Enzyme Treatment Time Research Articles

Investigating the physicochemical properties and air-water interface adsorption behavior of transglutaminase-crosslinking rapeseed protein isolate

Improving the technical functionality to adapt to the application of complex food systems is an important challenge for the development of plant protein ingredients. Herein, the correlation between the physicochemical properties and interfacial adsorption behavior of rapeseed protein isolate (RPI) at the air–water interface after transglutaminase (TG) treatment was investigated. The results of cross-linking degree, Fourier transform infrared spectroscopy (FTIR) and sodium dodecyl sulphate–polyacrylamide gel electrophoresis (SDS-PAGE) showed that the TG enzyme was able to catalyse cross-linking between lysine and glutamine residues of RPI. The foaming capacity of RPI was enhanced from 120 % to 150 % after TG cross-linking 5 h, whereas the average size (210–219 nm) of the RPI determined by dynamic light scattering did not change significantly. Besides, the hydrophobicity tended to increase overall under the enzyme treatment, while the surface electrostatic potential decreased. The former indicates the unfolding of the protein and reduces the kinetic barriers to protein adsorption at the air–water interface, with a consequent increase in disulfide bonding and surface pressure. Furthermore, as the enzyme treatment time increased, a significant increase in protein content of foam by 33.86 %. These findings provide novel insight into the foaming mechanism of TG cross-linking RPI.

Nutritional composition of Cassava (Manihot esculenta) and its application to elder-friendly food based on enzyme treatment

ABSTRACT Cassava (Manihotesculenta) is known as one of the most nutritious root vegetables, but the texture is relatively hard and tough for the elderly, making it difficult to eat. So, this study attempted to identify the nutritional properties of Cassava and the change in texture according to enzyme treatment to confirm the possibility of using Cassava as anelder-friendly food suitable for the Korean Industrial Standard (KS).To this, the nutritional composition and physiological activity wereanalyzed, and the effect of enzymes (cellulase, polygalacturonase,and α-amylase) on the texture properties of Cassavas was studied. Asa result, Cassava contained various bioactive nutrients such asminerals, essential fatty acids, antioxidants, and anti-diabetessubstances. In all experimental groups, hardness was significantly decreased as the enzyme treatment time increased. Based on KS, when Cassava was treated with cellulase + α-amylase for 3.07 h, α-amylase + polygalacturonase for 3.69 h, and polygalacturonase + cellulase for 4.06 h or more, it showed soft hardness that could be chewed with theelderly's tongue. In addition, it was observed that the microstructure changed as the shape of the tissue was deformed, arrangement became irregular, and size and number of pores increased. In conclusion, root vegetables such as Cassava can be softened tosuit KS using enzymes to promote consumption of elderly consumers andhelp balance nutrition. In addition, considering that Korea isentering a super-aged society, it is thought that this study canprovide positive help to the development of the elder-friendly food industry.

장마 영여자 효소․주정 복합처리 추출물의 이화학적 특성 및 생리활성

The present study was performed to investigate the physicochemical properties and biological activity of extract from Dioscorea polystachya Turcz. bulbil (DPB), registered as novel food ingredients, via a combination treatment using enzyme and ethanol. The results indicated an increase in the degree of starch hydrolysis with an increase in the enzyme treatment time. Furthermore, the treatment time exerted a significant effect on the marked increase in browning index (BI), content of total soluble solids (TSS), and useful component content (p<0.001). The contents of total polyphenols (TP), total flavonoids, and crude saponin (CS) also increased with an increase in the enzyme treatment time (p<0.001). It was determined that enzyme treatment for more than 4 h was unnecessary. The increase in α-glucosidase inhibitory activity was affected by the presence of TP and CS during enzyme treatment. It was concluded that enzyme treatment was effective for a minimum of 30 min and a maximum of 4 h. The present work demonstrated the optimization of the useful and functional components of DPB via a complex treatment using enzyme and ethanol. These profiles provide valuable data in the selection and application of DPB for the development of functional food materials.

Enzyme-Assisted Ultrasonic Extraction of Total Flavonoids from Acanthopanax senticosus and Their Enrichment and Antioxidant Properties

Flavonoids are one of the important active ingredients from Acanthopanax senticosus, with a variety of biological functions, such as antioxidant and antibacterial properties. The aim of this work was to investigate enzyme-assisted ultrasonic extraction of A. senticosus flavonoids and their enrichment and antioxidant properties. We found that the optimal extraction process after Box–Behnken response surface optimization had the following parameters: a 3:2 ratio of cellulase to pectinase, enzyme mixture amount of 6960 U g−1, enzyme treatment time of 59.80 min; temperature of 53.70 °C, and pH value of 6.05. The yield of total flavonoids reached 36.95 ± 0.05 mg g−1. The results for different polar solvent enrichments showed that the highest flavonoid (61.0 ± 0.344 mg g−1), polyphenol (24.93 ± 0.234 mg g−1), and saponin (17.80 ± 0.586 mg g−1) contents were observed in the 1-butanol fraction, and the highest polysaccharide content (20.04 ± 0.783 mg g−1) was in the water fraction. Pearson correlation analysis revealed that the antioxidant potential of the extract was related to the higher amount of flavonoids and phenolics in the extract. We thus found an effective A. senticosus flavonoid extraction and enrichment procedure, which can serve as a reference method.

Understanding the evolution of cellulose fibers during enzyme treatment

Enzyme treatment is a potential strategy for producing cellulose fibrils but its evolution of the mesoscopic and microcosmic structures is not fully understood. In this work, the effect of the properties and microstructures of cellulose bleached hardwood kraft pulp (BHKP) subjected to different enzyme treatment times (0−10 h) on further fibrillation was explored by Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction (XRD). The results showed that the enzyme treatment did not change the crystal structure of cellulose but destroyed the intermolecular and intramolecular hydrogen bonds, leading to the increase of the crystal index and size. A thorough investigation on the relation between treatment and evolution of inter-/intra-molecular H-bonds in cellulose including content and cleave sequence of H-bonds was conducted by FTIR peak fitting, second derivative analysis and generalized two-dimensional correlation spectroscopy (2DCOS). Compared to intramolecular H-bonds, the intermolecular H-bonds was first broken with a significant decrease in content. In addition, enzyme treatment could promote the peeling of fibrils, and various properties such as yield, water retention value, aspect ratio, and degree of polymerization, etc. were gradually reduced over time relative to the original material, these discoveries provide a theoretical support to a more effective treatment method for the commercial production of cellulose fibrils.

Transcriptome analysis of gene expression changes upon enzymatic dissociation in skeletal myoblasts.

Single-cell RNA-sequencing analysis is one of the most effective tools for understanding specific cellular states. The use of single cells or pooled cells in RNA-seq analysis requires the isolation of cells from a tissue or culture. Although trypsin or more recently cold-active protease (CAP) has been used for cell dissociation, the extent to which the gene expression changes are suppressed has not been clarified. To this end, we conducted detailed profiling of the enzyme-dependent gene expression changes in mouse skeletal muscle progenitor cells, focusing on the enzyme treatment time, amount and temperature. We found that the genes whose expression was changed by the enzyme treatment could be classified in a time-dependent manner and that there were genes whose expression was changed independently of the enzyme treatment time, amount and temperature. This study will be useful as reference data for genes that should be excluded or considered for RNA-seq analysis using enzyme isolation methods.

Structural and physicochemical properties of enzymatically modified rice starch as influenced by the degree of enzyme treatment

The structure and physicochemical properties of rice starch modified with 4-α-glucanotransferase (4αGTase) were compared for different enzyme treatment times (1, 24, and 96 h). Specifically, the gelation properties of native rice starch and 4αGTase-treated rice starch (GS) were analyzed regarding their structural characteristics. The average molecular weight of GS decreased with increasing treatment time, and was 4.73 × 104 g/mol after 96 h of treatment. The chain length distribution was also broadened with the enzyme treatment, as 4αGTase transferred α-glucan from one chain to another. The enzyme treatment also altered the gelation properties and decreased the viscosity of the starch depending on the treatment time, perhaps due to the changes in molecular weight distribution and branched chain length distribution. Moreover, the overall characteristics of GS differed significantly from those of maltodextrin. The physicochemical characteristics of GS with different degrees of 4αGTase treatment suggest that it can be used in the food and pharmaceutical industries.

Faba bean protein in reduced fat/cholesterol mayonnaise: extraction and physico-chemical modification process.

Effect of faba bean enzymatic protein extraction process parameters were investigated at different ultrasound powers (200, 300 and 400W), sonication times (15, 25 and 35min), enzyme dosages (0.15, 0.3 and 0.45%) and enzyme treatment times (15, 25 and 35min). Physico-functional characterization of the protein samples through solubility, zeta potential, color, fat adsorption, emulsifying and foaming capacity measurements suggested faba protein as a promising substituent to egg yolk powder in reduced fat mayonnaise formulation. Reduced-fat mayonnaise formulation containing different faba protein/egg yolk powder ratios were prepared and characterized through rheological analyses as well as emulsion stability, texture, color and microstructural evaluations. The formulations containing equal compositions of faba bean protein and egg yolk powder (0.375%) and also the one with 0.5% faba bean protein and 0.25% egg yolk powder were finally suggested to substitute the conventional formulation.

Combustion behaviour and chemical structure changes of enzyme-treated coal

As one of the technologies for the improvement in coal quality, biological enzyme technology has received much attention. The enzyme product named 3EC was shown to enhance the power plant performance in our previous full-scale test. In this work, its effect on coal was explored. The results indicated that the enzyme product was beneficial in the removal of organic sulphur from coal, and the catalytic action of 3EC on the cleavage of C–C and C–S bonds was proven based on data from the dibenzothiophene decomposition test. Thus, when it was used to treat coal, the CH3-to-CH2 ratio changed from 0.81 to 0.32 with an increase in treatment time, which indicated that some chemical structures in the enzyme-treated coal changed. Because of these structural changes, the combustion behaviour of coal improved, indicated by the increase in the comprehensive combustion index from 2.958 × 106 to 3.113 × 106 %2 min−2 K−3 and the decrease in activation energy from 32.76 to 30.43 kJ mol−1. In addition, the optimum enzyme treatment time should be 4 days to ensure enough reaction time between the enzyme and the coal.

Biotechnological Preparation of Gelatines from Chicken Feet.

In the European Union (EU), about five tons of poultry by-product tissues are produced every year. Due to their high collagen content, they represent a significant raw material source for gelatine production. The aim of the paper was the biotechnological preparation of gelatine from chicken feet. The influence of selected process factors on the gelatine yield, gel strength, viscosity, and ash of gelatine was observed; a two-level factor design of experiments with three variable process factors (enzyme addition, enzyme treatment time, and gelatine extraction time) was applied. After grinding and separating soluble proteins and fat, the purified raw material was treated in water at pH 7.5 with the addition of endoprotease at 23 °C and after thorough washing with water at 80 °C, gelatine was extracted. By the suitable choice of process conditions, gelatine with high gel strength (220–320 bloom), low ash content (<2.0%) and viscosity of 3.5–7.3 mPa·s can be prepared. The extraction efficiency was 18–38%. The presented technology is innovative mainly by the enzymatic processing of the source raw material, which is economically, technologically, and environmentally beneficial for manufacturers. Chicken gelatines are a suitable alternative to gelatines made from mammals or fish, and can be used in many food, pharmaceutical, and biomedical applications.

Structural and functional modifications of kudzu starch modified by branching enzyme

ABSTRACTKudzu starch has been used as a natural healthy food worldwide. Low solubility, poor water dispensability, high paste viscosity and low fluidity limit its wholesome utility. In order to improve its processing properties and applicability, kudzu starch has been modified using a branching enzyme (BE) from Rhodothermus obamensis and in combination with maltogenic amylase (MA) from Bacillus stearothermophilus. The results indicated that amylose content and molecular weight decreased with enzyme treatment but the proportion of short chains and branch density increased. The natural A-starch type crystalline structure changes to V-type but with decreased crystallinity. The storage modulus and loss modulus depended on the enzyme treatment time. Overall, enzymatic modification results in starch fractions with increased solubility and paste transparency, reduced gelatinization temperature, gelatinization enthalpy, and viscosity. The outcome opens up new opportunities to develop more palatable and marketable products based on kudzu starch.

The effect of cellulase, microwave and ultrasonic methods on crude polysaccharides extraction from the spore of Vietnamese lingzhi (Ganoderma lucidum)

Ganoderma lucidum known as reishi in Japanese and lingzhi in Chinese, are commonly used in Vietnam with excellent beneficial health effects. Polysaccharides are usually considered as their main active components. In this study, the polysaccharides from the spore of Vietnamese lingzhi, collected from the south of Vietnam, were analyzed and compared based on monitoring the absorbance of the samples in 490 nm, as well as enzymatic, microwave and ultrasonic methods with different surveyed parameters, such as: concentration of cellulase, microwave frequencies, extraction time, extraction temperature, ratio of sample and water. The results showed that the highest crude polysaccharide was extracted when using cellulase in enzymatic method with the following variables for the best adequate extraction conditions: cellulase concentration of 2.3%, enzyme treatment time of 150 min. and treatment temperature of 50°C. The highest amount of extracted polysaccharide was 7,1971% when the complex method was applied with preheating, enzyme use, ultrasonic application and microwave treatment, respectively.

A study on the optimization and characteristics of enzymatic preparation of Artocarpus heterophyllus Lam (Jackfruit) seed resistant starch

Objective: With the development of the Artocarpus heterophyllus Lam (A. heterophyllus) processing industry, A. heterophyllus Lam seed as by-products, usually are cooked to eat or discarded, and no industrial application has yet been discovered in china. It is especially important to study the nutrients of A. heterophyllus Lam seed and to develop and utilize them. A. heterophyllus Lam seeds are rich in starch. At present, there are few reports on the processing of native starch of A. heterophyllus Lam seed and its modification as well as the application. To find the best way to prepare the resistant starch of A. heterophyllus Lam seed and to witness the changes in starch properties before and after the treated starch molecules. Methods: A. heterophyllus Lam seed starch was used as raw material in this paper and was treated by autoclaving and pullulanase debranching to produce resistant starch. Resistant starch content was confirmed by a resistant starch assay kit from Megazyme, Ireland, according to the AOAC 2002.02 standard method recommended by the American Society of Analytical Chemists. Taking resistant starch content as an indicator, the single factor and L9 (34) orthogonal experiment were used to optimize the processing parameters. Electronic scanning microscopy, X-diffraction and Differential scanning calorimetry were used to characterize native starch and treated starch molecules. Results: The optimal preparation process for preparing the resistant starch of A. heterophyllus Lam seed was starch milk concentration with the ratio of 15%, with enzyme15 ASPU/g, and with enzyme treatment time in 24 h, and starch retrograde time in 24 h. The resistant starch content was 25.82%. After being treated, A. heterophyllus Lam seed starch became a sheet with a large number of micropore. Crystal of starch changed from A type to B+V type, and the gelatinization temperature range became wider and gelatinization enthalpy value became decreaser. Conclusions: Resistant starch content of A. heterophyllus Lam seed starch was greatly improved after being treated. High resistant starch content of the treated starch indicates that it can be used as one of the carbohydrate components in diabetic foods to control blood sugar. The porous structure of the treated A. heterophyllus Lam seed starch indicates that it can be used for advanced controlled release of bioactive extracts.

Physicochemical properties of enzyme-treated waxy rice flour and expansion properties of Gangjung (a traditional Korean oil-puffed rice snack).

Long steeping process of waxy rice involved in Gangjung production is essential for obtaining good quality Gangjung, but it causes many related problems. The objective was to examine physiochemical properties of waxy rice flour and expansion properties of Gangjung manufactured using waxy rice flour treated with protease (P-flour), α-amylase (A-flour), or in combination of the two (PA-flour) over different durations. While crude protein and reducing sugar contents of P-flour and Aflour differed depending on enzyme treatment time, it was not observed for PA-flour. Gangjung made with P-flour or A-flour could show similar expansion rate to that of Gangjung made with waxy rice flour steeped under the optimal condition, however, Gangjung made with PA-flour showed lower expansion rate than of the optimal one. These findings indicate that treatment of waxy rice flour with either protease or α-amylase, but not both, could reduce the steeping time involved in Gangjung production.

Reduction of major peanut allergens Ara h 1 and Ara h 2, in roasted peanuts by ultrasound assisted enzymatic treatment

This study investigated the effects of ultrasound, enzyme concentration and enzyme treatment time on soluble protein and major allergenic proteins (Ara h 1 and Ara h 2) of roasted peanut kernels. A 3-factor, five-level orthogonal experimental design was implemented with various ultrasonication times, concentrations of trypsin or α-chymotrypsin and treatment times. The total soluble proteins were determined by the Bicinchoninic acid (BCA) method, Ara h 1 and Ara h 2 were evaluated by SDS–PAGE and sandwich ELISA. The IgE-binding of peanut extracts was analysed by a competitive inhibition ELISA. Results indicate that ultrasound treatment, followed by protease digestion of peanuts, significantly increased the solubility of peanut protein and decreased the concentrations of Ara h 1 and Ara h 2. The sequential treatment of peanuts by ultrasonication–trypsin–alpha chymotrypsin, resulted in maximum reductions of Ara h 1/Ara h 2, and lowest IgE-binding. This study provides an approach to significantly reduce allergenic proteins in peanut product.

A feasibility study for evaluation of mechanical properties of articular cartilage with a two-electrode electrical impedance method

BackgroundSince articular cartilage has important mechanical properties such as load-bearing, shock absorption and lubrication for activities in daily life, it is important to evaluate the mechanical properties of repaired cartilage in terms of whether those properties are the same as those of natural cartilage. The purpose of this study was to investigate the effectiveness of an electrical impedance method for quantitatively measuring the mechanical properties of cartilage. MethodsCartilage specimens were harvested from porcine knee joint, and two kinds of enzyme-treated cartilages were prepared to investigate the correlation between mechanical and electrical properties resulting from changes in the structure of the extracellular matrix. Collagenase solution and hyaluronidase solution were used to digest the collagen fibril and proteoglycan, respectively. Electrical impedance measurement, indentation test and biochemical analysis were carried out for the enzyme-treated cartilages. ResultsThe water content increased with enzyme treatment time, and the permeability of the treated cartilages increased with decreasing glycosaminoglycan content for both types of enzyme-treated cartilages. The aggregate modulus and the electrical resistivity for both types of enzyme-treated cartilages decreased with increasing permeability after 12-h treatment. The aggregate modulus and the electrical resistivity for both types of treated cartilages decreased with increasing water content and permeability after 24-h treatment. The electrical resistivity and the aggregate modulus of articular cartilage depended not only on the water content, but also on the permeability, and the electrical resistivity for both types of enzyme-treated cartilages was found to be significantly linearly correlated with the aggregate modulus. ConclusionsThese results showed that the aggregate modulus of articular cartilage can be estimated by measuring its electrical impedance.

Processing Optimization and Physicochemical Characteristics of Collagen from Scales of Yellowfin Tuna (Thunnus albacares)

This study was conducted to investigate the optimal conditions of collagen extraction from scales of yellowfin tuna (Thunnus albacares) using surface response methodology. Four independent variables of NaOH concentration and pretreatment fime in alkali pretreatment and enzyme concentration and treatment time in enzyme hydrolysis were used to predict a model equation for the collagen yield. The determinant coefficient (<TEX>$R^2$</TEX>) for the equation was 0.906. The values of the independent variables for the maximum yield were 0.32 N NaOH, 16.38 h alkali pretreatment time, 0.18% enzyme concentration, and 31.02 h enzyme treatment time. In the physicochemical properties of tuna scale collagen, sodium dodecyl sulfate-polyacrylamide gel electrophoresis of tuna scale collagen showed the same migration distances as that of calf skin collagen. The amide A, I, II, and III regions of tuna scale collagen in Fourier transform infrared measurements were shown in the peaks of 3,414 <TEX>$cm^{-1}$</TEX>, 1,645 <TEX>$cm^{-1}$</TEX>, 1,553 <TEX>$cm^{-1}$</TEX>, and 1,247 <TEX>$cm^{-1}$</TEX>, respectively. The amount of imino acids in tuna scale collagen was 18.97% and the collagen denaturation temperature was <TEX>$33^{\circ}C$</TEX>. The collagen solubility as a function of NaCl concentration decreased to 4% NaCl (w/v) and the collagen solubility as a function of pH was high at pH 2-4 and sharply decreased from pH 4 to pH 7. Viscosity of the collagen solution decreased continuously until <TEX>$30^{\circ}C$</TEX> and this decreasing rate slowed in the temperature range of <TEX>$35-50^{\circ}C$</TEX>.

A Simple Procedure for Mesophyll Protoplast Culture and Plant Regeneration in Brassica oleracea L. and Brassica napus L.

An improved protocol for Brassica protoplast culture and plant regeneration was developed. Isolated protoplasts from four-weeks-old in vitro shoot tip culture of Brassica oleracea var. botrytis cv. Siria F1 and Brassica napus doubled haploid of breeding line OP-1 were cultured at a density of 9.8&amp;ndash;11.2 &amp;times; 10&lt;sup&gt;4 &lt;/sup&gt;protoplasts/ml in darkness at 25&amp;deg;C in a modified medium containing 2% glucose, 0.25 mg/l 2,4-D, 1 mg/l BAP and 1 mg/l NAA. The first divisions of protoplasts were observed on the third day of culture in B. oleracea and on the fourth day in B. napus. The protoplast cultures were diluted with low osmotic medium on 7&lt;sup&gt;th&lt;/sup&gt; and 11&lt;sup&gt;th&lt;/sup&gt; day. The frequency of dividing cells was about 80% in B. oleracea and 50% in B. napus. After one month, the microcalli of approximately 0.5&amp;ndash;1 mm in size were transferred into an induction medium with various combinations of growth regulators. Minimum duration of enzyme treatment time and extended dark period in the initial phase of culture increased the survival rate of protoplasts. Organogenesis started when the calli enlarged in size on an induction medium (1 mg/l NAA, 0.02 mg/l GA&lt;sub&gt;3&lt;/sub&gt;, 1 mg/l 2iP) with 2% sucrose and 0.8% agar. Regeneration frequency of calli was found to be 69&amp;ndash;75% in B. oleracea and 2&amp;ndash;3% in B. napus. Well-developed shoots were transferred for rooting to a half-strength MS medium without growth regulators. More than 100 B. oleracea regenerants were transferred into soil, and they produced normal heads and set seeds. This very simple procedure is efficient and suitable mainly for B. oleracea var. botrytis and represents a background for fusion experiments. &amp;nbsp;

Rheology of protein gels synthesized through a combined enzymatic and heat treatment method

Whey protein gels prepared under acidic conditions (pH<4.6) remain largely unutilized because of their weak and brittle nature in contrast to the favorable elastic gels produced at neutral or basic conditions. However, such usage is important, as low pH food products are desirable due to their shelf stability and less stringent sterilization processes. In this study, we use a two-step process involving enzyme followed by heat treatment to produce whey protein gels at low pH (4.0). Dynamic rheological measurements reveal that the gel elastic modulus and yield stress increase substantially when heat treatment is supplemented with enzyme treatment. Both the elastic modulus and yield stress increase with increasing enzyme concentration or treatment time. In contrast, the dynamic yield strain decreases with enzyme concentration but increases with time of enzyme treatment. These results are explained in terms of the enzyme treatment time affecting the diffusion of the enzyme within the gel. This in turn leads to two types of gel microstructure at short and long enzyme treatment times, with the extent of enzyme diffusion modulating the structure at intermediate times.

Diffusion of Macromolecules in Polymer Solutions and Gels: A Laser Scanning Confocal Microscopy Study

Laser scanning confocal microscopy combined with fluorescence recovery after photobleaching is an effective tool to measure the diffusion coefficients of macromolecules in cross-linked hydrogels and polymer solutions. In this study, the effects of enzyme treatment on the diffusion of macromolecules (FITC-dextran) in guar solutions and titanium-guar hydrogels are examined. Enzyme treatment with β-mannanase, a polymer backbone cleaving enzyme, quickly increases the diffusion coefficient of the probe molecules in both solutions and hydrogels to that in water. Enzyme treatment of guar solutions and hydrogels with α-galactosidase, a side chain cleaving enzyme, displays a unique behavior due to changes in the fine structure of guar. The removal of galactose branches from the mannan backbone of guar creates additional hyperentanglements (i.e., cross-links), which reduce the water holding capacity of guar and induce syneresis. If the depth at which the diffusion coefficient is measured remains constant, a minimum is observed in the diffusion coefficient as α-galactosidase enzyme treatment time increases. At the site of measurement, the sample changes from a homogeneous guar system to a phase-separated polymer-rich hydrogel and finally to a dilute polymer phase as the polymer-rich hydrogel phase precipitates below the site of measurement. The diffusion coefficient in the dilute polymer phase increases to that in water, while the diffusion coefficient in the hydrogel phase continues to decrease to a value of approximately 6 × 10-8 cm2/s.