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  • 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, 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, 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 CF, 2018,

    Chemical-Reaction-Controlled Phase Separated Drops: Formation, Size Selection, and Coarsening

    , PHYSICAL REVIEW LETTERS, Vol: 120, ISSN: 0031-9007
  • 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.

  • Journal article
    Kral N, Hanna Ougolnikova A, Sena G, 2016,

    Externally imposed electric field enhances plant root tip regeneration

    , Regeneration, Vol: 3, Pages: 156-167, ISSN: 2052-4412

    In 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.

  • Journal article
    Jean L, Lee CF, Hodder P, Hawkins N, Vaux DJet al., 2016,

    Dynamics of the formation of a hydrogel by a pathogenic amyloid peptide: islet amyloid polypeptide

    , Scientific Reports, Vol: 6, ISSN: 2045-2322

    Many 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.

  • Journal article
    Lee CF, Pruessner G, 2016,

    Percolation mechanism drives actin gels to the critically connected state

    , Physical Review E, Vol: 93, ISSN: 1539-3755

    Cell 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.

  • Journal article
    Richards 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: 1091-6490

    Along 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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