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"Bates, Daniel"
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Garden
An exploration of Edelaar Mosayebi Inderbitzin Architects' interest in the garden as a topos and its meaning for their work, and a documentation of their temporary garden installation in Berlin in 2016.
Book
Robustness and parameter geography in post-translational modification systems
Biological systems are acknowledged to be robust to perturbations but a rigorous understanding of this has been elusive. In a mathematical model, perturbations often exert their effect through parameters, so sizes and shapes of parametric regions offer an integrated global estimate of robustness. Here, we explore this \"parameter geography\" for bistability in post-translational modification (PTM) systems. We use the previously developed \"linear framework\" for timescale separation to describe the steady-states of a two-site PTM system as the solutions of two polynomial equations in two variables, with eight non-dimensional parameters. Importantly, this approach allows us to accommodate enzyme mechanisms of arbitrary complexity beyond the conventional Michaelis-Menten scheme, which unrealistically forbids product rebinding. We further use the numerical algebraic geometry tools Bertini, Paramotopy, and alphaCertified to statistically assess the solutions to these equations at ∼109 parameter points in total. Subject to sampling limitations, we find no bistability when substrate amount is below a threshold relative to enzyme amounts. As substrate increases, the bistable region acquires 8-dimensional volume which increases in an apparently monotonic and sigmoidal manner towards saturation. The region remains connected but not convex, albeit with a high visibility ratio. Surprisingly, the saturating bistable region occupies a much smaller proportion of the sampling domain under mechanistic assumptions more realistic than the Michaelis-Menten scheme. We find that bistability is compromised by product rebinding and that unrealistic assumptions on enzyme mechanisms have obscured its parametric rarity. The apparent monotonic increase in volume of the bistable region remains perplexing because the region itself does not grow monotonically: parameter points can move back and forth between monostability and bistability. We suggest mathematical conjectures and questions arising from these findings. Advances in theory and software now permit insights into parameter geography to be uncovered by high-dimensional, data-centric analysis.
Journal Article
Global reference mapping of human transcription factor footprints
Combinatorial binding of transcription factors to regulatory DNA underpins gene regulation in all organisms. Genetic variation in regulatory regions has been connected with diseases and diverse phenotypic traits
1
, but it remains challenging to distinguish variants that affect regulatory function
2
. Genomic DNase I footprinting enables the quantitative, nucleotide-resolution delineation of sites of transcription factor occupancy within native chromatin
3
–
6
. However, only a small fraction of such sites have been precisely resolved on the human genome sequence
6
. Here, to enable comprehensive mapping of transcription factor footprints, we produced high-density DNase I cleavage maps from 243 human cell and tissue types and states and integrated these data to delineate about 4.5 million compact genomic elements that encode transcription factor occupancy at nucleotide resolution. We map the fine-scale structure within about 1.6 million DNase I-hypersensitive sites and show that the overwhelming majority are populated by well-spaced sites of single transcription factor–DNA interaction. Cell-context-dependent
cis
-regulation is chiefly executed by wholesale modulation of accessibility at regulatory DNA rather than by differential transcription factor occupancy within accessible elements. We also show that the enrichment of genetic variants associated with diseases or phenotypic traits in regulatory regions
1
,
7
is almost entirely attributable to variants within footprints, and that functional variants that affect transcription factor occupancy are nearly evenly partitioned between loss- and gain-of-function alleles. Unexpectedly, we find increased density of human genetic variation within transcription factor footprints, revealing an unappreciated driver of
cis
-regulatory evolution. Our results provide a framework for both global and nucleotide-precision analyses of gene regulatory mechanisms and functional genetic variation.
A high-density DNase I cleavage map from 243 human cell and tissue types provides a genome-wide, nucleotide-resolution map of human transcription factor footprints.
Journal Article
Identifiability and numerical algebraic geometry
A common problem when analyzing models, such as mathematical modeling of a biological process, is to determine if the unknown parameters of the model can be determined from given input-output data. Identifiable models are models such that the unknown parameters can be determined to have a finite number of values given input-output data. The total number of such values over the complex numbers is called the identifiability degree of the model. Unidentifiable models are models such that the unknown parameters can have an infinite number of values given input-output data. For unidentifiable models, a set of identifiable functions of the parameters are sought so that the model can be reparametrized in terms of these functions yielding an identifiable model. In this work, we use numerical algebraic geometry to determine if a model given by polynomial or rational ordinary differential equations is identifiable or unidentifiable. For identifiable models, we present a novel approach to compute the identifiability degree. For unidentifiable models, we present a novel numerical differential algebra technique aimed at computing a set of algebraically independent identifiable functions. Several examples are used to demonstrate the new techniques.
Journal Article
Index and biological spectrum of human DNase I hypersensitive sites
DNase I hypersensitive sites (DHSs) are generic markers of regulatory DNA
1
–
5
and contain genetic variations associated with diseases and phenotypic traits
6
–
8
. We created high-resolution maps of DHSs from 733 human biosamples encompassing 438 cell and tissue types and states, and integrated these to delineate and numerically index approximately 3.6 million DHSs within the human genome sequence, providing a common coordinate system for regulatory DNA. Here we show that these maps highly resolve the
cis
-regulatory compartment of the human genome, which encodes unexpectedly diverse cell- and tissue-selective regulatory programs at very high density. These programs can be captured comprehensively by a simple vocabulary that enables the assignment to each DHS of a regulatory barcode that encapsulates its tissue manifestations, and global annotation of protein-coding and non-coding RNA genes in a manner orthogonal to gene expression. Finally, we show that sharply resolved DHSs markedly enhance the genetic association and heritability signals of diseases and traits. Rather than being confined to a small number of distal elements or promoters, we find that genetic signals converge on congruently regulated sets of DHSs that decorate entire gene bodies. Together, our results create a universal, extensible coordinate system and vocabulary for human regulatory DNA marked by DHSs, and provide a new global perspective on the architecture of human gene regulation.
High-resolution maps of DNase I hypersensitive sites from 733 human biosamples are used to identify and index regulatory DNA within the human genome.
Journal Article
A Comprehensive Algorithm for Management of Neuropathic Pain
Abstract
Background
The objective of this review was to merge current treatment guidelines and best practice recommendations for management of neuropathic pain into a comprehensive algorithm for primary physicians. The algorithm covers assessment, multidisciplinary conservative care, nonopioid pharmacological management, interventional therapies, neurostimulation, low-dose opioid treatment, and targeted drug delivery therapy.
Methods
Available literature was identified through a search of the US National Library of Medicine’s Medline database, PubMed.gov. References from identified published articles also were reviewed for relevant citations.
Results
The algorithm provides a comprehensive treatment pathway from assessment to the provision of first- through sixth-line therapies for primary care physicians. Clear indicators for progression of therapy from firstline to sixth-line are provided. Multidisciplinary conservative care and nonopioid medications (tricyclic antidepressants, serotonin norepinephrine reuptake inhibitors, gabapentanoids, topicals, and transdermal substances) are recommended as firstline therapy; combination therapy (firstline medications) and tramadol and tapentadol are recommended as secondline; serotonin-specific reuptake inhibitors/anticonvulsants/NMDA antagonists and interventional therapies as third-line; neurostimulation as a fourth-line treatment; low-dose opioids (no greater than 90 morphine equivalent units) are fifth-line; and finally, targeted drug delivery is the last-line therapy for patients with refractory pain.
Conclusions
The presented treatment algorithm provides clear-cut tools for the assessment and treatment of neuropathic pain based on international guidelines, published data, and best practice recommendations. It defines the benefits and limitations of the current treatments at our disposal. Additionally, it provides an easy-to-follow visual guide of the recommended steps in the algorithm for primary care and family practitioners to utilize.
Journal Article