scholarly journals Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination

2021 ◽  
Author(s):  
J. F. Cass ◽  
S. J. Hogan
Keyword(s):  
Motor Coordination ◽  
Nonlinear Damping ◽  
Numerical Continuation ◽  
Arbitrary Parameter ◽  
Relevant Parameter ◽  
Coupling Coefficients ◽  
Dimensionless Parameters ◽  
Biologically Relevant ◽  
Mechanical Analogue ◽  
Partner Interaction

AbstractThe widely cited Haken–Kelso–Bunz (HKB) model of motor coordination is used in an enormous range of applications. In this paper, we show analytically that the weakly damped, weakly coupled HKB model of two oscillators depends on only two dimensionless parameters; the ratio of the linear damping coefficient and the linear coupling coefficient and the ratio of the combined nonlinear damping coefficients and the combined nonlinear coupling coefficients. We illustrate our results with a mechanical analogue. We use our analytic results to predict behaviours in arbitrary parameter regimes and show how this led us to explain and extend recent numerical continuation results of the full HKB model. The key finding is that the HKB model contains a significant amount of behaviour in biologically relevant parameter regimes not yet observed in experiments or numerical simulations. This observation has implications for the development of virtual partner interaction and the human dynamic clamp, and potentially for the HKB model itself.

Dynamic Stability of a Base-Excited Thin Beam With Top Mass

2006 ◽  
Author(s):  
Niels J. Mallon ◽  
Rob H.-B. Fey ◽  
Henk Nijmeijer
Keyword(s):  
Dynamic Stability ◽  
Finite Element Modelling ◽  
Nonlinear Damping ◽  
Basis Functions ◽  
Numerical Continuation ◽  
Series Expansions ◽  
Thin Beam ◽  
Taylor Series Expansions ◽  
Numerical Tools ◽  
Top Mass

This paper deals with a base-excited clamped-clamped vertical thin beam carrying a top mass. The thin beam is considered to be inextensible and initially not perfectly straight. Based on Taylor series expansions of the inextensibility constraint and the exact curvature, and by using one or more basis functions, a semi-analytical model is derived. This model is numerically validated through a comparison with quasi-static and modal analysis results obtained using finite element modelling. The steady-state nonlinear dynamics of the base-excited beam are investigated using numerical continuation of periodic solutions and bifurcations. Using these numerical tools, the dynamic stability of the beam is investigated for various parameter settings, including the effect of nonlinear damping. The continuation of bifurcations appears to be very suitable to determine whether or not parametric resonance occurs for certain parameter settings.

scholarly journals Fluid dynamics in heart development: effects of hematocrit and trabeculation

2017 ◽  
Vol 35 (4) ◽  
pp. 493-516 ◽  
Author(s):  
Nicholas A Battista ◽  
Andrea N Lane ◽  
Jiandong Liu ◽  
Laura A Miller
Keyword(s):  
Heart Development ◽  
Genetic Regulatory Networks ◽  
Vortical Flow ◽  
Immersed Boundary ◽  
Relevant Parameter ◽  
Womersley Number ◽  
Biologically Relevant ◽  
Morphogen Gradients ◽  
Stage Of Development

Abstract Recent in vivo experiments have illustrated the importance of understanding the haemodynamics of heart morphogenesis. In particular, ventricular trabeculation is governed by a delicate interaction between haemodynamic forces, myocardial activity, and morphogen gradients, all of which are coupled to genetic regulatory networks. The underlying haemodynamics at the stage of development in which the trabeculae form is particularly complex, given the balance between inertial and viscous forces. Small perturbations in the geometry, scale, and steadiness of the flow can lead to changes in the overall flow structures and chemical morphogen gradients, including the local direction of flow, the transport of morphogens, and the formation of vortices. The immersed boundary method was used to solve the two-dimensional fluid-structure interaction problem of fluid flow moving through a two chambered heart of a zebrafish (Danio rerio), with a trabeculated ventricle, at 96 hours post fertilization (hpf). Trabeculae heights and hematocrit were varied, and simulations were conducted for two orders of magnitude of Womersley number, extending beyond the biologically relevant range (0.2–12.0). Both intracardial and intertrabecular vortices formed in the ventricle for biologically relevant parameter values. The bifurcation from smooth streaming flow to vortical flow depends upon the trabeculae geometry, hematocrit, and Womersley number, $Wo$. This work shows the importance of hematocrit and geometry in determining the bulk flow patterns in the heart at this stage of development.

scholarly journals Bursting noise in gene expression dynamics: linking microscopic and mesoscopic models

2016 ◽  
Vol 13 (114) ◽  
pp. 20150772 ◽  
Author(s):  
Yen Ting Lin ◽  
Tobias Galla
Keyword(s):  
Regulatory Networks ◽  
Coarse Grained ◽  
Relevant Parameter ◽  
Piecewise Deterministic Markov Process ◽  
Biologically Relevant ◽  
Coarse Grained Model ◽  
Mesoscopic Models ◽  
Gene Expression Dynamics ◽  
Gene Regulatory ◽  
Noise In Gene Expression

The dynamics of short-lived mRNA results in bursts of protein production in gene regulatory networks. We investigate the propagation of bursting noise between different levels of mathematical modelling and demonstrate that conventional approaches based on diffusion approximations can fail to capture bursting noise. An alternative coarse-grained model, the so-called piecewise deterministic Markov process (PDMP), is seen to outperform the diffusion approximation in biologically relevant parameter regimes. We provide a systematic embedding of the PDMP model into the landscape of existing approaches, and we present analytical methods to calculate its stationary distribution and switching frequencies.

scholarly journals Spatial structure governs the mode of tumour evolution

2019 ◽  
Author(s):  
Robert Noble ◽  
Dominik Burri ◽  
Jakob Nikolas Kather ◽  
Niko Beerenwinkel
Keyword(s):  
Early Stage ◽  
Mechanistic Explanation ◽  
Cell Interaction ◽  
Colorectal Adenomas ◽  
Neutral Evolution ◽  
Relevant Parameter ◽  
Biologically Relevant ◽  
Wide Range ◽  
Sequencing Studies ◽  
Parameter Ranges

AbstractCharacterizing the mode – the way, manner, or pattern – of evolution in tumours is important for clinical forecasting and optimizing cancer treatment. DNA sequencing studies have inferred various modes, including branching, punctuated and neutral evolution, but it is unclear why a particular pattern predominates in any given tumour.1, 2Here we propose that differences in tumour architecture alone can explain the variety of observed patterns. We examine this hypothesis using spatially explicit population genetic models and demonstrate that, within biologically relevant parameter ranges, human tumours are expected to exhibit four distinct onco-evolutionary modes (oncoevotypes): rapid clonal expansion (predicted in leukaemia); progressive diversification (in colorectal adenomas and early-stage colorectal carcinomas); branching evolution (in invasive glandular tumours); and effectively almost neutral evolution (in certain non-glandular and poorly differentiated solid tumours). We thus provide a simple, mechanistic explanation for a wide range of empirical observations. Oncoevotypes are governed by the mode of cell dispersal and the range of cell-cell interaction, which we show are essential factors in accurately characterizing, forecasting and controlling tumour evolution.

scholarly journals Mutation Rates, Mutation Frequencies, and Proofreading-Repair Activities in RNA Virus Genetics

Viruses ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1882 ◽  
Author(s):  
Esteban Domingo ◽  
Carlos García-Crespo ◽  
Rebeca Lobo-Vega ◽  
Celia Perales
Keyword(s):  
Error Rate ◽  
Rna Virus ◽  
Error Rates ◽  
Viral Rna ◽  
Mutation Rates ◽  
Relevant Parameter ◽  
Dna Viruses ◽  
Biologically Relevant ◽  
Host Interactions ◽  
The Stability

The error rate displayed during template copying to produce viral RNA progeny is a biologically relevant parameter of the replication complexes of viruses. It has consequences for virus–host interactions, and it represents the first step in the diversification of viruses in nature. Measurements during infections and with purified viral polymerases indicate that mutation rates for RNA viruses are in the range of 10−3 to 10−6 copying errors per nucleotide incorporated into the nascent RNA product. Although viruses are thought to exploit high error rates for adaptation to changing environments, some of them possess misincorporation correcting activities. One of them is a proofreading-repair 3′ to 5′ exonuclease present in coronaviruses that may decrease the error rate during replication. Here we review experimental evidence and models of information maintenance that explain why elevated mutation rates have been preserved during the evolution of RNA (and some DNA) viruses. The models also offer an interpretation of why error correction mechanisms have evolved to maintain the stability of genetic information carried out by large viral RNA genomes such as the coronaviruses.

scholarly journals How sequence populations persist inside bacterial genomes

Genetics ◽  
2021 ◽  
Vol 217 (4) ◽  
Author(s):  
Hye Jin Park ◽  
Chaitanya S Gokhale ◽  
Frederic Bertels
Keyword(s):  
Gene Transfer ◽  
Horizontal Gene Transfer ◽  
Population Size ◽  
Repetitive Sequences ◽  
Host Genome ◽  
Parameter Range ◽  
Relevant Parameter ◽  
Bacterial Genomes ◽  
Bacterial Host ◽  
Biologically Relevant

AbstractCompared to their eukaryotic counterparts, bacterial genomes are small and contain extremely tightly packed genes. Repetitive sequences are rare but not completely absent. One of the most common repeat families is REPINs. REPINs can replicate in the host genome and form populations that persist for millions of years. Here, we model the interactions of these intragenomic sequence populations with the bacterial host. We first confirm well-established results, in the presence and absence of horizontal gene transfer (hgt) sequence populations either expand until they drive the host to extinction or the sequence population gets purged from the genome. We then show that a sequence population can be stably maintained, when each individual sequence provides a benefit that decreases with increasing sequence population size. Maintaining a sequence population of stable size also requires the replication of the sequence population to be costly to the host, otherwise the sequence population size will increase indefinitely. Surprisingly, in regimes with high hgt rates, the benefit conferred by the sequence population does not have to exceed the damage it causes to its host. Our analyses provide a plausible scenario for the persistence of sequence populations in bacterial genomes. We also hypothesize a limited biologically relevant parameter range for the provided benefit, which can be tested in future experiments.

scholarly journals Variations on the Theme of Synaptic Filtering: A Comparison of Integrate-and-Express Models of Synaptic Plasticity for Memory Lifetimes

2016 ◽  
Vol 28 (11) ◽  
pp. 2393-2460 ◽  
Author(s):  
Terry Elliott
Keyword(s):  
Synaptic Plasticity ◽  
Parameter Space ◽  
Signal To Noise Ratio ◽  
First Passage Time ◽  
Passage Time ◽  
Memory Storage ◽  
Relevant Parameter ◽  
Filter Model ◽  
Biologically Relevant ◽  
Consecutive Number

Integrate-and-express models of synaptic plasticity propose that synapses integrate plasticity induction signals before expressing synaptic plasticity. By discerning trends in their induction signals, synapses can control destabilizing fluctuations in synaptic strength. In a feedforward perceptron framework with binary-strength synapses for associative memory storage, we have previously shown that such a filter-based model outperforms other, nonintegrative, “cascade”-type models of memory storage in most regions of biologically relevant parameter space. Here, we consider some natural extensions of our earlier filter model, including one specifically tailored to binary-strength synapses and one that demands a fixed, consecutive number of same-type induction signals rather than merely an excess before expressing synaptic plasticity. With these extensions, we show that filter-based models outperform nonintegrative models in all regions of biologically relevant parameter space except for a small sliver in which all models encode memories only weakly. In this sliver, which model is superior depends on the metric used to gauge memory lifetimes (whether a signal-to-noise ratio or a mean first passage time). After comparing and contrasting these various filter models, we discuss the multiple mechanisms and timescales that underlie both synaptic plasticity and memory phenomena and suggest that multiple, different filtering mechanisms may operate at single synapses.

The biologically relevant parameter in nerve impulse trains

1970 ◽  
Vol 6 (5) ◽  
pp. 168-170 ◽  
Author(s):  
T. A. McKean ◽  
R. E. Poppele ◽  
N. P. Rosenthal ◽  
C. A. Terzuolo
Keyword(s):  
Nerve Impulse ◽  
Relevant Parameter ◽  
Biologically Relevant

scholarly journals Explicit flock solutions for Quasi-Morse potentials

2014 ◽  
Vol 25 (5) ◽  
pp. 553-578 ◽  
Author(s):  
J. A. CARRILLO ◽  
Y. HUANG ◽  
S. MARTIN
Keyword(s):  
Interacting Particle Systems ◽  
Mean Field ◽  
Relevant Parameter ◽  
Biologically Relevant ◽  
Interacting Particle ◽  
Short Range Repulsion ◽  
Pattern Formations ◽  
Mean Field Limits ◽  
Three Space ◽  
Morse Potentials

We consider interacting particle systems and their mean-field limits, which are frequently used to model collective aggregation and are known to demonstrate a rich variety of pattern formations. The interaction is based on a pairwise potential combining short-range repulsion and long-range attraction. We study particular solutions, which are referred to as flocks in the second-order models, for the specific choice of the Quasi-Morse interaction potential. Our main result is a rigorous analysis of continuous, compactly supported flock profiles for the biologically relevant parameter regime. Existence and uniqueness are proven for three space dimensions, while existence is shown for the two-dimensional case. Furthermore, we numerically investigate additional Morse-like interactions to complete the understanding of this class of potentials.

Impact Assessment Using the Before-After-Control-Impact (BACI) Model: Concerns and Comments

1993 ◽  
Vol 50 (3) ◽  
pp. 627-637 ◽  
Author(s):  
Eric P. Smith ◽  
David R. Orvos ◽  
John Cairns Jr.
Keyword(s):  
Power Plant ◽  
Statistical Model ◽  
Impact Assessment ◽  
Control Site ◽  
Irregular Sampling ◽  
Relevant Parameter ◽  
Biologically Relevant ◽  
Before And After ◽  
Long Term Impact

The effect of a change in an ecosystem can often be assessed through the use of a statistical model that incorporates the change. A sensible approach for assessing the effects of an industrial or power plant on the aquatic environment is to sample the environment both before and after the plant starts operation and test for a change in some biologically relevant parameter. To improve sensitivity, samples may be taken at a control site as well as at sites receiving the plant effluent. While this provides a powerful means for assessing effects, the implementation of the design is important and subsequent analysis of the collected data depends on proper implementation. Problems such as trends in the measurements, failure to meet the assumptions of the model, irregular sampling, confounding factors, and changes in the habitat can influence results, as we illustrate using a long-term impact assessment of a power plant on fish populations. In long-term studies, it may be difficult to separate effects due to the plant from effects due to other sources. Sound design requires both a good statistical model and an understanding of the underlying biological processes (what to measure) and careful planning (how to measure it well).

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