Pulse propagation in discrete systems of coupled excitable cells

Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast. We give an asymptotic construction of pulses for spatially discrete FitzHugh-Nagumo systems which agrees well with numerical simulations and discuss evolution of initial data into pulses and pulse generation at a boundary. Formulas for the speed and length of pulses are also obtained.Comment: 16 pages, 10 figures, to appear in SIAM J. Appl. Mat

An obstruction to K-fold splitting

Abstract. For a transformation T , if the sum of the K-th root of its partial mixing with the K-th root of its partial rigidity exceeds 1, then the transformation can have no factor isomorphic to a K-fold cartesian product. The inspiration for this note is Nat Friedman's result, Say that transformation T : X → X K-fold splits if T is a K-fold cartesian product S 1 ×· · ·×S K where none of the S k live on a 1-point space. [Our context is that of bi-measure preserving maps of a Lebesgue probability space.] We now define the notions of partial rigidity and mixing. Given a sequence of integers s = {s[k]} ∞ k=1 going to infinity, define four quantities where the above infimums are taken over all sets A, B ⊂ X of positive measure. When T is understood, we suppress T and write m( s) for m(T ; s). Say that sequence n is an (eventual) subsequence of s, written n ≺ s, if after discarding finitely many terms from n the resulting sequence is an actual subset of s. The quantity m(T ; s) is called the partial mixing of T along s and is also written as mix(T ; s). For T , the partial rigidity along s is rig(T ; s) := sup n: n≺ s r(T ; n). In both the above, when s = N we write mix(T ) and rig(T ), respectively

The Structure of the Cataract-Causing P23T Mutant of Human γD-Crystallin Exhibits Distinctive Local Conformational and Dynamic Changes†,‡

Crystallins are major proteins of the eye lens and essential for lens transparency. Mutations and aging of crystallins cause cataracts, the predominant cause of blindness in the world. In human γD-crystallin, the P23T mutant is associated with congenital cataracts. Until now, no atomic structural information has been available for this variant. Biophysical analyses of this mutant protein have revealed dramatically reduced solubility compared to that of the wild-type protein due to self-association into higher-molecular weight clusters and aggregates that retain a nativelike conformation within the monomers [Pande, A., et al. (2005) Biochemistry 44, 2491−2500]. To elucidate the structure and local conformation around the mutation site, we have determined the solution structure and characterized the protein’s dynamic behavior by NMR. Although the global structure is very similar to the X-ray structure of wild-type γD-crystallin, pivotal local conformational and dynamic differences are caused by the threonine substitution. In particular, in the P23T mutant, the imidazole ring of His22 switches from the predominant Nε2 tautomer in the wild-type protein to the Nδ1 tautomer, and an altered motional behavior of the associated region in the protein is observed. The data support structural changes that may initiate aggregation or polymerization by the mutant protein.National Institutes of Health (U.S.) (Grant GM 17980)National Eye Institute (Grant EY 015834

Investigation of the STR loci noise distributions of PowerSeq Auto System

AimTo characterize the noise and stutter distribution of 23 short tandem repeats (STRs) included in the PowerSeqTM Auto System. MethodsRaw FASTQ files were analyzed using STRait Razor v2s to display alleles and coverage. The sequence noise was divided into several categories: noise at allele position, noise at -1 repeat position, and artifact. The average relative percentages of locus coverage for each noise, stutter, and allele were calculated from the samples used for this locus noise analysis. ResultsStutter products could be routinely observed at the -2 repeat position, -1 repeat position, and +1 repeat position of alleles. Sequence noise at the allele position ranged from 10.22% to 28.81% of the total locus coverage. At the allele position, individual noise reads were relatively low. ConclusionThe data indicate that noise generally will be low. In addition, the PowerSeqTM Auto System could capture nine flanking region single nucleotide polymorphisms (SNPs) that would not be observed by other current kits for massively parallel sequencing (MPS) of STRs

First assessment of geophysical sensitivities from spaceborne Galileo and BeiDou GNSS-Reflectometry data collected by the UK TechDemoSat-1 Mission

The UK’s TechDemoSat-1 (TDS-1), launched 2014, has demonstrated the use of global positioning system (GPS) signals for monitoring ocean winds and sea ice. Here it is shown, for the first time, that Galileo and BeiDou signals detected by TDS-1 show similar promise. TDS-1 made seven raw data collections, recovering returns from Galileo and BeiDou, between November 2015 and March 2019. The retrieved open ocean delay Doppler maps (DDMs) are similar to those from GPS. Over sea ice, the Galileo DDMs show a distinctive triple peak. Analysis, adapted from that for GPS DDMs, gives Galileo’s signal-to-noise ratio (SNR), which is found to be inversely sensitive to wind speed, as for GPS. A Galileo track transiting from open ocean to sea ice shows a strong instantaneous SNR response. These results demonstrate the potential of future spaceborne constellations of GNSS-R (global navigation satellite system–reflectometry) instruments for exploiting signals from multiple systems: GPS, Galileo, and BeiDou