RD System Research Articles

Simulation analysis of the effects of the simultaneous release of quanta of acetylcholine on the endplate current at the neuromuscular junction

Arrival of an action potential to a nerve terminal at the neuromuscular junction induces the release of a few hundred quanta of acetylcholine (ACh) into the synaptic cleft, resulting in depolarization of the muscle cell which is observed as the endplate current (EPC). The release of each quantum of ACh invokes the miniature endplate current (MEPC), so that an EPC could be generated by summation of the MEPCs both in time during evolution of the EPC and in space for a certain area of the post-synaptic membrane. In this study, a mathematical model for EPC generation is developed as a reaction–diffusion system (RD system) which represents the dynamic behavior of ACh in the chemical transmission process with the simultaneous quantum release of ACh. The RD system for ACh is mathematically expressed by a two-dimensional diffusion equation with nonlinear reaction terms due to the rate processes for acetylcholinesterase (AChE) and ACh receptor (AChR). Numerical solution of the governing equation with the method of lines and the Gear method yields temporal changes in relative concentrations of the open channel form of AChR which is assumed to be equivalent to the EPC. Analysis of the behavior of the RD system with respect to the various distances between the release sites of ACh on the pre-synaptic membrane demonstrates that the amplitude of EPC is quite sensitive to the distances around 0.5 μm, but independent of the values of the diffusion coefficient of ACh in the synaptic cleft.

Serum thrombopoietin levels in acute myeloid leukaemia.

To improve our understanding of the regulation of circulating platelet counts (PC) by thrombopoietin (TPO), we studied serum TPO levels and PC before and after myelosuppressive chemotherapy in 12 patients with acute myeloid leukaemia (AML). Serum TPO levels were measured by the quantitative sandwich enzyme-linked immunosorbent assay (Quantikine, RD Systems). At the start of the induction chemotherapy, the patients had a median serum TPO level of 199 pg/ml (range 120-2,150 pg/ml), while 10 to 12 days after the end of chemotherapy, their TPO levels were substantially increased, the median value being 1,907 pg/ml (range 1,049-4,194 pg/ml). The correlation between PC and TPO was statistically significant prior to chemotherapy (p < 0.03) and insignificant after chemotherapy. As a result of chemotherapy, the patients developed aplasia; after the administration of platelet transfusions, their median PC increased to 21 x 10(9)/l (range 5-55 x 10(9)/l), while the median TPO value decreased by 300 pg/ml (range 11-1,125 pg/ml). Our results suggest that platelet mass directly regulates serum TPO levels in acute leukaemia patients prior to chemotherapy and after the administration of platelet transfusions. Serum TPO levels may also be influenced by the cytokine response during complicating infections in patients with chemotherapy-induced cytopenia.

C REACTIVE PROTEIN IN PATIENTS WITH CHRONIC RENAL DISEASES

Base-line serum levels of plasma C-reactive protein (CRP) are predictive of future myocardial infarction and sudden cardiac death in apparently healthy subjects, suggesting the hypothesis that chronic inflammation might be important in the pathogenesis of atherothrombosis. CRP production is mediated by several inflammatory mediators: interleukin 6 (IL-6) is currently felt to be the major cytokine influencing the acute phase response. CRP and other acute phase proteins are elevated in dialysis patients and cardiovascular diseases represent the single largest cause of mortality in chronic renal failure patients. Little information is available, however regarding CRP and IL-6 plasma levels in pre-dialysis renal failure. Plasma CRP was determined by a modification of the laser nephelometry technique; IL-6 by immunoassay (RD System); and fibrinogen, serum albumin, cholesterol, triglycerides, hematocrit, white blood cell count, erythrocytic sedimentation rate (ESR) and urinary protein levels by standard laboratory techniques. Results were obtained in 102 chronic pre-dialysis patients whose mean age was 53 ± 5.8 years with a mean creatinine clearance (CCr) of 52 ± 37 mL/min). CRP was greater than 5 mg/L in 25% of the global population. CRP and IL-6 were 4.0 ± 4.6 mg/L and 5.8 ± 5.6 pg/mL, respectively and were not significantly correlated (r = 0.11, p = n.s.). CRP and IL-6 were however related with renal function (CRP versus CCr r = −0.40 p < 0.001; IL-6 versus CCr r = −0.45; p < 0.001). When patients were divided in two groups according to renal function, CRP resulted 7.4 ± 6.3 mg/L in the group of patients with a CCr lower than 20 mL/min (n = 32) and 2.76 ± 4.35 in the group of patients with a CCr higher than 20mL/min (n = 70) (p < 0.0001). CRP and IL-6 were positively related with ESR (r = 0.32 and 0.46 respectively). Serum albumin levels were not significantly different in the two groups of patients (3.2 ± 0.4 versus 3.0 ± 0.5 g/dL). CRP and serum albumin were not significantly related (r = 0.17). CRP and IL-6 correlated positively with ESR (r = 0.32 and 0.46 respectively). In pre-dialysis patients we have demonstrated an increase in both CRP and IL-6 that occurs as renal function decreases. These data provided evidence of the activation – even in the predialysis phase of renal failure – of mechanisms known to contribute to the enhanced cardiovascular morbidity and mortality of the uremic syndrome.

Self-replicating spots in reaction-diffusion systems

In this article we discuss the self-replicating spot, a particlelike phenomenon that occurs in reaction-diffusion ~RD! systems @1#. The spots consist of localized regions in which the concentrations of the reactants differ from the surrounding concentration fields. They grow, reaching a critical size at which time they divide in two. The two resulting spots again grow and divide. This process, which is visually similar to cell division, continues indefinitely. The long-time behavior depends on the precise values of the external control parameters, but typically consists of a chaotic ‘‘soup’’ in which many spots compete for resources as illustrated in Fig. 1. Those spots that find adequate resources continue to grow and divide. Those that are unable to find adequate resources decay into the background. The spots observed in @1# were found during an attempt to model labyrinthine patterns in the ferrocyanide-iodate-sulfate ~FIS! reaction @2#. Since then, replicating spot patterns have been observed both numerically and experimentally in the FIS reaction @3,4#. There are obvious differences in the Gaspar-Showalter model of the FIS reaction @5# and of the models discussed by us and others. This fact suggests that replication is a generic feature characterizing a broad class of reaction-diffusion systems. In @6#, we presented some arguments in support of this proposition. These arguments included both a heuristic description of the process of replication and demonstrations of analytic features common to several related model RD systems. It turns out that replication is more general than our analysis accounts for. Nevertheless, we think it worthwhile to spell out the details of the theory presented in @6#. We remark here that various aspects of the replication phenomenon have been discussed by other authors @7,8#. Kerner and Osipov have a large body of work on largeamplitude dissipative structures including an analysis of the static division of one-dimensional pulses as the system size is changed. Gurevich and Mints have a body of work on replication of thermal hot spots in composite superconductors. In the article by Petrov, Scott, and Showalter replication

A two-dimensional compartment model for the reaction-diffusion system of acetylcholine in the synaptic cleft at the neuromuscular junction

A minimal compartment model of the reaction-diffusion system (RD system) of a neurotransmitter in a two-dimensional space of axis-symmetrical disc is proposed to represent the chemical transmission process of a quantum of acetylcholine (ACh) in the synaptic cleft at the neuromuscular junction. The behavior of the RD system for ACh is expressed by a two-dimensional diffusion equation with nonlinear reaction terms due to the rate processes for ACh receptor and acetylcholinesterase. The simulation analysis of the RD system reveals that the radial diffusion process of ACh has more distinctive effects on spontaneous generation of the miniature endplate current (MEPC) than the transverse process. The anisotropic diffusion is effective in the RD system since the diffusion coefficient of ACh in the radial direction is evaluated to be about 1.0×10 −6 cm 2 sec −1 for appropriate characterization of the MEPC, on which the diffusion coefficient in the transverse direction larger than 2.0×10 −6 cm 2 sec −1 has virtually no effects. The compartment model is thus appropriately constructed to comprise three elements on the transverse coordinate and ten elements on the radial coordinate in the disc with 500 nm of radius and 50 nm of height.

Ergodicity for an infinite particle system in Rd of jump type with hard core interaction

Ergodicity for an infinite particle system in Rd of jump type with hard core interaction

Limit Theorems for Supercritical Branching Random Fields

An infinite particle system in Rd is considered where the initial distribution is POISSONian and each initial particle gives rise to a supercritical age-dependent branching process with the particles moving randomly in space. Our approach differs from the usual: instead of the point measures determined by the locations of the particles at each time, we take the particles at a “final time” and observe the past histories of their ancestry lines. A law of large numbers and a central limit theorem are proved under a space-time scaling representing high density of particles and small mean particle lifetime. The fluctuation limit is a generalized GAUSS-MARKOV process with continuous trajectories and satisfies a deterministic evolution equation with generalized random initial condition. A more precise form of the central limit theorem is obtained in the case of particles performing BROWNian motion and having exponentially distributed lifetime.

On the Independence of Velocities in a System of Noninteracting Particles

1. Main result. Consider a particle system in Rd (de N) which is locally finite at each time, and let the positions at time 0 be given by a point process d. Further suppose that each particle moves with constant speed, and that the velocities at time 0 are independent of the positions and distributed according to some common nondegenerate probability measure pu on Rd. At first sight, one might expect the velocities to remain independent and identically distributed independently of the positions, but it turns out that the independence will normally be destroyed. In fact, we shall prove that independence with a common velocity distribution at two or more epochs implies that e is a Cox process (cf. [2]) of a very special structure. This strengthens a result by Thedeen ((1967), Corollary 5. 1) (cf. Theorem 5.3 in [3]), who draws an equivalent conclusion under the additional hypothesis of time stationarity of the process of positions and velocities. For a precise statement of our result, let S be the support of Pa, and write H for the closed additive group generated by S-S. Note that H has more than one point since , is nondegenerate. The positions and velocities of the particles at a fixed epoch are most conveniently described by a point process in the phase space R2d = Rd x Rd = {(p, q)}, where p and q denote the velocity and position of a particle. It is sometimes helpful to consider the evolution of the system as a line process in the space-time diagram Rd+1 = Rd x R = {(q, t)}. Note that a time shift corresponds to a p-preserving linear shear in the phase space and to a translation in the space-time diagram. THEOREM. Let t t 0 be arbitrary butfixed. Then the velocities of the particles at time t are independent of the positions and mutually independent with a common distribution, iff e is a Cox process directed by some random measure y which is a.s. tH-invariant, apart from a factor of the form er with r e Rd. Note that, if the hypothesis of the theorem is fulfilled for two rationally

Bearings for Sulzer Slow‐Speed Diesel Engines

In a paper to the Institute of Marine Engineers in London on 14th November, Dr. P. E. A. Borgeaud (Technical Director, Diesel Engine Department, Sulzer Brothers Ltd., Winterthur) presented some detailed developments in the RND range of Sulzer slow‐speed Diesel engines which, a few years ago superseded the RD series. The main difference in the new range was in the super‐charging arrangement: pulse system for RD and constant pressure system for RND. Service experiences have caused various refinements and improvements, and in connection with bearings, the author had this to say.