9,647 research outputs found
Potentials of Mean Force for Protein Structure Prediction Vindicated, Formalized and Generalized
Understanding protein structure is of crucial importance in science, medicine
and biotechnology. For about two decades, knowledge based potentials based on
pairwise distances -- so-called "potentials of mean force" (PMFs) -- have been
center stage in the prediction and design of protein structure and the
simulation of protein folding. However, the validity, scope and limitations of
these potentials are still vigorously debated and disputed, and the optimal
choice of the reference state -- a necessary component of these potentials --
is an unsolved problem. PMFs are loosely justified by analogy to the reversible
work theorem in statistical physics, or by a statistical argument based on a
likelihood function. Both justifications are insightful but leave many
questions unanswered. Here, we show for the first time that PMFs can be seen as
approximations to quantities that do have a rigorous probabilistic
justification: they naturally arise when probability distributions over
different features of proteins need to be combined. We call these quantities
reference ratio distributions deriving from the application of the reference
ratio method. This new view is not only of theoretical relevance, but leads to
many insights that are of direct practical use: the reference state is uniquely
defined and does not require external physical insights; the approach can be
generalized beyond pairwise distances to arbitrary features of protein
structure; and it becomes clear for which purposes the use of these quantities
is justified. We illustrate these insights with two applications, involving the
radius of gyration and hydrogen bonding. In the latter case, we also show how
the reference ratio method can be iteratively applied to sculpt an energy
funnel. Our results considerably increase the understanding and scope of energy
functions derived from known biomolecular structures
Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment
The optical properties of slab-like photonic crystals are often discussed on the basis of effective index (EI) approximations, where a 2-D effective refractive index profile replaces the actual 3-D structure. Our aim is to assess this approximation by analogous steps that reduce finite 2-D waveguide Bragg-gratings (to be seen as sections through 3-D PC slabs and membranes) to 1-D problems, which are tractable by common transfer matrix methods. Application of the EI method is disputable in particular in cases where locally no guided modes are supported, as in the holes of a PC membrane. A variational procedure permits to derive suitable effective permittivities even in these cases. Depending on the structural properties, these values can well turn out to be lower than one, or even be negative. Both the “standard” and the variational procedures are compared with reference data, generated by a rigorous 2-D Helmholtz solver, for a series of example structures.\u
A mass action model of a fibroblast growth factor signaling pathway and its simplification
We consider a kinetic law of mass action model for Fibroblast Growth Factor (FGF) signaling, focusing on the induction of the RAS-MAP kinase pathway via GRB2 binding. Our biologically simple model suffers a combinatorial explosion in the number of differential equations required to simulate the system. In addition to numerically solving the full model, we show that it can be accurately simplified. This requires combining matched asymptotics, the quasi-steady state hypothesis, and the fact subsets of the equations decouple asymptotically. Both the full and simplified models reproduce the qualitative dynamics observed experimentally and in previous stochastic models. The simplified model also elucidates both the qualitative features of GRB2 binding and the complex relationship between SHP2 levels, the rate SHP2 induces dephosphorylation and levels of bound GRB2. In addition to providing insight into the important and redundant features of FGF signaling, such work further highlights the usefulness of numerous simplification techniques in the study of mass action models of signal transduction, as also illustrated recently by Borisov and co-workers (Borisov et al. in Biophys. J. 89, 951–66, 2005, Biosystems 83, 152–66, 2006; Kiyatkin et al. in J. Biol. Chem. 281, 19925–9938, 2006). These developments will facilitate the construction of tractable models of FGF signaling, incorporating further biological realism, such as spatial effects or realistic binding stoichiometries, despite a more severe combinatorial explosion associated with the latter
Unbounded Human Learning: Optimal Scheduling for Spaced Repetition
In the study of human learning, there is broad evidence that our ability to
retain information improves with repeated exposure and decays with delay since
last exposure. This plays a crucial role in the design of educational software,
leading to a trade-off between teaching new material and reviewing what has
already been taught. A common way to balance this trade-off is spaced
repetition, which uses periodic review of content to improve long-term
retention. Though spaced repetition is widely used in practice, e.g., in
electronic flashcard software, there is little formal understanding of the
design of these systems. Our paper addresses this gap in three ways. First, we
mine log data from spaced repetition software to establish the functional
dependence of retention on reinforcement and delay. Second, we use this memory
model to develop a stochastic model for spaced repetition systems. We propose a
queueing network model of the Leitner system for reviewing flashcards, along
with a heuristic approximation that admits a tractable optimization problem for
review scheduling. Finally, we empirically evaluate our queueing model through
a Mechanical Turk experiment, verifying a key qualitative prediction of our
model: the existence of a sharp phase transition in learning outcomes upon
increasing the rate of new item introductions.Comment: Accepted to the ACM SIGKDD Conference on Knowledge Discovery and Data
Mining 201
- …