On the formal theory of pseudomonads and pseudodistributive laws

We contribute to the formal theory of pseudomonads, i.e. the analogue for pseudomonads of the formal theory of monads. In particular, we solve a problem posed by Steve Lack by proving that, for every Gray-category K, there is a Gray-category Psm(K) of pseudomonads, pseudomonad morphisms, pseudomonad transformations and pseudomonad modifications in K. We then establish a triequivalence between Psm(K) and the Gray-category of pseudomonads introduced by Marmolejo. Finally, these results are applied to give a clear account of the coherence conditions for pseudodistributive laws. 40 pages. Comments welcome.Comment: This submission replaces arXiv:0907:1359v1, titled "On the coherence conditions for pseudo-distributive laws". 40 page

Distributive laws for relative monads

We introduce the notion of a distributive law between a relative monad and a monad. We call this a relative distributive law and define it in any 2-category $\mathcal{K}$. In order to do that, we introduce the 2-category of relative monads in a 2-category $\mathcal{K}$ with relative monad morphisms and relative monad transformations as 1- and 2-cells, respectively. We relate our definition to the 2-category of monads in $\mathcal{K}$ defined by Street. Thanks to this view we prove two Beck-type theorems regarding relative distributive laws. We also describe what does it mean to have Eilenberg-Moore and Kleisli objects in this context and give examples in the 2-category of locally small categories.Comment: 32 page

A skew approach to enrichment for Gray-categories

It is well known that the category of Gray-categories does not admit a monoidal biclosed structure that models weak higher-dimensional transformations. In this paper, the first of a series on the topic, we describe several skew monoidal closed structures on the category of Gray-categories, one of which captures higher lax transformations, and another which models higher pseudo-transformations.Comment: Minor updates. Submitted for publicatio

Dynamic Electromagnetic Field Measurements of Clustered Hall Thrusters

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77192/1/AIAA-2006-4996-870.pd

A Method of Measuring Transient Plume Properties

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76522/1/AIAA-2008-4650-871.pd

Evaluation and Active Control of Clustered Hall Thruster Discharge Oscillations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77203/1/AIAA-2005-3679-597.pd

NMR studies on the nucleosome and chromatin factors

Chromatin is vital to compaction and regulation of the DNA in eukaryotes and is intimately involved in DNA expression, replication, and repair. As one of the cell’s biggest polymers, chromatin forms a multi-scale structure consisting of DNA and protein. At the smallest level, the nucleosome forms the repeating unit of chromatin, consisting of two copies of four different histones and around 150 base pair of DNA. A central question in chromatin biology is how chromatin, DNA binding proteins, chromatin factors and environmental factors work together to regulate all DNA-mediated processes. The underlying molecular mechanisms not only involve interactions between the smallest units, e.g. proteins and the nucleosome, but also the interplay of the complex higher-order organization of chromatin and these molecular interactions. These aspects converge in the case of chromatin remodelers. These enzymes interact with nucleosomes to alter higher-order chromatin structure directly, by reshuffling the position of nucleosomes in the genome. Chapter 1 reviews the basic components of the nucleosome and gives a first glance at factors involved in the higher order organization of chromatin including ionic strength and chromatin remodeling proteins. In chapter 2 we expand on this first glance by reviewing nucleosome-protein interactions in higher order chromatin structures. The increasing availability of high-resolution nucleosome-protein structures allowed us to shed light on how chromatin factors operate in this complex higher order chromatin environment. In chapter 3 we investigate the effect of the currently highest permanent magnetic field of 28.2 Tesla in the context of chromatin. We investigated the performance of methyl-TROSY NMR at 1.2 GHz, using the nucleosome as a test sample. We find that the increased resolution of the 1.2 GHz system allows to resolve small asymmetries in amino acid sidechain conformation between symmetry-related copies of the histone proteins. We further observe significant magnetic field alignment of the nucleosome at 1.2 GHz, giving rise to methyl 1H-13C residual dipolar couplings (RDCs) that can be used for assignment and structural characterization. We show that these histone methyl group RDCs can be used to aid assignment and to determine the overall conformation of the nucleosomal DNA, revealing a significant unwrapping of the DNA from the histone core. In chapter 4 we applied nuclear magnetic resonance to study nucleosomes with mono- and divalent ions using a methyl labeling approach. An increase in ionic strength resulted in a decrease in core residue signals but did not decrease the tail residue signal. Our data point to an increase in effective size of the nucleosome particle due to tail DNA interactions between nucleosome particles. In chapter 5 we studied the conformational dynamics of ISWI and the nucleosome-ISWI complex using methyl-TROSY solution NMR spectroscopy. We find that the free enzyme is highly dynamic throughout the protein. Our data indicate that binding of an active ISWI construct to the nucleosome induces conformational changes through the histone octamer, affecting histone-DNA and histone-histone contacts. These findings provide strong support for histone plasticity during remodeling to facilitate DNA translocation and further highlight the histone octamer as an allosteric unit