Deriving structural information from non-coding ribonucleic acids by mass spectrometry

The purpose of this study is to describe the development of application of mass spectrometry for the structural analyses of non-coding ribonucleic acids during past decade. Mass spectrometric methods are compared of traditional gel electrophoretic methods, the characteristics of performance of mass spectrometric, analyses are studied and the future trends of mass spectrometry of ribonucleic acids are discussed. Non-coding ribonucleic acids are short polymeric biomolecules which are not translated to proteins, but which may affect the gene expression in all organisms. Regulatory ribonucleic acids act through transient interactions with key molecules in signal transduction pathways. Interactions are mediated through specific secondary and tertiary structures. Posttranscriptional modifications in the structures of molecules may introduce new properties to the organism, such as adaptation to environmental changes or development of resistance to antibiotics. In the scope of this study, the structural studies include i) determination of the sequence of nucleobases in the polymer chain, ii) characterisation and localisation of posttranscriptional modifications in nucleobases and in the backbone structure, iii) identification of ribonucleic acid-binding molecules and iv) probing of higher order structures in the ribonucleic acid molecule. Bacteria, archaea, viruses and HeLa cancer cells have been used as target organisms. Synthesised ribonucleic acids consisting of structural regions of interest have been frequently used. Electrospray ionisation (ESI) and matrix-assisted laser desorption ionisation (MALDI) have been used for ionisation of ribonucleic analytes. Ammonium acetate and 2-propanol are common solvents for ESI. Trihydroxyacetophenone is the optimal MALDI matrix for ionisation of ribonucleic acids and peptides. Ammonium salts are used in ESI buffers and MALDI matrices as additives to remove cation adducts. Reverse phase high performance liquid chromatography has been used for desalting and fractionation of analytes either off-line of on-line, coupled with ESI source. Triethylamine and triethylammonium bicarbonate are used as ion pair reagents almost exclusively. Fourier transform ion cyclotron resonance analyser using ESI coupled with liquid chromatography is the platform of choice for all forms of structural analyses. Time-of-flight (TOF) analyser using MALDI may offer sensitive, easy-to-use and economical solution for simple sequencing of longer oligonucleotides and analyses of analyte mixtures without prior fractionation. Special analysis software is used for computer-aided interpretation of mass spectra. With mass spectrometry, sequences of 20-30 nucleotides of length may be determined unambiguously. Sequencing may be applied to quality control of short synthetic oligomers for analytical purposes. Sequencing in conjunction with other structural studies enables accurate localisation and characterisation of posttranscriptional modifications and identification of nucleobases and amino acids at the sites of interaction. High throughput screening methods for RNA-binding ligands have been developed. Probing of the higher order structures has provided supportive data for computer-generated three dimensional models of viral pseudoknots. In conclusion. mass spectrometric methods are well suited for structural analyses of small species of ribonucleic acids, such as short non-coding ribonucleic acids in the molecular size region of 20-30 nucleotides. Structural information not attainable with other methods of analyses, such as nuclear magnetic resonance and X-ray crystallography, may be obtained with the use of mass spectrometry. Sequencing may be applied to quality control of short synthetic oligomers for analytical purposes. Ligand screening may be used in the search of possible new therapeutic agents. Demanding assay design and challenging interpretation of data requires multidisclipinary knowledge. The implement of mass spectrometry to structural studies of ribonucleic acids is probably most efficiently conducted in specialist groups consisting of researchers from various fields of science.

Micropillar Array Based Microchips for Electrospray Ionization Mass Spectrometry, Microreactors, and Liquid Chromatographic Separation

This dissertation deals with the design, fabrication, and applications of microscale electrospray ionization chips for mass spectrometry. The microchip consists of microchannel, which leads to a sharp electrospray tip. Microchannel contain micropillars that facilitate a powerful capillary action in the channels. The capillary action delivers the liquid sample to the electrospray tip, which sprays the liquid sample to gas phase ions that can be analyzed with mass spectrometry. The microchip uses a high voltage, which can be utilized as a valve between the microchip and mass spectrometry. The microchips can be used in various applications, such as for analyses of drugs, proteins, peptides, or metabolites. The microchip works without pumps for liquid transfer, is usable for rapid analyses, and is sensitive. The characteristics of performance of the single microchips are studied and a rotating multitip version of the microchips are designed and fabricated. It is possible to use the microchip also as a microreactor and reaction products can be detected online with mass spectrometry. This property can be utilized for protein identification for example. Proteins can be digested enzymatically on-chip and reaction products, which are in this case peptides, can be detected with mass spectrometry. Because reactions occur faster in a microscale due to shorter diffusion lengths, the amount of protein can be very low, which is a benefit of the method. The microchip is well suited to surface activated reactions because of a high surface-to-volume ratio due to a dense micropillar array. For example, titanium dioxide nanolayer on the micropillar array combined with UV radiation produces photocatalytic reactions which can be used for mimicking drug metabolism biotransformation reactions. Rapid mimicking with the microchip eases the detection of possibly toxic compounds in preclinical research and therefore could speed up the research of new drugs. A micropillar array chip can also be utilized in the fabrication of liquid chromatographic columns. Precisely ordered micropillar arrays offer a very homogenous column, where separation of compounds has been demonstrated by using both laser induced fluorescence and mass spectrometry. Because of small dimensions on the microchip, the integrated microchip based liquid chromatography electrospray microchip is especially well suited to low sample concentrations. Overall, this work demonstrates that the designed and fabricated silicon/glass three dimensionally sharp electrospray tip is unique and facilitates stable ion spray for mass spectrometry.

SU-8-Based Microchips for Capillary Electrophoresis and Electrospray Ionization Mass Spectrometry

Miniaturization of analytical instrumentation is attracting growing interest in response to the explosive demand for rapid, yet sensitive analytical methods and low-cost, highly automated instruments for pharmaceutical and bioanalyses and environmental monitoring. Microfabrication technology in particular, has enabled fabrication of low-cost microdevices with a high degree of integrated functions, such as sample preparation, chemical reaction, separation, and detection, on a single microchip. These miniaturized total chemical analysis systems (microTAS or lab-on-a-chip) can also be arrayed for parallel analyses in order to accelerate the sample throughput. Other motivations include reduced sample consumption and waste production as well as increased speed of analysis. One of the most promising hyphenated techniques in analytical chemistry is the combination of a microfluidic separation chip and mass spectrometer (MS). In this work, the emerging polymer microfabrication techniques, ultraviolet lithography in particular, were exploited to develop a capillary electrophoresis (CE) separation chip which incorporates a monolithically integrated electrospray ionization (ESI) emitter for efficient coupling with MS. An epoxy photoresist SU-8 was adopted as structural material and characterized with respect to its physicochemical properties relevant to chip-based CE and ESI/MS, namely surface charge, surface interactions, heat transfer, and solvent compatibility. As a result, SU-8 was found to be a favorable material to substitute for the more commonly used glass and silicon in microfluidic applications. In addition, an infrared (IR) thermography was introduced as direct, non-intrusive method to examine the heat transfer and thermal gradients during microchip-CE. The IR data was validated through numerical modeling. The analytical performance of SU-8-based microchips was established for qualitative and quantitative CE-ESI/MS analysis of small drug compounds, peptides, and proteins. The CE separation efficiency was found to be similar to that of commercial glass microchips and conventional CE systems. Typical analysis times were only 30-90 s per sample indicating feasibility for high-throughput analysis. Moreover, a mass detection limit at the low-attomole level, as low as 10E+5 molecules, was achieved utilizing MS detection. The SU-8 microchips developed in this work could also be mass produced at low cost and with nearly identical performance from chip to chip. Until this work, the attempts to combine CE separation with ESI in a chip-based system, amenable to batch fabrication and capable of high, reproducible analytical performance, have not been successful. Thus, the CE-ESI chip developed in this work is a substantial step toward lab-on-a-chip technology.

Heated Nebulizer Microchips for Mass Spectrometry

Miniaturized analytical devices, such as heated nebulizer (HN) microchips studied in this work, are of increasing interest owing to benefits like faster operation, better performance, and lower cost relative to conventional systems. HN microchips are microfabricated devices that vaporize liquid and mix it with gas. They are used with low liquid flow rates, typically a few µL/min, and have previously been utilized as ion sources for mass spectrometry (MS). Conventional ion sources are seldom feasible at such low flow rates. In this work HN chips were developed further and new applications were introduced. First, a new method for thermal and fluidic characterization of the HN microchips was developed and used to study the chips. Thermal behavior of the chips was also studied by temperature measurements and infrared imaging. An HN chip was applied to the analysis of crude oil – an extremely complex sample – by microchip atmospheric pressure photoionization (APPI) high resolution mass spectrometry. With the chip, the sample flow rate could be reduced significantly without loss of performance and with greatly reduced contamination of the MS instrument. Thanks to its suitability to high temperature, microchip APPI provided efficient vaporization of nonvolatile compounds in crude oil. The first microchip version of sonic spray ionization (SSI) was presented. Ionization was achieved by applying only high (sonic) speed nebulizer gas to an HN microchip. SSI significantly broadens the range of analytes ionizable with the HN chips, from small stable molecules to labile biomolecules. The analytical performance of the microchip SSI source was confirmed to be acceptable. The HN microchips were also used to connect gas chromatography (GC) and capillary liquid chromatography (LC) to MS, using APPI for ionization. Microchip APPI allows efficient ionization of both polar and nonpolar compounds whereas with the most popular electrospray ionization (ESI) only polar and ionic molecules are ionized efficiently. The combination of GC with MS showed that, with HN microchips, GCs can easily be used with MS instruments designed for LC-MS. The presented analytical methods showed good performance. The first integrated LC–HN microchip was developed and presented. In a single microdevice, there were structures for a packed LC column and a heated nebulizer. Nonpolar and polar analytes were efficiently ionized by APPI. Ionization of nonpolar and polar analytes is not possible with previously presented chips for LC–MS since they rely on ESI. Preliminary quantitative performance of the new chip was evaluated and the chip was also demonstrated with optical detection. A new ambient ionization technique for mass spectrometry, desorption atmospheric pressure photoionization (DAPPI), was presented. The DAPPI technique is based on an HN microchip providing desorption of analytes from a surface. Photons from a photoionization lamp ionize the analytes via gas-phase chemical reactions, and the ions are directed into an MS. Rapid analysis of pharmaceuticals from tablets was successfully demonstrated as an application of DAPPI.

Thin-Layer Chromatography with Ultraviolet and Mass Spectrometric Detection: From Preparative-Layer to Miniaturized Ultra-Thin-Layer Technique

The present challenge in drug discovery is to synthesize new compounds efficiently in minimal time. The trend is towards carefully designed and well-characterized compound libraries because fast and effective synthesis methods easily produce thousands of new compounds. The need for rapid and reliable analysis methods is increased at the same time. Quality assessment, including the identification and purity tests, is highly important since false (negative or positive) results, for instance in tests of biological activity or determination of early-ADME parameters in vitro (the pharmacokinetic study of drug absorption, distribution, metabolism, and excretion), must be avoided. This thesis summarizes the principles of classical planar chromatographic separation combined with ultraviolet (UV) and mass spectrometric (MS) detection, and introduces powerful, rapid, easy, low-cost, and alternative tools and techniques for qualitative and quantitative analysis of small drug or drug-like molecules. High performance thin-layer chromatography (HPTLC) was introduced and evaluated for fast semi-quantitative assessment of the purity of synthesis target compounds. HPTLC methods were compared with the liquid chromatography (LC) methods. Electrospray ionization mass spectrometry (ESI MS) and atmospheric pressure matrix-assisted laser desorption/ionization MS (AP MALDI MS) were used to identify and confirm the product zones on the plate. AP MALDI MS was rapid, and easy to carry out directly on the plate without scraping. The PLC method was used to isolate target compounds from crude synthesized products and purify them for bioactivity and preliminary ADME tests. Ultra-thin-layer chromatography (UTLC) with AP MALDI MS and desorption electrospray ionization mass spectrometry (DESI MS) was introduced and studied for the first time. Because of the thinner adsorbent layer, the monolithic UTLC plate provided 10 100 times better sensitivity in MALDI analysis than did HPTLC plates. The limits of detection (LODs) down to low picomole range were demonstrated for UTLC AP MALDI and UTLC DESI MS. In a comparison of AP and vacuum MALDI MS detection for UTLC plates, desorption from the irregular surface of the plates with the combination of an external AP MALDI ion source and an ion trap instrument provided clearly less variation in mass accuracy than the vacuum MALDI time-of-flight (TOF) instrument. The performance of the two-dimensional (2D) UTLC separation with AP MALDI MS method was studied for the first time. The influence of the urine matrix on the separation and the repeatability was evaluated with benzodiazepines as model substances in human urine. The applicability of 2D UTLC AP MALDI MS was demonstrated in the detection of metabolites in an authentic urine sample.

Liquid Chromatography-Mass Spectrometry in Studies of Drug Metabolism and Permeability

Poor pharmacokinetics is one of the reasons for the withdrawal of drug candidates from clinical trials. There is an urgent need for investigating in vitro ADME (absorption, distribution, metabolism and excretion) properties and recognising unsuitable drug candidates as early as possible in the drug development process. Current throughput of in vitro ADME profiling is insufficient because effective new synthesis techniques, such as drug design in silico and combinatorial synthesis, have vastly increased the number of drug candidates. Assay technologies for larger sets of compounds than are currently feasible are critically needed. The first part of this work focused on the evaluation of cocktail strategy in studies of drug permeability and metabolic stability. N-in-one liquid chromatography-tandem mass spectrometry (LC/MS/MS) methods were developed and validated for the multiple component analysis of samples in cocktail experiments. Together, cocktail dosing and LC/MS/MS were found to form an effective tool for increasing throughput. First, cocktail dosing, i.e. the use of a mixture of many test compounds, was applied in permeability experiments with Caco-2 cell culture, which is a widely used in vitro model for small intestinal absorption. A cocktail of 7-10 reference compounds was successfully evaluated for standardization and routine testing of the performance of Caco-2 cell cultures. Secondly, cocktail strategy was used in metabolic stability studies of drugs with UGT isoenzymes, which are one of the most important phase II drug metabolizing enzymes. The study confirmed that the determination of intrinsic clearance (Clint) as a cocktail of seven substrates is possible. The LC/MS/MS methods that were developed were fast and reliable for the quantitative analysis of a heterogenous set of drugs from Caco-2 permeability experiments and the set of glucuronides from in vitro stability experiments. The performance of a new ionization technique, atmospheric pressure photoionization (APPI), was evaluated through comparison with electrospray ionization (ESI), where both techniques were used for the analysis of Caco-2 samples. Like ESI, also APPI proved to be a reliable technique for the analysis of Caco-2 samples and even more flexible than ESI because of the wider dynamic linear range. The second part of the experimental study focused on metabolite profiling. Different mass spectrometric instruments and commercially available software tools were investigated for profiling metabolites in urine and hepatocyte samples. All the instruments tested (triple quadrupole, quadrupole time-of-flight, ion trap) exhibited some good and some bad features in searching for and identifying of expected and non-expected metabolites. Although, current profiling software is helpful, it is still insufficient. Thus a time-consuming largely manual approach is still required for metabolite profiling from complex biological matrices.

Quality Assessment of a Forest Inventory Based on Airborne Laser Scanning

In this study, a quality assessment method based on sampling of primary laser inventory units (microsegments) was analysed. The accuracy of a laser inventory carried out in Kuhmo was analysed as a case study. Field sample plots were measured on the sampled microsegments in the Kuhmo inventory area. Two main questions were considered. Did the ALS based inventory meet the accuracy requirements set for the provider and how should a reliable, cost-efficient and independent quality assessment be undertaken. The agreement between control measurement and ALS based inventory was analysed in four ways: 1) The root mean squared errors (RMSEs) and bias were calculated. 2) Scatter plots with 95% confidence intervals were plotted and the placing of identity lines was checked. 3) Bland-Altman plots were drawn so that the mean difference of attributes between the control method and ALS-method was calculated and plotted against average value of attributes. 4) The tolerance limits were defined and combined with Bland-Altman plots. The RMSE values were compared to a reference study from which the accuracy requirements had been set to the service provider. The accuracy requirements in Kuhmo were achieved, however comparison of RMSE values proved to be difficult. Field control measurements are costly and time-consuming, but they are considered to be robust. However, control measurements might include errors, which are difficult to take into account. Using the Bland-Altman plots none of the compared methods are considered to be completely exact, so this offers a fair way to interpret results of assessment. The tolerance limits to be set on order combined with Bland-Altman plots were suggested to be taken in practise. In addition, bias should be calculated for total area. Some other approaches for quality control were briefly examined. No method was found to fulfil all the required demands of statistical reliability, cost-efficiency, time efficiency, simplicity and speed of implementation. Some benefits and shortcomings of the studied methods were discussed.

Microbial life and deposits in paper machine circuits

Väitöskirjani käsittele mikrobien ja erilaisten kemikaalien rooleja saostumien ja biofilmien muodostumisessa paperi- ja kartonkikoneilla. "Saostuma" tässä työssä tarkoittaa kiinteän aineen kertymää konepinnoille tai rajapinnoille konekierroissa, jotka on tarkoitettu massasulppujen, lietteiden, vesien tai ilman kuljetukseen. Saostumasta tulee "biofilmi" silloin kun sen oleellinen rakennekomponentti on mikrobisolut tai niiden tuotteet. Väitöstyöni työhypoteesina oli, että i. tietämys saostumien koostumuksesta, sekä ii. niiden rakenteesta, biologisista, fysikaalis-kemiallisista ja teknisistä ominaisuuksista ohjaavat tutkijaa löytämään ympäristöä säästäviä keinoja estää epätoivottujen saostumien muodostus tai purkaa jo muodostuneita saostumia. Selvittääkseni saostumien koostumista ja rakennetta käytin monia erilaisia analytiikan työkaluja, kuten elektronimikroskopiaa, konfokaali-laser mikroskopiaa (CLSM), energiadispersiivistä röntgenanalyysiä (EDX), pyrolyysi kaasukromatografiaa yhdistettynä massaspektrometriaan (Py-GCMS), joninvaihtokromatografiaa, kaasukromatografiaa ja mikrobiologisia analyysejä. Osallistuin aktiivisesti innovatiivisen, valon takaisinsirontaan perustuvan sensorin kehittämistyöhön, käytettäväksi biofilmin kasvun mittaukseen suoraan koneen vesikierroista ja säiliöistä. Työni osoitti, että monet paperinvalmistuksessa käytetyistä kemikaaleista reagoivat keskenään tuottaen orgaanisia tahmakerroksia konekiertojen teräspinnoille. Löysin myös kerrostumia, jotka valomikroskooppisessa tarkastelussa oli tulkittu mikrobeiksi, mutta jotka elektronimikroskopia paljasti alunasta syntyneiksi, alumiinihydroksidiksi joka saostui pH:ssa 6,8 kiertokuitua käyttävän koneen viiravesistä. Monet paperintekijät käyttävät vieläkin alunaa kiinnitysaineena vaikka prosessiolot ovat muuttuneet happamista neutraaleiksi. Sitä pidetään paperitekijän "aspiriinina", mutta väitöstutkimukseni osoitti sen riskit. Löysin myös orgaanisia saostumia, joiden alkuperä oli aineiden, kuten pihkan, saippuoituminen (kalsium saippuat) niin että muodostui tahmankasvua ylläpitävä alusta monilla paperi- ja kartonkikoneilla. Näin solumuodoiltaan Deinococcus geothermalista muistuttavia bakteereita kasvamassa lujasti teräskoepalojen pintaan kiinnittyneinä pesäkkeinä, kun koepaloja upotettiin paperikoneiden vesikiertoihin. Nämä deinokokkimaiset pesäkkeet voivat toimia jalustana, tarttumisalustana muiden mikrobien massoille, joka selittäisi miksi saostumat yleisesti sisältävät deinokokkeja pienenä, muttei koskaan pääasiallisena rakenneosana. Kun paperikoneiden käyttämien vesien (raakavedet, lämminvesi, biologisesti puhdistettu jätevesi) laatua tutkitaan, mittausmenetelmällä on suuri merkitys. Koepalan upotusmenetelmällä todettu biofilmikasvu ja viljelmenetelmällä mitattu bakteerisaastuneisuus korreloivat toisiinsa huonosti etenkin silloin kun likaantumisessa oli mukana rihmamaiseti kasvavia bakteereja. Huoli ympäristöstä on pakottanut paperi- ja kartonkikoneiden vesikiertojen sulkemiseen. Vesien kierrätys ja prosessivesien uudelleenkäyttö nostavat prosessilämpötilaa ja lisäävät koneella kiertävien kolloidisten ja liuenneiden aineiden määriä. Tutkin kiertovesien pitoisuuksia kolmessa eriasteisesti suljetussa tehtaassa, joiden päästöt olivat 0 m3, 0,5 m3 ja 4 m3 jätevettä tuotetonnia kohden, perustuen puhdistetun jäteveden uudelleen käyttöön. Nollapäästöisellä tehtaalla kiertovesiin kertyi paljon orgaanisesti sidottua hiiltä (> 10 g L-1), etenkin haihtuvina happoina (maito-, etikka-, propioni- ja voi-). Myös sulfaatteja, klorideja, natriumia ja kalsiumia kertyi paljon, > 1 g L-1 kutakin. Pääosa (>40%) kaikista bakteereista oli 16S rRNA geenisekvenssianalyysien tulosten perusteella sukua, joskin etäistä (< 96%) ainoastaan Enterococcus cecorum bakteerille. 4 m3 päästävältä tehtaalta löytyi lisäksi Bacillus thermoamylovorans ja Bacillus coagulans. Tehtaiden saostumat sisälsivät arkkeja suurina pitoisuuksina, ≥ 108 g-1, mutta tunnistukseen riittävää sekvenssisamanlaisuutta löytyi vain yhteen arkkisukuun, Methanothrix. Tutkimustulokset osoittivat että tehtaan vesikiertojen sulkeminen vähensi rajusti mikrobiston monimuotoisuutta, muttei estänyt liuenneen aineen ja kiintoaineen mineralisoitumista.

Multiangular Spectrometry and Optical Properties of Debris Covered Surfaces

Due to the recent development in CCD technology aerial photography is now slowly changing from film to digital cameras. This new aspect in remote sensing allows and requires also new automated analysis methods. Basic research on reflectance properties of natural targets is needed so that computerized processes could be fully utilized. For this reason an instrument was developed at Finnish Geodetic Institute for measurement of multiangular reflectance of small remote sensing targets e.g. forest understorey or asphalt. Finnish Geodetic Institute Field Goniospectrometer (FiGIFiGo) is a portable device that is operated by 1 or 2 persons. It can be reassembled to a new location in 15 minutes and after that a target's multiangular reflectance can be measured in 10 - 30 minutes (with one illumination angle). FiGIFiGo has effective spectral range approximately from 400 nm to 2000 nm. The measurements can be made either outside with sunlight or in laboratory with 1000 W QTH light source. In this thesis FiGIFiGo is introduced and the theoretical basis of such reflectance measurements are discussed. A new method is introduced for extraction of subcomponent proportions from reflectance of a mixture sample, e.g. for retrieving proportion of lingonberry's reflectance in observation of lingonberry-lichen sample. This method was tested by conducting a series of measurements on reflectance properties of artificial samples. The component separation method yielded sound results and brought up interesting aspects in targets' reflectances. The method and the results still need to be verified with further studies, but the preliminary results imply that this method could be a valuable tool in analysis of such mixture samples.

Cavity-enhanced laser spectroscopic studies of vibrational overtones of acetylene

This thesis contains five experimental spectroscopic studies that probe the vibration-rotation energy level structure of acetylene and some of its isotopologues. The emphasis is on the development of laser spectroscopic methods for high-resolution molecular spectroscopy. Three of the experiments use cavity ringdown spectroscopy. One is a standard setup that employs a non-frequency stabilised continuous wave laser as a source. In the other two experiments, the same laser is actively frequency stabilised to the ringdown cavity. This development allows for increased repetition rate of the experimental signal and thus the spectroscopic sensitivity of the method is improved. These setups are applied to the recording of several vibration-rotation overtone bands of both H(12)C(12)CH and H(13)C(13)CH. An intra-cavity laser absorption spectroscopy setup that uses a commercial continuous wave ring laser and a Fourier transform interferometer is presented. The configuration of the laser is found to be sub-optimal for high-sensitivity work but the spectroscopic results are good and show the viability of this type of approach. Several ro-vibrational bands of carbon-13 substituted acetylenes are recorded and analysed. Compared with earlier work, the signal-to-noise ratio of a laser-induced dispersed infrared fluorescence experiment is enhanced by more than one order of magnitude by exploiting the geometric characteristics of the setup. The higher sensitivity of the spectrometer leads to the observation of two new symmetric vibrational states of H(12)C(12)CH. The precision of the spectroscopic parameters of some previously published symmetric states is also improved. An interesting collisional energy transfer process is observed for the excited vibrational states and this phenomenon is explained by a simple step-down model.