Periodic dynamics of coupled cell networks I: rigid patterns of synchrony and phase relations

It has recently been proved by Golubitsky and coworkers that in any network of coupled dynamical systems, the possible 'rigid' patterns of synchrony of hyperbolic equilibria are determined by purely combinatorial properties of the network, known as 'balanced equivalence relations'. A pattern is 'rigid' if it persists under small 'admissible' perturbations of the differential equation — ones that respect the network structure. We discuss a natural generalisation of these ideas to time-periodic states, and motivate two basic conjectures, the Rigid Synchrony Conjecture and the Rigid Phase Conjecture. These conjectures state that for rigid hyperbolic time-periodic patterns, cells with synchronous dynamics must have synchronous input cells, and cells with phase-related dynamics must have input cells that have the same phase relations. We provide evidence supporting the two conjectures, by proving them for a special class of periodic orbits, which we call 'tame', under strong assumptions on the network architecture and the symmetries of the periodic state. The discussion takes place in the formal setting of coupled cell networks. We prove that rigid patterns of synchrony are balanced, together with the analogous result for rigid patterns of phase relations. The assumption on the network architecture simplifies the geometry of admissible vector fields, while tameness rules out patterns with non-trivial local or multilocal symmetry. The main idea is to perturb an admissible vector field in a way that retains sufficient control over the associated perturbed periodic orbit. We present two techniques for constructing these perturbations, both using a general theorem on groupoid-symmetrisation of vector fields, which has independent interest. In particular we introduce a method of 'patching' that makes local changes to an admissible vector field. Having established these results for all-to-all coupled networks and tame periodic orbits we prove more general versions that require these assumptions only on a suitable quotient network. These conditions are weaker and encompass a larger class of networks and periodic orbits. We give an example to show that rigidity cannot be relaxed to hyperbolicity. We also prove, without any technical assumptions, that rigidly synchronous or phase-related cells must be input-isomorphic, a necessary precondition for the two conjectures to hold.     

High Throughput Primer Walking of cDNA Clones

Primer walking of cloned DNA is a standard research tool. It has been used in the past to determine the sequence of individual clones of interest. With the expansion of DNA sequencing capacity the need to be able to walk larger numbers of clones has become necessary. Our laboratory is a mid-sized genomics facility. In conjunction with the Advanced Biomedical Computing Center (ABCC) we have developed methods for automating the primer selection, DNA sequencing, contig assembly and sequence analysis for clones arrayed in microtiter format. This approach has allowed us to walk 475 clones (five microtiter plates) selected from a cDNA library.     

Elucidation of mitochondrial effects by tetrahydroaminoacridine (tacrine) in rat, dog, monkey and human hepatic parenchymal cells

Tetrahydroaminoacridine (tacrine) causes morphological and functional changes in the endoplasmic reticulum, ribosomes, and mitochondria in the liver of humans and animals. In order to investigate species differences as well as to understand the morphological changes, we examined the effects of tacrine on respiration and electron transport in mitochondria isolated from rat, dog, monkey, and human liver. Tacrine produced significantly decreased respiratory control ratios (RCR) in all species at concentrations ranging from 5 to 25 microg/ml. Human mitochondria were more sensitive to tacrine effects with RCR decreased 24% at 5 microg/ml while other species were unaffected at this concentration. The tacrine effects were characterized by increased hepatic mitochondrial State 4 respiration in rats and decreased State 3 respiration in humans. Mitochondria from aged rats were more sensitive to the effects of tacrine than mitochondria from young animals, with significantly decreased RCR at 10 microg/ml in aged rats while mitochondria from young rats were unaffected at this concentration. Concomitant with the respiratory changes, mitochondrial DNA synthesis was impaired. Since tacrine undergoes extensive biotransformation, we also explored the possibility that metabolites could exert detrimental effects. The ranking order of potency for decreasing RCR caused by monohydroxylated metabolites was: tacrine > 4-OH and 7-OH > 2-OH, 1-OH, and velnacrine with the latter group of metabolites having no effect on mitochondrial respiration at concentrations up to 50 microg/ml. In vivo administration of 20 mg/kg tacrine to rats for up to 20 days caused a paradoxical increase in RCR and P/O on Day 1 and decreased RCR on Days 9 and 20, the later findings being consistent with in vitro data. From these data we propose that tacrine does not necessarily have to be metabolized to exert effects on mitochondria at different sites in the electron transport chain that differ among species. These effects are exacerbated in mitochondria from older animals and humans appear to be more sensitive than the laboratory animals studied.     

Serologic evidence of previous Campylobacter jejuni infection in patients with the Guillain-Barré syndrome

OBJECTIVE: To determine if patients with the Guillain-Barré syndrome are likely to have had Campylobacter jejuni infection before onset of neurologic symptoms. DESIGN: A case-control study. SETTING: Several university medical centers. PATIENTS: Case patients met clinical criteria for the Guillain-Barré syndrome between 1983 and 1990 and had a serum sample collected and frozen within 3 weeks after onset of neurologic symptoms (n = 118). Disease controls were patients with other neurologic illnesses (n = 56); healthy controls were hospital employees or healthy family members of patients (n = 47). MEASUREMENTS: Serum IgA, IgG, and IgM antibodies to C. jejuni were determined by enzyme-linked immunosorbent assays. Assays were done in a blinded manner. RESULTS: Optical density ratios > or = 2 in two or more immunoglobulin classes were seen in 43 (36%) of patients with the Guillain-Barré syndrome and in 10 (10%) of controls (odds ratio, 5.3; 95% CI, 2.4 to 12.5; P < 0.001). Increasing the optical density ratio or the number of immunoglobulin classes necessary to yield a positive result increased the strength of the association. The number of patients with the Guillain-Barré syndrome who had positive serologic responses was greatest from September to November (P = 0.02). Male patients were three times more likely to have serologic evidence of C. jejuni infection (P = 0.009); the proportion of patients with the syndrome who had a positive serologic response increased with age. CONCLUSIONS: Patients with the Guillain-Barré syndrome are more likely than controls to have serologic evidence of C. jejuni infection in the weeks before onset of neurologic symptoms. Campylobacter jejuni may play a role in the initiation of the Guillain-Barré syndrome in many patients.     

Motor learning by field approximation

We investigated how human subjects adapt to forces perturbing the motion of their ams. We found that this kind of learning is based on the capacity of the central nervous system (CNS) to predict and therefore to cancel externally applied perturbing forces. Our experimental results indicate: (i) that the ability of the CNS to compensate for the perturbing forces is restricted to those spatial locations where the perturbations have been experienced by the moving arm. The subjects also are able to compensate for forces experienced at neighboring workspace locations. However, adaptation decays smoothly and quickly with distance from the locations where disturbances had been sensed by the moving limb. (ii) Our experiments also how that the CNS builds an internal model of the external perturbing forces in intrinsic (muscles and / or joints) coordinates.     

In vivo characterization of cytotoxic intracellular edema by multicomponent analysis of transverse magnetization decay curves

The precise measurement of low numbers of leukocyte below 0.1 WBC/microliter in filtered red cell or platelet suspensions meet both aims: to check the compliance with previously determined requirements and to evaluate the performances of novel filtering material (5 log depletion or more), justified by more and more important clinical use. The reliability of results, obtained with the chosen method, is ensured by applying of validation protocol, including training of technologist, assessment of the analytical range and the detection limit, assessment of precision and accuracy. The flow cytometry (FC) and Nageotte Chamber (NC) method are the both techniques which are currently used in routine Quality Control (QC) and validated by multicenter studies. Recent developments are made for increasing the sensibility of these counting methods, thanks to higher concentration or volume of the sample to be analysed. Among the experimental techniques, requiring more advances before implementing in QC program, quantitative PCR must become essential as reference method for evaluating the efficiency of filtration, in the future.