281 research outputs found
Association constants for the binding of vancomycin and teicoplanin to N-acetyl-d-alanyl-d-alanine and N-acetyl-d-alanyl-d-serine
Computability, G\"odel's Incompleteness Theorem, and an inherent limit on the predictability of evolution
The process of evolutionary diversification unfolds in a vast genotypic space
of potential outcomes. During the past century there have been remarkable
advances in the development of theory for this diversification, and the
theory's success rests, in part, on the scope of its applicability. A great
deal of this theory focuses on a relatively small subset of the space of
potential genotypes, chosen largely based on historical or contemporary
patterns, and then predicts the evolutionary dynamics within this pre-defined
set. To what extent can such an approach be pushed to a broader perspective
that accounts for the potential open-endedness of evolutionary diversification?
There have been a number of significant theoretical developments along these
lines but the question of how far such theory can be pushed has not been
addressed. Here a theorem is proven demonstrating that, because of the digital
nature of inheritance, there are inherent limits on the kinds of questions that
can be answered using such an approach. In particular, even in extremely simple
evolutionary systems a complete theory accounting for the potential
open-endedness of evolution is unattainable unless evolution is progressive.
The theorem is closely related to G\"odel's Incompleteness Theorem and to the
Halting Problem from computability theory.Comment: Journal of the Royal Society, Interface 201
Revised interpretation of the sequence containing the murE gene encoding the UDP-N-acetylmuramyl-tripeptide synthetase of Escherichia coli
When logic meets engineering: introduction to logical issues in the history and philosophy of computer science
Introduction to a Journal Special issue on Logical Issues in the History and Philosophy of Computer Scienc
Identification and in vitro Analysis of the GatD/MurT Enzyme-Complex Catalyzing Lipid II Amidation in Staphylococcus aureus
The peptidoglycan of Staphylococcus aureus is characterized by a high degree of crosslinking and almost completely lacks free carboxyl groups, due to amidation of the D-glutamic acid in the stem peptide. Amidation of peptidoglycan has been proposed to play a decisive role in polymerization of cell wall building blocks, correlating with the crosslinking of neighboring peptidoglycan stem peptides. Mutants with a reduced degree of amidation are less viable and show increased susceptibility to methicillin. We identified the enzymes catalyzing the formation of D-glutamine in position 2 of the stem peptide. We provide biochemical evidence that the reaction is catalyzed by a glutamine amidotransferase-like protein and a Mur ligase homologue, encoded by SA1707 and SA1708, respectively. Both proteins, for which we propose the designation GatD and MurT, are required for amidation and appear to form a physically stable bi-enzyme complex. To investigate the reaction in vitro we purified recombinant GatD and MurT His-tag fusion proteins and their potential substrates, i.e. UDP-MurNAc-pentapeptide, as well as the membrane-bound cell wall precursors lipid I, lipid II and lipid II-Gly5. In vitro amidation occurred with all bactoprenol-bound intermediates, suggesting that in vivo lipid II and/or lipid II-Gly5 may be substrates for GatD/MurT. Inactivation of the GatD active site abolished lipid II amidation. Both, murT and gatD are organized in an operon and are essential genes of S. aureus. BLAST analysis revealed the presence of homologous transcriptional units in a number of gram-positive pathogens, e.g. Mycobacterium tuberculosis, Streptococcus pneumonia and Clostridium perfringens, all known to have a D-iso-glutamine containing PG. A less negatively charged PG reduces susceptibility towards defensins and may play a general role in innate immune signaling
A Schwarz lemma for K\"ahler affine metrics and the canonical potential of a proper convex cone
This is an account of some aspects of the geometry of K\"ahler affine metrics
based on considering them as smooth metric measure spaces and applying the
comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a
version for K\"ahler affine metrics of Yau's Schwarz lemma for volume forms. By
a theorem of Cheng and Yau there is a canonical K\"ahler affine Einstein metric
on a proper convex domain, and the Schwarz lemma gives a direct proof of its
uniqueness up to homothety. The potential for this metric is a function
canonically associated to the cone, characterized by the property that its
level sets are hyperbolic affine spheres foliating the cone. It is shown that
for an -dimensional cone a rescaling of the canonical potential is an
-normal barrier function in the sense of interior point methods for conic
programming. It is explained also how to construct from the canonical potential
Monge-Amp\`ere metrics of both Riemannian and Lorentzian signatures, and a mean
curvature zero conical Lagrangian submanifold of the flat para-K\"ahler space.Comment: Minor corrections. References adde
Nominal Henkin Semantics: simply-typed lambda-calculus models in nominal sets
We investigate a class of nominal algebraic Henkin-style models for the
simply typed lambda-calculus in which variables map to names in the denotation
and lambda-abstraction maps to a (non-functional) name-abstraction operation.
The resulting denotations are smaller and better-behaved, in ways we make
precise, than functional valuation-based models.
Using these new models, we then develop a generalisation of \lambda-term
syntax enriching them with existential meta-variables, thus yielding a theory
of incomplete functions. This incompleteness is orthogonal to the usual notion
of incompleteness given by function abstraction and application, and
corresponds to holes and incomplete objects.Comment: In Proceedings LFMTP 2011, arXiv:1110.668
The good, the bad and the ugly
This paper discusses the neo-logicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neo-logicist school, present a generic form of the Bad Company objection and introduce an epistemic issue connected to this general problem that will be the focus of the rest of the paper. In the third section, we present an alternative approach within philosophy of mathematics, a view that emerges from Hilbert's Grundlagen der Geometrie (1899, Leipzig: Teubner; Foundations of geometry (trans.: Townsend, E.). La Salle, Illinois: Open Court, 1959.). We will argue that Bad Company-style worries, and our concomitant epistemic issue, also affects this conception and other foundationalist approaches. In the following sections, we then offer various ways to address our epistemic concern, arguing, in the end, that none resolves the issue. The final section offers our own resolution which, however, runs against the foundationalist spirit of the Scottish neo-logicist program
Simplivariate Models: Uncovering the Underlying Biology in Functional Genomics Data
One of the first steps in analyzing high-dimensional functional genomics data is an exploratory analysis of such data. Cluster Analysis and Principal Component Analysis are then usually the method of choice. Despite their versatility they also have a severe drawback: they do not always generate simple and interpretable solutions. On the basis of the observation that functional genomics data often contain both informative and non-informative variation, we propose a method that finds sets of variables containing informative variation. This informative variation is subsequently expressed in easily interpretable simplivariate components
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