蛋白质聚集过程动力学建模和实验研究
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摘要
随着检测理论和技术的不断发展，检测的对象已经从传统的检测领域延伸到图像、化学、生物、医药等领域，在生物制药、食品、化工等领域，蛋白质聚集现象是普遍存在的。对它动态的聚集过程进行检测一直是学者们研究的热点之一。对他的研究将对生物药中蛋白质聚集导致药效的降低、是否引起免疫应答、相关的毒理学效应、药的保质期等研究都有着重要的意义。
目前蛋白质的聚集过程主要依赖于经验公式、质量作用定律、相关的数学模型来预测其聚集结果。若能在生产中不断地控制初始条件，加上对中间结果的检测来修正初始条件，这样的闭环控制就能尽最大可能防止蛋白质的聚集。如何控制初始条件？聚集过程中哪个时间点更能有效地来修正初始条件？都要依赖于聚集过程的动力学方程。目前的聚集动力学方程的模型都是假定：1蛋白质是某一形貌，如：球状、杆状等简单的几何形状；2在假定某种形貌的基础上，计算聚集体的尺寸。3聚集过程是个动态的，它包含成核、聚集、生长和解聚行为，在前两个基础上，再对模型参数进行识别，即获得方程的初始条件。这无疑缺少普适性，蛋白质的形貌是复杂的，甚至是变化的。本文采用了分形维来描述和表达聚集体的形貌，而不是假定某一几何形貌，以此建立了新的聚集体动力学模型，这一模型可以同时反映出聚集体的尺寸和分形维两个特征。增加了使用的普适性。同时对模型的初始条件，即模型参数进行了参数估计和辨识。并用仿真和实验进行了验证工作。并给出了较满意的结果。
本文的主要工作可归纳如下：
1.采用分形理论和群体粒子衡算方程(Population Balance Equation,PBE)，提出了描述蛋白质聚集过程的动力学模型，推导了动力学模型的增长函数和成核函数。并通过计算机仿真实现了动态尺寸模拟、动态分形维模拟。该模型可以同时给出蛋白质聚集体的尺寸和分形维两个关键参数的动态尺寸。针对聚集体尺寸和分形维的计算中存在的问题，应用有限元盖拉金法编制了计算机软件求解了动力学方程。
2.在闭环控制中，要不停修正初始条件即模型参数。在模型参数的辨识过程中，提出了一种新的基于K-L信息距离的蛋白质聚集过程模型参数辨识方法。通过优化算法，给出了蛋白质聚集过程的初始条件和实验检测时间点，该方法将指导实验验证工作中的实验设计，并选择了具有普适性意义溶菌酶的聚集实验。
3.将上述方法应用于溶菌酶的聚集过程控制，利用参数辨识给出的初始条件、时间检测点，分别应用激光粒度仪和密度计测定溶菌酶冷却聚集过程中尺寸和浓度变化的一般规律。根据这些变化规律，精确拟合聚集动力学参数的基于尺寸和浓度变化规律。实验证明，采用分形理论和PBE方程提出描述蛋白质聚集过程的仿真动力学模型可以有效预测聚集体形貌及其分布。
4.针对聚集过程中难以测量存在的宏观聚集现象，研究了大尺寸分形维测量问题。以不同稀释条件的添加凝乳酶牛奶溶液为实验材料，提出了一种基于PBE模拟模型的致密聚集体分形维测量新方法，方法在不建立聚集体互相关函数的情况下，测量了蛋白质聚集体大尺寸分形维。
5.建立蛋白质聚集体过程测量系统，该系统验证了论文中所提出的的观点，利用所提出的模型，研究了鸡蛋清溶菌酶间歇冷却聚集过程中，温度条件、pH值条件对聚集过程的影响。实验测量发现溶菌酶在不同温度、pH值条件下，聚集过程差异较大，而提出的模型能很好地预测这一点。进一步研究了聚集体光散射特性和分形特性、聚集体尺寸分布、分形维分布和聚集体粒子数之间的关系，为研究聚集体聚集过程检测仪器奠定了基础。
With the continuous development of detection theory and technology,detection object has extended to image, chemistry, biology, medicine and otherfields from the traditional detection field, protein aggregation phenomenon iswidespread in the field of biological pharmacy, food, chemical and so on. Studyon protein dynamic accumulation process is one of hot topics in the study ofscholars, the research is of great significance for protein accumulation resultingin a loss of efficacy, cause immune response, related toxicological effect, such asthe shelf life of medicine in biological medicine.
The protein aggregation process mainly depends on experience formula, thelaw of mass action, the relevant mathematical model to predict the results. If wecan continuously control initial conditions in the production process, using thetested intermediate results to modify initial conditions, the closed loop controlcan prevent protein concentrations as much as possible. How to control the initialcondition and which time points in the process of aggregation is more effective tomodify initial conditions, depends on dynamic equation of the accumulationprocess. At present, the models of accumulation dynamics equation are allassumed:1protein belongs to a particular morphology, such as spherical, rodsand other simple geometric shapes;2On the basis of assumption that certainmorphology, calculate the size of aggregate particles;3Accumulation is adynamic process and it includes nucleation, aggregation, growth anddepolymerization behavior, on the basis of the former two behaviors,identification of model parameters, obtain the initial conditions of equation, itcan be seen that this method is lack of universality, because of the topography ofprotein is complex and changing. In this paper, fractal dimension method is usedto describe and express the aggregation morphology, instead of assuming ageometric shape, in order to establish a new aggregate dynamic model. Thismodel can reflect aggregate size and fractal dimensions characteristics at the same time, increase the universality, initial conditions of the model, parameterestimation and identification of model parameters at the same time, simulationand experimental work is used for verify the proposed model and the satisfactoryresult is given.
In this research, the main work can be summarized as follows:
1. Adopt fractal theory and population balance equation (PBE), dynamicmodel is proposed for describe protein aggregation process, the growth functionand kernel function of dynamic model was deduced. The proposed modelaccomplishment dynamic size and dynamic fractal dimension simulation bycomputer simulation. The model can parse the size and fractal dimension ofprotein aggregation at the same time. In view of calculation problems ofaggregate size and fractal dimension, finite element cover Larkin method is usedto compile computer software and the purpose is to solve dynamic equations.
2. In the process of closed loop control, constantly revised initial conditions,that is model parameters. Aim at the identification problem of aggregationdynamic model, a kind of protein aggregation process model parameteridentification method is proposed based on K-L information distance, optimizingthe algorithm, initial conditions and experimental testing point of proteinaggregation process were given, this method can guide the experimental designof experimental verification work and select lysozyme aggregate experiment ofuniversal significance.
3. This method was applied to lysozyme aggregation process control, makeuse of the given initial conditions, time check points by parameter identificationmethod, using a laser granulometer and density gauge measuring general rule ofsize and concentration change during lysozyme cooling gathered process,according to the change rule, precise fitting size and concentration change rulebased on aggregation kinetics parameters. Experiments show that dynamic modelof describe protein aggregation process based on fractal theory and populationbalance equation (PBE) is proposed, the model can effectively predict theaggregation morphology and distribution.
4. Aimed at the Macro aggregation phenomenon in the process ofaggregation is difficult to measured, large size particles fractal dimensionmeasurement problem is studied, with different dilution condition to add rennetin milk solution as the experimental materials, a new dense aggregates fractal dimension measuring method based on PBE simulation model is proposed, in thecase of don't build aggregation cross-correlation function, measuring proteinaggregation large size fractal dimension.
5. Establish a protein aggregation process measurement system, the systemis used to verify the effectiveness of the proposed method in the dissertation, inthe process of hen egg white lysozyme intermittent cooling condition, theinfluence of temperature, pH value and other condition on the accumulationprocess is studied by the proposed model. The results showed that lysozymeaccumulation process difference is bigger under the condition of differenttemperature and pH value, the PBE mathematical model has a good predictionwith accumulation process difference. Systematically studied the relationshipbetween protein aggregation light scattering characteristics and fractal features、aggregation size distribution、 fractal dimension distribution and proteinaggregate particles, the article proposed method laid a foundation for the study ofaggregation process instrumentation.
目前蛋白质的聚集过程主要依赖于经验公式、质量作用定律、相关的数学模型来预测其聚集结果。若能在生产中不断地控制初始条件，加上对中间结果的检测来修正初始条件，这样的闭环控制就能尽最大可能防止蛋白质的聚集。如何控制初始条件？聚集过程中哪个时间点更能有效地来修正初始条件？都要依赖于聚集过程的动力学方程。目前的聚集动力学方程的模型都是假定：1蛋白质是某一形貌，如：球状、杆状等简单的几何形状；2在假定某种形貌的基础上，计算聚集体的尺寸。3聚集过程是个动态的，它包含成核、聚集、生长和解聚行为，在前两个基础上，再对模型参数进行识别，即获得方程的初始条件。这无疑缺少普适性，蛋白质的形貌是复杂的，甚至是变化的。本文采用了分形维来描述和表达聚集体的形貌，而不是假定某一几何形貌，以此建立了新的聚集体动力学模型，这一模型可以同时反映出聚集体的尺寸和分形维两个特征。增加了使用的普适性。同时对模型的初始条件，即模型参数进行了参数估计和辨识。并用仿真和实验进行了验证工作。并给出了较满意的结果。
本文的主要工作可归纳如下：
1.采用分形理论和群体粒子衡算方程(Population Balance Equation,PBE)，提出了描述蛋白质聚集过程的动力学模型，推导了动力学模型的增长函数和成核函数。并通过计算机仿真实现了动态尺寸模拟、动态分形维模拟。该模型可以同时给出蛋白质聚集体的尺寸和分形维两个关键参数的动态尺寸。针对聚集体尺寸和分形维的计算中存在的问题，应用有限元盖拉金法编制了计算机软件求解了动力学方程。
2.在闭环控制中，要不停修正初始条件即模型参数。在模型参数的辨识过程中，提出了一种新的基于K-L信息距离的蛋白质聚集过程模型参数辨识方法。通过优化算法，给出了蛋白质聚集过程的初始条件和实验检测时间点，该方法将指导实验验证工作中的实验设计，并选择了具有普适性意义溶菌酶的聚集实验。
3.将上述方法应用于溶菌酶的聚集过程控制，利用参数辨识给出的初始条件、时间检测点，分别应用激光粒度仪和密度计测定溶菌酶冷却聚集过程中尺寸和浓度变化的一般规律。根据这些变化规律，精确拟合聚集动力学参数的基于尺寸和浓度变化规律。实验证明，采用分形理论和PBE方程提出描述蛋白质聚集过程的仿真动力学模型可以有效预测聚集体形貌及其分布。
4.针对聚集过程中难以测量存在的宏观聚集现象，研究了大尺寸分形维测量问题。以不同稀释条件的添加凝乳酶牛奶溶液为实验材料，提出了一种基于PBE模拟模型的致密聚集体分形维测量新方法，方法在不建立聚集体互相关函数的情况下，测量了蛋白质聚集体大尺寸分形维。
5.建立蛋白质聚集体过程测量系统，该系统验证了论文中所提出的的观点，利用所提出的模型，研究了鸡蛋清溶菌酶间歇冷却聚集过程中，温度条件、pH值条件对聚集过程的影响。实验测量发现溶菌酶在不同温度、pH值条件下，聚集过程差异较大，而提出的模型能很好地预测这一点。进一步研究了聚集体光散射特性和分形特性、聚集体尺寸分布、分形维分布和聚集体粒子数之间的关系，为研究聚集体聚集过程检测仪器奠定了基础。
With the continuous development of detection theory and technology,detection object has extended to image, chemistry, biology, medicine and otherfields from the traditional detection field, protein aggregation phenomenon iswidespread in the field of biological pharmacy, food, chemical and so on. Studyon protein dynamic accumulation process is one of hot topics in the study ofscholars, the research is of great significance for protein accumulation resultingin a loss of efficacy, cause immune response, related toxicological effect, such asthe shelf life of medicine in biological medicine.
The protein aggregation process mainly depends on experience formula, thelaw of mass action, the relevant mathematical model to predict the results. If wecan continuously control initial conditions in the production process, using thetested intermediate results to modify initial conditions, the closed loop controlcan prevent protein concentrations as much as possible. How to control the initialcondition and which time points in the process of aggregation is more effective tomodify initial conditions, depends on dynamic equation of the accumulationprocess. At present, the models of accumulation dynamics equation are allassumed:1protein belongs to a particular morphology, such as spherical, rodsand other simple geometric shapes;2On the basis of assumption that certainmorphology, calculate the size of aggregate particles;3Accumulation is adynamic process and it includes nucleation, aggregation, growth anddepolymerization behavior, on the basis of the former two behaviors,identification of model parameters, obtain the initial conditions of equation, itcan be seen that this method is lack of universality, because of the topography ofprotein is complex and changing. In this paper, fractal dimension method is usedto describe and express the aggregation morphology, instead of assuming ageometric shape, in order to establish a new aggregate dynamic model. Thismodel can reflect aggregate size and fractal dimensions characteristics at the same time, increase the universality, initial conditions of the model, parameterestimation and identification of model parameters at the same time, simulationand experimental work is used for verify the proposed model and the satisfactoryresult is given.
In this research, the main work can be summarized as follows:
1. Adopt fractal theory and population balance equation (PBE), dynamicmodel is proposed for describe protein aggregation process, the growth functionand kernel function of dynamic model was deduced. The proposed modelaccomplishment dynamic size and dynamic fractal dimension simulation bycomputer simulation. The model can parse the size and fractal dimension ofprotein aggregation at the same time. In view of calculation problems ofaggregate size and fractal dimension, finite element cover Larkin method is usedto compile computer software and the purpose is to solve dynamic equations.
2. In the process of closed loop control, constantly revised initial conditions,that is model parameters. Aim at the identification problem of aggregationdynamic model, a kind of protein aggregation process model parameteridentification method is proposed based on K-L information distance, optimizingthe algorithm, initial conditions and experimental testing point of proteinaggregation process were given, this method can guide the experimental designof experimental verification work and select lysozyme aggregate experiment ofuniversal significance.
3. This method was applied to lysozyme aggregation process control, makeuse of the given initial conditions, time check points by parameter identificationmethod, using a laser granulometer and density gauge measuring general rule ofsize and concentration change during lysozyme cooling gathered process,according to the change rule, precise fitting size and concentration change rulebased on aggregation kinetics parameters. Experiments show that dynamic modelof describe protein aggregation process based on fractal theory and populationbalance equation (PBE) is proposed, the model can effectively predict theaggregation morphology and distribution.
4. Aimed at the Macro aggregation phenomenon in the process ofaggregation is difficult to measured, large size particles fractal dimensionmeasurement problem is studied, with different dilution condition to add rennetin milk solution as the experimental materials, a new dense aggregates fractal dimension measuring method based on PBE simulation model is proposed, in thecase of don't build aggregation cross-correlation function, measuring proteinaggregation large size fractal dimension.
5. Establish a protein aggregation process measurement system, the systemis used to verify the effectiveness of the proposed method in the dissertation, inthe process of hen egg white lysozyme intermittent cooling condition, theinfluence of temperature, pH value and other condition on the accumulationprocess is studied by the proposed model. The results showed that lysozymeaccumulation process difference is bigger under the condition of differenttemperature and pH value, the PBE mathematical model has a good predictionwith accumulation process difference. Systematically studied the relationshipbetween protein aggregation light scattering characteristics and fractal features、aggregation size distribution、 fractal dimension distribution and proteinaggregate particles, the article proposed method laid a foundation for the study ofaggregation process instrumentation.
引文
[1]董健.单抗类药物的免疫原性问题及其控制[J].中国执业药师,2012,9(9):15-20.
[2] Sauerborn M, Brinks V, Jiskoot W, et al. Immunological mechanismunderlying the immune response to recombinant human proteintherapeutics[J]. Trends in pharmacological sciences,2010,31(2):53-59.
[3] Barnard J G, Singh S, Randolph T W, et al. Subvisible particle countingprovides a sensitive method of detecting and quantifying aggregation ofmonoclonal antibody caused by freeze‐thawing: Insights into the roles ofparticles in the protein aggregation pathway[J]. Journal of pharmaceuticalsciences,2011,100(2):492-503.
[4] Berkowitz S A, Engen J R, Mazzeo J R, et al. Analytical tools forcharacterizing biopharmaceuticals and the implications for biosimilars[J].Nature Reviews Drug Discovery,2012,11(7):527-540.
[5]张麟,卢滇楠,刘铮.高分子抑制蛋白质聚集的动态Monte Carlo模拟[J].化工学报.2008,58(1):153-154.
[6] Monsellier E, Chiti F. Prevention of amyloid-like aggregation as a drivingforce of protein evolution[J]. EMBO reports,2007,8(8):737-742.
[7] V á zquez‐Rey M, Lang D A. Aggregates in monoclonal antibodymanufacturing processes[J]. Biotechnology and bioengineering,2011,108(7):1494-1508.
[8] Hulse W, Forbes R. A Taylor dispersion analysis method for the sizing oftherapeutic proteins and their aggregates using nanolitre samplequantities[J]. International journal of pharmaceutics,2011,416(1):394-397.
[9] D. A. Weitz, M. Oliveria. Fractal Structures Formed by KineticAggregation of Aqueous Gold Colloids[J]. Physical Review Letters,1983,52(16):1433-1436
[10] Singh S K, Afonina N, Awwad M, et al. An industry perspective on themonitoring of subvisible particles as a quality attribute for proteintherapeutics[J]. Journal of pharmaceutical sciences,2010,99(8):3302-3321.
[11] Rubin J, San Miguel A, Bommarius A S, et al. Correlating AggregationKinetics and Stationary Diffusion in Protein-Sodium Salt SystemsObserved with Dynamic Light Scattering[J]. The Journal of physicalchemistry. B,2010,114(12):4383-4387.
[12] Weiss W F, Young T M, Roberts C J. Principles, approaches, andchallenges for predicting protein aggregation rates and shelf life[J].Journal of pharmaceutical sciences,2009,98(4):1246-1277.
[13] Arakawa T, Ejima D, Li T, et al. The critical role of mobile phasecomposition in size exclusion chromatography of proteinpharmaceuticals[J]. Journal of pharmaceutical sciences,2010,99(4):1674-1692.
[14] Goetz H, Kuschel M, Wulff T, et al. Comparison of selected analyticaltechniques for protein sizing, quantitation and molecular weightdetermination[J]. Journal of biochemical and biophysical methods,2004,60(3):281-293.
[15] Andrews J M, Weiss IV W F, Roberts C J. Nucleation, growth, andactivation energies for seeded and unseeded aggregation of α-chymotrypsinogen A[J]. Biochemistry,2008,47(8):2397-2403.
[16] Rabe M, Verdes D, Seeger S. Surface-induced spreading phenomenon ofprotein clusters[J]. Soft matter,2009,5(5):1039-1047.
[17] Modler A J, Gast K, Lutsch G, et al. Assembly of amyloid protofibrils viacritical oligomers--a novel pathway of amyloid formation[J]. Journal ofmolecular biology,2003,325(1):135.
[18] Gibson T J, Murphy R M. Design of peptidyl compounds that affect β-amyloid aggregation: importance of surface tension and context[J].Biochemistry,2005,44(24):8898-8907.
[19] Andrews J M, Roberts C J. A Lumry-Eyring nucleated polymerizationmodel of protein aggregation kinetics:1. Aggregation with pre-equilibrated unfolding[J]. The Journal of Physical Chemistry B,2007,111(27):7897-7913.
[20] Roberts C J, Das T K, Sahin E. Predicting solution aggregation rates fortherapeutic proteins: Approaches and challenges[J]. International journal ofpharmaceutics,2011,418(2):318-333．
[21] Cohen S I A, Vendruscolo M, Welland M E, et al. Nucleatedpolymerization with secondary pathways. I. Time evolution of theprincipal moments[J]. The Journal of chemical physics,2011,135:065105.
[22]李文涓,李芳,唐燕红等.溶液中金属盐对溶菌酶高级结构的影响[J].化学研究与应用,2009,21(3):423-426.
[23]关婧,李辉,邹志远等.氯化钠促进溶菌酶聚集机制的分子动力学研究[J].东北师大学报(自然科学版),2011,43（3）:117-120.
[24]宋有涛,于东润,徐利楠等.氯化镁促进溶菌酶淀粉样聚集的分子机制研究[J].辽宁大学学报(自然科学版),2012,39(2):97-101.
[25] Stéphane Bénazet, Guy Jacob, Gérard Pèpe. Molecular Modeling inCrystal Engineering for Processing of Energetic Materials [J]. Propellants,Explosives, Pyrotechnics,2003,28（6）:287-295.
[26] Dongxu Zhou, Arturo A. Keller, Bren. Role of morphology in theaggregation kinetics of ZnO nanoparticles[J]. Water Research,2010,44（9）:2548-2556.
[27] Chi E Y, Krishnan S, Randolph T W, et al. Physical stability of proteins inaqueous solution: mechanism and driving forces in nonnative proteinaggregation[J]. Pharmaceutical research,2003,20(9):1325-1336.
[28] J. Baldyga, W. Orciuch, L. A Systematic Evaluation of the Role ofIsomerism and Steric Factors in Determining Crystal Packing andNano/Microcrystal Morphologies [J]. Cryst. Growth Des.,2010：10(6),pp2571–2580.
[29] Nico A. J. M.Sommerdijk. Crystal Design and Crystal Engineering [J].Angew. Chem. Int. Ed.2003,42：3572-3574.
[30]苏军伟,顾兆林.离散相系统群体平衡模型的求解算法[J].中国科学:化学,2010(2):144-160.
[31] M. Kostoglou, A.G. Konstandopoulos. Evolution of aggregate size andfractal dimension during Brownian coagulation [J]. Aerosol Sci.,2001,32:1399-1401.
[32] Puel F.,Fevotte G.,Klein J.P.. Simulation and analysis of industrialcrystallization processes through multidimensional population balanceequations.Partl:a resolution algorithm based on the method of classes [J].Chemical Engineering Science,2003a,58(16):3715-3727..
[33] Fran ois Févotte, Gilles Févotte. A method of characteristics for solvingPopulation Balance Equations (PBE) describing the adsorption ofimpurities during crystallization processes [J]. Chemical EngineeringScience,2010,65(10):3191-3197.
[34] GerstiauerA.,GahnC.,ZhouH., et al. Application of population balances inthe chemical industry current status and future needs [J]. ChemicalEngineering Science,2006,61（1）:205-217.
[35] J. Kumar, c, M. Peglowb, G. Warneckea, et al. A discretized model fortracer population balance equation: Improved accuracy and convergence[J]. Computers&Chemical Engineering,2006,15（8）:1278-1292.
[36] Kumar J, Peglow M, Warnecke G, et al. The cell average technique forsolving multi-dimensional aggregation population balance equations[J].Computers&Chemical Engineering,2008,32(8):1810-1830.
[37] Wan J, Wang X Z, Ma C Y. Particle shape manipulation and optimizationin cooling crystallization involving multiple crystal morphologicalforms[J]. AIChE Journal,2009,55(8):2049-2061.
[38] Jing J. Liu, Cai Y. Ma2，Yang D. Hu, et al. Morphological PopulationBalance Model for Studying the Effects of Seed Loading and CoolingRates on Crystal Size and Shape Distribution in Protein Crystallisation [C].20th European Symposium on Computer Aided Process Engineering,2010,pp:4262-4277.
[39] López‐Fidalgo J, Tommasi C, Trandafir P C. An optimal experimentaldesign criterion for discriminating between non‐normal models[J].Journal of the Royal Statistical Society: Series B (Statistical Methodology),2007,69(2):231-242.
[40] Cheon M, Chang I, Hall C K. Extending the PRIME model for proteinaggregation to all20amino acids[J]. Proteins: Structure, Function, andBioinformatics,2010,78(14):2950-2960.
[41] Lee C C, Walters R H, Murphy R M. Reconsidering the mechanism ofpolyglutamine peptide aggregation[J]. Biochemistry,2007,46(44):12810-12820.
[42] Nagy Z K, Fujiwara M, Woo X Y, et al. Determination of the kineticparameters for the crystallization of paracetamol from water usingmetastable zone width experiments[J]. Industrial&Engineering ChemistryResearch,2008,47(4):1245-1252.
[43] Bernacki J P, Murphy R M. Model discrimination and mechanisticinterpretation of kinetic data in protein aggregation studies[J]. Biophysicaljournal,2009,96(7):2871-2887.
[44] Ucinski D, Bogacka B. T-optimum designs for multiresponse dynamicheteroscedastic models[M] mODa7-Advances in Model-Oriented Designand Analysis. Physica-Verlag HD,2004:191-199.
[45] Jain R, Knorr A L, Bernacki J, et al. Investigation of bacteriophage MS2viral dynamics using model discrimination analysis and the implicationsfor phage therapy[J]. Biotechnology progress,2006,22(6):1650-1658.
[46] Mélykúti B, August E, Papachristodoulou A, et al. Discriminating betweenrival biochemical network models: three approaches to optimal experimentdesign[J]. BMC systems biology,2010,4(1):38.
[47] Phelps E M, Hall C K. Structural transitions and oligomerization alongpolyalanine fibril formation pathways from computer simulations[J].Proteins: Structure, Function, and Bioinformatics,2012,80(6):1582-1597.
[48] Myung J I, Pitt M A. Optimal experimental design for modeldiscrimination[J]. Psychological review,2009,116(3):499.
[49] Balsa-Canto E, Alonso A A, Banga J R. Computational procedures foroptimal experimental design in biological systems[J]. Systems Biology,IET,2008,2(4):163-172.
[50] López‐Fidalgo J, Tommasi C, Trandafir P C. An optimal experimentaldesign criterion for discriminating between non‐normal models[J].Journal of the Royal Statistical Society: Series B (Statistical Methodology),2007,69(2):231-242.
[51] Skanda D, Lebiedz D. A robust optimization approach to experimentaldesign for model discrimination of dynamical systems[J]. MathematicalProgramming,2012:1-29.
[52] Lin M Y, Lindsay H M, Weitz D A, et al. Universality of fractal aggregatesas probed by light scattering[J]. Proceedings of the Royal Society ofLondon. A. Mathematical and Physical Sciences,1989,423(1864):71-87.
[53] Ehrl L, Soos M, Morbidelli M. Dependence of aggregate strength,structure, and light scattering properties on primary particle size underturbulent conditions in stirred tank[J]. Langmuir,2008,24(7):3070-3081.
[54] Schr der J M, Becker A, Wiegand S. Suppression of multiple scatteringfor the critical mixture polystyrene/cyclohexane: Application of the one-beam cross correlation technique[J]. The Journal of chemical physics,2003,118:11307.
[55] Rozé C, Girasole T, Gréhan G, et al. Average crossing parameter andforward scattering ratio values in four-flux model for multiple scatteringmedia[J]. Optics communications,2001,194(4):251-263.
[56] Lattuada M, Ehrl L. Scattering properties of dense clusters of colloidalnanoparticles[J]. The Journal of Physical Chemistry B,2009,113(17):5938-5950.
[57] Buitenhuis J, Dhont J K G, Lekkerkerker H N W. Scattering of light fromcylindrical particles: Coupled dipole method calculations and the range ofvalidity of the Rayleigh-Gans-Debye approximation[J]. Journal of colloidand interface science,1994,162:19-24.
[58] Liu F, Smallwood G J. Radiative properties of numerically generatedfractal soot aggregates: the importance of configuration averaging[J].Journal of heat transfer,2010,132(2).
[59] Botet R, Rannou P, Cabane M. Mean-field approximation of Miescattering by fractal aggregates of identical spheres[J]. Applied optics,1997,36(33):8791-8797.
[60] Ehrl L, Soos M, Lattuada M. Generation and geometrical analysis of denseclusters with variable fractal dimension[J]. The Journal of PhysicalChemistry B,2009,113(31):10587-10599.
[61] Roberts C J, Das T K, Sahin E. Predicting solution aggregation rates fortherapeutic proteins: Approaches and challenges[J]. International journalof pharmaceutics,2011,418(2):318-333．
[62] Li Y, Weiss W F, Roberts C J. Characterization of high‐molecular‐weight nonnative aggregates and aggregation kinetics by size exclusionchromatography with inline multi‐angle laser light scattering[J]. Journalof pharmaceutical sciences,2009,98(11):3997-4016.
[63] Roberts C J, Darrington R T, Whitley M B. Irreversible aggregation ofrecombinant bovine granulocyte‐colony stimulating factor (bG‐CSF)and implications for predicting protein shelf life[J]. Journal ofpharmaceutical sciences,2003,92(5):1095-1111.
[64] Andrews J M, Roberts C J. Non-native aggregation of α-chymotrypsinogen occurs through nucleation and growth with competingnucleus sizes and negative activation energies[J]. Biochemistry,2007,46(25):7558-7571.
[65] Brummitt R K, Nesta D P, Chang L, et al. Nonnative aggregation of anIgG1antibody in acidic conditions: Part1. Unfolding, colloidalinteractions, and formation of high‐molecular‐weight aggregates[J].Journal of pharmaceutical sciences,2011,100(6):2087-2103.
[66] Weiss W F, Hodgdon T K, Kaler E W, et al. Nonnative protein polymers:Structure, morphology, and relation to nucleation and growth[J].Biophysical journal,2007,93(12):4392-4403.
[67] Powers E T, Powers D L. The kinetics of nucleated polymerizations athigh concentrations: amyloid fibril formation near and above the“supercritical concentration”[J]. Biophysical journal,2006,91(1):122-132.
[68] Korevaar P A, George S J, Markvoort A J, et al. Pathway complexity insupramolecular polymerization[J]. Nature,2012,481(7382):492-496.
[69] Morris A.M., Watzky M.A., Agar J.N., Finke R.G. Fitting neurologicalprotein aggregation kinetic data via a2-step, Minimal “Ockham's Razor”model: the Finke-Watzky mechanism of nucleation followed byautocatalytic surface growth. Biochemistry.2008,47:2413–2427.
[70] Chen Y.D., Bjornson K., Redick S.D., Erickson H.P. A rapid fluorescenceassay for FtsZ assembly indicates cooperative assembly with a dimernucleus. Biophys. J.2005,88:505–514.
[71] Morris A M, Watzky M A, Finke R G. Protein aggregation kinetics,mechanism, and curve-fitting: a review of the literature[J]. Biochimica etBiophysica Acta (BBA)-Proteins&Proteomics,2009,1794(3):375-397.
[72] Chi E Y, Kendrick B S, Carpenter J F, et al. Population balance modelingof aggregation kinetics of recombinant human interleukin‐1receptorantagonist[J]. Journal of pharmaceutical sciences,2005,94(12):2735-2748.
[73] Alford J R, Kendrick B S, Carpenter J F, et al. High concentrationformulations of recombinant human interleukin‐1receptor antagonist: II.aggregation kinetics[J]. Journal of pharmaceutical sciences,2008,97(8):3005-3021.
[74] Da Silva B, Dufour P, Sheibat-Othman N, et al. Model predictive controlof free surfactant concentration in emulsion polymerization[C].Proceedings of the17th International Federation of Automatic Control(IFAC) World Congress2008.2008, pp.8375-8380.
[75] Narayan S. Tavare. Industrial Crystallization: Process SimulationAnalysis and Design [M]. New York, Springer.1995.
[76] Witkowski W R, Miller S M, Rawlings J B. Light scattering measurementsto estimate kinetic parameters of crystallization[C].Crystallization as aseparation process, ACS Symposium Series.1990,438:102.
[77] Monnier O, Fevotte G, Hoff C, et al. Model identification of batch coolingcrystallizations through calorimetry and image analysis[J]. Chemicalengineering science,1997,52(7):1125-1139.
[78] Santos G G B, Antonello R T, McKenna T F, et al. Population balanceequations for particle size distributions in semibatch emulsionpolymerizations[J]. Latin American applied research,2006,36(4):269-275.
[79] S.H. Kim, K.S. Woo, B.Y. L., et al. Method of measuring chargedistribution of nanosized aerosols [J]. Journal of Colloid and InterfaceScience.2005,282:46-57.
[80] Gherras Nesrine, Fevotte Gillesa. On the Use of Process AnalyticalTechnologies (PAT) and Population Balance Equations for the Estimationof Crystallization Kinetics. A Case Study [J]. AIChEJournal.2012,58(9):7421-7429.
[81] Toufik Bakir, Sami Othman, Franc ois Puel, et al. Continuous-discreteobserver for crystal size distribution of batch crystallization process [C].Proceedings of the44th IEEE Conference on Decision and Control, andthe European Control Conference，Seville,2005,pp.6240-6244.
[82] Neha B. Raikar, Surita R. Bhatiaa, Michael F. Malone, et al. Self-similarinverse population balance modeling for turbulently prepared batchemulsions: Sensitivity to measurement errors [J]. Chemical EngineeringScienee.2006,61:7421-7435.
[83] Cédric Damour, Michel Benne, Brigitte Grondin-Perez, et al. Modelbased Soft-Sensor for Industrial Crystallization: On-line Mass of Crystalsand Solubility Measurement [C]. World Academy of Science, Engineeringand Technology30，Denver,2009,pp.196-200.
[84] C.SWeeger. Morphology,evolution and other characteristics of gibbsitecrystals grown from pure and impure aqueous sodium aluminatesolutions[J].Jouenal of Crystal Growth,2001,233:567-582
[85] YolotaM,SatoA, Kubota.A. Simple method for evaluating kinetleparameters in non-isothermal batch crystalization[J].Chemical EngineermgScienee.2000,55:717-722.
[86] A.H. Alexopoulos, A.Roussosb, C.Kiparissides. Part V:Dynamic evolutionof the multivariate particle size distribution undergoing combined particlegrowth and aggregation [J]. Chemical Engineermg Scienee.2009,64:3260-3269.
[87] Y. Adachi, K. Aoki. Restructuring of small flocs of polystyrene latex withpolyelectrolyte [J]. Colloids and Surfaces A: Physico-chemical andEngineering Aspects.2009,24:342-344.
[88]陈绮,周明全，耿国华等.基于分形的蛋白质三维空间结构复杂性研究.计算机应用与软件，2008，25（8）：42-43.
[89] Oh C, Sorensen C M. Light scattering study of fractal cluster aggregationnear the free molecular regime[J]. Journal of aerosol science,1997,28(6):937-957.
[90] Elimelech M, Jia X, Gregory J, et al. Particle deposition&aggregation:measurement, modelling and simulation[M]. Butterworth-Heinemann,1998.
[91] M. Soos, J. Sefcik, M. Morbidelli. Investigation of aggregation, breakageand restructuring kinetics of colloidal dispersions in turbulent flows bypopulation balance modelling and static light scattering [J]. Chem. Eng.Sci.,2006,61:2348-2349.
[92] S. di Stasio. Observation of restructuring of nanoparticle soot aggregatesin a diffusion flame by static light scattering [J]. J. Aerosol Sci.，2001，32:509-511.
[93] M. Y. Lin, H. M. Lindsay, D. A. Weitz, et al. Universality in colloidaggregation [J]. Nature,1989,339:360-362.
[94] Rosner D E, Yu S. MC simulation of aerosol aggregation and simultaneousspheroidization[J]. AIChE journal,2001,47(3):545-561.
[95] Kostoglou M, Konstandopoulos A G, Friedlander S K. Bivariatepopulation dynamics simulation of fractal aerosol aggregate coagulationand restructuring[J]. Journal of aerosol science,2006,37(9):1102-1115.
[96] Liu J J, Ma C Y, Hu Y D, et al. Morphological Population Balance Modelsfor the Dynamic Evolution of Particle Shape and Size Distribution inProtein Crystallization[J]. Computer Aided Chemical Engineering,2009,27:1911-1916.
[97] Grimes B A, Dorao C A, Simon S, et al. Analysis of dynamic surfactantmass transfer and its relationship to the transient stabilization ofcoalescing liquid–liquid dispersions[J]. Journal of colloid and interfacescience,2010,348(2):479-490.
[98] Attarakih M M, Drumm C, Bart H J. Solution of the population balanceequation using the sectional quadrature method of moments (SQMOM)[J].Chemical Engineering Science,2009,64(4):742-752.
[99] Silva L, Damian R B, Lage P L C. Implementation and analysis ofnumerical solution of the population balance equation in CFD packages[J].Computers&Chemical Engineering,2008,32(12):2933-2945.
[100] Mesbah A, Kramer H J M, Huesman A E M, et al. A control oriented studyon the numerical solution of the population balance equation forcrystallization processes[J]. Chemical Engineering Science,2009,64(20):4262-4277.
[101] Gu Y T, Liu G R. A meshless local Petrov-Galerkin (MLPG) formulationfor static and free vibration analyses of thin plates[J]. Computer Modelingin Engineering and Sciences,2001,2(4):463-476.
[102] Roussos A I, Alexopoulos A H, Kiparissides C. Part III: Dynamicevolution of the particle size distribution in batch and continuousparticulate processes: A Galerkin on finite elements approach[J]. Chemicalengineering science,2005,60(24):6998-7010.
[103] M tzler C. Thermal microwave radiation: applications for remotesensing[M]. Institution of Engineering and Technology,2006.
[104] G. chliveros, M.A. rodrigues and D.cooper, Modelling Populations ofProkaryotic Cells: the n-Layered mRDG Approximation[C].17thEuropean Simulation Multiconference SCS Europe BVBA,2003.
[105] Trevor Cickovski, Santanu Chatterjee, Jacob Wenger, et al. MDLab: Amolecular dynamics simulation prototyping environment [J]. Journal ofComputational Chemistry,2010,31（7）:1345-1356.
[106]戴国亮,于泳,康琦等.溶菌酶晶体生长前期溶液中聚集体研究[J].化学学报,2004,62(8):757-761.
[107]王翾,于泳,刘玉红.溶菌酶分子聚集状态对蛋白质晶体生长[J].生物物理学报，2010，26（5）：380-388.
[108] Sassi P, Onori G, Giugliarelli A, et al. Conformational changes in theunfolding process of lysozyme in water and ethanol/water solutions[J].Journal of Molecular Liquids,2011,159(1):112-116.
[109] Kurihara K, Miyashita S, Sazaki G, et al. Interferometric study on thecrystal growth of tetragonal lysozyme crystal[J]. Journal of crystal growth,1996,166(1):904-908.
[110] Monaco L A, Rosenberger F. Growth and etching kinetics of tetragonallysozyme[J]. Journal of crystal growth,1993,129(3):465-484.
[111]刘晶晶.蛋白质结晶过程的模拟优化和实验研究[D].中国海洋大学博士学位论文.2010.
[112] Park T Y, Froment G F. Kinetic modeling of the methanol to olefinsprocess.2. Experimental results, model discrimination, and parameterestimation[J]. Industrial&engineering chemistry research,2001,40(20):4187-4196.
[113]夏辉,李富石,陈智全等.低相干动态光散射研究浓悬浮液中布朗运动粒子的扩散特性[J].光学学报,2010(10):3059-3063.
[114] Bohren C F, Huffman D R. Absorption and scattering of light by smallparticles[M]. Wiley-Vch,2008.
[115] Mischenko M I, Travis L D, Lacis A A. Scattering, absorption, andemission of light by small particles[M]. Cambridge university press,2002.
[116] Hagiwara T, Kumagai H, Matsunaga, et al. Analysis of aggregate structurein food protein gels with the concept of fractal[J]. Bioscience,biotechnology, and biochemistry,1997,61(10):1663-1667.
[117] Wei L, Liu H, Chen L, et al. The determination and application of fractaldimension on zinc polysilicate flocculation process[C] Remote Sensing,Environment and Transportation Engineering (RSETE),2011InternationalConference on. IEEE,2011:8639-8642.
[118] Meng Z, Hashmi S M, Elimelech M. Aggregation rate and fractaldimension of fullerene nanoparticles via simultaneous multiangle staticand dynamic light scattering measurement[J]. Journal of Colloid andInterface Science,2013,392:27-33.
[119] Molina-Bolivar J A, Galisteo-Gonzalez F, Hidalgo-Alvarez R. Fractalaggregates induced by antigen-antibody interaction[J]. Langmuir,2001,17(8):2514-2520.
[120] Li X, Leung R P C. Determination of the fractal dimension of microbialflocs from the change in their size distribution after breakage[J].Environmental science&technology,2005,39(8):2731-2735.
[121] Chakraborti R K, Gardner K H, Atkinson J F, et al. Changes in fractaldimension during aggregation[J]. Water Research,2003,37(4):873-883.
[122] Roberts C J, Das T K, Sahin E. Predicting solution aggregation rates fortherapeutic proteins: Approaches and challenges[J]. International journalof pharmaceutics,2011,418(2):318-333.
[123] Mroczka J, Wozniak M, Onofri F R A. Algorithms and methods foranalysis of the optical structure factor of fractal aggregates[J].Metrol.Meas. Syst.,2012,3:459-470.
[124] Lee J. Effect of structure factor on aggregate number concentrationestimated using Rayleigh–Debye–Gans scattering theory[J]. OpticaApplicata,2011,41(3):519-525.
[125]陶风云,张新妙,马润宇.溶菌酶结晶的研究进展[J]. Journal of BeijingUnion University (Natural Sciences),2006,20(3):65.
[126]杨晓飞,马启敏,江翠芸.扩散限制凝聚过程的计算机模拟研究[J].中国海洋大学学报(自然科学版),2007,37：139-142.
[127] Di Stasio S, Konstandopoulos A G, Kostoglou M. Cluster–cluster
aggregation kinetics and primary particle growth of soot nanoparticles in
flame by light scattering and numerical simulations[J]. Journal of colloid
and interface science,2002,247(1):33-46.
[2] Sauerborn M, Brinks V, Jiskoot W, et al. Immunological mechanismunderlying the immune response to recombinant human proteintherapeutics[J]. Trends in pharmacological sciences,2010,31(2):53-59.
[3] Barnard J G, Singh S, Randolph T W, et al. Subvisible particle countingprovides a sensitive method of detecting and quantifying aggregation ofmonoclonal antibody caused by freeze‐thawing: Insights into the roles ofparticles in the protein aggregation pathway[J]. Journal of pharmaceuticalsciences,2011,100(2):492-503.
[4] Berkowitz S A, Engen J R, Mazzeo J R, et al. Analytical tools forcharacterizing biopharmaceuticals and the implications for biosimilars[J].Nature Reviews Drug Discovery,2012,11(7):527-540.
[5]张麟,卢滇楠,刘铮.高分子抑制蛋白质聚集的动态Monte Carlo模拟[J].化工学报.2008,58(1):153-154.
[6] Monsellier E, Chiti F. Prevention of amyloid-like aggregation as a drivingforce of protein evolution[J]. EMBO reports,2007,8(8):737-742.
[7] V á zquez‐Rey M, Lang D A. Aggregates in monoclonal antibodymanufacturing processes[J]. Biotechnology and bioengineering,2011,108(7):1494-1508.
[8] Hulse W, Forbes R. A Taylor dispersion analysis method for the sizing oftherapeutic proteins and their aggregates using nanolitre samplequantities[J]. International journal of pharmaceutics,2011,416(1):394-397.
[9] D. A. Weitz, M. Oliveria. Fractal Structures Formed by KineticAggregation of Aqueous Gold Colloids[J]. Physical Review Letters,1983,52(16):1433-1436
[10] Singh S K, Afonina N, Awwad M, et al. An industry perspective on themonitoring of subvisible particles as a quality attribute for proteintherapeutics[J]. Journal of pharmaceutical sciences,2010,99(8):3302-3321.
[11] Rubin J, San Miguel A, Bommarius A S, et al. Correlating AggregationKinetics and Stationary Diffusion in Protein-Sodium Salt SystemsObserved with Dynamic Light Scattering[J]. The Journal of physicalchemistry. B,2010,114(12):4383-4387.
[12] Weiss W F, Young T M, Roberts C J. Principles, approaches, andchallenges for predicting protein aggregation rates and shelf life[J].Journal of pharmaceutical sciences,2009,98(4):1246-1277.
[13] Arakawa T, Ejima D, Li T, et al. The critical role of mobile phasecomposition in size exclusion chromatography of proteinpharmaceuticals[J]. Journal of pharmaceutical sciences,2010,99(4):1674-1692.
[14] Goetz H, Kuschel M, Wulff T, et al. Comparison of selected analyticaltechniques for protein sizing, quantitation and molecular weightdetermination[J]. Journal of biochemical and biophysical methods,2004,60(3):281-293.
[15] Andrews J M, Weiss IV W F, Roberts C J. Nucleation, growth, andactivation energies for seeded and unseeded aggregation of α-chymotrypsinogen A[J]. Biochemistry,2008,47(8):2397-2403.
[16] Rabe M, Verdes D, Seeger S. Surface-induced spreading phenomenon ofprotein clusters[J]. Soft matter,2009,5(5):1039-1047.
[17] Modler A J, Gast K, Lutsch G, et al. Assembly of amyloid protofibrils viacritical oligomers--a novel pathway of amyloid formation[J]. Journal ofmolecular biology,2003,325(1):135.
[18] Gibson T J, Murphy R M. Design of peptidyl compounds that affect β-amyloid aggregation: importance of surface tension and context[J].Biochemistry,2005,44(24):8898-8907.
[19] Andrews J M, Roberts C J. A Lumry-Eyring nucleated polymerizationmodel of protein aggregation kinetics:1. Aggregation with pre-equilibrated unfolding[J]. The Journal of Physical Chemistry B,2007,111(27):7897-7913.
[20] Roberts C J, Das T K, Sahin E. Predicting solution aggregation rates fortherapeutic proteins: Approaches and challenges[J]. International journal ofpharmaceutics,2011,418(2):318-333．
[21] Cohen S I A, Vendruscolo M, Welland M E, et al. Nucleatedpolymerization with secondary pathways. I. Time evolution of theprincipal moments[J]. The Journal of chemical physics,2011,135:065105.
[22]李文涓,李芳,唐燕红等.溶液中金属盐对溶菌酶高级结构的影响[J].化学研究与应用,2009,21(3):423-426.
[23]关婧,李辉,邹志远等.氯化钠促进溶菌酶聚集机制的分子动力学研究[J].东北师大学报(自然科学版),2011,43（3）:117-120.
[24]宋有涛,于东润,徐利楠等.氯化镁促进溶菌酶淀粉样聚集的分子机制研究[J].辽宁大学学报(自然科学版),2012,39(2):97-101.
[25] Stéphane Bénazet, Guy Jacob, Gérard Pèpe. Molecular Modeling inCrystal Engineering for Processing of Energetic Materials [J]. Propellants,Explosives, Pyrotechnics,2003,28（6）:287-295.
[26] Dongxu Zhou, Arturo A. Keller, Bren. Role of morphology in theaggregation kinetics of ZnO nanoparticles[J]. Water Research,2010,44（9）:2548-2556.
[27] Chi E Y, Krishnan S, Randolph T W, et al. Physical stability of proteins inaqueous solution: mechanism and driving forces in nonnative proteinaggregation[J]. Pharmaceutical research,2003,20(9):1325-1336.
[28] J. Baldyga, W. Orciuch, L. A Systematic Evaluation of the Role ofIsomerism and Steric Factors in Determining Crystal Packing andNano/Microcrystal Morphologies [J]. Cryst. Growth Des.,2010：10(6),pp2571–2580.
[29] Nico A. J. M.Sommerdijk. Crystal Design and Crystal Engineering [J].Angew. Chem. Int. Ed.2003,42：3572-3574.
[30]苏军伟,顾兆林.离散相系统群体平衡模型的求解算法[J].中国科学:化学,2010(2):144-160.
[31] M. Kostoglou, A.G. Konstandopoulos. Evolution of aggregate size andfractal dimension during Brownian coagulation [J]. Aerosol Sci.,2001,32:1399-1401.
[32] Puel F.,Fevotte G.,Klein J.P.. Simulation and analysis of industrialcrystallization processes through multidimensional population balanceequations.Partl:a resolution algorithm based on the method of classes [J].Chemical Engineering Science,2003a,58(16):3715-3727..
[33] Fran ois Févotte, Gilles Févotte. A method of characteristics for solvingPopulation Balance Equations (PBE) describing the adsorption ofimpurities during crystallization processes [J]. Chemical EngineeringScience,2010,65(10):3191-3197.
[34] GerstiauerA.,GahnC.,ZhouH., et al. Application of population balances inthe chemical industry current status and future needs [J]. ChemicalEngineering Science,2006,61（1）:205-217.
[35] J. Kumar, c, M. Peglowb, G. Warneckea, et al. A discretized model fortracer population balance equation: Improved accuracy and convergence[J]. Computers&Chemical Engineering,2006,15（8）:1278-1292.
[36] Kumar J, Peglow M, Warnecke G, et al. The cell average technique forsolving multi-dimensional aggregation population balance equations[J].Computers&Chemical Engineering,2008,32(8):1810-1830.
[37] Wan J, Wang X Z, Ma C Y. Particle shape manipulation and optimizationin cooling crystallization involving multiple crystal morphologicalforms[J]. AIChE Journal,2009,55(8):2049-2061.
[38] Jing J. Liu, Cai Y. Ma2，Yang D. Hu, et al. Morphological PopulationBalance Model for Studying the Effects of Seed Loading and CoolingRates on Crystal Size and Shape Distribution in Protein Crystallisation [C].20th European Symposium on Computer Aided Process Engineering,2010,pp:4262-4277.
[39] López‐Fidalgo J, Tommasi C, Trandafir P C. An optimal experimentaldesign criterion for discriminating between non‐normal models[J].Journal of the Royal Statistical Society: Series B (Statistical Methodology),2007,69(2):231-242.
[40] Cheon M, Chang I, Hall C K. Extending the PRIME model for proteinaggregation to all20amino acids[J]. Proteins: Structure, Function, andBioinformatics,2010,78(14):2950-2960.
[41] Lee C C, Walters R H, Murphy R M. Reconsidering the mechanism ofpolyglutamine peptide aggregation[J]. Biochemistry,2007,46(44):12810-12820.
[42] Nagy Z K, Fujiwara M, Woo X Y, et al. Determination of the kineticparameters for the crystallization of paracetamol from water usingmetastable zone width experiments[J]. Industrial&Engineering ChemistryResearch,2008,47(4):1245-1252.
[43] Bernacki J P, Murphy R M. Model discrimination and mechanisticinterpretation of kinetic data in protein aggregation studies[J]. Biophysicaljournal,2009,96(7):2871-2887.
[44] Ucinski D, Bogacka B. T-optimum designs for multiresponse dynamicheteroscedastic models[M] mODa7-Advances in Model-Oriented Designand Analysis. Physica-Verlag HD,2004:191-199.
[45] Jain R, Knorr A L, Bernacki J, et al. Investigation of bacteriophage MS2viral dynamics using model discrimination analysis and the implicationsfor phage therapy[J]. Biotechnology progress,2006,22(6):1650-1658.
[46] Mélykúti B, August E, Papachristodoulou A, et al. Discriminating betweenrival biochemical network models: three approaches to optimal experimentdesign[J]. BMC systems biology,2010,4(1):38.
[47] Phelps E M, Hall C K. Structural transitions and oligomerization alongpolyalanine fibril formation pathways from computer simulations[J].Proteins: Structure, Function, and Bioinformatics,2012,80(6):1582-1597.
[48] Myung J I, Pitt M A. Optimal experimental design for modeldiscrimination[J]. Psychological review,2009,116(3):499.
[49] Balsa-Canto E, Alonso A A, Banga J R. Computational procedures foroptimal experimental design in biological systems[J]. Systems Biology,IET,2008,2(4):163-172.
[50] López‐Fidalgo J, Tommasi C, Trandafir P C. An optimal experimentaldesign criterion for discriminating between non‐normal models[J].Journal of the Royal Statistical Society: Series B (Statistical Methodology),2007,69(2):231-242.
[51] Skanda D, Lebiedz D. A robust optimization approach to experimentaldesign for model discrimination of dynamical systems[J]. MathematicalProgramming,2012:1-29.
[52] Lin M Y, Lindsay H M, Weitz D A, et al. Universality of fractal aggregatesas probed by light scattering[J]. Proceedings of the Royal Society ofLondon. A. Mathematical and Physical Sciences,1989,423(1864):71-87.
[53] Ehrl L, Soos M, Morbidelli M. Dependence of aggregate strength,structure, and light scattering properties on primary particle size underturbulent conditions in stirred tank[J]. Langmuir,2008,24(7):3070-3081.
[54] Schr der J M, Becker A, Wiegand S. Suppression of multiple scatteringfor the critical mixture polystyrene/cyclohexane: Application of the one-beam cross correlation technique[J]. The Journal of chemical physics,2003,118:11307.
[55] Rozé C, Girasole T, Gréhan G, et al. Average crossing parameter andforward scattering ratio values in four-flux model for multiple scatteringmedia[J]. Optics communications,2001,194(4):251-263.
[56] Lattuada M, Ehrl L. Scattering properties of dense clusters of colloidalnanoparticles[J]. The Journal of Physical Chemistry B,2009,113(17):5938-5950.
[57] Buitenhuis J, Dhont J K G, Lekkerkerker H N W. Scattering of light fromcylindrical particles: Coupled dipole method calculations and the range ofvalidity of the Rayleigh-Gans-Debye approximation[J]. Journal of colloidand interface science,1994,162:19-24.
[58] Liu F, Smallwood G J. Radiative properties of numerically generatedfractal soot aggregates: the importance of configuration averaging[J].Journal of heat transfer,2010,132(2).
[59] Botet R, Rannou P, Cabane M. Mean-field approximation of Miescattering by fractal aggregates of identical spheres[J]. Applied optics,1997,36(33):8791-8797.
[60] Ehrl L, Soos M, Lattuada M. Generation and geometrical analysis of denseclusters with variable fractal dimension[J]. The Journal of PhysicalChemistry B,2009,113(31):10587-10599.
[61] Roberts C J, Das T K, Sahin E. Predicting solution aggregation rates fortherapeutic proteins: Approaches and challenges[J]. International journalof pharmaceutics,2011,418(2):318-333．
[62] Li Y, Weiss W F, Roberts C J. Characterization of high‐molecular‐weight nonnative aggregates and aggregation kinetics by size exclusionchromatography with inline multi‐angle laser light scattering[J]. Journalof pharmaceutical sciences,2009,98(11):3997-4016.
[63] Roberts C J, Darrington R T, Whitley M B. Irreversible aggregation ofrecombinant bovine granulocyte‐colony stimulating factor (bG‐CSF)and implications for predicting protein shelf life[J]. Journal ofpharmaceutical sciences,2003,92(5):1095-1111.
[64] Andrews J M, Roberts C J. Non-native aggregation of α-chymotrypsinogen occurs through nucleation and growth with competingnucleus sizes and negative activation energies[J]. Biochemistry,2007,46(25):7558-7571.
[65] Brummitt R K, Nesta D P, Chang L, et al. Nonnative aggregation of anIgG1antibody in acidic conditions: Part1. Unfolding, colloidalinteractions, and formation of high‐molecular‐weight aggregates[J].Journal of pharmaceutical sciences,2011,100(6):2087-2103.
[66] Weiss W F, Hodgdon T K, Kaler E W, et al. Nonnative protein polymers:Structure, morphology, and relation to nucleation and growth[J].Biophysical journal,2007,93(12):4392-4403.
[67] Powers E T, Powers D L. The kinetics of nucleated polymerizations athigh concentrations: amyloid fibril formation near and above the“supercritical concentration”[J]. Biophysical journal,2006,91(1):122-132.
[68] Korevaar P A, George S J, Markvoort A J, et al. Pathway complexity insupramolecular polymerization[J]. Nature,2012,481(7382):492-496.
[69] Morris A.M., Watzky M.A., Agar J.N., Finke R.G. Fitting neurologicalprotein aggregation kinetic data via a2-step, Minimal “Ockham's Razor”model: the Finke-Watzky mechanism of nucleation followed byautocatalytic surface growth. Biochemistry.2008,47:2413–2427.
[70] Chen Y.D., Bjornson K., Redick S.D., Erickson H.P. A rapid fluorescenceassay for FtsZ assembly indicates cooperative assembly with a dimernucleus. Biophys. J.2005,88:505–514.
[71] Morris A M, Watzky M A, Finke R G. Protein aggregation kinetics,mechanism, and curve-fitting: a review of the literature[J]. Biochimica etBiophysica Acta (BBA)-Proteins&Proteomics,2009,1794(3):375-397.
[72] Chi E Y, Kendrick B S, Carpenter J F, et al. Population balance modelingof aggregation kinetics of recombinant human interleukin‐1receptorantagonist[J]. Journal of pharmaceutical sciences,2005,94(12):2735-2748.
[73] Alford J R, Kendrick B S, Carpenter J F, et al. High concentrationformulations of recombinant human interleukin‐1receptor antagonist: II.aggregation kinetics[J]. Journal of pharmaceutical sciences,2008,97(8):3005-3021.
[74] Da Silva B, Dufour P, Sheibat-Othman N, et al. Model predictive controlof free surfactant concentration in emulsion polymerization[C].Proceedings of the17th International Federation of Automatic Control(IFAC) World Congress2008.2008, pp.8375-8380.
[75] Narayan S. Tavare. Industrial Crystallization: Process SimulationAnalysis and Design [M]. New York, Springer.1995.
[76] Witkowski W R, Miller S M, Rawlings J B. Light scattering measurementsto estimate kinetic parameters of crystallization[C].Crystallization as aseparation process, ACS Symposium Series.1990,438:102.
[77] Monnier O, Fevotte G, Hoff C, et al. Model identification of batch coolingcrystallizations through calorimetry and image analysis[J]. Chemicalengineering science,1997,52(7):1125-1139.
[78] Santos G G B, Antonello R T, McKenna T F, et al. Population balanceequations for particle size distributions in semibatch emulsionpolymerizations[J]. Latin American applied research,2006,36(4):269-275.
[79] S.H. Kim, K.S. Woo, B.Y. L., et al. Method of measuring chargedistribution of nanosized aerosols [J]. Journal of Colloid and InterfaceScience.2005,282:46-57.
[80] Gherras Nesrine, Fevotte Gillesa. On the Use of Process AnalyticalTechnologies (PAT) and Population Balance Equations for the Estimationof Crystallization Kinetics. A Case Study [J]. AIChEJournal.2012,58(9):7421-7429.
[81] Toufik Bakir, Sami Othman, Franc ois Puel, et al. Continuous-discreteobserver for crystal size distribution of batch crystallization process [C].Proceedings of the44th IEEE Conference on Decision and Control, andthe European Control Conference，Seville,2005,pp.6240-6244.
[82] Neha B. Raikar, Surita R. Bhatiaa, Michael F. Malone, et al. Self-similarinverse population balance modeling for turbulently prepared batchemulsions: Sensitivity to measurement errors [J]. Chemical EngineeringScienee.2006,61:7421-7435.
[83] Cédric Damour, Michel Benne, Brigitte Grondin-Perez, et al. Modelbased Soft-Sensor for Industrial Crystallization: On-line Mass of Crystalsand Solubility Measurement [C]. World Academy of Science, Engineeringand Technology30，Denver,2009,pp.196-200.
[84] C.SWeeger. Morphology,evolution and other characteristics of gibbsitecrystals grown from pure and impure aqueous sodium aluminatesolutions[J].Jouenal of Crystal Growth,2001,233:567-582
[85] YolotaM,SatoA, Kubota.A. Simple method for evaluating kinetleparameters in non-isothermal batch crystalization[J].Chemical EngineermgScienee.2000,55:717-722.
[86] A.H. Alexopoulos, A.Roussosb, C.Kiparissides. Part V:Dynamic evolutionof the multivariate particle size distribution undergoing combined particlegrowth and aggregation [J]. Chemical Engineermg Scienee.2009,64:3260-3269.
[87] Y. Adachi, K. Aoki. Restructuring of small flocs of polystyrene latex withpolyelectrolyte [J]. Colloids and Surfaces A: Physico-chemical andEngineering Aspects.2009,24:342-344.
[88]陈绮,周明全，耿国华等.基于分形的蛋白质三维空间结构复杂性研究.计算机应用与软件，2008，25（8）：42-43.
[89] Oh C, Sorensen C M. Light scattering study of fractal cluster aggregationnear the free molecular regime[J]. Journal of aerosol science,1997,28(6):937-957.
[90] Elimelech M, Jia X, Gregory J, et al. Particle deposition&aggregation:measurement, modelling and simulation[M]. Butterworth-Heinemann,1998.
[91] M. Soos, J. Sefcik, M. Morbidelli. Investigation of aggregation, breakageand restructuring kinetics of colloidal dispersions in turbulent flows bypopulation balance modelling and static light scattering [J]. Chem. Eng.Sci.,2006,61:2348-2349.
[92] S. di Stasio. Observation of restructuring of nanoparticle soot aggregatesin a diffusion flame by static light scattering [J]. J. Aerosol Sci.，2001，32:509-511.
[93] M. Y. Lin, H. M. Lindsay, D. A. Weitz, et al. Universality in colloidaggregation [J]. Nature,1989,339:360-362.
[94] Rosner D E, Yu S. MC simulation of aerosol aggregation and simultaneousspheroidization[J]. AIChE journal,2001,47(3):545-561.
[95] Kostoglou M, Konstandopoulos A G, Friedlander S K. Bivariatepopulation dynamics simulation of fractal aerosol aggregate coagulationand restructuring[J]. Journal of aerosol science,2006,37(9):1102-1115.
[96] Liu J J, Ma C Y, Hu Y D, et al. Morphological Population Balance Modelsfor the Dynamic Evolution of Particle Shape and Size Distribution inProtein Crystallization[J]. Computer Aided Chemical Engineering,2009,27:1911-1916.
[97] Grimes B A, Dorao C A, Simon S, et al. Analysis of dynamic surfactantmass transfer and its relationship to the transient stabilization ofcoalescing liquid–liquid dispersions[J]. Journal of colloid and interfacescience,2010,348(2):479-490.
[98] Attarakih M M, Drumm C, Bart H J. Solution of the population balanceequation using the sectional quadrature method of moments (SQMOM)[J].Chemical Engineering Science,2009,64(4):742-752.
[99] Silva L, Damian R B, Lage P L C. Implementation and analysis ofnumerical solution of the population balance equation in CFD packages[J].Computers&Chemical Engineering,2008,32(12):2933-2945.
[100] Mesbah A, Kramer H J M, Huesman A E M, et al. A control oriented studyon the numerical solution of the population balance equation forcrystallization processes[J]. Chemical Engineering Science,2009,64(20):4262-4277.
[101] Gu Y T, Liu G R. A meshless local Petrov-Galerkin (MLPG) formulationfor static and free vibration analyses of thin plates[J]. Computer Modelingin Engineering and Sciences,2001,2(4):463-476.
[102] Roussos A I, Alexopoulos A H, Kiparissides C. Part III: Dynamicevolution of the particle size distribution in batch and continuousparticulate processes: A Galerkin on finite elements approach[J]. Chemicalengineering science,2005,60(24):6998-7010.
[103] M tzler C. Thermal microwave radiation: applications for remotesensing[M]. Institution of Engineering and Technology,2006.
[104] G. chliveros, M.A. rodrigues and D.cooper, Modelling Populations ofProkaryotic Cells: the n-Layered mRDG Approximation[C].17thEuropean Simulation Multiconference SCS Europe BVBA,2003.
[105] Trevor Cickovski, Santanu Chatterjee, Jacob Wenger, et al. MDLab: Amolecular dynamics simulation prototyping environment [J]. Journal ofComputational Chemistry,2010,31（7）:1345-1356.
[106]戴国亮,于泳,康琦等.溶菌酶晶体生长前期溶液中聚集体研究[J].化学学报,2004,62(8):757-761.
[107]王翾,于泳,刘玉红.溶菌酶分子聚集状态对蛋白质晶体生长[J].生物物理学报，2010，26（5）：380-388.
[108] Sassi P, Onori G, Giugliarelli A, et al. Conformational changes in theunfolding process of lysozyme in water and ethanol/water solutions[J].Journal of Molecular Liquids,2011,159(1):112-116.
[109] Kurihara K, Miyashita S, Sazaki G, et al. Interferometric study on thecrystal growth of tetragonal lysozyme crystal[J]. Journal of crystal growth,1996,166(1):904-908.
[110] Monaco L A, Rosenberger F. Growth and etching kinetics of tetragonallysozyme[J]. Journal of crystal growth,1993,129(3):465-484.
[111]刘晶晶.蛋白质结晶过程的模拟优化和实验研究[D].中国海洋大学博士学位论文.2010.
[112] Park T Y, Froment G F. Kinetic modeling of the methanol to olefinsprocess.2. Experimental results, model discrimination, and parameterestimation[J]. Industrial&engineering chemistry research,2001,40(20):4187-4196.
[113]夏辉,李富石,陈智全等.低相干动态光散射研究浓悬浮液中布朗运动粒子的扩散特性[J].光学学报,2010(10):3059-3063.
[114] Bohren C F, Huffman D R. Absorption and scattering of light by smallparticles[M]. Wiley-Vch,2008.
[115] Mischenko M I, Travis L D, Lacis A A. Scattering, absorption, andemission of light by small particles[M]. Cambridge university press,2002.
[116] Hagiwara T, Kumagai H, Matsunaga, et al. Analysis of aggregate structurein food protein gels with the concept of fractal[J]. Bioscience,biotechnology, and biochemistry,1997,61(10):1663-1667.
[117] Wei L, Liu H, Chen L, et al. The determination and application of fractaldimension on zinc polysilicate flocculation process[C] Remote Sensing,Environment and Transportation Engineering (RSETE),2011InternationalConference on. IEEE,2011:8639-8642.
[118] Meng Z, Hashmi S M, Elimelech M. Aggregation rate and fractaldimension of fullerene nanoparticles via simultaneous multiangle staticand dynamic light scattering measurement[J]. Journal of Colloid andInterface Science,2013,392:27-33.
[119] Molina-Bolivar J A, Galisteo-Gonzalez F, Hidalgo-Alvarez R. Fractalaggregates induced by antigen-antibody interaction[J]. Langmuir,2001,17(8):2514-2520.
[120] Li X, Leung R P C. Determination of the fractal dimension of microbialflocs from the change in their size distribution after breakage[J].Environmental science&technology,2005,39(8):2731-2735.
[121] Chakraborti R K, Gardner K H, Atkinson J F, et al. Changes in fractaldimension during aggregation[J]. Water Research,2003,37(4):873-883.
[122] Roberts C J, Das T K, Sahin E. Predicting solution aggregation rates fortherapeutic proteins: Approaches and challenges[J]. International journalof pharmaceutics,2011,418(2):318-333.
[123] Mroczka J, Wozniak M, Onofri F R A. Algorithms and methods foranalysis of the optical structure factor of fractal aggregates[J].Metrol.Meas. Syst.,2012,3:459-470.
[124] Lee J. Effect of structure factor on aggregate number concentrationestimated using Rayleigh–Debye–Gans scattering theory[J]. OpticaApplicata,2011,41(3):519-525.
[125]陶风云,张新妙,马润宇.溶菌酶结晶的研究进展[J]. Journal of BeijingUnion University (Natural Sciences),2006,20(3):65.
[126]杨晓飞,马启敏,江翠芸.扩散限制凝聚过程的计算机模拟研究[J].中国海洋大学学报(自然科学版),2007,37：139-142.
[127] Di Stasio S, Konstandopoulos A G, Kostoglou M. Cluster–cluster
aggregation kinetics and primary particle growth of soot nanoparticles in
flame by light scattering and numerical simulations[J]. Journal of colloid
and interface science,2002,247(1):33-46.