Molecular weight determination of heparin and dermatan sulfate by size exclusion chromatography with a triple detector array

The determination of molecular weight (M) and molecular weight distribution (MD) of heparins by a novel approach, consisting of a high performance size exclusion chromatography (HP-SEC) combined with a triple detector array (TDA) is described. HP-SEC/TDA permits the evaluation of MD of polymeric samples through a combined and simultaneous action of three on-line detectors, right-angle laser light scattering (RALLS), refractometer (RI), and viscometer. The method does not require any chromatographic column calibration, thus overcoming also the difficulty to obtain adequate reference standards. It permits the size determination also of small molecules, even when scattering dissimmetry is not observable. Unfractionated heparins, eight fractions of a size fractionated heparin, and dermatan sulfates were analyzed by HP-SEC/TDA. The M values found for the heparin fractions were used to build up a calibration curve of a conventional HP-SEC system: the results obtained analyzing unfractionated heparin samples with both HP-SEC/TDA and HP-SEC were in excellent agreement, suggesting the possibility to use the TDA data to generate standard samples with known MD and intrinsic viscosity [eta]. Moreover, HP-SEC/TDA can successfully be employed also for the determination of the Mark-Houwink a and k parameters.     

Characterization of gelatine and acid soluble collagen by size exclusion chromatography coupled with multi angle light scattering (SEC-MALS)

Acid soluble collagen (ASC) and a cattle hide gelatine were analyzed by size exclusion chromatography (SEC) coupled with multi angle light scattering (MALS). The SEC system was calibrated with ASC and its cyan bromide cleavage products. The accuracy of calibration was confirmed by MALS by measuring the mass-average molar masses (Mw). ASC acted as a mixture of two polymer standards of Mw = 90 and 180 kg/mol, respectively. The elution behavior of the gelatine in SEC-MALS was similar to that of ASC. Therefore, the determination of the molar mass distribution of this gelatine was possible either by SEC, using a calibration curve, or by MALS by direct measurement of Mw. According to the scaling law (1/2) = KMalpha, alpha = 0.78 was determined for the gelatine. This alpha could reflect a structure in solution, which is more similar to an ellipsoid than to a random coil.     

Molecular weight and related properties of lily amylose determined by monitoring of elution from TSK-GEL PW high performance gel chromatography columns by the low-angle laser light scattering technique and precision differential refractometry

Amylose was fractionated according to its molecular weight by high performance gel chromatography using columns of a TSK-GEL PW series. Elution from the columns was monitored with a low-angle laser light scattering photometer and a precision differential refractometer. The following results were obtained indicating that the procedure is highly efficient for characterizing an amylose preparation with respect to its molecular weight: 1) the weight-average molecular weight of lily amylose used as a test material was determined to be 786,000 +/- 26,000 (n = 7); 2) the molecular weight distribution curve of the amylose was worked out from the chromatographic data; and 3) based on the concept of the universal calibration curve, the Mark-Houwink-Sakurada equation of the amylose was presumed to be [eta] = 2.27 X 10(-4)M0.62 (dl/g). The technique saves time and sample significantly compared with the conventional ones, and consequently enables the characterization of amylose in aqueous solvents without either the degradation or association peculiar to the amylose molecule.     

Evaluation of radius of gyration and intrinsic viscosity molar mass dependence and stiffness of hyaluronan

Nine hyaluronan (HA) samples were fractionated by size-exclusion chromatography, and molar mass (M), radius of gyration (Rg), and intrinsic viscosity ([eta]) were measured in 0.15 M NaCl at 37 degrees C by on-line multiangle light scattering and viscometer detectors. Using such method, we investigated the Rg and [eta] molar mass dependence for HA over a very wide range of molar masses: M ranging from 4 x 10(4) to 5.5 x 10(6) g/mol. The Rg and the [eta] molar mass dependence found for HA showed a meaningful difference. The Rg = f(M) power law was substantially linear in the whole range of molar masses explored with a constant slope of 0.6. In contrast, the [eta] = f(M) power law (Mark-Houwink-Sakurada plot) showed a marked curve shape, and a linear regression over the whole range of molar masses does not make sense. Also the persistence length (stiffness) for HA was estimated. The persistence length derived by using both the Odijk's model (7.5 nm from Rg vs M data) and the Bohdanecky's plot (6.8 nm from [eta] vs M data) were quite similar. These persistence length values are congruent with a semistiff conformation of HA macromolecules.     

Fractionation and characterization of a Polysaccharide from the sclerotia of Pleurotus tuber-regium by preparative size-exclusion chromatography

A kind of regenerated cellulose gel (RCG) particles were treated by toluene to obtain particles with smaller mean pore size, then was mixed with the cellulose gel with pore size of 370 and 525 nm. A preparative size-exclusion chromatography (SEC) column (700 x 20 mm) packed with three gel particles was used to fractionate water-soluble polysaccharide (WEP) extracted from the sclerotia of Pleurotus tuber-regium by aqueous solution. The exclusion limit and fractionation range of the stationary phase of the preparative SEC were molecular mass 8 x 10(5) and 5 x 10(3) to 8 x 10(5), respectively. The calibration curve of the preparative SEC was represented as: log M=13.96-0.53 Ve. The WEP sample (weight-average molecular mass M(w)=2.2 x 10(4), polydispersity=2.4) was divided into three fractions with M(w) ranging from 1.4 x 10(4) to 3.4 x 10(4) by the preparative SEC column, and the fractions were characterized by gas chromatography GC, SEC combined with laser light scattering (SEC-LLS) and viscometry. The unfractionated WEP exhibited triple peaks due to different molecular mass, but each fraction exhibited single peak with the polydispersity of 1.1-1.8 in the SEC patterns. The results indicated that the preparative SEC was efficient for fractionation of polysaccharides having low molecular weight and for determination of their molecular mass.     

Distribution of elements binding to molecules with different molecular weights in aqueous extract of Antarctic krill by size-exclusion chromatography coupled with inductively coupled plasma mass spectrometry

The distribution of silver, arsenic, cadmium, cobalt, chromium, copper, iron, manganese, nickel, lead, selenium and zinc binding to species with different molecular weight in aqueous extract of krill was studied by on-line size-exclusion chromatography (SEC)/inductively coupled plasma mass spectrometry (ICP-MS). The extract was fractionated in three fractions with different molecular weight (MW) ranges (>20,000 relative molecular mass (rel. mol. mass), 2000-20,000 rel. mol. mass and <2000 rel. mol. mass), which were further analyzed by SEC with columns having different optimum fractionation ranges in order to obtain more detailed information about the MW distribution of the elements. Various distribution profiles for the target elements among different MW ranges were observed. The results obtained indicated that manganese, zinc, silver, cadmium and lead species were mostly distributed in the higher MW range (>20,000 rel. mol. mass). In the case of chromium, iron, cobalt, arsenic and selenium, most of them bind to species with lower MW (<2000 rel. mol. mass). Only copper and nickel species was predominantly present in middle MW range (2000-20,000 rel. mol. mass). Further speciation of arsenic compounds in the small MW fraction was carried out with anion exchange chromatography (AEC) coupled with ICP-MS. The results showed that the dominant arsenic species in this fraction is As(III) (63% of extractable arsenic), while As(V) (13%) and two unknown arsenic species (19% and 5%, respectively) are present in lower amounts.     

Effect of molecular mass on antitumor activity of heteropolysaccharide from Poria cocos

A water-soluble heteropolysaccharide ac-PCM0 from Poria cocos was successfully fractionated using a preparative size exclusion chromatography (SEC) column, and their weight-average molecular mass (M(w)) was characterized by analytical SEC combined with laser light scattering (SEC-LLS). The results indicate that the fractions having relatively high M(w) exhibited higher inhibition ratio in vivo antitumor activity than those having M(w) below 3.29 x 10(4). However, the relatively low molecular mass was beneficial to the in vitro antitumor activity. Moreover, ac-PCM0 has a significantly higher enhancement ratio of the body weight than 5-fluorouracil, and its 50% lethal dose is above 1250 mg/kg, indicating a nontoxic nature.     

Speciation of Al in human serum by convective-interaction media fast-monolithic chromatography with inductively coupled plasma mass spectrometric detection

A new analytical procedure using anion-exchange separation support based on convective-interaction media (CIM) was developed for the speciation of Al in human serum. The separation of proteins was performed on a weak anion-exchange CIM diethylamine (DEAE) fast-monolithic disk. To prevent co-elution of low molecular mass (LMM) Al species with high molecular mass (HMM) Al compounds on CIM disk serum proteins were first separated from LMM-Al species by the use of size exclusion chromatography (SEC). For this purpose 1 mL of serum was injected onto SEC (Superdex 75 HR 10/30) column. Isocratic elution using 0.05 M TRIS-HCl+0.03 M NaHCO(3) was applied and separation of proteins was followed by UV detection at 278 nm. It was experimentally proven that proteins were eluted in 5.5 mL peak that was collected into a polyethylene cup. A 0.1 mL of the sample aliquot was then injected onto the CIM DEAE disk. The separation of serum proteins was obtained in 10 min by applying linear gradient elution from 100% buffer A (0.05 M TRIS-HCl+0.03 M NaHCO(3)) to 100% buffer B (A+1M NH(4)Cl) and followed by UV detection at 278 nm. Separated Al species were detected on-line by inductively coupled plasma mass spectrometry (ICP-MS). Well-resolved protein peaks were obtained. It was experimentally proven that 90+/-3% of Al in spiked serum of renal patient was eluted under the transferrin peak. The proposed speciation procedure removes LMM-Al species and enables reliable determination of the concentration and composition of Al bound to proteins by CIM DEAE-ICP-MS when the concentration of Al in serum is higher than 5 ng mL(-1). In comparison to chromatographic columns CIM disks enable faster separation and simpler manipulation during cleaning procedure and coupling to ICP-MS.     

Isolation and characterization of water-soluble hemicelluloses from flax shive

Partially depolymerized, water-soluble hemicelluloses were solubilized from flax shive employing hydrothermal microwave treatment and thereafter subjected to ion-exchange chromatography, enzymatic purification and/or size-exclusion chromatography (SEC). The oligo- and polysaccharide fractions thus obtained were characterized with respect to molar mass, molar mass distribution, degree of polymerization (DP) and degree of substitution with acetyl moieties (DSAc) by employing SEC in combination with MALDI-TOF mass spectrometry. The major portion of the water-soluble flax hemicellulose consisted of an O-acetyl-4-O-methylglucuronoxylan exhibiting a DPp value (i.e., peak-average DP) of 28. When the DSAc for this O-acetyl-4-O-methylglucuronoxylan was calculated on the basis of the MALDI-MS spectra obtained without and following deacetylation, a value of 0.7 was obtained. In addition, an O-acetyl-glucomannan (DPp=9, DS=0.4) and minor quantities of small neutral O-acetyl-xylooligosaccharides were also isolated from the mixture of water-soluble hemicelluloses released from the flax shive by microwave treatment.     

Mechanistic investigation of a starch-branching enzyme using hydrodynamic volume SEC analysis

Two linear alpha-(1,4)-D-glucans substrates, of degrees of polymerization DP approximately 150 and 6000, were exposed to maize starch-branching enzyme IIa (mSBEIIa) in vitro. The resulting branched alpha-glucans and their constituent chains (obtained by debranching) were analyzed by nuclear magnetic resonance (NMR) and size-exclusion chromatography (SEC). SEC data for the debranched species are presented as chain-length distributions, while those for branched species are presented as hydrodynamic volume distributions (HVDs), which is the most meaningful way to present such data (because SEC separates by size, not molar mass, and a sample of branched polymers with the same size can have a range of molar masses). A rigorous interpretation of the HVDs of the substrate and its branched product show that at least part of the branching is an interchain transfer mechanism in both the short- and long-chain substrate cases. A bimodal HVD of the in vitro branched alpha-glucan derived from the short-chain substrate was observed, and it is postulated that the divergence of the two populations is due to very small chains being unable to undergo branching. In the case of the in vitro branching of the long-chain substrate, the formation of maltohexaose during the reaction and the presence of a monomodal HVD were observed, suggesting a distinct mode of action of mSBEIIa on this substrate. Quantification of the branching level by NMR showed the branched glucans from both substrates had substantial amounts of branching (2.1-4.5%), ascribed to the intrinsic nature of the action of mSBEIIa on the two substrates. It is postulated that differences in the degrees of substrate association affect the pattern of branching catalyzed by the enzyme, and a putative active site structure is proposed based on the appearance of maltohexaose. The molar mass distribution of the constituent chains of the in vitro branched alpha-glucans obtained by isoamylase treatment reveals the transfer of chains of specific size and supports the supposition given in the literature that mSBEIIa is responsible for short-chain branching in amylopectin. It is suggested that hydrodynamic volume SEC analysis should be used as a tool for the mechanistic investigation of SBEs, allowing SEC data of in vitro branched alpha-glucans to be both comparable and quantitative.     

Measurement of the molecular weight distribution of debranched starch

Combining molecular weight distribution (MWD) data for linear chains of debranched starch from capillary electrophoresis and from size exclusion chromatography (SEC) with detection by differential refractive index and by multi-angle laser light scattering has enabled Mark-Houwink parameters to be determined for linear starch chains. For accurate results, it was found to be important to take SEC band broadening into account, and a methodology for implementing this is presented. This deconvolution technique can be used to reveal features such as maxima or shoulders in the MWD which have qualitative as well as quantitative significance. Remarkably, these data show that the empirical Mark-Houwink relation between molecular weight and hydrodynamic volume is, for linear debranched starch, valid for much lower molecular weights than synthetic polymers. This implies that these Mark-Houwink parameters can be used with "universal calibration" to enable SEC to be used with relative ease to provide MWDs for debranched starch for essentially any degree of polymerization.     

On-line characterization of monoclonal antibody variants by liquid chromatography-mass spectrometry operating in a two-dimensional format

Recombinant monoclonal antibodies (MAbs) have become one of the most rapidly growing classes of biotherapeutics in the treatment of human disease. MAbs are highly heterogeneous proteins, thereby requiring a battery of analytical technologies for their characterization. However, incompatibility between separation and subsequent detection is often encountered. Here we demonstrate the utility of a generic on-line liquid chromatography–mass spectrometry (LC-MS) method operated in a two-dimensional format toward the rapid characterization of MAb charge and size variants. Using a single chromatographic system capable of running two independent gradients, up to six fractions of interest from an ion exchange (IEC) or size exclusion (SEC) separation can be identified by trapping and desalting the fractions onto a series of reversed phase trap cartridges with subsequent on-line analysis by mass spectrometry. Analysis of poorly resolved and low-level peaks in the IEC or SEC profile was facilitated by preconcentrating fractions on the traps using multiple injections. An on-line disulfide reduction step was successfully incorporated into the workflow, allowing more detailed characterization of modified MAbs by providing chain-specific information. The system is fully automated, thereby enabling high-throughput analysis with minimal sample handling. This technology provides rapid data turnaround time, a much needed feature during product characterization and development of multiple biotherapeutic proteins.     

A complete set of hyaluronan fragments obtained from hydrolysis catalyzed by hyaluronidase: Application to studies of hyaluronan mass distribution by simple HPLC devices

Hyaluronan (HA) has different biological functions according to its molar mass; short HA fragments are involved in inflammation processes and angiogenesis, whereas native HA is not. Physicochemically, studies of native HA hydrolysis catalyzed by bovine testicular hyaluronidase (HAase) have suggested that kinetic parameters depend on HA chain length. To study the influence of HA chain length in more detail, and to try to correlate the physicochemical and biological properties of HA, HA hydrolysis catalyzed by HAase was used in a new procedure to obtain HA fragments of different molar masses. HA fragments (10-mg scale) with a molar mass from 800 to 300,000 g mol(-1) were prepared, purified using low-pressure size exclusion chromatography (SEC), lyophilized, and characterized in molar mass by either mass spectrometry or HPLC-SEC-multiangle laser light scattering. The polydispersity index of the purified fractions was less than 1.25. The complete set of HA standards obtained was used to calibrate our routine HPLC-SEC device using only a refractive index (RI) detector. We showed that the N-acetyl-d-glucosamine reducing end assay and the calibrated HPLC-SEC-RI gave equivalent kinetic data. In addition, the HPLC-SEC-RI furnished the mass distribution of the polysaccharide during its hydrolysis.     

A new approach for studying correlations between the chemical structure and the rheological properties in carboxymethyl cellulose

Two model sodium carboxymethyl celluloses (CMC) with similar monomer composition but with significant differences in the viscoelastic properties, that could not be assigned to variations in the average molar mass or molar mass distribution, were investigated with respect to the fraction of nonsubstituted cellulose segments in the polymers. The CMCs were hydrolyzed by a purified highly selective endoglucanase. The average molar mass and molar mass distribution of the enzyme products, as measured by size-exclusion chromatography with online multi-angle light scattering and refractive index detection (SEC/MALS/RI), revealed that the enzyme-catalyzed hydrolysis was more effective on one of the CMCs. To investigate whether this was due to a higher fraction of nonsubstituted cellulose segments in the polymer, the concentrations of nonsubstituted enzyme products, e.g., cellotetraose and cellopentaose, were measured by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS). It was concluded that the two CMCs displayed significant differences in the fraction of nonsubstituted cellulose segments. Furthermore, the CMC with the strongest attractive intermolecular interactions, according to rheometry, also contained the highest fraction of nonsubstituted cellulose segments.     

Evaluation of Multi-tRNA Synthetase Complex by Multiple Reaction Monitoring Mass Spectrometry Coupled with Size Exclusion Chromatography

Eight aminoacyl-tRNA synthetases (M, K, Q, D, R, I, EP and LARS) and three auxiliary proteins (AIMP1, 2 and 3) are known to form a multi-tRNA synthetase complex (MSC) in mammalian cells. We combined size exclusion chromatography (SEC) with reversed-phase liquid chromatography multiple reaction monitoring mass spectrometry (RPLC-MRM-MS) to characterize MSC components and free ARS proteins in human embryonic kidney (HEK 293T) cells. Crude cell extract and affinity-purified proteins were fractionated by SEC in non-denaturing state and ARSs were monitored in each fraction by MRM-MS. The eleven MSC components appeared mostly in earlier SEC fractions demonstrating their participation in complex formation. TARSL2 and AIMP2-DX2, despite their low abundance, were co-purified with KARS and detected in the SEC fractions, where MSC appeared. Moreover, other large complex-forming ARS proteins, such as VARS and FARS, were detected in earlier fractions. The MRM-MS results were further confirmed by western blot analysis. Our study demonstrates usefulness of combined SEC-MRM analysis for the characterization of protein complexes and in understanding the behavior of minor isoforms or variant proteins.     

Direct and Indirect Methods for Molar-Mass Analysis of Fragments of the Capsular Polysaccharide ofHaemophilus influenzaeType b

Two methods are described for direct molar-mass measurement of low-molar-mass fragments obtained by oxidative cleavage of the capsular polysaccharide ofHaemophilus influenzaetype b. Absolute molar masses were determined by size-exclusion chromatography (SEC) with detection by multiangle laserlight-scattering photometry (MALLS) and differential refractometry (RI). The end-group structure of the polysaccharide fragments allowed the direct measurement of average chain length by quantitative¹H NMR, from which molar masses were derived. Variation between the molar masses obtained by the two methods ranged from 5 to 7%. When molar masses estimated by indirect methods were compared to SEC-MALLS/RI data, significant deviations were observed. Analysis by SEC with secondary calibration with dextran standards gave molar masses that exceeded the SEC-MALLS/RI data by as much as 2.5-fold. Molar masses estimated by a combination of colorimetric assays varied from the SEC-MALLS/RI data by as much as 50%. These results demonstrated the applicability and superior accuracy of the direct methods of molar-mass determination of the polysaccharide fragments.     

Application of size-exclusion chromatography-inductively coupled plasma mass spectrometry for fractionation of element species in seeds of legumes

Fractionation of soluble species of P, Mn, Fe, Co, Ni, Cu, Zn, Se and Mo in pea and lentil seeds was made by on-line hyphenation of size-exclusion chromatography (SEC) and inductively coupled plasma mass spectrometry. Seed samples were extracted with 0.02 mol l(-1) Tris-HCl buffer solution, pH 7.5. SEC was performed on Superdex 75 and Superdex Peptide columns (300 x 10 mm) with the same buffer solution as the mobile phase. Monitoring of oxide ion 47(PO)+ was used for detection of phosphorus compounds. Other elements were detected as ions of 55Mn, 57Fe, 59Co, 62Ni, 65Cu, 66Zn, 82Se and 95Mo nuclides. Elements in individual elution zones were quantified using external calibration. Complete chromatographic recoveries of elements were found in cases of phosphorus, nickel and copper. Substantial parts of manganese and zinc, as well as traces of cobalt, selenium and molybdenum are retained on the column. Injection of EDTA solution removes these elements from the column. Chromatographic profiles of pea and lentil samples are very similar for all elements except Mo. Main element species in the high-molecular-mass region (approx. 190,000 rel. mol. mass unit) were detected in case of Fe. Low-molecular-mass species (<2000 rel. mol. mass unit) as major element forms are typical for Cu and Zn.     

"Top Down" characterization is a complementary technique to peptide sequencing for identifying protein species in complex mixtures

At present, mass spectrometry provides a rapid and sensitive means for making conclusive protein identifications from complex mixtures. Sequencing tryptic peptides derived from proteolyzed protein samples, also known as the "Bottom Up" approach, is the mass spectrometric gold standard for identifying unknowns. An alternative technology, "Top Down" characterization, is emerging as a viable option for protein identifications, which involves analyzing the intact unknowns for accurate mass and amino acid sequence tags. In this paper, both characterization methods were employed to more comprehensively differentiate two early-eluting peaks in a process-scale size-exclusion chromatography (SEC) step for a recombinant, immunoglobulin gamma-1 (IgG-1) fusion protein. The contents of each SEC peak were enzymatically digested, and the resulting peptides were mapped using reversed-phase (RP) HPLC-ion trap MS. Many low-level UV signals were observed among the fusion protein-related peptide peaks. These unknowns were collected, concentrated, and analyzed using nanoelectrospray (nanoES) collision-induced dissociation (CID) tandem (MS/MS) mass spectrometry for identification. The peptide sequencing experiments resulted in the identification of twenty host cell-related proteins. Following peptide mapping, the contents of the two SEC peaks were protein mass profiled using on-line RP HPLC coupled to a high-resolution, quadrupole time-of-flight (Qq/TOF) MS. Unknown proteins were also collected, concentrated, and dissociated using nanoES CID MS/MS. Intact protein CID experiments and accurate molecular weight information allowed for the identification of three full length host cell-derived proteins and numerous clips from these and additional proteins. The accurate molecular weight values allowed for the assignment of N- and C-terminal processing, which is difficult to conclusively access from peptide mapping data. The peptide-mapping experiments proved to be far more effective for making protein identifications from complex mixtures, whereas the protein mass profiling was useful for assessing modifications and distinguishing protein clips from full length species.     

Kinetic comparison of ricin immunotoxins: biricin conjugate has potentiated cytotoxicity

The plant toxin ricin was chemically coupled to an anti-Thy-1.1 antibody, and the resultant conjugates were fractionated by gel filtration. The cytotoxicity of the conjugate possessing two ricin molecules per immunoglobulin, yielding a first-order inactivation rate of protein synthesis of -0.4 log/h at 200 ng/mL, was well above that expected just from the increase in ricin per unit mass of conjugate, when compared to a conjugate possessing only one ricin per immunoglobulin. On a conjugate molar scale the biricin immunotoxin was determined to be 8 times more potent than the monoricin conjugate; thus, relative to the number of ricin molecules, the coupling of a second ricin to the immunoglobulin quadrupled the observed potency. The concentration of immunotoxin and the resultant inactivation rates of protein synthesis were found to be related through a power function. Additionally, the inactivation kinetics of these conjugates were found to be similar to those of native ricin.     

Intrinsic kinetics of continuous growth and ethanol production of a flocculating fusant yeast strain SPSC01

The intrinsic kinetics of continuous yeast cell growth and ethanol production for a self-flocculating fusant yeast strain SPSC01 was investigated by means of mechanically dispersing the flocs and correspondingly established floc size distribution on-line monitoring technique using the focused beam reflectance measurement system, through which the floc intra-particle mass transfer limitation was effectively eliminated, but its ethanol formation metabolism was not affected. Modified kinetic models were developed, which can be used to predict the continuous kinetic behaviors of SPSC01, especially when low dilution rates are applied and limiting substrate concentrations are undetectable and almost all kinetic models developed previously are failed in predicting corresponding kinetic behaviors. Both substrate and product inhibitions reported for freely suspended yeast cell ethanol production were also observed for SPSC01 when high gravity media were fed and relatively high levels of residual sugar and ethanol presented. Model parameters were evaluated through numerical calculation method and validated by experimental data mu = 0.584C(s)/0.155 + C(s) + C(2)(s)/160.7(1 -P/125)(3.68) + 0.004 for growth, nu = 1.998C(s)/0.427 + C(s) + C(2)(s)/366.7(1- P/125)(1.72) + 0.060 for ethanol production These intrinsic kinetic models can be further used to develop the observed kinetic models that quantitatively correlate the impact of the self-flocculating yeast cell size distributions on their apparent rates for yeast cell growth, substrate uptake and ethanol production and optimize the ethanol production process.