生物大分子结晶过程的动力学

2006.23№4化学与生物工程Chemistry BioengineeringThe Kinetics of Crystallization Process of Biological MacromoleculeGUI Lin, LI Lin, HU Song-qing, CHEN Ling, FAN Zhi-guo, LI Jian-bin(College of Light Industry and Food Technology, South China University ofTechnology, Guangzhou 510640, China)Abstract: In this paper the crystallization process of biological macromolecules was presented, and themechanisms and kinetics of crystallization were analyzedKeywords: biological macromolecule; crystallization; kineticsrowth1 ntroduction2 Crystallization processes of biological macroBiological macromolecules are one of the mainmoleculesmolecular families in living matter, for example, erzymes, nucleic acids, polysaccharides, toxins, hor- 2. 1 Saturation and supersaturationmones, antibodies and their complexes with proteinThe supersaturated state can be divided into threeviruses and ribosomes. The detailed understanding of loosely defined zones( Figure 1). The first zone is calledthe structure of such compounds is important in the the stable zone, where no crystallization occurs. Nextdesign ofmedicines and for engineering mole- comes the metastable zone, where growthexisticules with improved properties for industrial applica- crystals and formation of new nuclei occur simultaneousThe three-dimensional structure elucidly. The third zone is the labile zone, where new nucleition of biological macromolecules is essential for an form spontaneously from a clear solutionunderstanding of their complex biological functions.X-ray diffraction is the most reliable method todetermine the three-dimensional structure of all molLabileecules, but it can only be applied when suitable crystals are provided. Obtaining good ordered crystalsis currently the major barrier to structure determination. The task of overcoming the bottleneck to produce suitable crystals is tackled by two approachesFig. 1 Illustration of the three characteristic zones exhibitingone approach concentrates on empirical methods fordifferent crystallization behaviorproducing X-ray quality crystals; the second approachfocuses on studies concerning the understanding ofIt is useful to define the degree of supersaturacrystal growth on a molecular level[ 6]. Such studies tion using the following equationsare of fundamental importanceMacromolecular crystallization also represents anACD=CACAimportant separation/ purification step in a number ofchemical and biotechnological processes , /,B. The author highlights the thermodynamics of crystallizationIn these equations, Sp is the degree of saturaprocesses of biological macromolecules, and analyzes tionconcentration of solute A in solutionthe mechanisms and kinetics of crystallization for im中国煤化工 A at thproving crystal quality by control of nucleation and point:CNMHG基金项目:国家自然科学基金项目(20276021),华南理工大学高水平大学建设项目收稿日期:2006-01-18作者简介:桂林(1975—),男,湖北武汉人,博士研究生,研究方向为生物化工。电话:020-22837026,E-mail:foodgui(163.com桂林等:生物大分子结晶过程的动力学/2006年第4期The rate at which crystallization occur is directly tering free energy is given byrelated to the degree of supersaturation, as this facto--nkTInaRTypifies the driving force for solid-phase formationWhere R is the universal gas constant and T isThe maximum value of the degree of supersaturathe absolute temperature. The product of the boltztion, however, is often dictated by the type of nuclenann constant (k)and the number of moles undergation observed2.2 Nucleation phenomenang the phase change (n) can be replaced by the solidThe solid phase can be created by homogeneousdensity p, the molecular weight Mw, and the volumeof the spherical solid formed. Putting these terms toheterogeneous, secondary, or attritive nucleation. Ingether, we realize that if c is greater than c, theindustrial practice, the most unlikely of these processes is homogeneous nucleation, which requires a pertwo terms have opposite signs. Thus a maximum valfectly clean vessel with no rough surfaces. In heterue of the free energy must exist for a given particlesize. To ensure that a solid phase is created, the rageneous nucleation, the process is affected by thevessels wall morphology or the presence of insoludius of the solid particle must exceed the critical radibles, such as dust particles in the mother liquor. Seeus,r, dictated by the free energy maximum. Thisding a crystallizer can be the best method in commerfree energy maximum is given by the following equaalas the growth on the seedown as secondary nucleation, leads to large, well△Gmx=rys16y,MiR2T2(formed crystals. In a highly agitated vessel, crystalsBecause the free energy must be supplied ascan break; the fragment formed then serve as surork, we can see that nucleation is analogous to re-faces for growth by attritive nucleation o, Jaction kinetics. Thus we can use an Arrhenius-typeHomogeneous nucleation occurs when macro- expression to obtain the rate of nuclei formationmoleculles cluster and undergo a phase transitiondN=aeT=Aexp16ry. Mithereby creating a solid surface. This process is easiRTBpR2 T(In Sp)2/(8ly analyzed on a thermodynamic and transport basisIn equation 8the rate of nuclei formationand then this assessment can be used to build models A is the Arrhenius preexponential constant, and N isfor the more complex heterogeneous, secondary, andthe cumulative number of crystals per unit volumeattritive nucleation phenomena. The free energyIt is usually very convenient to use the linearchange upon crystal formation during homogeneous growth rate G, which is equal to the rate of change ofnucleation is the sum of the free energy from surface a characteristic dimension of a crystal, L. We use theformation and the entropically driven process of mo- chain rulelecular aggregation to form a solid phase△ homogeneous=△Gto obtain the following equatioThe free energy of surface formation for a sphericalparticle is given by the product of the interfacial area andthe surface tension of the solid-liquid interfaceIn equation 10, the term n, which is called thesurfarepopulation density of nuclei, is used to define theIn this equation, r is the particle radius and ychange in the number of crystals per unit crystalthe surface tension of the solid-liquid interface.中国煤化工 r growth rate is geThe free energy associated with the creation of a erallyCNMHGSaturationcluster of solid material can be defined as the energy 2. 3 Growth of crystalsof transferring n moles from the liquid to the solidBefore modelling the processes occurring in thellihclei fothe ratio of the activity coefficients is unity, the clus- should be understood. It is not possible to faithfully桂林等:生物大分子结晶过程的动力学/2006年第4期account for each of these phenomena and generate a cumulative mass of crystals per unit volume), we calmodel that unambiguously determines each of the ad- culate the mass of a crystal using the density of thejustable parameters. Instead, we must rely on the crystal.P, and a shape factor k,power law function once againTo determine the cumulative mass. we then emThe exponential factor g usually lies between 0 ploy the population balance in the integral shown innd 2. 5, and commonly has a value of 1. This value Equations 21-25, where W is defined as the totaluggests that a linear mass transfer process or a first- mass for all crystal sizesorder surface reaction is the rate-limiting step in thedI(20)overall process. It should be emphasized that equation 11 assumes that the linear growth rate is indeSet 1pendent of crystal size. When this assumption isG tLGvalid, we can rely on an empirical relationship knoM=oak, nG6r(3)I(2)as the Abegg-Stevens-Larson equationG=G"(1+aL)(-b)L2. 4 Crvstal size distributionBoIGI IG(GLGTwo quantities are especially relevant when exber of crystals per unit volume L, and M. the cumu2(2)lative mass of crystals per unit volume L. Of thesetwo quantitiesthe most readily obtained. As itM=wk b gtis simply the integral of the population density withAlthough complex, these equations suggest thatrespect to L N is easily calculated for Set 1 and Setthe cumulative mass can be modeled as a function of2 boundary conditionscrystal length, using a polynomial expression. Alsothe total mass depends on time and growth rate as aN一(-2[1-()] .3) power law expression2. 5 Growth rate dispersionN=nt1It is unrealistic to assume that crystallization canmaintain a constant growth rate because the degree of suSet 2persaturation chanof a run as a simBxp (G)dL=5 -exp(G)(16) ple approach to deal with this effect, we can modelN=B[(-b)(-)variation in the growth rate as a dispersion termND.D = Bt(18)Through this calculation, we find that the totalow that it includes the growth rate dispersion termnumber of crystals is proportional to time and either for a spiked seeding of the batch crystallizer, the popula-the growth rate or the nucleation rate, depending on tion der中国煤化工 stribution as a functwhether seeding takes place. Note that the equationof件HCNMHGan be solved using thefor N contain the unit step function u(t-L/G). following boundary and initial conditionswhere u=0 from t=0 to t=L/G, and u= 1 when t isatt=0,n=0;atL=0,n=n0(t);atI→∞,nisgreater than L/GfiniteTo obtain the easily measured quantity M(theThe resulting expression for n takes the form of a桂林等:生物大分子结晶过程的动力学/2006年第4期Gaussian or normal distribution with respect to timenomenallization these methods are in(L-G)tended to guide the operation of batch and contiexp 4LDindustrial crystallizers. It has not been given that adetailed analysis of specific conditions for crystallizingThis expression is obtained via Laplace transforms certain types of biomolecules, Rather. our discussionand van der Laan's theorem. From the Laplace transform has focused on the general methods through which aof the population density, we can read the cumulativestate of supersaturation can be created. These methlumber and mass distributions differ from the results ods include solvent evaporation, cooling, and diluentpreviously obtained without the use of the growth rateaddition, which are used in nearly all industrially reledispersion term. Based on our definition of N, we needvant crystallization strategiesto calculate the following integralReferencesL-(r)1 Chernov AA. Protein crystals and their growth[J]. Journal of4πLD。(27)[2] McPherson A. Introduction to protein crystallization[J]. Meth-The cumulative mass of crystals can also be calods,2004,34:254-26culated using the following integral[3 McPherson A Crystallization of Biological Macromolecules [MG-L expGNew York: Cold Spring Harbor Laboratory Press, 1999: 1-29.ALDG dL(28)[4 Gilliland G L, Ladner J E. Crystallization of biological macromeecules for X-ray diffraction studies[J]. Current Opinion in Struc-As L approaches infinity in Equation 28, the toural Biology, 1996.6: 595-603tal weight of crystals can be found[5 Curcio E, Profio G D, Drioli E Membrane crystallization of mac-Introducing the growth rate dispersion term intmolecular solutions[J]. Desalination, 2002,145:173-17the calculations demonstrates that crystals of differ[6 Rosenberger F, Meehan EJ. Control of nucleation and growth inent sizes grow at different rate. Although growthprotein crystal growth[J] Journal of Crystal Growth, 1988.90rate dispersion can still beurring, continuo[7 Profio G D, Curcio E, Cassetta A, et al. Membrane crystalliza-crystallizers can be operated in a manner that closelyion of lysozyme: kinetic aspects[J]. Journal of Crystal Growthapproximates the process that results in a small in2003,257:359-36cremental change in crystal size. This small, differ- [8 McPherson A Current approaches to macrential crystal growth method allows for the measureon[J]. European Journal of Biochemistry,1990,189: 1-23ent of the linear growth rate. Size-dependent[9] Haas C, Drenth J. Understanding protein crystallization on thebasis of the phase diagram[J]. Journal of Crystal Growth,1999growth and growth rate dispersion factors can also be196:388-394.considered as part of the analysis, thereby enabling [10] Baird J K, Hill S C, Clunie JC. Kinetics of protein crystal nuto model industrial crystallizerslation and growth in the batch method[J]. Journal of CrystalGrowth,1999,196:220-2253 Summary[11] Rodriguez C F, Rodriguez FF, Morales S A, et al. Crystalliza-tion simulation in macromolecular crystals[J]. Journal of CrystaIt has been emphasized the development of anaGrowth,2000,220:130-134lytical models that incorporate an understanding of the生物大分子结晶过程的动力学中国煤化工桂林,李琳,胡松青,陈玲,CNMHG(华南理工大学轻工与食品学院,广水摘要:阐述了生物大分子结晶的一般过程,分析了结晶的机制和动力学。关键词:生物大分子;结晶;动力学中图分类号:Q51文献标识码:A文章编号:1672-5425(2006)04-0022-04