19 research outputs found
Role of spatial heterogeneity on the collective dynamics of cilia beating in a minimal 1D model
Cilia are elastic hairlike protuberances of the cell membrane found in
various unicellular organisms and in several tissues of most living organisms.
In some tissues such as the airway tissues of the lung, the coordinated beating
of cilia induce a fluid flow of crucial importance as it allows the continuous
cleaning of our bronchia, known as mucociliary clearance. While most of the
models addressing the question of collective dynamics and metachronal wave
consider homogeneous carpets of cilia, experimental observations rather show
that cilia clusters are heterogeneously distributed over the tissue surface.
The purpose of this paper is to investigate the role of spatial heterogeneity
on the coherent beating of cilia using a very simple one dimensional model for
cilia known as the rower model. We systematically study systems consisting of a
few rowers to hundreds of rowers and we investigate the conditions for the
emergence of collective beating. When considering a small number of rowers, a
phase drift occurs, hence a bifurcation in beating frequency is observed as the
distance between rowers clusters is changed. In the case of many rowers, a
distribution of frequencies is observed. We found in particular the pattern of
the patchy structure that shows the best robustness in collective beating
behavior, as the density of cilia is varied over a wide range.Comment: 16 pages, 22 figures including appendi
Spatial Structures and Giant Number Fluctuations in Models of Active Matter
The large scale fluctuations of the ordered state in active matter systems
are usually characterised by studying the "giant number fluctuations" of
particles in any finite volume, as compared to the expectations from the
central limit theorem. However, in ordering systems, the fluctuations in
density ordering are often captured through their structure functions deviating
from Porod law. In this paper we study the relationship between giant number
fluctuations and structure functions, for different models of active matter as
well as other non-equilibrium systems. A unified picture emerges, with
different models falling in four distinct classes depending on the nature of
their structure functions. For one class, we show that experimentalists may
find Porod law violation, by measuring subleading corrections to the number
fluctuations.Comment: 5 pages, 3 figure
Role of cilia activity and surrounding viscous fluid on properties of metachronal waves
Large groups of active cilia collectively beat in a fluid medium as
metachronal waves, essential for some microorganisms motility and for flow
generation in mucociliary clearance. Several models can predict the emergence
of metachronal waves, but what controls the properties of metachronal waves is
still unclear. Here, we investigate numerically a simple model for cilia in the
presence of noise on regular lattices in one- and two-dimensions. We
characterize the wave using spatial correlation and the frequency of collective
beating. Our results clearly show that the viscosity of the fluid medium does
not affect the wavelength; the activity of the cilia does. These numerical
results are supported by a dimensional analysis, which is expected to be robust
against the model for active force generation, unless surrounding fluid
influences the cilia activity. Interestingly, enhancement of cilia activity
increases the wavelength and decreases the beating frequency, keeping the wave
velocity almost unchanged. These results might have significance in
understanding paramecium locomotion and mucociliary clearance diseases.Comment: 6 pages, 5 figure
Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator
In a system of non-linear chemical reactions called the Brusselator, we show
that {\it intrinsic noise} can be regulated to drive it to exhibit resonance in
the presence of a sub-threshold signal. The phenomena of periodic stochastic
resonance and aperiodic stochastic resonance, hitherto studied mostly with
extrinsic noise, is demonstrated here to occur with inherent systemic noise
using exact stochastic simulation algorithm due to Gillespie. The role of
intrinsic noise in a couple of other phenomena is also discussed.Comment: 7 pages, 5 figure
Effect of transcription factor resource sharing on gene expression noise
Gene expression is intrinsically a stochastic (noisy) process with important implications for cellular functions. Deciphering the underlying mechanisms of gene expression noise remains one of the key challenges of regulatory biology. Theoretical models of transcription often incorporate the kinetics of how transcription factors (TFs) interact with a single promoter to impact gene expression noise. However, inside single cells multiple identical gene copies as well as additional binding sites can compete for a limiting pool of TFs. Here we develop a simple kinetic model of transcription, which explicitly incorporates this interplay between TF copy number and its binding sites. We show that TF sharing enhances noise in mRNA distribution across an isogenic population of cells. Moreover, when a single gene copy shares it\u27s TFs with multiple competitor sites, the mRNA variance as a function of the mean remains unaltered by their presence. Hence, all the data for variance as a function of mean expression collapse onto a single master curve independent of the strength and number of competitor sites. However, this result does not hold true when the competition stems from multiple copies of the same gene. Therefore, although previous studies showed that the mean expression follows a universal master curve, our findings suggest that different scenarios of competition bear distinct signatures at the level of variance. Intriguingly, the introduction of competitor sites can transform a unimodal mRNA distribution into a multimodal distribution. These results demonstrate the impact of limited availability of TF resource on the regulation of noise in gene expression
Short-range interaction vs long-range correlation in bird flocks
Bird flocks are a paradigmatic example of collective motion. One of the
prominent experimental traits discovered about flocks is the presence of long
range velocity correlations between individuals, which allow them to influence
each other over the large scales, keeping a high level of group coordination. A
crucial question is to understand what is the mutual interaction between birds
generating such nontrivial correlations. Here we use the Maximum Entropy (ME)
approach to infer from experimental data of natural flocks the effective
interactions between birds. Compared to previous studies, we make a significant
step forward as we retrieve the full functional dependence of the interaction
on distance and find that it decays exponentially over a range of a few
individuals. The fact that ME gives a short-range interaction even though its
experimental input is the long-range correlation function, shows that the
method is able to discriminate the relevant information encoded in such
correlations and single out a minimal number of effective parameters. Finally,
we show how the method can be used to capture the degree of anisotropy of
mutual interactions.Comment: 21 pages, 7 figures, 1 tabl
Critical behavior of loops and biconnected clusters on fractals of dimension d < 2
We solve the O(n) model, defined in terms of self- and mutually avoiding
loops coexisting with voids, on a 3-simplex fractal lattice, using an exact
real space renormalization group technique. As the density of voids is
decreased, the model shows a critical point, and for even lower densities of
voids, there is a dense phase showing power-law correlations, with critical
exponents that depend on n, but are independent of density. At n=-2 on the
dilute branch, a trivalent vertex defect acts as a marginal perturbation. We
define a model of biconnected clusters which allows for a finite density of
such vertices. As n is varied, we get a line of critical points of this
generalized model, emanating from the point of marginality in the original loop
model. We also study another perturbation of adding local bending rigidity to
the loop model, and find that it does not affect the universality class.Comment: 14 pages,10 figure
Lattice models for ballistic aggregation in one dimension
We propose two lattice models in one dimension, with stochastically hopping particles which aggregate on contact. The hops are guided by “velocity rates" which themselves evolve according to the rules of ballistic aggregation as in a sticky gas in continuum. Our lattice models have both velocity and density fields and an appropriate real time evolution, such that they can be compared directly with event-driven molecular dynamics (MD) results for the sticky gas. We demonstrate numerically that the long-time and large-distance behavior of the lattice models is identical to that of the MD, and some exact results known for the sticky gas. In particular, the exactly predicted form of the non-Gaussian tail of the velocity distribution function is clearly exhibited. This correspondence of the lattice models and the sticky gas in continuum is nontrivial, as the latter has a deterministic dynamics with a local kinematic constraint, in contrast with the former; yet the spatial velocity profiles (with shocks) of the lattice models and the MD have a striking match