Multi-peak Distribution Research Articles

A Mathematical Model of Protein Degradation by the Proteasome

The proteasome is the major protease for intracellular protein degradation. The influx rate of protein substrates and the exit rate of the fragments/products are regulated by the size of the axial channels. Opening the channels is known to increase the overall degradation rate and to change the length distribution of fragments. We develop a mathematical model with a flux that depends on the gate size and a phenomenological cleavage mechanism. The model has Michaelis-Menten kinetics with a V max that is inversely related to the length of the substrate, as observed in the in vitro experiments. We study the distribution of fragment lengths assuming that proteasomal cleavage takes place at a preferred distance from the ends of a protein fragment, and find multipeaked fragment length distributions similar to those found experimentally. Opening the gates in the model increases the degradation rate, increases the average length of the fragments, and increases the peak in the distribution around a length of 8–10 amino acids. This behavior is also observed in immunoproteasomes equipped with PA28. Finally, we study the effect of re-entry of processed fragments in the degradation kinetics and conclude that re-entry is only expected to affect the cleavage dynamics when short fragments enter the proteasome much faster than the original substrate. In summary, the model proposed in this study captures the known characteristics of proteasomal degradation, and can therefore help to quantify MHC class I antigen processing and presentation.

Ac-induced thermal vortex escape in magnetic-field-embedded long annular Josephson junctions

We investigate theoretically the thermal escape behavior of trapped magnetic fluxons in long annular Josephson junctions in dc magnetic fields, and perturbed by a probing ac current. The study is motivated by recently published experimental data that show multipeaked escape distributions for increasing bias current in the extreme low temperature regime when the system is perturbed by an ac current. We demonstrate that the observed behavior of multipeaked escape distributions can be reproduced and predicted in the entirely classical, thermally driven sine-Gordon model, which is widely accepted as accurately describing the experimental system. We interpret the observed multipeaked distributions as being directly induced by dynamical resonances between the applied ac perturbation and the natural oscillation frequency of a trapped fluxon.

Kerr nonlinear effects in AlGaAs multimode waveguides

We have experimentally investigated the linear and nonlinear characteristics of AlGaAs multimode waveguides. By varying the angle of incidence and∕or the intensity of the input beam, it is possible to change the multipeak intensity distributions at the output facet in a controllable fashion. Numerical simulations have reproduced the main features of the intensity profiles observed at the waveguide output over a range of intensities and angles.

Control of Deep Tectonics on the Superlarge Deposits in China

Abstract Seventy‐three large‐superlarge deposits in China were formed in 4 metallogenic epochs, and located in 6 metallogenic domains. By combing their time‐space distribution and the relevant data of crustal thickness, we discuss the control conditions of deep tectonics on superlarge deposits. The various spatial variation of the crustal thickness where deposits locate is closely related to their different tectonic setting. The crustal thickness of the region where deposits are in the Precambrian metallogenic epoch is 37.1 km and shows double‐peak distribution, which is related to the different tectonic‐mineralization processes in the Tarim‐North China and Yangtze metallogenic domains. The crustal thickness of the region where deposits are in the Paleoproterozoic metallogenic epoch is 43.4 km and shows normal distribution, which is the result of “pure” mineralization setting. The crustal thickness of the region where deposits are in the Late Palaeozoic‐Early Mesozoic metallogenic epoch is about 41.2 km and shows multi‐peak distribution, which can be related with dispersing distribution in the metallogenic domain of these superlarge deposits. The crustal thickness of the region where deposits are in the post‐Indosinian metallogenic epoch is 37.3 km, and shows skew distribution, which resulted from different tectonic settings in eastern and western China.

Coupling of optical modes in GaN‐based laser‐diodes

The optical waveguiding in GaN-based laser-diodes grown on sapphire substrates is investigated. Modes mainly guided either in the GaN buffer layer or between the AlGaN cladding layers interact with each other. This results in minima of the confinement factor at periodic intervals of the buffer layer thickness and in a multi-peak far field distribution. It is shown that the mode coupling can hardly be suppressed by a variation of either the thickness or the composition of the AlGaN cladding layers. Instead, the use of an AlGaN buffer layer or an InGaN waveguide is suggested. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Auditory scene analysis based on time‐frequency integration of shared FM and AM (I): Lagrange differential features and frequency‐axis integration

AbstractWe will propose in this paper a new algorithm for a computational implementation of auditory scene analysis. This algorithm forms a three‐layer structure of (1) subband decomposition by wavelet transform, (2) characterization of subband signal fragments by instantaneous frequency, frequency change rate, and amplitude change rate, and (3) frequency integration of subband signal features by voting method. We will perform the grouping and integration by voting the subband signal fragments into a nonparametric multipeak probability density distribution expressing “possibility of streams”; and then the recognition of the streams and the extraction of the stream parameters are realized by tracing its greatest point. It is confirmed from basic experiments for synthesized sounds and voices that the fundamental frequency/frequency change rate/amplitude change rate can be separated and estimated from multiple streams. © 2002 Wiley Periodicals, Inc. Syst Comp Jpn, 33(11): 95–106, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.1167

Auditory scene analysis based on time‐frequency integration of shared FM and AM (II): Optimum time‐domain integration and stream sound reconstruction

AbstractIn the preceding paper, we have proposed a method for auditory scene analysis, in which the instantaneous frequency, frequency change rate, and amplitude change rate in time‐frequency space are intensified into a multipeak probability density distribution by voting method and the grouping into streams of mixed sounds is realized. In this paper, as the main point of the second half of this method, we will introduce the assumption that the stream parameters vary slowly according to the known dynamics and propose an integration method on the time axis, in which the probability density distribution of the stream parameters is optimally estimated in time series by a nonparametric Kalman filter. By doing so, the mechanism of higher auditory scene analysis such as enhancement of the accuracy of the stream parameters, interpolation and connection of the breaks of the streams, and introduction of a priori knowledge into stream selection can be realized. Moreover, the separation and reconstruction system of sounds which correspond to streams is constructed, and the proposed technique is verified by fundamental experiments for synthesized sounds or musical sounds and voices. © 2002 Wiley Periodicals, Inc. Syst Comp Jpn, 33(10): 83–94, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.1160

Lipid membrane phase behaviour elucidated in real time by controlled environment atomic force microscopy.

Lipids are integral components of all biological membranes. Understanding the physical and chemical properties of these lipids is critical to our understanding of membrane functions. We developed a new atomic force microscope (AFM) approach to visualize in real time the temperature-induced lipid phase transition and domain separation processes in 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) membranes and estimate the thermodynamics of the phase transition process. The gel and liquid crystalline phases of DMPC coexisted over a broad temperature range (approximately 10 degrees C). Equal partitioning into two phases occurred at a transition temperature (Tm) of 28.5 degrees C. We developed a mathematical model to analyse AFM-derived DMPC membrane height changes as multi-peak Gaussian distributions. This approach allowed us to estimate the DMPC domain size, N, as 18-75 molecules per leaflet corresponding to a -4.2 nm diameter circular nanodomain. Lipid nanodomains may organize into microdomains or rafts which, in concert with proteins and other lipid components, play an important dynamic role in many biomedically important processes.

How to improve a random number generator

It is demonstrated that the one-dimensional random walk is sensitive both to short and long correlation of random numbers. In the case of correlated random numbers, the walker is trapped in the vicinity of the correlation. The result is a multipeak range distribution of the walker. Hence, the one-dimensional random walk can be used as a supplement to the standard tests for revealing long correlations of the generated random numbers. By implementing variety of tests to several generators we have shown that the quality can be improved by using a double randomization technique only if the random numbers, to be sampled from, are of a good quality. The sampling generator is less important. We propose, as well, a generator that produces high-quality random numbers for many stochastic processes.

Analysis of T cell clonality by CDR3 size of T-cell antigen receptor Vβ repertoire in HCL and c-All

Objective: To analyze the distribution and clonality of TCR Vβsubfamily T cells in hairy cell leukemia (HCL) and common-acute lymphoblastic leukemia (c-ALL). Methods: Peripheral blood mononuclear cell samples from 3 cases of HCL and 1 case of c-ALL were investigated for analysis of complementarity determining region 3 (CDR3) size of T cell receptor Vβ repertoire using reverse transcriptasepolymerase chain reaction (RT-PCR). The products were further analyzed by genescan to identify T cell clonality. Results: Some Vβ subfamily PCR products from 4 patients contained monopeak (monoclone) or a dominant peak (oligoclone). In contrast, multipeak (polyclone) distributions were found in all Vβ subfamily PCR products from normal control cases. Conclusion: T cell clonal expansion may be found in HCL and c-ALL cases that may indicate a host response directed against leukemia related antigen. In addition, it may be useful to detect the minimal residual disease.

Multiple scattering analysis of airborne POLDER image data over the sea

The authors have made a multiple scattering analysis of the airborne polarization and directionality of Earth reflectances (POLDER) data over the Mediterranean Sea, which was obtained in the Medimar campaign in 1991. Assuming an atmosphere-ocean system with an anisotropic Cox-Munk sea surface, the radiance and linear polarization in the upwelling radiation have been numerically evaluated for several typical aerosol models by using the adding and doubling method, in which multiple scatterings within the atmosphere and, multiple reflections at the atmosphere-ocean interface are fully taken into account. Major results based on this study are summarized as follows, (1) For the first time, the Medimar airborne POLDER data was analyzed from the linear polarization point of view by this study. Several typical aerosol models, namely, the Haze M, water-soluble, oceanic, maritime, continental and Junge-type models were fully tested against both the observed reflectance and linear polarization data at 0.85 /spl mu/m in the principal plane, as well as in the image form with various viewing angle information. (2) By examining various combinations of aerosol's complex refractive indices and wind speeds, the authors found that only the water-soluble model and Junge-type models with /spl nu/=3.5, 4.0, and 4.5 can satisfy the observed reflectance data, but they also found that these models, satisfying the observed reflectance constraints, fail to satisfy the observed linear polarization features in the backward scattering directions. (3) Any aerosol models deduced from the reflectance data analysis should be tested against the polarization data. This study was the first such attempt and all the major aerosol models with a single-peaked size distribution function were rejected, as an appropriate model over the Mediterranean Sea at the Medimar experiment time because they all failed to satisfy the observed polarization data. (4) More studies are certainly needed to find an appropriate aerosol model which can satisfy both the observed reflectance and polarization features. Other types of aerosol models with a multipeaked size distribution function should be fully examined in the future.

Experimental and theoretical investigation of recombination-pumped x-ray lasers driven by high-intensity, short-pulse lasers

We have experimentally investigated a recombination-pumped soft-x-ray laser on a Lyman-α transition (135 Å) of hydrogenlike lithium. Furthermore, we have modeled the dynamics of this system, including the effects of the multipeaked electron distribution function that is obtained from the sequential, optical-field ionization of an atom. We compare the predictions of our model and our experimental results.

Dynamics of optical-field-ionized plasmas for x-ray lasers.

The success of recombination-pumped x-ray laser schemes is determined by the kinetics of ions in plasmas with relatively dense, cold-electron distributions. We examine how laser gain in such systems is affected by a multipeaked electron distribution generated by sequential ionization of atoms using high-intensity, ultrashort-pulse lasers. We also investigate the role of heating processes that modify electron energy distributions during the recombination and the accompanying collisional cascade. We find that conditions for the success of these schemes are critically modified by the inclusion of these effects.

Distribution of excitatory junction potential amplitude in cat cerebral arteries: Examination of its quantal nature and modulation by opiates

We used scorpion venom to release small amounts of an excitatory neurotransmitter from adventitial nerves in cat left anterior descending cerebral artery. We used glass microelectrodes to measure and record postsynaptic electrical events of minimal amplitude. These events were similar to postsynaptic spontaneous and electrically evoked excitatory junction potentials (ejp's) seen in skeletal muscle. We performed a frequency analysis of the ejp amplitudes to determine if they fit a unimodal or multimodal distribution. We also investigated the effects of phentolamine, norepinephrine, hydromorphone, and morphine on ejp amplitude and frequency in the artery. Statistical analysis of the ejp frequency and amplitude revealed a multipeaked distribution with decreasing peaks. These results were similar to the distribution reported for acetylcholine release in skeletal muscle. The ejps were inhibited by phentolamine, which suggested that these events were adrenergically mediated. Norepinephrine and the opiates, hydromorphone and morphine, reduced the frequency and amplitude of the ejp's. The vessels also constricted to increasing doses of norepinephrine both under control conditions and in the presence of opiate. These results suggest that norepinephrine blocks the ejp's by a feedback mechanism at the presynaptic membrane and that endorphins and/or enkephalins, also acting at this presynaptic site, may modulate neurotransmission in the cerebral circulation.

Anisotropy and anharmonicity of atomic fluctuations in proteins: analysis of a molecular dynamics simulation.

Positional probability density functions (pdf) for the atomic fluctuations are determined from a molecular dynamics simulation for hen egg-white lysozyme. Most atoms are found to have motions that are highly anisotropic but only slightly anharmonic. The largest deviations from harmonic motion are in the direction of the largest rms fluctuations in the local principal axis frame. Backbone atoms tend to be more nearly harmonic than sidechain atoms. The atoms with the largest anharmonicities tend to have pdfs with multiple peaks, each of which is close to harmonic. Several model pdfs are evaluated on the basis of how well they fit probability densities from the dynamics simulations when parameterized in terms of the moments of the distribution. Gram-Charlier and Edgeworth perturbation expansions, which have been successful in describing the motions of small molecules in crystals, are shown to be inadequate for the distributions found in the dynamics of proteins. Multipeaked distribution functions are found to be more appropriate.

FAST-ION EXPANSION IN A SPHERICALLY SYMMETRICAL LASER-PLASMA

The fast expansion processes in a spherically symmetrical laser-plasma are investigated. The analytic expressions for the density, velocity and energy scaling law of fast ions under ambipolar acceleration are found. Explanations are given on various possible mechanisms which are responsible for the formation of the multipeaked distribution of ion kinetic energies.

Polyploidy in the murine colonic pericryptal fibroblast sheath.

The cause of the apparently paradoxical occurrence of relatively high levels of labelling and low levels of mitotic activity in the pericryptal fibroblast sheath (PCFS) was investigated. Analysis of the distribution of grain densities over epithelial cells and the PCFS in the colon demonstrated that, although the former had a unimodal peak, the PCFS had a multi-peak distribution. The PCFS nuclei with the higher grain densities gradually disappeared with time, due not to proliferation but to lateral migration into the lamina propria. Photodensitometric analysis confirmed the existence of polyploid cells in the colonic PCFS, but not in the epithelium.

On the presynaptic nature of the quantal subunit

Amplitude distributions of spontaneous miniature endplate potentials from the frog neuromuscular junction show several peaks which indicate the existence of quantal subunits. Such multipeaked distributions are even more pronounced when recording from a small length of the synapse thus excluding spatial factors as responsible. When increasing the mean quantal amplitude by blocking the acetylcholine esterase the amplitude of the subunit is increased, whereas the mean number of subunits in a single quantum remains unchanged. Though not providing direct evidence, these results support the hypothesis that quantal subunits are produced at the presynaptic level.

Deviations from simple binomial predictions of transmitter release at frog neuromuscular junctions

Measurements of transmitter release at frog neuromuscular junctions have produced multi-peaked amplitude distributions not in accord with either Poisson or binomial predictions. The phenomenon is attributed to intermittent branch failure within the synapses which are thus suggested to be functionally heterogeneous.

Long time behavior in locally activated random walks

We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient: emergence of a non-Gaussian mul-tipeaked probability distribution and a dynamical transition to an absorbing static state. We compute the generator and we study the partial differential equation which involves its adjoint. We discuss global existence and blow-up of the solution to this latter equation.