Adaptive behaviour and learning in slime moulds: the role of oscillations.

The slime mould Physarum polycephalum, an aneural organism, uses information from previous experiences to adjust its behaviour, but the mechanisms by which this is accomplished remain unknown. This article examines the possible role of oscillations in learning and memory in slime moulds. Slime moulds share surprising similarities with the network of synaptic connections in animal brains. First, their topology derives from a network of interconnected, vein-like tubes in which signalling molecules are transported. Second, network motility, which generates slime mould behaviour, is driven by distinct oscillations that organize into spatio-temporal wave patterns. Likewise, neural activity in the brain is organized in a variety of oscillations characterized by different frequencies. Interestingly, the oscillating networks of slime moulds are not precursors of nervous systems but, rather, an alternative architecture. Here, we argue that comparable information-processing operations can be realized on different architectures sharing similar oscillatory properties. After describing learning abilities and oscillatory activities of P. polycephalum, we explore the relation between network oscillations and learning, and evaluate the organism's global architecture with respect to information-processing potential. We hypothesize that, as in the brain, modulation of spontaneous oscillations may sustain learning in slime mould. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

Biomechanical Aspects of Actin Bundle Dynamics.

Lamellipodial and filopodial protrusions are two of the main aggregate types of filamentous actin in living cells. Even though filopodia are essential to a range of vital cell functions, the mechanisms leading to their formation are still debated. Filopodia are relatively stiff and rod-like structures that are embedded in the highly dynamic framework of the backward flowing meshwork of the lamellipodium. Phenomena such as lateral filopodia drift and collision events suggest that mechanical aspects play a significant role in filopodia dynamics. In this paper, we systematically analyze the interplay between the backward flow of actin in the lamellipodium and the drift velocity of actin bundles, that we identify to be filopodia, in a quantitative manner in cells of given morphology and controlled myosin activity. Moreover, we study mechanical aspects of fusion of actin bundles drifting laterally in the lamellipodium. We find that the dynamics of actin bundles drift and fusion can be captured in a mechanical framework, which leads to a model of actin bundles orientation.

Mitochondrial numbers increase during glucose deprivation in the slime mold Physarum polycephalum.

Glucose deprivation in the slime mold Physarum polycephalum leads to a specific morphotype, a highly motile mesoplasmodium. We investigated the ultrastructure of both mesoplasmodia and non-starved plasmodia and found significantly increased numbers of mitochondria in glucose-deprived mesoplasmodia. The volume of individual mitochondria was the same in both growth forms. We conjecture that the number of mitochondria correlates with the metabolic state of the cell: When glucose is absent, the slime mold is forced to switch to different metabolic pathways, which occur inside mitochondria. Furthermore, a catabolic cue (such as AMP-activated protein kinase (AMPK)) could stimulate mitochondrial biogenesis.

A lumped parameter model of endoplasm flow in Physarum polycephalum explains migration and polarization-induced asymmetry during the onset of locomotion.

The plasmodial slime mold Physarum polycephalum exhibits strong, periodic flow of cytoplasm through the veins of its network. In the special case of mesoplasmodia, a newly described starvation-induced, shape-constant morphotype, this periodic endoplasm streaming is the basis of locomotion. Furthermore, we presume that cytoplasm flow is also involved in signal transmission and signal processing. Mesoplasmodia motility resembles amoeboid locomotion. In contrast to other amoebae, however, mesoplasmodia move without extending pseudopods and retain a coherent, fan-shaped morphology throughout their steady locomotion. Attaining sizes of up to 2 mm2, mesoplasmodia are also much bigger than other amoebae. We characterize this particular type of locomotion and identify patterns of movement. By using the analogy between pulsatile fluid flow through a network of elastic tubes and electrical circuits, we build a lumped model that explains observed fluid flow patterns. Essentially, the mesoplasmodium acts as a low-pass filter, permitting only low-frequency oscillations to propagate from back to front. This frequency selection serves to optimize flow and reduces power dissipation. Furthermore, we introduce a distributed element into the lumped model to explain cell polarization during the onset of chemotaxis: Biochemical cues (internal or external) lead to a local softening of the actin cortex, which in turn causes an increased flow of cytoplasm into that area and, thus, a net forward movement. We conclude that the internal actin-enclosed vein network gives the slime mold a high measure of control over fluid transport, especially by softening or hardening, which in turn leads to polarization and net movement.

Nonlinear compliance of elastic layers to indentation.

Thin samples adherent to a rigid substrate are considerably less compliant to indentation when compared to specimens that are not geometrically confined. Analytical corrections to this so-called substrate effect exist for various types of indenters but are not applicable when large deformations are possible, as is the case in biological materials. To overcome this limitation, we construct a nonlinear scaling model characterized by one single exponent, which we explore employing a parametric finite element analysis. The model is based on asymptotes of two length scales in relation to the sample thickness, i.e., indentation depth and radius of the contact area. For small indentation depth, we require agreement with analytical, linear models, whereas for large indentation depth and extensive contact area, we recognize similarity to uniaxial deformation, indicating a divergent force required to indent nonlinear materials. In contrast, we find linear materials not to be influenced by the substrate effect beyond first order, implying that nonlinear effects originating from either the material or geometric confinement are clearly separated only in thin samples. Furthermore, in this regime the scaling model can be derived by following a heuristic argument extending a linear model to large indentation depths. Lastly, in a large indentation setting where the contact is small in comparison with sample thickness, we observe nonlinear effects independent of material type that we attribute to a higher-order influence of geometrical confinement. In this regime, we define a scalar as the ratio of strains along principal axes as obtained by comparison with the case of a point force on a half-space. We find this scalar to be in quantitative agreement with the scaling exponent, indicating an approach to distinguish between nonlinear effects in the scaling model. While we conjecture our findings to be applicable to other flat-ended indenters, we focus on the case of a flat-ended cylinder in normal contact with a thin layer. The analytical solution for small indentation associated with this problem has been given by Hayes et al. (J Biomech 5:541-551, 1972), for which we provide a convenient numerical implementation.

Correlation and Comparison of Cortical and Hippocampal Neural Progenitor Morphology and Differentiation through the Use of Micro- and Nano-Topographies.

Neuronal morphology and differentiation have been extensively studied on topography. The differentiation potential of neural progenitors has been shown to be influenced by brain region, developmental stage, and time in culture. However, the neurogenecity and morphology of different neural progenitors in response to topography have not been quantitatively compared. In this study, the correlation between the morphology and differentiation of hippocampal and cortical neural progenitor cells was explored. The morphology of differentiated neural progenitors was quantified on an array of topographies. In spite of topographical contact guidance, cell morphology was observed to be under the influence of regional priming, even after differentiation. This influence of regional priming was further reflected in the correlations between the morphological properties and the differentiation efficiency of the cells. For example, neuronal differentiation efficiency of cortical neural progenitors showed a negative correlation with the number of neurites per neuron, but hippocampal neural progenitors showed a positive correlation. Correlations of morphological parameters and differentiation were further enhanced on gratings, which are known to promote neuronal differentiation. Thus, the neurogenecity and morphology of neural progenitors is highly responsive to certain topographies and is committed early on in development.

Fronts and waves of actin polymerization in a bistability-based mechanism of circular dorsal ruffles.

During macropinocytosis, cells remodel their morphologies for the uptake of extracellular matter. This endocytotic mechanism relies on the collapse and closure of precursory structures, which are propagating actin-based, ring-shaped vertical undulations at the dorsal (top) cell membrane, a.k.a. circular dorsal ruffles (CDRs). As such, CDRs are essential to a range of vital and pathogenic processes alike. Here we show, based on both experimental data and theoretical analysis, that CDRs are propagating fronts of actin polymerization in a bistable system. The theory relies on a novel mass-conserving reaction-diffusion model, which associates the expansion and contraction of waves to distinct counter-propagating front solutions. Moreover, the model predicts that under a change in parameters (for example, biochemical conditions) CDRs may be pinned and fluctuate near the cell boundary or exhibit complex spiral wave dynamics due to a wave instability. We observe both phenomena also in our experiments indicating the conditions for which macropinocytosis is suppressed.

Spatiotemporal Patterns of Noise-Driven Confined Actin Waves in Living Cells.

Cells utilize waves of polymerizing actin to reshape their morphologies, which is central to physiological and pathological processes alike. Here, we force dorsal actin waves to propagate on one-dimensional domains with periodic boundary conditions, which results in striking spatiotemporal patterns with a clear signature of noise-driven dynamics. We show that these patterns can be very closely reproduced with a noise-driven active medium at coherence resonance.

Dynamics of actin waves on patterned substrates: a quantitative analysis of circular dorsal ruffles.

Circular Dorsal Ruffles (CDRs) have been known for decades, but the mechanism that organizes these actin waves remains unclear. In this article we systematically analyze the dynamics of CDRs on fibroblasts with respect to characteristics of current models of actin waves. We studied CDRs on heterogeneously shaped cells and on cells that we forced into disk-like morphology. We show that CDRs exhibit phenomena such as periodic cycles of formation, spiral patterns, and mutual wave annihilations that are in accord with an active medium description of CDRs. On cells of controlled morphologies, CDRs exhibit extremely regular patterns of repeated wave formation and propagation, whereas on random-shaped cells the dynamics seem to be dominated by the limited availability of a reactive species. We show that theoretical models of reaction-diffusion type incorporating conserved species capture partially the behavior we observe in our data.

Myosin 1E localizes to actin polymerization sites in lamellipodia, affecting actin dynamics and adhesion formation.

Because the actin network in active lamellipodia is continuously assembling at the edge, moving inward and disassembling, there is a question as to how actin-binding proteins and other components are transported to the leading edge and how nascent adhesions are stabilized. Active transport could play a significant role in these functions but the components involved are unknown. We show here that Myosin 1E (a long tailed Myosin 1 isoform) rapidly moves to the tips of active lamellipodia and to actin-rich early adhesions, unlike Myosin 1G, 1B or 1C (short tailed isoforms). Myosin 1E co-localizes with CARMIL, FHOD1, Arp3 and ß3-integrin in those early adhesions. But these structures precede stable paxillin-rich adhesions. Myosin 1E movement depends upon actin-binding domains and the presence of an SH3 oligomerization domain. Overexpression of a Myosin 1E deletion mutant without the extreme C-terminal interacting (SH3) domain (Myosin 1EΔSH3) increases edge fluctuations and decreases stable adhesion lifetimes. In contrast, overexpression of Myosin 1E full tail domain (TH1+TH2+TH3/SH3) decreases edge fluctuation. In Myosin 1E knockdown cells, and more prominently in cells treated with Myosin 1 inhibitor, cell-matrix adhesions are also short-lived and fail to mature. We suggest that, by moving to actin polymerization sites and early adhesion sites in active lamellipodia, Myosin 1E might play important roles in transporting not only important polymerizing proteins but also proteins involved in adhesion stabilization.

Physarum polycephalum percolation as a paradigm for topological phase transitions in transportation networks.

We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. It is generally applicable to percolation as seen, e.g., in vascular networks.

Adhesion patterns in early cell spreading.

Mouse embryonic fibroblasts explore the chemical suitability before spreading on a given substrate. We find this early phase of cell spreading to be characterized by transient adhesion patches with a typical mean size of (1.0 ± 0.4) µm and a lifetime of (33 ± 12) s. Eventually, these patches fuse to initiate extensive spreading of the cell. We monitor cell adhesion using reflection interference contrast and total internal reflection fluorescence microscopy. Digital time lapse movies are analysed employing spatio-temporal correlation functions of adhesion patterns. Correlation length and time can be scaled to obtain a master curve at the fusion point.

Quantification of cell edge velocities and traction forces reveals distinct motility modules during cell spreading.

Actin-based cell motility and force generation are central to immune response, tissue development, and cancer metastasis, and understanding actin cytoskeleton regulation is a major goal of cell biologists. Cell spreading is a commonly used model system for motility experiments -- spreading fibroblasts exhibit stereotypic, spatially-isotropic edge dynamics during a reproducible sequence of functional phases: 1) During early spreading, cells form initial contacts with the surface. 2) The middle spreading phase exhibits rapidly increasing attachment area. 3) Late spreading is characterized by periodic contractions and stable adhesions formation. While differences in cytoskeletal regulation between phases are known, a global analysis of the spatial and temporal coordination of motility and force generation is missing. Implementing improved algorithms for analyzing edge dynamics over the entire cell periphery, we observed that a single domain of homogeneous cytoskeletal dynamics dominated each of the three phases of spreading. These domains exhibited a unique combination of biophysical and biochemical parameters -- a motility module. Biophysical characterization of the motility modules revealed that the early phase was dominated by periodic, rapid membrane blebbing; the middle phase exhibited continuous protrusion with very low traction force generation; and the late phase was characterized by global periodic contractions and high force generation. Biochemically, each motility module exhibited a different distribution of the actin-related protein VASP, while inhibition of actin polymerization revealed different dependencies on barbed-end polymerization. In addition, our whole-cell analysis revealed that many cells exhibited heterogeneous combinations of motility modules in neighboring regions of the cell edge. Together, these observations support a model of motility in which regions of the cell edge exhibit one of a limited number of motility modules that, together, determine the overall motility function. Our data and algorithms are publicly available to encourage further exploration.

Lamellipodial actin mechanically links myosin activity with adhesion-site formation.

Cell motility proceeds by cycles of edge protrusion, adhesion, and retraction. Whether these functions are coordinated by biochemical or biomechanical processes is unknown. We find that myosin II pulls the rear of the lamellipodial actin network, causing upward bending, edge retraction, and initiation of new adhesion sites. The network then separates from the edge and condenses over the myosin. Protrusion resumes as lamellipodial actin regenerates from the front and extends rearward until it reaches newly assembled myosin, initiating the next cycle. Upward bending, observed by evanescence and electron microscopy, results in ruffle formation when adhesion strength is low. Correlative fluorescence and electron microscopy shows that the regenerating lamellipodium forms a cohesive, separable layer of actin above the lamellum. Thus, actin polymerization periodically builds a mechanical link, the lamellipodium, connecting myosin motors with the initiation of adhesion sites, suggesting that the major functions driving motility are coordinated by a biomechanical process.

Lateral membrane waves constitute a universal dynamic pattern of motile cells.

We have monitored active movements of the cell circumference on specifically coated substrates for a variety of cells including mouse embryonic fibroblasts and T cells, as well as wing disk cells from fruit flies. Despite having different functions and being from multiple phyla, these cell types share a common spatiotemporal pattern in their normal membrane velocity; we show that protrusion and retraction events are organized in lateral waves along the cell membrane. These wave patterns indicate both spatial and temporal long-range periodic correlations of the actomyosin gel.

Continuous membrane-cytoskeleton adhesion requires continuous accommodation to lipid and cytoskeleton dynamics.

The plasma membrane of most animal cells conforms to the cytoskeleton and only occasionally separates to form blebs. Previous studies indicated that many weak interactions between cytoskeleton and the lipid bilayer kept the surfaces together to counteract the normal outward pressure of cytoplasm. Either the loss of adhesion strength or the formation of gaps in the cytoskeleton enables the pressure to form blebs. Membrane-associated cytoskeleton proteins, such as spectrin and filamin, can control the movement and aggregation of membrane proteins and lipids, e.g., phosphoinositol phospholipids (PIPs), as well as blebbing. At the same time, lipids (particularly PIPs) and membrane proteins affect cytoskeleton and signaling dynamics. We consider here the roles of the major phosphatidylinositol-4,5-diphosphate (PIP2) binding protein, MARCKS, and PIP2 levels in controlling cytoskeleton dynamics. Further understanding of dynamics will provide important clues about how membrane-cytoskeleton adhesion rapidly adjusts to cytoskeleton and membrane dynamics.

Force sensing and generation in cell phases: analyses of complex functions.

Cellular morphology is determined by motility, force sensing, and force generation that must be finely controlled in a dynamic fashion. Contractile and extensile functions are integrated with the overall cytoskeleton, including linkages from the cytoplasmic cytoskeleton to the extracellular matrix and other cells by force sensing. During development, as cells differentiate, variations in protein expression levels result in morphological changes. There are two major explanations for motile behavior: either cellular motility depends in a continuous fashion on cell composition or it exhibits phases wherein only a few protein modules are activated locally for a given time. Indeed, in support of the latter model, the quantification of cell spreading and other motile activities shows multiple distinct modes of behavior, which we term "phases" because there exist abrupt transitions between them. Cells in suspension have a basal level of motility that enables them to probe their immediate environment. After contacting a matrix-coated surface, they rapidly transition to an activated spreading phase. After the development of a significant contact area, the cells contract repeatedly to determine the rigidity of the substrate and then develop force on matrix contacts. When cells are fully spread, extension activity is significantly decreased and focal complexes start to assemble near the cell periphery. For each of these phases, there are significant differences in protein activities, which correspond to differences in function. Thus overall morphological change of a tissue is driven by chemical signals and force-dependent activation of one or more motile phases in limited cell regions for defined periods.

Dynamic phase transitions in cell spreading.

We monitored isotropic spreading of mouse embryonic fibroblasts on fibronectin-coated substrates. Cell adhesion area versus time was measured via total internal reflection fluorescence microscopy. Spreading proceeds in well-defined phases. We found a power-law area growth with distinct exponents in three sequential phases, which we denote as basal, continuous, and contractile spreading. High resolution differential interference contrast microscopy was used to characterize local membrane dynamics at the spreading front. Fourier power spectra of membrane velocity reveal the sudden development of periodic membrane retractions at the transition from continuous to contractile spreading. We propose that the classification of cell spreading into phases with distinct functional characteristics and protein activity serves as a paradigm for a general program of a phase classification of cellular phenotype.

Periodic lamellipodial contractions correlate with rearward actin waves.

Cellular lamellipodia bind to the matrix and probe its rigidity through forces generated by rearward F-actin transport. Cells respond to matrix rigidity by moving toward more rigid matrices using an unknown mechanism. In spreading and migrating cells we find local periodic contractions of lamellipodia that depend on matrix rigidity, fibronectin binding and myosin light chain kinase (MLCK). These contractions leave periodic rows of matrix bound beta3-integrin and paxillin while generating waves of rearward moving actin bound alpha-actinin and MLCK. The period between contractions corresponds to the time for F-actin to move across the lamellipodia. Shortening lamellipodial width by activating cofilin decreased this period proportionally. Increasing lamellipodial width by Rac signaling activation increased this period. We propose that an actin bound, contraction-activated signaling complex is transported locally from the tip to the base of the lamellipodium, activating the next contraction/extension cycle.

Nanometer analysis of cell spreading on matrix-coated surfaces reveals two distinct cell states and STEPs.

When mouse embryonic fibroblasts in suspension contact a matrix-coated surface, they rapidly adhere and spread. Using total internal reflection fluorescence microscopy of dye-loaded fibroblasts to quantify cell-substrate contact, we found that increasing the surface matrix density resulted in faster spreading initiation whereas lamellipodial dynamics during spreading were unaltered. After spreading initiation, most cells spread in an anisotropic manner through stochastic, transient extension periods (STEPs) with approximately 30 STEPs over 10 min to reach an area of 1300 micro m(2) +/- 300 micro m(2). A second mode of spreading, increased in serum-deprived cells, lacked STEPs and spread in a rapid, isotropic manner for 1-4 min. This isotropic mode was characterized by a high rate of area increase, 340 micro m(2)/min with 78% of the cell edge extending. Anisotropic cells spread slower via STEPs, 126 micro m(2)/min with 34% of the edge extending. During the initial 2-4 min of fast, isotropic spreading, centripetal flow of actin was low (0.8 micro m/min) whereas in anisotropic cells it was high from early times (4.7 micro m/min). After initial isotropic spreading, rearward actin movement increased and isotropic cells displayed STEPs similar to anisotropic cells. Thus, the two cell states display dramatically different spreading whereas long-term motility is based on STEPs.