stability of nonequilibrium steady states. This shows that in a multistable system, all else being equal, the steady state with the highest entropy production is favored, with a number of implications for the evolution of biological, physical, and geological systems.

  • Journal article
    Micali G, Colin R, Sourjik V, Endres RGet al., 2017,

    Drift and behavior of E. coli cells

    , Biophysical Journal, Vol: 113, Pages: 2321-2325, ISSN: 0006-3495

    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.

  • Journal article
    Richards DM, Endres RG, 2017,

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

    , Reports on Progress in Physics, Vol: 80, ISSN: 0034-4885

    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.

  • Journal article
    Yap L, Endres RG, 2017,

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

    , Soft Matter, Vol: 13, Pages: 8089-8095, ISSN: 1744-683X

    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.

  • Journal article
    Rotrattanadumrong R, Endres RG, 2017,

    Emergence of cooperativity in a model biofilm

    , Journal of Physics D: Applied Physics, Vol: 50, ISSN: 0022-3727

    Evolution 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.

  • Journal article
    Weber CA, Lee CF, Juelicher F, 2017,

    Droplet ripening in concentration gradients

    , New Journal of Physics, Vol: 19, ISSN: 1367-2630

    Living 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.

  • Journal article
    De 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: 1544-9173

    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.

  • Journal article
    Ojkic N, Lopez-Garrido J, Pogliano K, Endres RGet al., 2016,

    Cell-wall remodeling drives engulfment during Bacillus subtiliss porulation

    , eLife, Vol: 5, ISSN: 2050-084X

    When 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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