Size-dependent self-avoidance enables superdiffusive migration in macroscopic unicellulars

Many cells face search problems, such as finding food, mates, or shelter, where their success depends on their search strategy. In contrast to other unicellular organisms, the slime mold Physarum polycephalum forms a giant network-shaped plasmodium while foraging for food. What is the advantage of the giant cell on the verge of multicellularity? We experimentally study and quantify the migration behavior of P. polycephalum plasmodia on the time scale of days in the absence and presence of food. We develop a model which successfully describes its migration in terms of ten data-derived parameters. Using the mechanistic insights provided by our data-driven model, we find that regardless of the absence or presence of food, P. polycephalum achieves superdiffusive migration by performing a self-avoiding run-and-tumble movement. In the presence of food, the run duration statistics change, only controlling the short-term migration dynamics. However, varying organism size, we find that the long-term superdiffusion arises from self-avoidance determined by cell size, highlighting the potential evolutionary advantage that this macroscopically large cell may have.

Calcium regulates cortex contraction inPhysarum polycephalum

The tubular network-forming slime moldPhysarum polycephalumis able to maintain long-scale contraction patterns driven by an actomyosin cortex. The resulting shuttle streaming in the network is crucial for the organism to respond to external stimuli and reorganize its body mass giving rise to complex behaviors. However, the chemical basis of the self-organized flow pattern is not fully understood. Here, we present ratiometric measurements of free intracellular calcium in simple morphologies ofPhysarumnetworks. The spatiotemporal patterns of the free calcium concentration reveal a nearly anti-correlated relation to the tube radius, suggesting that calcium is indeed a key regulator of the actomyosin activity. We compare the experimentally observed phase relation between the radius and the calcium concentration to the predictions of a theoretical model including calcium as an inhibitor. Numerical simulations of the model suggest that calcium indeed inhibits the contractions inPhysarum, although a quantitative difference to the experimentally measured phase relation remains. Unraveling the mechanism underlying the contraction patterns is a key step in gaining further insight into the principles ofPhysarum's complex behavior.

Alkaline vents recreated in two dimensions to study pH gradients, precipitation morphology, and molecule accumulation

Alkaline vents (AVs) are hypothesized to have been a setting for the emergence of life, by creating strong gradients across inorganic membranes within chimney structures. In the past, three-dimensional chimney structures were formed under laboratory conditions; however, no in situ visualization or testing of the gradients was possible. We develop a quasi-two-dimensional microfluidic model of AVs that allows spatiotemporal visualization of mineral precipitation in low-volume experiments. Upon injection of an alkaline fluid into an acidic, iron-rich solution, we observe a diverse set of precipitation morphologies, mainly controlled by flow rate and ion concentration. Using microscope imaging and pH-dependent dyes, we show that finger-like precipitates can facilitate formation and maintenance of microscale pH gradients and accumulation of dispersed particles in confined geometries. Our findings establish a model to investigate the potential of gradients across a semipermeable boundary for early compartmentalization, accumulation, and chemical reactions at the origins of life.

Network topology enables efficient response to environment inPhysarum polycephalum

The network-shaped body plan distinguishes the unicellular slime mouldPhysarum polycephalumin body architecture from other unicellular organisms. Yet, network-shaped body plans dominate branches of multi-cellular life such as in fungi. What survival advantage does a network structure provide when facing a dynamic environment with adverse conditions? Here, we probe how network topology impactsP. polycephalum's avoidance response to an adverse blue light. We stimulate either an elongated, I-shaped amoeboid or a Y-shaped networked specimen and subsequently quantify the evacuation process of the light-exposed body part. The result shows that Y-shaped specimen complete the avoidance retraction in a comparable time frame, even slightly faster than I-shaped organisms, yet, at a lower almost negligible increase in migration velocity. Contraction amplitude driving mass motion is further only locally increased in Y-shaped specimen compared to I-shaped-providing further evidence that Y-shaped's avoidance reaction is energetically more efficient than in I-shaped amoeboid organisms. The difference in the retraction behaviour suggests that the complexity of network topology provides a key advantage when encountering adverse environments. Our findings could lead to a better understanding of the transition from unicellular to multicellularity.

Flow-driven control of pulse width in excitable media

Models of pulse formation in nerve conduction have provided manifold insight not only into neuronal dynamics but also the nonlinear dynamics of pulse formation in general. Recent observation of neuronal electrochemical pulses also driving mechanical deformation of the tubular neuronal wall, and thereby generating ensuing cytoplasmic flow, now question the impact of flow on the electrochemical dynamics of pulse formation. Here, we theoretically investigate the classical Fitzhugh-Nagumo model, now accounting for advective coupling between the pulse propagator typically describing membrane potential and triggering mechanical deformations, and thus governing flow magnitude, and the pulse controller, a chemical species advected with the ensuing fluid flow. Employing analytical calculations and numerical simulations, we find that advective coupling allows for a linear control of pulse width while leaving pulse velocity unchanged. We therefore uncover an independent control of pulse width by fluid flow coupling.

Vein fate determined by flow-based but time-delayed integration of network architecture

Veins in vascular networks, such as in blood vasculature or leaf networks, continuously reorganize, grow or shrink, to minimize energy dissipation. Flow shear stress on vein walls has been set forth as the local driver for a vein's continuous adaptation. Yet, shear feedback alone cannot account for the observed diversity of vein dynamics - a puzzle made harder by scarce spatiotemporal data. Here, we resolve network-wide vein dynamics and shear rate during spontaneous reorganization in the prototypical vascular networks of Physarum polycephalum. Our experiments reveal a plethora of vein dynamics (stable, growing, shrinking) where the role of shear is ambiguous. Quantitative analysis of our data reveals that (a) shear rate indeed feeds back on vein radius, yet, with a time delay of 1-3 min. Further, we reconcile the experimentally observed disparate vein fates by developing a model for vein adaptation within a network and accounting for the observed time delay. The model reveals that (b) vein fate is determined by parameters - local pressure or relative vein resistance - which integrate the entire network's architecture, as they result from global conservation of fluid volume. Finally, we observe avalanches of network reorganization events that cause entire clusters of veins to vanish. Such avalanches are consistent with network architecture integrating parameters governing vein fate as vein connections continuously change. As the network architecture integrating parameters intrinsically arise from laminar fluid flow in veins, we expect our findings to play a role across ow-based vascular networks.

Memory capacity of adaptive flow networks

Biological flow networks adapt their network morphology to optimize flow while being exposed to external stimuli from different spatial locations in their environment. These adaptive flow networks retain a memory of the stimulus location in the network morphology. Yet, what limits this memory and how many stimuli can be stored are unknown. Here, we study a numerical model of adaptive flow networks by applying multiple stimuli subsequently. We find strong memory signals for stimuli imprinted for a long time into young networks. Consequently, networks can store many stimuli for intermediate stimulus duration, which balance imprinting and aging.

Dispersive transport dynamics in porous media emerge from local correlations

Understanding and controlling transport through complex media is central for a plethora of processes ranging from technical to biological applications. Yet, the effect of micro-scale manipulations on macroscopic transport dynamics still poses conceptual conundrums. Here, we demonstrate the predictive power of a conceptual shift in describing complex media by local micro-scale correlations instead of an assembly of uncorrelated minimal units. Specifically, we show that the non-linear dependency between microscopic morphological properties and macroscopic transport characteristics in porous media is captured by transport statistics on the level of pore junctions instead of single pores. Probing experimentally and numerically transport through two-dimensional porous media while gradually increasing flow heterogeneity, we find a non-monotonic change in transport efficiency. Using analytic arguments, we built physical intuition on how this non-monotonic dependency emerges from junction statistics. The shift in paradigm presented here broadly affects our understanding of transport within the diversity of complex media.

Dispersive transport through complex media, relevant for semiconductors, liquid crystals, and biological soft matter, is influenced by their microscopic, porous structure. The authors consider the statistics of pore-junction units, in contrast to individual pores, to link morphology and macroscopic transport characteristics.

Changing Flows Balance Nutrient Absorption and Bacterial Growth along the Gut

Small intestine motility and its ensuing flow of luminal content impact both nutrient absorption and bacterial growth. To explore this interdependence we introduce a biophysical description of intestinal flow and absorption. Rooted in observations of mice we identify the average flow velocity as the key control of absorption efficiency and bacterial growth, independent of the exact contraction pattern. We uncover self-regulation of contraction and flow in response to nutrients and bacterial levels to promote efficient absorption while restraining detrimental bacterial overgrowth.

Memory Formation in Adaptive Networks

The continuous adaptation of networks like our vasculature ensures optimal network performance when challenged with changing loads. Here, we show that adaptation dynamics allow a network to memorize the position of an applied load within its network morphology. We identify that the irreversible dynamics of vanishing network links encode memory. Our analytical theory successfully predicts the role of all system parameters during memory formation, including parameter values which prevent memory formation. We thus provide analytical insight on the theory of memory formation in disordered systems.

Spatial transcriptomic and single-nucleus analysis reveals heterogeneity in a gigantic single-celled syncytium

In multicellular organisms, the specification, coordination, and compartmentalization of cell types enable the formation of complex body plans. However, some eukaryotic protists such as slime molds generate diverse and complex structures while remaining in a multinucleate syncytial state. It is unknown if different regions of these giant syncytial cells have distinct transcriptional responses to environmental encounters and if nuclei within the cell diversify into heterogeneous states. Here, we performed spatial transcriptome analysis of the slime mold Physarum polycephalum in the plasmodium state under different environmental conditions and used single-nucleus RNA-sequencing to dissect gene expression heterogeneity among nuclei. Our data identifies transcriptome regionality in the organism that associates with proliferation, syncytial substructures, and localized environmental conditions. Further, we find that nuclei are heterogenous in their transcriptional profile and may process local signals within the plasmodium to coordinate cell growth, metabolism, and reproduction. To understand how nuclei variation within the syncytium compares to heterogeneity in single-nucleus cells, we analyzed states in single Physarum amoebal cells. We observed amoebal cell states at different stages of mitosis and meiosis, and identified cytokinetic features that are specific to nuclei divisions within the syncytium. Notably, we do not find evidence for predefined transcriptomic states in the amoebae that are observed in the syncytium. Our data shows that a single-celled slime mold can control its gene expression in a region-specific manner while lacking cellular compartmentalization and suggests that nuclei are mobile processors facilitating local specialized functions. More broadly, slime molds offer the extraordinary opportunity to explore how organisms can evolve regulatory mechanisms to divide labor, specialize, balance competition with cooperation, and perform other foundational principles that govern the logic of life.

Emergence of behaviour in a self-organized living matter network

What is the origin of behaviour? Although typically associated with a nervous system, simple organisms also show complex behaviours. Among them, the slime mold Physarum polycephalum, a giant single cell, is ideally suited to study emergence of behaviour. Here, we show how locomotion and morphological adaptation behaviour emerge from self-organized patterns of rhythmic contractions of the actomyosin lining of the tubes making up the network-shaped organism. We quantify the spatio-temporal contraction dynamics by decomposing experimentally recorded contraction patterns into spatial contraction modes. Notably, we find a continuous spectrum of modes, as opposed to a few dominant modes. Our data suggests that the continuous spectrum of modes allows for dynamic transitions between a plethora of specific behaviours with transitions marked by highly irregular contraction states. By mapping specific behaviours to states of active contractions, we provide the basis to understand behaviour’s complexity as a function of biomechanical dynamics.

Gut microbiota-motility interregulation: insights from in vivo, ex vivo and in silico studies

The human gastrointestinal tract is home to trillions of microbes. Gut microbial communities have a significant regulatory role in the intestinal physiology, such as gut motility. Microbial effect on gut motility is often evoked by bioactive molecules from various sources, including microbial break down of carbohydrates, fibers or proteins. In turn, gut motility regulates the colonization within the microbial ecosystem. However, the underlying mechanisms of such regulation remain obscure. Deciphering the inter-regulatory mechanisms of the microbiota and bowel function is crucial for the prevention and treatment of gut dysmotility, a comorbidity associated with many diseases. In this review, we present an overview of the current knowledge on the impact of gut microbiota and its products on bowel motility. We discuss the currently available techniques employed to assess the changes in the intestinal motility. Further, we highlight the open challenges, and incorporate biophysical elements of microbes-motility interplay, in an attempt to lay the foundation for describing long-term impacts of microbial metabolite-induced changes in gut motility.

Living System Adapts Harmonics of Peristaltic Wave for Cost-Efficient Optimization of Pumping Performance

Wavelike patterns driving transport are ubiquitous in life. Peristaltic pumps are a paradigm of efficient mass transport by contraction driven flows-often limited by energetic constraints. We show that a cost-efficient increase in pumping performance can be achieved by modulating the phase difference between harmonics to increase occlusion. In experiments we find a phase difference shift in the living peristalsis model P. polycephalum as dynamic response to forced mass transport. Our findings provide a novel metric for wavelike patterns and demonstrate the crucial role of nonlinearities in life.

Robust Increase in Supply by Vessel Dilation in Globally Coupled Microvasculature

Neuronal activity induces changes in blood flow by locally dilating vessels in the brain microvasculature. How can the local dilation of a single vessel increase flow-based metabolite supply, given that flows are globally coupled within microvasculature? Solving the supply dynamics for rat brain microvasculature, we find one parameter regime to dominate physiologically. This regime allows for robust increase in supply independent of the position in the network, which we explain analytically. We show that local coupling of vessels promotes spatially correlated increased supply by dilation.

Feedback from Tissue Mechanics Self-Organizes Efficient Outgrowth of Plant Organ

Plant organ outgrowth superficially appears like the continuous mechanical deformation of a sheet of cells. Yet, how precisely cells as individual mechanical entities can act to morph a tissue reliably and efficiently into three dimensions during outgrowth is still puzzling, especially when cells are tightly connected as in plant tissue. In plants, the mechanics of cells within a tissue is particularly well-defined because individual cell growth is essentially the mechanical yielding of the cell wall in response to internal turgor pressure. Cell-wall stiffness is controlled by biological signaling, which is impacted by stresses, and hence, cell growth is observed to respond to mechanical stresses building up within a tissue. What is the role of the mechanical feedback during morphing of tissue in three dimensions? Here, we develop a three-dimensional vertex model to investigate tissue mechanics at the onset of organ outgrowth at the tip of a plant shoot. We find that organ height is primarily governed by the ratio of growth rates of faster-growing cells initiating the organ versus slower-growing cells surrounding them. Remarkably, the outgrowth rate is higher when cell growth responds to the tissue-wide mechanical stresses. Our quantitative analysis of simulation data shows that tissue mechanical feedback on cell growth can act via a twofold mechanism. First, the feedback guides patterns of cellular growth. Second, the feedback modifies the stress patterns on the cells, consequently amplifying and propagating growth anisotropies. This mechanism may allow plants to grow organs efficiently out of the meristem by reorganizing the cellular growth rather than inflating growth rates.

Order parameter allows classification of planar graphs based on balanced fixed points in the Kuramoto model

Phase balanced states are a highly underexplored class of solutions of the Kuramoto model and other coupled oscillator models on networks. So far, coupled oscillator research focused on phase synchronized solutions. Yet, global constraints on oscillators may forbid synchronized state, rendering phase balanced states as the relevant stable state. If, for example, oscillators are driving the contractions of a fluid filled volume, conservation of fluid volume constrains oscillators to balanced states as characterized by a vanishing Kuramoto order parameter. It has previously been shown that stable, balanced patterns in the Kuramoto model exist on circulant graphs. However, which noncirculant graphs first of all allow for balanced states and what characterizes the balanced states is unknown. Here, we derive rules of how to build noncirculant, planar graphs allowing for balanced states from the simple cycle graph by adding loops or edges to it. We thereby identify different classes of small planar networks allowing for balanced states. Investigating the balanced states' characteristics, we find that the variance in basin stability scales linearly with the size of the graph for these networks. We introduce the balancing ratio as an order parameter based on the basin stability approach to classify balanced states on networks and evaluate it analytically for a subset of the network classes. Our results offer an analytical description of noncirculant graphs supporting stable, balanced states and may thereby help to understand the topological requirements on oscillator networks under global constraints.

Fluid flows shaping organism morphology

A dynamic self-organized morphology is the hallmark of network-shaped organisms like slime moulds and fungi. Organisms continuously reorganize their flexible, undifferentiated body plans to forage for food. Among these organisms the slime mould Physarum polycephalum has emerged as a model to investigate how an organism can self-organize their extensive networks and act as a coordinated whole. Cytoplasmic fluid flows flowing through the tubular networks have been identified as the key driver of morphological dynamics. Inquiring how fluid flows can shape living matter from small to large scales opens up many new avenues for research. This article is part of the theme issue 'Self-organization in cell biology'.

Flow rate of transport network controls uniform metabolite supply to tissue

Life and functioning of higher organisms depends on the continuous supply of metabolites to tissues and organs. What are the requirements on the transport network pervading a tissue to provide a uniform supply of nutrients, minerals or hormones? To theoretically answer this question, we present an analytical scaling argument and numerical simulations on how flow dynamics and network architecture control active spread and uniform supply of metabolites by studying the example of xylem vessels in plants. We identify the fluid inflow rate as the key factor for uniform supply. While at low inflow rates metabolites are already exhausted close to flow inlets, too high inflow flushes metabolites through the network and deprives tissue close to inlets of supply. In between these two regimes, there exists an optimal inflow rate that yields a uniform supply of metabolites. We determine this optimal inflow analytically in quantitative agreement with numerical results. Optimizing network architecture by reducing the supply variance over all network tubes, we identify patterns of tube dilation or contraction that compensate sub-optimal supply for the case of too low or too high inflow rate.

Local Pore Size Correlations Determine Flow Distributions in Porous Media

The relationship between the microstructure of a porous medium and the observed flow distribution is still a puzzle. We resolve it with an analytical model, where the local correlations between adjacent pores, which determine the distribution of flows propagated from one pore downstream, predict the flow distribution. Numerical simulations of a two-dimensional porous medium verify the model and clearly show the transition of flow distributions from δ-function-like via Gaussians to exponential with increasing disorder. Comparison to experimental data further verifies our numerical approach.

Pruning to Increase Taylor Dispersion in Physarum polycephalum Networks

How do the topology and geometry of a tubular network affect the spread of particles within fluid flows? We investigate patterns of effective dispersion in the hierarchical, biological transport network formed by Physarum polycephalum. We demonstrate that a change in topology-pruning in the foraging state-causes a large increase in effective dispersion throughout the network. By comparison, changes in the hierarchy of tube radii result in smaller and more localized differences. Pruned networks capitalize on Taylor dispersion to increase the dispersion capability.

Leaf growth is conformal

Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a later stage. Based on the mapping we predict the local displacement field in the leaf blade and find it to agree with the experimentally measured displacement field to 92%. This approach is applicable to any two-dimensional system with locally isotropic growth, enabling the deduction of the whole growth field just from observation of the tissue contour.

Matrix elasticity of void-forming hydrogels controls transplanted-stem-cell-mediated bone formation

The effectiveness of stem cell therapies has been hampered by cell death and limited control over fate. These problems can be partially circumvented by using macroporous biomaterials that improve the survival of transplanted stem cells and provide molecular cues to direct cell phenotype. Stem cell behaviour can also be controlled in vitro by manipulating the elasticity of both porous and non-porous materials, yet translation to therapeutic processes in vivo remains elusive. Here, by developing injectable, void-forming hydrogels that decouple pore formation from elasticity, we show that mesenchymal stem cell (MSC) osteogenesis in vitro, and cell deployment in vitro and in vivo, can be controlled by modifying, respectively, the hydrogel's elastic modulus or its chemistry. When the hydrogels were used to transplant MSCs, the hydrogel's elasticity regulated bone regeneration, with optimal bone formation at 60 kPa. Our findings show that biophysical cues can be harnessed to direct therapeutic stem cell behaviours in situ.

Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual

Individuals can function as integrated organisms only when information and resources are shared across a body. Signals and substrates are commonly moved using fluids, often channeled through a network of tubes. Peristalsis is one mechanism for fluid transport and is caused by a wave of cross-sectional contractions along a tube. We extend the concept of peristalsis from the canonical case of one tube to a random network. Transport is maximized within the network when the wavelength of the peristaltic wave is of the order of the size of the network. The slime mold Physarum polycephalum grows as a random network of tubes, and our experiments confirm peristalsis is used by the slime mold to drive internal cytoplasmic flows. Comparisons of theoretically generated contraction patterns with the patterns exhibited by individuals of P. polycephalum demonstrate that individuals maximize internal flows by adapting patterns of contraction to size, thus optimizing transport throughout an organism. This control of fluid flow may be the key to coordinating growth and behavior, including the dynamic changes in network architecture seen over time in an individual.

Quantitative analysis of the nanopore translocation dynamics of simple structured polynucleotides

Nanopore translocation experiments are increasingly applied to probe the secondary structures of RNA and DNA molecules. Here, we report two vital steps toward establishing nanopore translocation as a tool for the systematic and quantitative analysis of polynucleotide folding: 1), Using α-hemolysin pores and a diverse set of different DNA hairpins, we demonstrate that backward nanopore force spectroscopy is particularly well suited for quantitative analysis. In contrast to forward translocation from the vestibule side of the pore, backward translocation times do not appear to be significantly affected by pore-DNA interactions. 2), We develop and verify experimentally a versatile mesoscopic theoretical framework for the quantitative analysis of translocation experiments with structured polynucleotides. The underlying model is based on sequence-dependent free energy landscapes constructed using the known thermodynamic parameters for polynucleotide basepairing. This approach limits the adjustable parameters to a small set of sequence-independent parameters. After parameter calibration, the theoretical model predicts the translocation dynamics of new sequences. These predictions can be leveraged to generate a baseline expectation even for more complicated structures where the assumptions underlying the one-dimensional free energy landscape may no longer be satisfied. Taken together, backward translocation through α-hemolysin pores combined with mesoscopic theoretical modeling is a promising approach for label-free single-molecule analysis of DNA and RNA folding.

Regulatory role of cell division rules on tissue growth heterogeneity

The coordination of cell division and cell expansion are critical to normal development of tissues. In plants, cell wall mechanics and the there from arising cell shapes and mechanical stresses can regulate cell division and cell expansion and thereby tissue growth and morphology. Limited by experimental accessibility it remains unknown how cell division and expansion cooperatively affect tissue growth dynamics. Employing a cell-based two dimensional tissue simulation we investigate the regulatory role of a range of cell division rules on tissue growth dynamics and in particular on the spatial heterogeneity of growth. We find that random cell divisions only add noise to the growth and therefore increase growth heterogeneity, while cell divisions following the shortest new wall or along the direction of maximal mechanical stress reduce growth heterogeneity by actively enhancing the regulation of growth by mechanical stresses. Thus, we find that, beyond tissue geometry and topology, cell divisions affect the dynamics of growth, and that their signature is embedded in the statistics of tissue growth.

Quantitative predictions on auxin-induced polar distribution of PIN proteins during vein formation in leaves

The dynamic patterning of the plant hormone auxin and its efflux facilitator the PIN protein are the key regulators for the spatial and temporal organization of plant development. In particular auxin induces the polar localization of its own efflux facilitator. Due to this positive feedback, auxin flow is directed and patterns of auxin and PIN arise. During the earliest stage of vein initiation in leaves auxin accumulates in a single cell in a rim of epidermal cells from which it flows into the ground meristem tissue of the leaf blade. There the localized auxin supply yields the successive polarization of PIN distribution along a strand of cells. We model the auxin and PIN dynamics within cells with a minimal canalization model. Solving the model analytically we uncover an excitable polarization front that triggers a polar distribution of PIN proteins in cells. As polarization fronts may extend to opposing directions from their initiation site, we suggest a possible resolution to the puzzling occurrence of bipolar cells, thus we offer an explanation for the development of closed, looped veins. Employing non-linear analysis, we identify the role of the contributing microscopic processes during polarization. Furthermore, we deduce quantitative predictions on polarization fronts establishing a route to determine the up to now largely unknown kinetic rates of auxin and PIN dynamics.

Buckling of stiff polymer rings in weak spherical confinement

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.

Buckling of stiff polymer rings in weak spherical confinement

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.

Excluded volume effects on semiflexible ring polymers

Two-dimensional semiflexible polymer rings are studied both by imaging circular DNA adsorbed on a mica surface and by Monte Carlo simulations of phantom polymers as well as of polymers with finite thickness. Comparison of size and shape of the different models over the full range of flexibilities shows that excluded volume caused by finite thickness induces an anisotropic increase of the main axes of the conformations, a change of shape, accomplished by an enhanced correlation along the contour.

Shapes of semiflexible polymer rings

The shape of semiflexible polymer rings is studied over their whole range of flexibility. Investigating the joint distribution of asphericity and the nature of asphericity as well as their respective averages, we find two distinct shape regimes depending on the flexibility of the polymer. For a small perimeter to persistence length the fluctuating rings exhibit only planar, elliptical configurations. At higher flexibilities three-dimensional, crumpled structures arise. Analytic calculations confirm the qualitative behavior of the averaged shape parameters and the elliptical shape in the stiff regime.

Fluctuating semiflexible polymer ribbon constrained to a ring

Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling in addition to twist-bend coupling. Furthermore, due to the geometric constraint the polymer's effective bending stiffness increases. A new parameter for experimental investigations of polymer bundles is proposed: the mean square diameter of a ribbonlike ring, which is determined analytically in the semiflexible limit. Monte Carlo simulations are performed which affirm the model's prediction up to high flexibility.