On a class of n-Leibniz deformations of the simple Filippov algebras

We study the problem of the infinitesimal deformations of all real, simple, finite-dimensional Filippov (or n-Lie) algebras, considered as a class of n-Leibniz algebras characterized by having an n-bracket skewsymmetric in its n-1 first arguments. We prove that all n>3 simple finite-dimensional Filippov algebras are rigid as n-Leibniz algebras of this class. This rigidity also holds for the Leibniz deformations of the semisimple n=2 Filippov (i.e., Lie) algebras. The n=3 simple FAs, however, admit a non-trivial one-parameter infinitesimal 3-Leibniz algebra deformation. We also show that the $n\geq 3$ simple Filippov algebras do not admit non-trivial central extensions as n-Leibniz algebras of the above class.Comment: 19 pages, 30 refs., no figures. Some text rearrangements for better clarity, misprints corrected. To appear in J. Math. Phy

A role of topoisomerase II in linking DNA replication to chromosome condensation

The condensin complex and topoisomerase II (topo II) have different biochemical activities in vitro, and both are required for mitotic chromosome condensation. We have used Xenopus egg extracts to investigate the functional interplay between condensin and topo II in chromosome condensation. When unreplicated chromatin is directly converted into chromosomes with single chromatids, the two proteins must function together, although they are independently targeted to chromosomes. In contrast, the requirement for topo II is temporarily separable from that of condensin when chromosome assembly is induced after DNA replication. This experimental setting allows us to find that, in the absence of condensin, topo II becomes enriched in an axial structure within uncondensed chromatin. Subsequent addition of condensin converts this structure into mitotic chromosomes in an ATP hydrolysis–dependent manner. Strikingly, preventing DNA replication by the addition of geminin or aphidicolin disturbs the formation of topo II–containing axes and alters the binding property of topo II with chromatin. Our results suggest that topo II plays an important role in an early stage of chromosome condensation, and that this function of topo II is tightly coupled with prior DNA replication

Self-assembly mechanism of pH-responsive glycolipids : micelles, fibers, vesicles, and bilayers

A set of four structurally related glycolipids are described: two of them have one glucose unit connected to either stearic or oleic acid, and two other ones have a diglucose headgroup (sophorose) similarly connected to either stearic or oleic acid. The self-assembly properties of these compounds, poorly known, are important to know due to their use in various fields of application from cleaning to cosmetics to medical. At basic pH, they all form mainly small micellar aggregates. At acidic pH, the oleic and stearic derivatives of the monoglucose form, respectively, vesicles and bilayer, while the same derivatives of the sophorose headgroup form micelles and twisted ribbons. We use pH-resolved in situ small angle X-ray scattering (SAXS) under synchrotron radiation to characterize the pH-dependent mechanism of evolution from micelles to the more complex aggregates at acidic pH. By pointing out the importance of the COO-/COOH ratio, the melting temperature, T-m, of the lipid moieties, hydration of the glycosidic headgroup, the packing parameter, membrane rigidity, and edge stabilization, we are now able to draw a precise picture of the full self-assembly mechanism. This work is a didactical illustration of the complexity of the self-assembly process of a stimuli-responsive amphiphile during which many concomitant parameters play a key role at different stages of the process

Dense Neural Networks for Predicting Chromatin Conformation

Background  DNA inside eukaryotic cells wraps around histones to form the 11nm chromatin fiber that can further fold into higher-order DNA loops, which may depend on the binding of architectural factors. Predicting how the DNA will fold given a distribution of bound factors, here viewed as a type of sequence, is currently an unsolved problem and several heterogeneous polymer models have shown that many features of the measured structure can be reproduced from simulations. However a model that determines the optimal connection between sequence and structure and that can rapidly assess the effects of varying either one is still lacking. Results  Here we train a dense neural network to solve for the local folding of chromatin, connecting structure, represented as a contact map, to a sequence of bound chromatin factors. The network includes a convolutional filter that compresses the large number of bound chromatin factors into a single 1D sequence representation that is optimized for predicting structure. We also train a network to solve the inverse problem, namely given only structural information in the form of a contact map, predict the likely sequence of chromatin states that generated it. Conclusions  By carrying out sensitivity analysis on both networks, we are able to highlight the importance of chromatin contexts and neighborhoods for regulating long-range contacts, along with critical alterations that affect contact formation. Our analysis shows that the networks have learned physical insights that are informative and intuitive about this complex polymer problem

Probing Long-Range Interactions by Extracting Free Energies From Genome-Wide Chromosome Conformation Capture Data

Background A variety of DNA binding proteins are involved in regulating and shaping the packing of chromatin. They aid the formation of loops in the DNA that function to isolate different structural domains. A recent experimental technique, Hi-C, provides a method for determining the frequency of such looping between all distant parts of the genome. Given that the binding locations of many chromatin associated proteins have also been measured, it has been possible to make estimates for their influence on the long-range interactions as measured by Hi-C. However, a challenge in this analysis is the predominance of non-specific contacts that mask out the specific interactions of interest. Results We show that transforming the Hi-C contact frequencies into free energies gives a natural method for separating out the distance dependent non-specific interactions. In particular we apply Principal Component Analysis (PCA) to the transformed free energy matrix to identify the dominant modes of interaction. PCA identifies systematic effects as well as high frequency spatial noise in the Hi-C data which can be filtered out. Thus it can be used as a data driven approach for normalizing Hi-C data. We assess this PCA based normalization approach, along with several other normalization schemes, by fitting the transformed Hi-C data using a pairwise interaction model that takes as input the known locations of bound chromatin factors. The result of fitting is a set of predictions for the coupling energies between the various chromatin factors and their effect on the energetics of looping. We show that the quality of the fit can be used as a means to determine how much PCA filtering should be applied to the Hi-C data. Conclusions We find that the different normalizations of the Hi-C data vary in the quality of fit to the pairwise interaction model. PCA filtering can improve the fit, and the predicted coupling energies lead to biologically meaningful insights for how various chromatin bound factors influence the stability of DNA loops in chromatin

An evaluation of the effect of illustrations on comprehension in the first and second grades.

Thesis (Ed.M.)--Boston Universit