【正文】 ml, 1 FBG is the amount of enzyme required under the standard condition (30℃, pH , reaction time 30 min) to degrade barley b glucan to reducing carbohydrates with a reduction power corresponding to 1 mmol glucose/min. All the other reagents were of analytical grade.. Defatting of oat branOat bran was defatted by intermittent shaking with hexane at a 1:3 (v/w) brantosolvent ratio for 1 h at room temperature. The slurry was filtered, the solids washed on a Buchner funnel with hexane and airdried. The moisture content on a wet basis was, approximately, 10 g/100 g in defatted oat bran (DOB). The weight of DOB was calculated on a dry basis in the following studies. Enzymatic pretreatmentTo each 10 g of DOB sample, 100 ml of deionized water was added to obtain homogeneous slurry. After the pH of the slurries was adjusted to the presetted values (–), viscozyme L was added. The slurries containing enzymes were incubated in a water bath thermostatic vibrator (HZSH Model, Donglian Electronic and Technology Development Co., China) at 200 rpm for the desired period of time and temperature (35–55℃). The details of the independent variables used are presented in Tables 1 and 2. . Protein extractionSubsequent to the enzymatic pretreatment, the slurries were immediately adjusted to pH with 2 mol/L NaOH, and further incubated for 30 min at 50 ℃. The resultant suspensions were centrifuged at 4000g for 30 min, and the supernatants were used for protein determination. . Determination of protein content The protein contents of oat bran, enzyme, and supernatants were determined by the Kjeldahl analysis using a nitrogen to protein conversion factor of . The extracted proteins were expressed as follows:. Experimental design A five level, four variable central posite rotatable design (CCRD) (Cochran amp。 Cox, 1992) with 31 individual design points was employed to determine the best bination of enzymatic pretreatment variables for protein extraction in this study. The choice of variables and their levels was based on the preliminary experiments (data not shown). The variables Xi were coded as xi according to the following Eq. (1): xi=(XiX0)/△Xiwhere xi is the coded value of an independent variable, Xi is the real value of an independent variable, X0 is the real value of an independent variable at the center point, and △Xi is the step change value. The independent variables and their levels, with both real values and coded values investigated in this study, are presented in Table 1. Each experiment was replicated twice and the average of protein extracted was taken as the response, Y.. Statistical analysisThe Response Surface Regression (RSREG) Procedure of Statistical Analysis System (SAS )was used to fit the experimental data to the second order polynomial equation to obtain coefficients of the Eq. (2).where Y is the response variable, xi and xj are the coded independent variable。 and β0, βi, βii and βij are the regression coefficients of variables for intercept, linear, quadratic and interaction regression terms, respectively. The quality of the fit of the second order polynomial equation was expressed by the multiple coefficient of determination, R2, and its significance was tested by an Ftest at a probability ( p) of . The significance of each coefficient was tested using the Student ttest and p value.. Optimization by PSO algorithmsThe standard Particle Swarm Optimization and Quantumbehaved Particle Swarm Optimization were employed to optimize the enzymatic pretreatment conditions. The methods were programmed in MATLAB (The Math Works Inc., 2000).. Standard particle swarm optimizationStandard Particle Swarm Optimization (SPSO) (Kennedy amp。 Eberhart, 1995) is a populationbased evolutionary optimization method, inspired by the collective behaviors of birds and flocks. Through cooperation and petition among the population, populationbased optimization approaches often can find very good solutions efficiently and effectively. In the SPSO model, each particle flies in a Ddimensional space S according to its own historical experience and that of other particles. The velocity and location for the ith particle is represented as and search process of the particles is according to the Eqs. (3) and (4):where xid is the dth dimension location for ith particle, also vid is the dth dimension velocity for ith particle, c1 and c2 are acceleration constants。 rand() are random values between 0 and 1。 the vector pi is the best position giving the best fitness value of the particle i。 the vector pg is the position of the best particle among all the particles in the population。 and w is the inertia weight (Shi amp。 Eberhart, 1999) to balance the global and local search ability. The position of particle is updated using its velocity vector as shown in Eq. (4). Clerc and Kennedy (2002) further analyzed the trajectory and proved that, whichever model is employed in the SPSO algorithm, each particle in the SPSO system converges to its local point p, whose coordinates are so that the best previous position of all particles will converge to an exclusive global position at t→∞, where φ1, φ2 are random numbers distributed uniformly on [0,1]. The basic flowchart of SPSO algorithm can be described as Fig. 1.. Quantumbehaved particle swarm optimization Quantumbehaved Particle Swarm Optimization (QPSO) has been proposed, which introduced quantum theory into SPSO (Sun, Feng, amp。 Xu, 2004). In the quantum model of a PSO, the state of a particle is depicted by wave function,instead of position and velocity .The dynamic behavior of the particle is widely divergent from that of the particle in traditional SPSO systems in that the exact values of position and velocity cannot be determined simultaneously. The probability of the particle39。s appearing in position from probability density function ,the form of which depends on the potentia