ResearchPad - traveling-waves https://www.researchpad.co Default RSS Feed en-us © 2020 Newgen KnowledgeWorks <![CDATA[Agent-based and continuous models of hopper bands for the Australian plague locust: How resource consumption mediates pulse formation and geometry]]> https://www.researchpad.co/article/elastic_article_14654 Locusts aggregate in swarms that threaten agriculture worldwide. Initially these aggregations form as aligned groups, known as hopper bands, whose individuals alternate between marching and paused (associated with feeding) states. The Australian plague locust (for which there are excellent field studies) forms wide crescent-shaped bands with a high density at the front where locusts slow in uneaten vegetation. The density of locusts rapidly decreases behind the front where the majority of food has been consumed. Most models of collective behavior focus on social interactions as the key organizing principle. We demonstrate that the formation of locust bands may be driven by resource consumption. Our first model treats each locust as an individual agent with probabilistic rules governing motion and feeding. Our second model describes locust density with deterministic differential equations. We use biological observations of individual behavior and collective band shape to identify numerical values for the model parameters and conduct a sensitivity analysis of outcomes to parameter changes. Our models are capable of reproducing the characteristics observed in the field. Moreover, they provide insight into how resource availability influences collective locust behavior that may eventually aid in disrupting the formation of locust bands, mitigating agricultural losses.

]]>
<![CDATA[Further empirical data for torsion on bowed strings]]> https://www.researchpad.co/article/5c61e932d5eed0c48496f96e

Research on bowed string motion focuses on transverse waves rather than on torsional waves. These are believed to play only a minor role for stabilizing vibrations and no role for perception. Here, torsion is measured on both sides of the bow contact point for a variety of bridge-bow distances on a cello string. Every periodic string release is preceeded by a reverse torsional motion independent from bowing position or dynamics. Transverse and torsional motions are coupled and there are cases of stabilization, but also cases of perturbation or surrender. Structural and timing analyses of torsional waves suggest that the earlier concepts of differential slipping can be essentially confirmed while the concept of Schelleng ripples cannot be confirmed and the concept of subharmonics is under question.

]]>
<![CDATA[Colony Expansion of Socially Motile Myxococcus xanthus Cells Is Driven by Growth, Motility, and Exopolysaccharide Production]]> https://www.researchpad.co/article/5989da30ab0ee8fa60b8448a

Myxococcus xanthus, a model organism for studies of multicellular behavior in bacteria, moves exclusively on solid surfaces using two distinct but coordinated motility mechanisms. One of these, social (S) motility is powered by the extension and retraction of type IV pili and requires the presence of exopolysaccharides (EPS) produced by neighboring cells. As a result, S motility requires close cell-to-cell proximity and isolated cells do not translocate. Previous studies measuring S motility by observing the colony expansion of cells deposited on agar have shown that the expansion rate increases with initial cell density, but the biophysical mechanisms involved remain largely unknown. To understand the dynamics of S motility-driven colony expansion, we developed a reaction-diffusion model describing the effects of cell density, EPS deposition and nutrient exposure on the expansion rate. Our results show that at steady state the population expands as a traveling wave with a speed determined by the interplay of cell motility and growth, a well-known characteristic of Fisher’s equation. The model explains the density-dependence of the colony expansion by demonstrating the presence of a lag phase–a transient period of very slow expansion with a duration dependent on the initial cell density. We propose that at a low initial density, more time is required for the cells to accumulate enough EPS to activate S-motility resulting in a longer lag period. Furthermore, our model makes the novel prediction that following the lag phase the population expands at a constant rate independent of the cell density. These predictions were confirmed by S motility experiments capturing long-term expansion dynamics.

]]>
<![CDATA[Modelling Chemotactic Motion of Cells in Biological Tissues]]> https://www.researchpad.co/article/5989da1cab0ee8fa60b7d25d

Developmental processes in biology are underlined by proliferation, differentiation and migration of cells. The latter two are interlinked since cellular differentiation is governed by the dynamics of morphogens which, in turn, is affected by the movement of cells. Mutual effects of morphogenetic and cell movement patterns are enhanced when the movement is due to chemotactic response of cells to the morphogens. In this study we introduce a mathematical model to analyse how this interplay can result in a steady movement of cells in a tissue and associated formation of travelling waves in a concentration field of morphogen. Using the model we have identified four chemotactic scenarios for migration of single cell or homogeneous group of cells in a tissue. Such a migration can take place if moving cells are (1) repelled by a chemical produced by themselves or (2) attracted by a chemical produced by the surrounding cells in a tissue. Furthermore, the group of cells can also move if cells in surrounding tissue are (3) repelled by a chemical produced by moving cells or (4) attracted by a chemical produced by surrounding cells themselves. The proposed mechanisms can underlie migration of cells during embryonic development as well as spread of metastatic cells.

]]>
<![CDATA[Rescaling of Spatio-Temporal Sensing in Eukaryotic Chemotaxis]]> https://www.researchpad.co/article/5989daf2ab0ee8fa60bc1caa

Eukaryotic cells respond to a chemoattractant gradient by forming intracellular gradients of signaling molecules that reflect the extracellular chemical gradient—an ability called directional sensing. Quantitative experiments have revealed two characteristic input-output relations of the system: First, in a static chemoattractant gradient, the shapes of the intracellular gradients of the signaling molecules are determined by the relative steepness, rather than the absolute concentration, of the chemoattractant gradient along the cell body. Second, upon a spatially homogeneous temporal increase in the input stimulus, the intracellular signaling molecules are transiently activated such that the response magnitudes are dependent on fold changes of the stimulus, not on absolute levels. However, the underlying mechanism that endows the system with these response properties remains elusive. Here, by adopting a widely used modeling framework of directional sensing, local excitation and global inhibition (LEGI), we propose a hypothesis that the two rescaling behaviors stem from a single design principle, namely, invariance of the governing equations to a scale transformation of the input level. Analyses of the LEGI-based model reveal that the invariance can be divided into two parts, each of which is responsible for the respective response properties. Our hypothesis leads to an experimentally testable prediction that a system with the invariance detects relative steepness even in dynamic gradient stimuli as well as in static gradients. Furthermore, we show that the relation between the response properties and the scale invariance is general in that it can be implemented by models with different network topologies.

]]>
<![CDATA[Paul Drude's Prediction of Nonreciprocal Mutual Inductance for Tesla Transformers]]> https://www.researchpad.co/article/5989d9dbab0ee8fa60b67737

Inductors, transmission lines, and Tesla transformers have been modeled with lumped-element equivalent circuits for over a century. In a well-known paper from 1904, Paul Drude predicts that the mutual inductance for an unloaded Tesla transformer should be nonreciprocal. This historical curiosity is mostly forgotten today, perhaps because it appears incorrect. However, Drude's prediction is shown to be correct for the conditions treated, demonstrating the importance of constraints in deriving equivalent circuits for distributed systems. The predicted nonreciprocity is not fundamental, but instead is an artifact of the misrepresentation of energy by an equivalent circuit. The application to modern equivalent circuits is discussed.

]]>
<![CDATA[Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions]]> https://www.researchpad.co/article/5989db52ab0ee8fa60bdc993

The Sine-Gordon equation in (1+3) dimensions has N-traveling front (“kink”, “domain wall”)- solutions for all N ≥ 1. A nonlinear functional of the solution, which vanishes on a single-front, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Each rod is localized in the vicinity of the intersection of two Sine-Gordon fronts. The rod systems are solutions of the linear wave equation, driven by a term that is constructed out of Sine-Gordon fronts. An additional linear operation maps multi-rod systems onto sets of blobs. Each blob is localized in the vicinity of rod intersection, and moves in space. The blob systems are solutions of the linear wave equation, driven by a term that is also constructed out of Sine-Gordon fronts. The temporal evolution of multi-blob solutions mimics elastic collisions of systems of spatially extended particles.

]]>
<![CDATA[The Coda of the Transient Response in a Sensitive Cochlea: A Computational Modeling Study]]> https://www.researchpad.co/article/5989da2eab0ee8fa60b835c6

In a sensitive cochlea, the basilar membrane response to transient excitation of any kind–normal acoustic or artificial intracochlear excitation–consists of not only a primary impulse but also a coda of delayed secondary responses with varying amplitudes but similar spectral content around the characteristic frequency of the measurement location. The coda, sometimes referred to as echoes or ringing, has been described as a form of local, short term memory which may influence the ability of the auditory system to detect gaps in an acoustic stimulus such as speech. Depending on the individual cochlea, the temporal gap between the primary impulse and the following coda ranges from once to thrice the group delay of the primary impulse (the group delay of the primary impulse is on the order of a few hundred microseconds). The coda is physiologically vulnerable, disappearing when the cochlea is compromised even slightly. The multicomponent sensitive response is not yet completely understood. We use a physiologically-based, mathematical model to investigate (i) the generation of the primary impulse response and the dependence of the group delay on the various stimulation methods, (ii) the effect of spatial perturbations in the properties of mechanically sensitive ion channels on the generation and separation of delayed secondary responses. The model suggests that the presence of the secondary responses depends on the wavenumber content of a perturbation and the activity level of the cochlea. In addition, the model shows that the varying temporal gaps between adjacent coda seen in experiments depend on the individual profiles of perturbations. Implications for non-invasive cochlear diagnosis are also discussed.

]]>
<![CDATA[Twisted states in nonlocally coupled phase oscillators with frequency distribution consisting of two Lorentzian distributions with the same mean frequency and different widths]]> https://www.researchpad.co/article/5c915f8ed5eed0c48420ab08

In globally coupled phase oscillators, the distribution of natural frequency has strong effects on both synchronization transition and synchronous dynamics. In this work, we study a ring of nonlocally coupled phase oscillators with the frequency distribution made up of two Lorentzians with the same center frequency but with different half widths. Using the Ott-Antonsen ansatz, we derive a reduced model in the continuum limit. Based on the reduced model, we analyze the stability of the incoherent state and find the existence of multiple stability islands for the incoherent state depending on the parameters. Furthermore, we numerically simulate the reduced model and find a large number of twisted states resulting from the instabilities of the incoherent state with respect to different spatial modes. For some winding numbers, the stability region of the corresponding twisted state consists of two disjoint parameter regions, one for the intermediate coupling strength and the other for the strong coupling strength.

]]>
<![CDATA[Large-scale modulation of reconstituted Min protein patterns and gradients by defined mutations in MinE’s membrane targeting sequence]]> https://www.researchpad.co/article/5989db5fab0ee8fa60be1112

The E. coli MinDE oscillator is a paradigm for protein self-organization and gradient formation. Previously, we reconstituted Min protein wave patterns on flat membranes as well as gradient-forming pole-to-pole oscillations in cell-shaped PDMS microcompartments. These oscillations appeared to require direct membrane interaction of the ATPase activating protein MinE. However, it remained unclear how exactly Min protein dynamics are regulated by MinE membrane binding. Here, we dissect the role of MinE’s membrane targeting sequence (MTS) by reconstituting various MinE mutants in 2D and 3D geometries. We demonstrate that the MTS defines the lower limit of the concentration-dependent wavelength of Min protein patterns while restraining MinE’s ability to stimulate MinD’s ATPase activity. Strikingly, a markedly reduced length scale—obtainable even by single mutations—is associated with a rich variety of multistable dynamic modes in cell-shaped compartments. This dramatic remodeling in response to biochemical changes reveals a remarkable trade-off between robustness and versatility of the Min oscillator.

]]>
<![CDATA[Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions]]> https://www.researchpad.co/article/5989d9d4ab0ee8fa60b6519d

Slower-than-light multi-front solutions of the Sine-Gordon in (1+2) dimensions, constructed through the Hirota algorithm, are mapped onto spatially localized structures, which emulate free, spatially extended, massive relativistic particles. A localized structure is an image of the junctions at which the fronts intersect. It propagates together with the multi-front solution at the velocity of the latter. The profile of the localized structure obeys the linear wave equation in (1+2) dimensions, to which a term that represents interaction with a slower-than-light, Sine-Gordon-multi-front solution has been added. This result can be also formulated in terms of a (1+2)-dimensional Lagrangian system, in which the Sine-Gordon and wave equations are coupled. Expanding the Euler-Lagrange equations in powers of the coupling constant, the zero-order part of the solution reproduces the (1+2)-dimensional Sine-Gordon fronts. The first-order part is the spatially localized structure. PACS: 02.30.Ik, 03.65.Pm, 05.45.Yv, 02.30.Ik.

]]>
<![CDATA[Tailoring the Blast Exposure Conditions in the Shock Tube for Generating Pure, Primary Shock Waves: The End Plate Facilitates Elimination of Secondary Loading of the Specimen]]> https://www.researchpad.co/article/5989d9efab0ee8fa60b6de14

The end plate mounted at the mouth of the shock tube is a versatile and effective implement to control and mitigate the end effects. We have performed a series of measurements of incident shock wave velocities and overpressures followed by quantification of impulse values (integral of pressure in time domain) for four different end plate configurations (0.625, 2, 4 inches, and an open end). Shock wave characteristics were monitored by high response rate pressure sensors allocated in six positions along the length of 6 meters long 229 mm square cross section shock tube. Tests were performed at three shock wave intensities, which was controlled by varying the Mylar membrane thickness (0.02, 0.04 and 0.06 inch). The end reflector plate installed at the exit of the shock tube allows precise control over the intensity of reflected waves penetrating into the shock tube. At the optimized distance of the tube to end plate gap the secondary waves were entirely eliminated from the test section, which was confirmed by pressure sensor at T4 location. This is pronounced finding for implementation of pure primary blast wave animal model. These data also suggest only deep in the shock tube experimental conditions allow exposure to a single shock wave free of artifacts. Our results provide detailed insight into spatiotemporal dynamics of shock waves with Friedlander waveform generated using helium as a driver gas and propagating in the air inside medium sized tube. Diffusion of driver gas (helium) inside the shock tube was responsible for velocity increase of reflected shock waves. Numerical simulations combined with experimental data suggest the shock wave attenuation mechanism is simply the expansion of the internal pressure. In the absence of any other postulated shock wave decay mechanisms, which were not implemented in the model the agreement between theory and experimental data is excellent.

]]>
<![CDATA[Global Neuromagnetic Cortical Fields Have Non-Zero Velocity]]> https://www.researchpad.co/article/5989dabbab0ee8fa60baed7d

Globally coherent patterns of phase can be obscured by analysis techniques that aggregate brain activity measures across-trials, whether prior to source localization or for estimating inter-areal coherence. We analyzed, at single-trial level, whole head MEG recorded during an observer-triggered apparent motion task. Episodes of globally coherent activity occurred in the delta, theta, alpha and beta bands of the signal in the form of large-scale waves, which propagated with a variety of velocities. Their mean speed at each frequency band was proportional to temporal frequency, giving a range of 0.06 to 4.0 m/s, from delta to beta. The wave peaks moved over the entire measurement array, during both ongoing activity and task-relevant intervals; direction of motion was more predictable during the latter. A large proportion of the cortical signal, measurable at the scalp, exists as large-scale coherent motion. We argue that the distribution of observable phase velocities in MEG is dominated by spatial filtering considerations in combination with group velocity of cortical activity. Traveling waves may index processes involved in global coordination of cortical activity.

]]>
<![CDATA[Individual-based modelling of population growth and diffusion in discrete time]]> https://www.researchpad.co/article/5989db51ab0ee8fa60bdc339

Individual-based models (IBMs) of human populations capture spatio-temporal dynamics using rules that govern the birth, behavior, and death of individuals. We explore a stochastic IBM of logistic growth-diffusion with constant time steps and independent, simultaneous actions of birth, death, and movement that approaches the Fisher-Kolmogorov model in the continuum limit. This model is well-suited to parallelization on high-performance computers. We explore its emergent properties with analytical approximations and numerical simulations in parameter ranges relevant to human population dynamics and ecology, and reproduce continuous-time results in the limit of small transition probabilities. Our model prediction indicates that the population density and dispersal speed are affected by fluctuations in the number of individuals. The discrete-time model displays novel properties owing to the binomial character of the fluctuations: in certain regimes of the growth model, a decrease in time step size drives the system away from the continuum limit. These effects are especially important at local population sizes of <50 individuals, which largely correspond to group sizes of hunter-gatherers. As an application scenario, we model the late Pleistocene dispersal of Homo sapiens into the Americas, and discuss the agreement of model-based estimates of first-arrival dates with archaeological dates in dependence of IBM model parameter settings.

]]>
<![CDATA[Traveling Pulses for a Two-Species Chemotaxis Model]]> https://www.researchpad.co/article/5989da56ab0ee8fa60b8efad

Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely described thanks to a mathematical model at the macroscopic scale. Such model was derived in [1] using a kinetic model based on an accurate description of the mesoscopic run-and-tumble process. We extend this approach to study the behavior of the interaction between two populations of E. Coli. Separately, each population travels with its own speed in the channel. When put together, a synchronization of the speed of the traveling pulses can be observed. We show that this synchronization depends on the fraction of the fast population. Our approach is based on mathematical analysis of a macroscopic model of partial differential equations. Numerical simulations in comparison with experimental observations show qualitative agreement.

]]>
<![CDATA[Parasites Sustain and Enhance RNA-Like Replicators through Spatial Self-Organisation]]> https://www.researchpad.co/article/5989dab8ab0ee8fa60badca6

In a prebiotic RNA world, parasitic behaviour may be favoured because template dependent replication happens in trans, thus being altruistic. Spatially extended systems are known to reduce harmful effects of parasites. Here we present a spatial system to show that evolution of replication is (indirectly) enhanced by strong parasites, and we characterise the phase transition that leads to this mode of evolution. Building on the insights of this analysis, we identify two scenarios, namely periodic disruptions and longer replication time-span, in which speciation occurs and an evolved parasite-like lineage enables the evolutionary increase of replication rates in replicators. Finally, we show that parasites co-evolving with replicators are selected to become weaker, i.e. worse templates for replication when the duration of replication is increased. We conclude that parasites may not be considered a problem for evolution in a prebiotic system, but a degree of freedom that can be exploited by evolution to enhance the evolvability of replicators, by means of emergent levels of selection.

]]>
<![CDATA[A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map]]> https://www.researchpad.co/article/5989da38ab0ee8fa60b86fc7

We describe a general Godunov-type splitting for numerical simulations of the Fisher–Kolmogorov–Petrovski–Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas.

]]>
<![CDATA[Spatiotemporal Dynamics of Virus Infection Spreading in Tissues]]> https://www.researchpad.co/article/5989dad9ab0ee8fa60bb9339

Virus spreading in tissues is determined by virus transport, virus multiplication in host cells and the virus-induced immune response. Cytotoxic T cells remove infected cells with a rate determined by the infection level. The intensity of the immune response has a bell-shaped dependence on the concentration of virus, i.e., it increases at low and decays at high infection levels. A combination of these effects and a time delay in the immune response determine the development of virus infection in tissues like spleen or lymph nodes. The mathematical model described in this work consists of reaction-diffusion equations with a delay. It shows that the different regimes of infection spreading like the establishment of a low level infection, a high level infection or a transition between both are determined by the initial virus load and by the intensity of the immune response. The dynamics of the model solutions include simple and composed waves, and periodic and aperiodic oscillations. The results of analytical and numerical studies of the model provide a systematic basis for a quantitative understanding and interpretation of the determinants of the infection process in target organs and tissues from the image-derived data as well as of the spatiotemporal mechanisms of viral disease pathogenesis, and have direct implications for a biopsy-based medical testing of the chronic infection processes caused by viruses, e.g. HIV, HCV and HBV.

]]>