24,512 research outputs found
Structurally robust biological networks
Background:
The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation.
Results:
In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature.
Conclusions:
The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters
Modeling Small Oscillating Biological Networks in Analog VLSI
We have used analog VLSI technology to model a class of small oscillating
biological neural circuits known as central pattern generators
(CPG). These circuits generate rhythmic patterns of activity
which drive locomotor behaviour in the animal. We have designed,
fabricated, and tested a model neuron circuit which relies on many
of the same mechanisms as a biological central pattern generator
neuron, such as delays and internal feedback. We show that this
neuron can be used to build several small circuits based on known
biological CPG circuits, and that these circuits produce patterns of
output which are very similar to the observed biological patterns
Differential analysis of biological networks
In cancer research, the comparison of gene expression or DNA methylation
networks inferred from healthy controls and patients can lead to the discovery
of biological pathways associated to the disease. As a cancer progresses, its
signalling and control networks are subject to some degree of localised
re-wiring. Being able to detect disrupted interaction patterns induced by the
presence or progression of the disease can lead to the discovery of novel
molecular diagnostic and prognostic signatures. Currently there is a lack of
scalable statistical procedures for two-network comparisons aimed at detecting
localised topological differences. We propose the dGHD algorithm, a methodology
for detecting differential interaction patterns in two-network comparisons. The
algorithm relies on a statistic, the Generalised Hamming Distance (GHD), for
assessing the degree of topological difference between networks and evaluating
its statistical significance. dGHD builds on a non-parametric permutation
testing framework but achieves computationally efficiency through an asymptotic
normal approximation. We show that the GHD is able to detect more subtle
topological differences compared to a standard Hamming distance between
networks. This results in the dGHD algorithm achieving high performance in
simulation studies as measured by sensitivity and specificity. An application
to the problem of detecting differential DNA co-methylation subnetworks
associated to ovarian cancer demonstrates the potential benefits of the
proposed methodology for discovering network-derived biomarkers associated with
a trait of interest
Rigidity and flexibility of biological networks
The network approach became a widely used tool to understand the behaviour of
complex systems in the last decade. We start from a short description of
structural rigidity theory. A detailed account on the combinatorial rigidity
analysis of protein structures, as well as local flexibility measures of
proteins and their applications in explaining allostery and thermostability is
given. We also briefly discuss the network aspects of cytoskeletal tensegrity.
Finally, we show the importance of the balance between functional flexibility
and rigidity in protein-protein interaction, metabolic, gene regulatory and
neuronal networks. Our summary raises the possibility that the concepts of
flexibility and rigidity can be generalized to all networks.Comment: 21 pages, 4 figures, 1 tabl
Non-Hermitian Localization in Biological Networks
We explore the spectra and localization properties of the N-site banded
one-dimensional non-Hermitian random matrices that arise naturally in sparse
neural networks. Approximately equal numbers of random excitatory and
inhibitory connections lead to spatially localized eigenfunctions, and an
intricate eigenvalue spectrum in the complex plane that controls the
spontaneous activity and induced response. A finite fraction of the eigenvalues
condense onto the real or imaginary axes. For large N, the spectrum has
remarkable symmetries not only with respect to reflections across the real and
imaginary axes, but also with respect to 90 degree rotations, with an unusual
anisotropic divergence in the localization length near the origin. When chains
with periodic boundary conditions become directed, with a systematic
directional bias superimposed on the randomness, a hole centered on the origin
opens up in the density-of-states in the complex plane. All states are extended
on the rim of this hole, while the localized eigenvalues outside the hole are
unchanged. The bias dependent shape of this hole tracks the bias independent
contours of constant localization length. We treat the large-N limit by a
combination of direct numerical diagonalization and using transfer matrices, an
approach that allows us to exploit an electrostatic analogy connecting the
"charges" embodied in the eigenvalue distribution with the contours of constant
localization length. We show that similar results are obtained for more
realistic neural networks that obey "Dale's Law" (each site is purely
excitatory or inhibitory), and conclude with perturbation theory results that
describe the limit of large bias g, when all states are extended. Related
problems arise in random ecological networks and in chains of artificial cells
with randomly coupled gene expression patterns
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