Maximum Entropy Method Analysis Research Articles

High resolution electron density mapping for LiF and NaF by maximum entropy method (MEM)

High resolution maximum entropy method (MEM) electron density maps have been elucidated for LiF and NaF using reported X-ray structure factors. The ionic nature of the bonding between constituent atoms in both the systems is found to be well pronounced and clearly seen from the electron density maps. The resolution of the present MEM maps is 0.063Å per pixel for LiF and 0.072Å per pixel for NaF along the three crystallographic axes. The electron density at the middle of the bond along [111] is found to be 0.0673e/Å3 for LiF and 0.003e/Å3 for NaF showing the different ionic strengths of the bonding. The electron density along [100] and [110] has also been drawn and analyzed. The inequality in the ionicity for the individual atoms and the electron content for different ionic radii have also been analyzed and compared with already published results. The wRMEM obtained from MEM analysis is 0.3% for LiF and 0.79% for NaF.

ENIGMA: maximum-entropy method program package for huge systems

ENIGMA(Electron and Nuclear Image Generator by Max-ent Analysis) is a program package to evaluate three-dimensional electron and nuclear density from X-ray and neutron diffraction data by using the maximum-entropy method (MEM). Compared with the previous program packageMEED,ENIGMAsaves computing time and frees memory space at the same time by employing parallel data processing. The fast Fourier transformation (FFT) technique is also implemented. As a consequence of these improvements, the MEM analysis byENIGMAbecomes applicable to huge systems, such as proteins and polymers, when the phased structure factors are provided. The package is transferable to a wide variety of parallel computers, because it is written in Fortran 90 and a standard message-passing interface (MPI).

Steady-State and Time-Resolved Fluorescence Studies on Wild Type and Mutant Chromatium vinosum High Potential Iron Proteins: Holo- and Apo-Forms

Detailed circular dichroism (CD), steady-state and time-resolved tryptophan fluorescence studies on the holo- and apo- forms of high potential iron protein (HiPIP) from Chromatium vinosum and its mutant protein have been carried out to investigate conformational properties of the protein. CD studies showed that the protein does not have any significant secondary structure elements in the holo- or apo- HiPIP, indicating that the metal cluster does not have any effect on formation of secondary structure in the protein. Steady-state fluorescence quenching studies however, suggested that removal of the iron-sulfur ([Fe 4S 4] 3+) cluster from the protein leads to an increase in the solvent accessibility of tryptophans, indicating change in the tertiary structure of the protein. CD studies on the holo- and apo- HiPIP also showed that removal of the metal prosthetic group drastically affects the tertiary structure of the protein. Time-resolved fluorescence decay of the wild type protein was fitted to a four-exponentials model and that of the W80N mutant was fitted to a three-exponentials model. The time-resolved fluorescence decay was also analyzed by maximum entropy method (MEM). The results of the MEM analysis agreed with those obtained from discrete exponentials model analysis. Studies on the wild type and mutants helped to assign the fast picosecond lifetime component to the W80 residue, which exhibits fast fluorescence energy transfer to the [Fe 4S 4] 3+ cluster of the protein. Decay-associated fluorescence spectra of each tryptophan residues were calculated from the time-resolved fluorescence results at different emission wavelengths. The results suggested that W80 is in the hydrophobic core of the protein, but W60 and W76 are partially or completely exposed to the solvent.

Frequency domain instrument for measuring phosphorescence lifetime distributions in heterogeneous samples

The luminescence lifetime distribution can be used to determine the distribution of quencher concentrations in a heterogeneous sample. We describe a frequency domain instrument for real-time measurements of phosphorescence lifetime distributions in microheterogeneous objects. In this system (1) an array of harmonics (typically 100–200 frequencies) is used to modulate the excitation source, a light emitting diode. Due to the relatively long triplet state lifetimes, the frequencies required for the modulation are typically below 40 000 kHz, which allows direct digitization of both excitation and emission signals. (2) The dependence of the phase/amplitude factor on the modulation frequency is determined by linear least-squares analysis of the emission signal, which is sampled and summed over the multiple excitation cycles. (3) The phase/amplitude relationship obtained is analyzed in real time using a “light” version of the maximum entropy algorithm, which provides a complete phosphorescence lifetime distribution. (4) The lifetime distribution is converted into the distribution of quencher concentrations using an appropriate model of quenching. The instrument is also capable of measuring phosphorescence in “single-frequency” mode, which is useful for rapid evaluation of apparent luminescence lifetimes. In this mode, a correction for an in-phase signal, which is due to backscattering and fluorescence, is applied to improve the accuracy of lifetime measurements. The instruments were tested in Stern–Volmer calibrations of Pd-porphyrin based phosphors for oxygen measurements and used for preliminary evaluation of oxygen distributions in rat tumor tissues. The instruments were found to be capable of accurate determination of lifetimes in the range of 10–3000 μs. The average duration of a single lifetime distribution measurement was about 15 s, depending on the sample and on the density of the lifetime grid in the maximum entropy method analysis. In the single-frequency mode, the measurement time was reduced to about 0.2–0.5 s. The instruments provide complete correction for the in-phase signal of up to 40% of the total emission intensity.

On the Rate Distribution Analysis of Kinetic Data Using the Maximum Entropy Method: Applications to Myoglobin Relaxation on the Nanosecond and Femtosecond Timescales

We discuss the application of the maximum entropy method (MEM) to the extraction of rate distributions from kinetics experiments on the nanosecond to femtosecond time scale. We first present simulations to show the effects of data truncation (typical of nanosecond experiments) on rate distributions recovered by MEM. The stretched exponential decay is considered as an example to demonstrate that if the true distribution of rates for the underlying process includes faster time scales than are contained within the experimental data set, MEM can introduce unwarranted features that extend into the slower regions of rate space. This observation has relevance to the application of MEM to obtain rate distributions from kinetic experiments involving the relaxation of complex molecules like proteins, where features in the distribution are sometimes interpreted as static distributions of protein conformational substates. As an experimental example, we present an MEM analysis of the temperature dependence of the geminate rebinding kinetics of carbonmonoxy myoglobin near room temperature and find a barrier height of 18 kJ/mol. We also consider the application of MEM to ultrafast pump-probe transient absorption data, where one needs to take into account the possibility of nonmonotonicity in the kinetics and the finite pulse autocorrelation width that effectively convolves into the observed material responses. The MEM analyses of the femtosecond photophysics of Mb and MbNO, monitored at several wavelengths in the visible region, are presented as examples.

Charge density study of C 60 superconductors by MEM/Rietveld analysis

The charge density study of alkali metal doped fullerenes, Rb 2CsC 60, K 2RbC 60, Na 2RbC 60 and Li 2CsC 60, was carried out at room temperature by MEM/Rietveld analysis, which is the combination of the Maximum Entropy Method (MEM) and Rietveld analysis using synchrotron radiation powder data. The distinctly different features of charge densities of the C 60 molecules relating to the superconducting properties were revealed in the obtained MEM charge densities. For Na 2RbC 60, K 2RbC 60 and Rb 2CsC 60, the rotations of the C 60 molecules were virtually quenched while the C 60 molecule in Li 2CsC 60 was in an orientational disorder. In the interatomic region, the overlapped charge density indicating the existence of a covalent bond was not found significantly between the C 60 molecules and doped metal atoms for the four materials. However, in the MEM charge densities, the relative differences among them were found significantly for the charge deficiencies of the doped metal atoms which should be associated with charge transfer from the metal atoms to the C 60 molecule.

Tryptophan rotamers that report the conformational dynamics of proteins

Abstract The binding of acetyl­pepstatin to the Q7K/L33I/L63I mutant of HIV-1 protease was studied by fluorescence, phosphorescence, and 500-ps molecular dynamics. The protease is a homodimer with two tryptophans per monomer. Maximum entropy method (MEM) analysis and acrylamide quenching results show two tryptophyl, tryptophan (Trp) populations in the apoenzyme that merge into one in the complex. These results are in agreement with molecular dynamics simulations indicative of Trp asymmetry in the apoenzyme as revealed by the occurrence of nonequivalent Trp42 indole rotamer interconversions, not observed for the complex. Analysis of the local Trp42B environments of the apoenzyme with respect to possible quencher groups shows that the c2 interconversions do not influence the lifetime, while the c1 interconversions do. Upon binding the inhibitor, Trp42B acquires a single conformation with the same lifetime and orientation as that of Trp42, and also with less quenching accessibility. Thus, protein conformational dynamics become constrained with inhibitor binding. This conclusion is supported by red-edge effect experiments and phosphorescence lifetime measurements. The low temperature tp (~5.8 s) is quenched to ~200 ms as protein motions become activated around the glass transition temperature. In the case of the complex, the phosphorescence lifetime data show a more cooperative activation of the quenching mechanisms.

Changes in ultra-low and very low frequency heart rate variability after coronary artery bypass grafting

This study was performed to assess the effects of coronary artery bypass grafting (CABG) on the ultra-low (ULF) and very low (VLF) frequency components of heart rate variability (HRV). Fortynine CABG patients (aged from 38 to 77 years) were examined by 24-h ambulatory electrocardiographic (AECG) monitoring, both preoperatively and 4 weeks after CABG. HRV spectral components were obtained by maximum entropy method analysis. Then the ULF, VLF, low frequency (LF), high frequency (HF) and total frequency (TF) components were compared before and after CABG. The average 24-h heart rate increased significantly after CABG (69 ± 11.5 vs 82.9 ± 10.9 beats per minute [bpm], P < 0.0001). The power of the ULF, VLF, and LF spectral components showed a decrease after surgery (2,859.9 vs 1,601.2 ms 2, P < 0.0001, 1,215.0 vs 572.3 ms 2, P < 0.0001, and 260.3 vs 125.9 ms 2, P < 0.002, respectively), but the HF power did not show any significant change (98.7 vs 125.9 ms 2, NS). Analysis of the normalized ratio of the ULF component (ULF/TF ratio) revealed a significant increase postoperatively (0.6496 ± 0.0931 vs 0.7003 ± 0.1338, P < 0.0001), but the VLF/TF and LF/TF ratios decreased after CABG (from 0.2671 ± 0.0689 to 0.2040 ± 0.0832, P < 0.0001 and from 0.0568 ± 0.0290 to 0.0429 ± 0.0232, P < 0.0088, respectively). In contrast, there was no significant alteration in the HF/TF ratio. These results suggest that recovery of cardiac autonomic activity is delayed after surgery. However, improvement of the ULF/TF ratio, one of the prognostic indicators for patients with cardiac disease, should be related to the relief of myocardial ischemia by CABG.

Redox-linked conformational changes in bovine heart cytochrome c oxidase: picosecond time-resolved fluorescence studies of cyanide complex.

Picosecond time-resolved fluorescence studies are carried out on cyanide-inhibited and heat-modified cytochrome c oxidase in aqueous lauryl maltoside surfactant solution, as well as in an aqueous vesicle, to understand the conformational changes associated with electron transfer and proton pumping activity of the enzyme. The tryptophan fluorescence decay profiles follow a four exponential model, which also matches the lifetime maxima obtained in a maximum entropy method analysis. The fast lifetime components are highly affected by the reduction and chemical modification of the enzyme. Changes in these lifetime components are related to the conformational changes in the vicinity of the heme centers of the enzyme. The cyanide-inhibited enzyme in the oxidized form shows a fluorescence decay profile similar to that of the native oxidized form, indicating that the conformational changes due to cyanide binding are very small. However, reduction of the cyanide-inhibited enzyme that leaves cyanide bound heme alpha3 oxidized causes a large increase in the fluorescence lifetimes, which indicates very significant conformational changes due to electron transfer to the dinuclear Cu(A) and heme alpha centers. A comparison of the tryptophan fluorescence decay of various other modified forms of the enzyme leads us to propose that the possible site of conformational coupling is located near heme alpha instead of the binuclear heme alpha3-Cu(B) center.

A Synchrotron Powder Diffraction Study of Na-LTA

The charge density distribution of Na-LTA is obtained by the Maximum Entropy Method (MEM) using synchrotron powder data. In the MEM map, all the components; framework, cations and absorbed water molecules, are all clearly shown even if the site occupation is very low, say less than 10%. A powder diffraction experiment is carried out by the transmission geometry with Imaging Plate (IP) detector at BL-6A2, PR In the analysis, a new method which is a iterative use of Rietveld refinement and MEM is applied in order to improve a structure model used in Rietveld refinement. An initial structure model used in Rietveld is just simple framework only. In the first Rietveld refinement, the agreement factor, RI, was very bad, i.e.37.4%. Following MEM analysis, however, gives the key information of how to improve next structure model for Rietveld refinement. Improvement of the structure model by the present method eventually lead to RI to be as low as 5.2%, which proves a great success of the method. The present method may lead a drastic change of structural studies of zeolite compounds when it is applied to high resolution and high intensity synchrotron powder data.

部分プロファイル緩和と最大エンロピー法を導入した粉末構造解析

A Rietveld-refinement program, RIETAN-98, has two advanced features: partial profile relaxation and whole-pat-tern fitting based on a maximum-entropy method (MEM). Partial profile relaxation means that primary profile parameters of isolated reflections can be locally refined independently of secondary profile parameters. It was combined with three split-type profile functions to obtain better fits between observed and calculated patterns, particularly in samples showing anisotropic pro-file broadening. Further, RIETAN-98 has been combined with a MEED program for the MEM to grow into a joint software named REMEDY, which makes it possible to carry out MEM analysis and whole-pattern fitting alternately. REMEDY is very useful for modifying incomplete structural models and analyzing highly disordered structures.

Ｘ線回折法による金属内包フラーレンの構造研究

Endohedral metallofullerenes are novel forms of fullerene-related materials, which encage metal atom inside a carbon cage. The recent X-ray structural studies of metallofullerenes, Sc@C82 and Sc2@C84, by the synchrotron powder diffraction experiment are presented to illustrate the usefulness of the MEM/Rietveld analysis, which is a self-consistent iterative way in combination with the MEM (Maximum Entropy Method) and Rietveld analyses. The obtained MEM charge densities clearly reveal the distinct features of encapsulated metals inside the fullerene cages as well as endohedral cage structures for Sc@C82 and Sc2@C84.

Density Profile and Fluctuation Measurements with Microwave Reflectometry on Gamma 10

The microwave reflectometry using FM and ultrashort-pulse radar techniques have been applied to GAMMA 10 in order to diagnose plasma density profile and fluctuations. The reliability of profile measurement using the FM reflectometer is investigated for various sweep times and local path length. It is demonstrated that the reconstructed density profiles seem to be improved when the sweep time is faster than 50–100 μs. The several reconstruction algorithms are introduced to analyze the fast time-varying data, such as, the maximum-entropy method and wavelet analysis as well as zero-cross fringe counting and digital complex demodulation method.The reflectometers are applied to the measurement of density/magnetic fluctuations. The space-and time-resolving spectra of rf waves as well as low-frequency waves are obtained. The density and magnetic-field fluctuations are evaluated from both the reflectometer and cross-polarization scattering diagnostic method.

Characterization of a partially unfolded structure of cytochrome c induced by sodium dodecyl sulphate and the kinetics of its refolding.

The mechanism of unfolding of ferricytochrome c induced by the surfactant sodium dodecyl sulfate has been studied by heme absorption, tryptophan fluorescence, circular dichroism, resonance Raman scattering, stopped-flow and time-resolved resonance energy transfer to obtain a comprehensive view of the whole process. Unfolding occurred at an almost specific molecular ratio of SDS/cytochrome c in the concentration range (20-50 microM) studied here. However there appears to be a point at approximately 0.6 mM SDS where unfolding begins to occur for lower cytochrome c concentrations. The kinetics of unfolding revealed only a single transition with a rate constant of 33 s(-1) (at 298 K, [SDS] = 8.7 mM) and activation energy barrier of approximately 16 kJ/mol, indicating that other associated steps, if any, are too fast to be significantly populated. The free energy change (deltaG(o)) involved with the unfolding transition was estimated to be about 16.8 kJ/mol. The CD spectrum at 220 nm of SDS-unfolded cytochrome c shows only a partial decrease (25%), indicating that a significant amount of helical structure remains folded in contrast to a complete loss of helical structure in GdnHCl-denatured cytochrome c. The heme structure in SDS-unfolded cytochrome c, as deduced from heme absorption and resonance Raman spectra, shows a major population (approximately 95%) of mis-ligated histidine to the heme which acts as a kinetic trap in the folding process. The structural changes associated with cytochrome c unfolding were also monitored by time-resolved resonance energy transfer which shows a drastic increase in tryptophan fluorescence lifetime from 12 ps in the native protein to 0.63 ns in the unfolded one, associated with a movement of Trp59 by 10 A away from heme. The maximum entropy method analysis of fluorescence decay indicated the growth of various conformational substates in SDS-unfolded cytochrome c in contrast to narrowly distributed conformations in the native protein. The refolding was comprised of three kinetic steps; the first was significantly fast (approximately 8 ms) and was assigned to the dissociation of His26 that paves the protein towards correct folding pathway. The other two slower steps probably arise from chain misorganization and prolyl isomerization. The absence of a burst-phase amplitude supports the idea that the burst phase observed in the folding from completely unfolded cytochrome c corresponds to a molecular collapse that produces significant secondary structure. The partially unfolded state represents a unique intermediate state in the folding pathway.

Magnetic and electronic state of Co in LaCoO 3

High-spin state of Co in LaCoO 3 was investigated by the X-ray diffraction (XRD) and submillimeter ESR method. The ESR signals of high-spin state Co 3+ were found in the frequency range above 150 GHz at temperatures above 25 K. They were discussed by the thermal activation and the crystal distortion model. The XRD and the maximum entropy method (MEM) analysis revealed the high density of electron distribution along the chain -O-Co-O-.

A Spectral Analysis of the Masuda Flare UsingYohkohHard X‐Ray Telescope Pixon Reconstruction

Masuda's discovery of a compact hard X-ray impulsive source at the apex of a flaring coronal loop has received a great deal of recent attention in the solar physics community. The Masuda flare, which occurred on 1992 January 13, exhibited evidence of energy deposition in a compact region some distance above the soft X-ray loop, suggesting, to some authors, a flare process similar to the classical model for two-ribbon flares proposed by Shibata et al. These conclusions were made on the basis of a maximum entropy method (MEM) reconstruction of the Yohkoh Hard X-Ray Telescope (HXT) observations. Recently, a new approach has been developed for reconstructing the spatial information from the HXT: that of pixon reconstruction, proposed by Metcalf et al. In this paper, we apply the pixon reconstruction technique to the event of 1992 January 13 and determine the temporal and spectral characteristics of the loop-top source. While our emphasis here is on the spectral properties of the Masuda flare, we also provide a brief comparison between the pixon reconstruction and that of MEM for the hard X-ray loop top. In carrying out the comparison between the methods, we have applied recent improvements to the instrument response functions and reconstruction algorithms. We have also identified a previously unknown effect of weak source suppression that was inherent in previous analyses and that significantly compromised the ability to study weak sources of hard X-ray emission in the presence of strong sources. The improved response functions and the better flux estimation used in this paper reduce (but do not eliminate) the effects of this suppression, and consequently, it should be noted that the MEM analysis presented in this paper is quite distinct from any that have been carried out previously. Our conclusions are that (a) a compact loop-top hard X-ray source exists with an impulsive temporal profile spanning the peak of the flare; (b) the loop-top source is nonthermal in nature at the peak of the flare; (c) there is a distinct dearth of HXT LO channel emission, relative to the higher energy channels, from the loop-top region, indicating either a very hard spectrum or the presence of a low-energy cutoff in the energetic electron spectrum; (d) the footpoint and loop-top emission during the impulsive phase of the flare are produced by two distinct particle populations; (e) following the main phase of this flare, the loop top is clearly thermal in nature with a peak temperature of ~40 MK that decreases with time as the event proceeds; and (f) the disparity between the present pixon results and previous MEM results is primarily due to the intrinsically better photometry achieved by the pixon method and the avoidance of suppression effects in the present analysis. These conclusions therefore support, in part, those made in previous works, confirming the existence of an impulsive source of hard X-rays in the corona above a flaring loop. Our analysis does, however, allow for a more comprehensive understanding of the temporal and spectral development of this event in the context of an alternative reconstruction technique.

Laurdan solvatochromism: solvent dielectric relaxation and intramolecular excited-state reaction

Absorption, steady-state, and time-resolved fluorescence measurements have been performed on laurdan dissolved either in white viscous apolar solvents or in ethanol as a function of temperature. The heterogeneity of the absorption spectra in white oils or in ethanol is consistent with semiempirical calculations performed previously on Prodan. From steady-state and time-resolved fluorescence measurements in apolar media, an excited state reaction is evidenced. The bimodal lifetime distribution determined from the maximum entropy method (MEM) analysis is attributed to the radiative deexcitation of a "locally excited" (LE) state and of a "charge transfer" (CT) state, whereas a very short component (20 ps), the sign and the amplitude of which depend on the emission wavelength, is attributed to the kinetics of the interconvertion reaction. The observation of an isoemissive point in the temperature range from -50 degrees C to -110 degrees C in ethanol suggests an interconvertion between two average excited-state populations: unrelaxed and solvent-relaxed CT states. A further decrease in temperature (-190 degrees C), leading to frozen ethanol, induces an additional and important blue shift. This low temperature spectrum is partly attributed to the radiative deexcitation of the LE state. Time-resolved emission spectra (TRES) measurements at -80 degrees C in the ethanol liquid phase show a large spectral shift of approximately 2500 cm(-1) (stabilization energy of the excited state: 7.1 kcal x M(-1)). The time-dependent fluorescence shift (TDFS) is described for its major part by a nanosecond time constant. The initial part of the spectral shift reveals, however, a subnanosecond process that can be due to fast internal solvent reorientation and/or to intramolecular excited-state reactions. These two relaxation times are also detected in the analysis of the fluorescence decays in the middle range of emission energy. The activation energy of the longest process is approximately 3 kcal x M(-1). At -190 degrees C, one subnanosecond and one nanosecond excited-state reactions are also evidenced. They are likely due to intramolecular rearrangements after the excitation, leading to the CT state and not to solvent relaxation, which is severely hindered in these temperature conditions. Therefore, both intramolecular and solvent relaxations are responsible for the large Stokes shift displayed by this probe as a function of solvent polarity. A possible scheme is proposed for the deexcitation pathway, taking into account the kinetics observed in these different solvents.

Charge density distribution in alkaline-earth cuprates with one- or two-dimensional arrangements of Cu [sbnd

We report the charge density distribution ϱ(r) ( = |φ(r)| 2 ; φ(r)wave function) of Ca 2CuO 3 with the one-dimensional Cu O chain and (Sr 0.15, Ca 0.85)CuO 2 with the two-dimensional CuO 2 plane, in comparison with that of superconducting YBa 2Cu 3O 6.9 with both the Cu O atomic arrangements. ϱ(r) was obtained by the Maximum-Entropy Method (MEM) analysis using laboratory X-ray powder diffraction data. The ϱ(r) in (Ca,Sr)CuO 2 is almost spherical, indicating that ionic features are dominant in the CuO 2 planes. This contrasts with the case of superconducting YBa 2Cu 3O 6.9, which shows remarkable overlapping between Cu 3d and O 2p orbitals. On the contrary, the ϱ(r) in Ca 2CuO 3 indicates substantial overlapping between Cu and O only along the single chain direction and no interaction between each Cu O chain.

Long-term features of drifting and standing non-dipole fields as determined from Holocene palaeomagnetic secular variations

Geomagnetic field motions of Holocene secular variations are investigated using a separation method. The palaeomagnetic secular variations from Britain, North America and Australia have been subjected to maximum-entropy method analyses. Based on the results of spectral analyses, the secular variations are separated by band-pass filters into low-frequency components, generally including the period band 1800-3600 yr, and high-frequency components, generally including the period band 1000-1200 yr. There is an interval, from 4200 to 1700 yr BP, which shows clockwise rotational motions in the low-frequency components of all three sites. Westward drifting of geomagnetic fields may be globally dominant. Swinging or elliptical looping motions constrained to a certain direction were observed in the low-frequency components of the British data. The time duration for the persistence of the swinging motion constrained to a certain direction was 3500 years or so, which could be the lifetime of an oscillating stationary field. The duration of the transitional motion was 1000-1300 years, which may indicate the recurrence time of a stationary field.

New technique for time series analysis combining the maximum entropy method and non-linear least squares method: its value in heart rate variability analysis.

A new technique for time series analysis, which is a combination of the maximum entropy method (MEM) for spectral analysis and the non-linear least squares method (LSM) for fitting analysis, is described. In this technique, the MEM power spectral density (MEMPSD) is calculated using a very large lag that could diminish the lag dependence of dominant periods estimated by the MEM analysis. The validity of this large lag is confirmed by the LSM, given that the ten dominant MEM periods are known quantities. To validate the MEM plus LSM technique, it is compared with autoregressive (AR) modelling, by analysing heart rate variability under pharmacological interventions (phenylephrine and trinitroglycerine), using 16 young males. The results indicate that the MEMPSD, when compared with the ARPSD, has numerous periods that could reproduce the original time series much more accurately, as revealed by the LSM analysis. However, both the low- and high-frequency powers with MEMPSD and ARPSDs shift in the expected directions in accordance with the pharmacological effects on the cardiovascular system. The implications of these results are discussed from the theoretical and practical standpoints of the MEM plus LSM technique, compared with AR modelling.