22,125 research outputs found
Getting started in probabilistic graphical models
Probabilistic graphical models (PGMs) have become a popular tool for
computational analysis of biological data in a variety of domains. But, what
exactly are they and how do they work? How can we use PGMs to discover patterns
that are biologically relevant? And to what extent can PGMs help us formulate
new hypotheses that are testable at the bench? This note sketches out some
answers and illustrates the main ideas behind the statistical approach to
biological pattern discovery.Comment: 12 pages, 1 figur
Efficient inference of parsimonious phenomenological models of cellular dynamics using S-systems and alternating regression
The nonlinearity of dynamics in systems biology makes it hard to infer them
from experimental data. Simple linear models are computationally efficient, but
cannot incorporate these important nonlinearities. An adaptive method based on
the S-system formalism, which is a sensible representation of nonlinear
mass-action kinetics typically found in cellular dynamics, maintains the
efficiency of linear regression. We combine this approach with adaptive model
selection to obtain efficient and parsimonious representations of cellular
dynamics. The approach is tested by inferring the dynamics of yeast glycolysis
from simulated data. With little computing time, it produces dynamical models
with high predictive power and with structural complexity adapted to the
difficulty of the inference problem.Comment: 14 pages, 2 figure
Positional information, positional error, and read-out precision in morphogenesis: a mathematical framework
The concept of positional information is central to our understanding of how
cells in a multicellular structure determine their developmental fates.
Nevertheless, positional information has neither been defined mathematically
nor quantified in a principled way. Here we provide an information-theoretic
definition in the context of developmental gene expression patterns and examine
which features of expression patterns increase or decrease positional
information. We connect positional information with the concept of positional
error and develop tools to directly measure information and error from
experimental data. We illustrate our framework for the case of gap gene
expression patterns in the early Drosophila embryo and show how information
that is distributed among only four genes is sufficient to determine
developmental fates with single cell resolution. Our approach can be
generalized to a variety of different model systems; procedures and examples
are discussed in detail
3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries
Recent advances in electron microscopy have enabled the imaging of single
cells in 3D at nanometer length scale resolutions. An uncharted frontier for in
silico biology is the ability to simulate cellular processes using these
observed geometries. Enabling such simulations requires watertight meshing of
electron micrograph images into 3D volume meshes, which can then form the basis
of computer simulations of such processes using numerical techniques such as
the Finite Element Method. In this paper, we describe the use of our recently
rewritten mesh processing software, GAMer 2, to bridge the gap between poorly
conditioned meshes generated from segmented micrographs and boundary marked
tetrahedral meshes which are compatible with simulation. We demonstrate the
application of a workflow using GAMer 2 to a series of electron micrographs of
neuronal dendrite morphology explored at three different length scales and show
that the resulting meshes are suitable for finite element simulations. This
work is an important step towards making physical simulations of biological
processes in realistic geometries routine. Innovations in algorithms to
reconstruct and simulate cellular length scale phenomena based on emerging
structural data will enable realistic physical models and advance discovery at
the interface of geometry and cellular processes. We posit that a new frontier
at the intersection of computational technologies and single cell biology is
now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies
available upon reques
Analysis of the lactose metabolism in E. coli using sum-of-squares decomposition
We provide a system-theoretic analysis of the mathematical model of lactose induction in E.coli which predicts the level of lactose induction into the cell for specified values of external lactose. Depending on the levels of external lactose and other parameters, the Lac operon is known to have a low steady state in which it is said to be turned off and high steady state where it is said to be turned on. Furthermore, the model has been shown experimentally to exhibit a bi-stable behavior. Using ideas from Lyapunov stability theory and sum-of-squares decomposition, we characterize the reachable state
space for different sets of initial conditions, calculating estimates of the regions of attraction of the biologically relevant equilibria of this system. The changes in the basins of attraction with changes in model parameters can be used to provide biological insight. Specifically, we explain the crucial role played by a small basal transcription rate in the Lac operon. We show that if the basal rate is below a threshold, the region of attraction of the low steady state grows significantly, indicating that system is trapped in the (off) mode, showing the importance of the basal rate of transcription
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Cavitation in soft matter
Cavitation is the sudden, unstable expansion of a void or bubble within a liquid or solid subjected to a negative hydrostatic stress. Cavitation rheology is a field emerging from the development of a suite of materials characterization, damage quantification, and therapeutic techniques that exploit the physical principles of cavitation. Cavitation rheology is inherently complex and broad in scope with wide-ranging applications in the biology, chemistry, materials, and mechanics communities. This perspective aims to drive collaboration among these communities and guide discussion by defining a common core of high-priority goals while highlighting emerging opportunities in the field of cavitation rheology. A brief overview of the mechanics and dynamics of cavitation in soft matter is presented. This overview is followed by a discussion of the overarching goals of cavitation rheology and an overview of common experimental techniques. The larger unmet needs and challenges of cavitation in soft matter are then presented alongside specific opportunities for researchers from different disciplines to contribute to the field
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