colloidal aspects of yeast flocculation: a review - Wiley Online Library

/. Inst. Brew., November-December, 1992, Vol. 98, pp. 525-531

COLLOIDAL ASPECTS OF YEAST FLOCCULATION: A REVIEW

By R. Alex Speers1, Marvin A. Tung2, Timothy D. Durance3 and Graham G. Stewart4 (l Department of Food Science, Acadia University, Wolfville, Nova Scotia, BOP 1XO; 2Department of Food Science and Technology, Technical University of Nova Scotia, P. O. Box 1000, Halifax, Nova

Scotia, B3J 2X4; 3Department of Food Science, University of British Columbia, 6650 N. XV. Marine Drive, Vancouver, British Columbia, V6T1W5; ^Production Research Department, Labatt Brewing Company Limited, 150 Simcoe Street, London, Ontario, N6A 4M3) Received 17 March 1992

In this review, areas of colloid science including the DLVO theory, flocculation kinetics and suspension rheology are outlined and their applicability to the study of yeast flocculation discussed. Specifically, fundamental methods of predicting cell-cell interaction energies, orthokinetic flocculation rates and rheological flow properties of flocculent suspensions are detailed. While the application of these theor ies to brewing systems is somewhat difficult, they may aid our understanding of brewing yeast floccu lation. The limited information available on the colloidal nature and properties of brewing yeast cells is also summarized.

Key Words: Brewing yeast, flocculation, aggregation, colloid, review.

©

Introduction Despite the vast amount of effort that has been expended studying the phenomenon of how brewing yeast cells floccul ate, much controversy about the mechanism still exists in

© © © o

the brewing literature56. When examining the flocculation

process from a colloidal rather than a biochemical or micro biological point of view, it is apparent that a number of tenets of colloid science might be successfully applied to help increase our understanding of the process. However, surprisingly few researchers have examined brewing yeast flocculation from a colloidal viewpoint. It is the purpose of this review to detail a number of principles of colloid science and examine their application to the study of brewing yeast flocculation. Apart from the volume of literature in the brewing sciences concerned with yeast flocculation, examination of the phenomenon in light of current colloidal theory can help clarify our understanding of how yeast cells associate. While largely ignored in the past, two central tenets of colloid science, "DVLO" (after Derjaguin, Landau, Verwey and

0 O

Shearing Piano Surface Potential

Overbeek21-49) and kinetic flocculation theories can be used

to: (1) predict the energy of interaction as two yeast cells approach one another and (2) predict the rate at which cells flocculate, respectively. A third area of colloid science, concerned with the flow behaviour or rheological properties of particulate suspensions, can also provide an insight into the flocculation state of brewing yeast cells. One definition of a colloid is a particle which does not settle out of a suspension under the force of gravity. Yeast cells and floes lie in the upper size limit of this definition. Colloid particles normally have diameters of 10 nm to about

1 jim49, however, numerous research teams have employed

colloid theories to explain the behaviour of cells of diameters Of 5 tO 10 JM17.9.10.16.19.24.67.70

Zeta Potential

Distance from Surface

Fig. 1. The Stern model for decay of the electrostatic potential across an electrical double layer.

DLVO Theory

In order to examine the energies involved when two charged cells approach each other, one must first understand

the concept of the double layer. In an ionic medium, nega tively charged particles will attract cations to their surfaces. The concentration of these ions will decline with distance from the particle surface and this will result in an electrostatic potential occurring as shown in Figure 1. While variations of this diagram exist, the one portrayed below, based on the Stern model, has been employed by many researchers". In this model, counter-ions are assumed to be adsorbed on the

surface of the particle forming a Stern layer about the radius of the adsorbed ion. Also indicated is the shear boundary

(the shear plane during flow) and the zeta potential (£), the potential between this shear plane and the particle surface. Building on the double layer concept, different equations for estimating the energies of attraction and repulsion have

been developed7-23-30-47. Equation 1 below applies to large

spheres with small double layers at 'long range' distances of

greater than 2 nm46. The contribution of electrostatic repul sion (VR) to the interaction energy is then:

This document is provided compliments of the Institute of Brewing and Distilling www.ibd.org.uk Copyright - Journal of the Institute of Brewing

526

YEAST FLOCUI.AT1ON

-»h )

(1)

where eo is the permittivity of free space, e is the dielectric constant of the medium, r is the particle radius, 0 is the surface potential (often taken to be £), k is the reciprocal of the double layer thickness and h is the distance between the two particles. The attractive potential energy, VA, due to van der Waals interactions can also be estimated by: VA = A/l[h,T)r/12h

(2)

where A/(h, T) is the Hamaker function, dependent on distance and temperature, but normally taken to be a con stant.

Summation of the VK and VA terms leads to the construc

tion of so called DLVO curves (Figs. 2a-2c), which relate the change in the potential energy of interaction with distance. Calculation of the potential energies of particles interacting under various conditions can give one a useful insight into the flocculation process. DLVO curves often have a primary minimum close to the particle, followed by a primary maximum where positive repulsion forces are predominant and then a secondary minimum at a greater separation where a relatively small negative energy of attraction occurs. Some colloid scientists reserve the term flocculation to apply to the reversible approach of particle to the secondary minimum and the term aggregation for particles tightly bound in the primary minimum. However, flocculation and aggregation will be taken to be equivalent in this discussion.

A

90-

50-

30-

"'■-...

■

-30-

' B

q:

\

70

\

S 50

| .0

f-,0

/TSi—

SM

«

'c

*****

80\

60-

2 nm47. Due to retardation effects, the theory also begins to overestimate the attractive energy above 10 nm27. As well,

values used for the Hamaker function, surface potential and dielectric constant are estimates and dramatically affect the total interaction energy, Vr. Finally, application of the theory assumes that the particles are smooth spheres. Since yeast

cells are rough prolate spheroids, application of the model may result in violation of some of its assumptions. For exam ple, any fimbriae present protruding from the surface can

affect the values used for the dielectric constant. Hamaker function and the zeta potential. Aside from this type of electrostatic repulsion and van der Waals attraction there also exist other types of interactions which can influence the flocculation of yeast cells. The first of these interactions is due to the presence of polymers on the cell wall. When these polymers prevent the approach of

adjacent cells (steric repulsion), flocculation may be pre vented. Alternately, when the polymer chains are more attracted to themselves than the suspending solvent, floccu lation may occur by interpenetration of adjacent polymer chains. Bridging of cells by extracellular polymers such as fimbriae may also occur. In flocculent ale or lager cells this may be due to either calcium salt bridging or lectin-like adhesion. In such cases, the adhesion structures may bridge cells where DLVO repulsion would otherwise prevent attach ment.

for the Hamaker function™ and zeta potentials reported for brewing yeasts (letting £ = if as suggested by Lawrence el al.*3). These curves indicate that changes of Hamaker and

-10-

»

DLVO theory has a number of limitations which, if not noted, could lead to erroneous conclusions. First, the use of various expressions for the estimation of VR and VA terms are subject to debate regarding the assumption of constant charge or constant potential during particle interactions'"1. Secondly, the theory only applies at distances greater than

While it is worthwhile recognizing the preceding concerns, it is still useful to estimate DLVO interaction energies. Fig ures 2a-2c represent such calculations using equations 1 and 2. The calculation assumed the cells were suspended in a "typical" flocculation assay buffer55, using various estimates

70-

10-

[J. Inst. Brew.

40-

20-

surface charge values can dramatically affect the attractive energies between the cells. According to these estimates, the

yeast cells would only approach to the limit of the secondary minimum (>4 nm). Despite the aforementioned limitations, DLVO theory is still useful for determining the qualitative importance of the van der Waals and electrostatic repulsion forces in yeast cell flocculation. In such flocculation studies, the effect of the suspending medium on yeast flocculation rates and on theor etical DLVO interaction energies could be compared. Corre lation of these factors would indicate the importance of electrostatic repulsion in flocculation.

While electrostatic and van der Walls forces are important in the flocculence of yeast cells, it is probable that special forms of interaction such as lectin-like and hydrophobic inter actions are involved in yeast flocculation. It has recently been postulated that all three mechanisms are involved in the

phenomenon2"'2-54.

-20-

Kinetic Theory A second branch of colloid science that can be usefully employed in the study of brewing yeast flocculation is that concerned with the rate at which particles collide and associ

-40-60-

/

-80-

)

2

4

6

6

10

12

14

16

18

20

Distance between cells (nm)

Fig. 2. Potential energy curves of typical brewing yeast cells for Hamaker values of (a) 5 x 10"22, (b) 10"21 and (c) 5 x 10"21 J (@25°C, Ionic strength = 0.02 M and cell radius = 4.5 /urn, solid line indicates a zcta potential of —5 mV, dotted line indi cates a zeta potential of -ISmV). Note different scales on ordinate axis & example of primary minimum (PM) & secondary maximum (SM) in Fig. 2b.

ate. There are essentially three mechanisms by which par ticles can associate: (1) by perikinetic aggregation due to Brownian motion, (2) by orthokinetic aggregation due to fluid flow and (3) so-called ballistic aggregation arising from collisions during the settling of cells or floes. Due to the relatively large size of yeast cells, perikinetic aggregation is not important in brewing conditions. One would expect that orthokinetic, and possibly ballistic, aggregation are respon sible for the majority of brewing yeast cell interactions.


Vol. 98, 1992]

YEAST FL0CUI.AT1ON

/. Laminar flow While orthokinetic aggregation can take place during either laminar or turbulent flow, complete theories have only been developed for the aggregation of particles in laminar flow fields. Within a laminar flow field a specific shear rate is

defined as the ratio of the velocity gradient across the slipping planes to the distance between the planes (i.e., JV/h or y) as shown in Fig. 3. Shear rates have units of reciprocal time

and are normally expressed in s"1.

An expression describing rate of flocculation of perfect spheres within a laminar shear field was first developed by von Smoluchowski in 191751 and later modified by van de

Ven and Mason67:

527

the zeta potential, Hamaker function, particle size, volume fraction, medium viscosity and shear rate are known, then an estimate of the capture coefficient could be calculated. Van de Ven and Mason calculated and graphically presented the dependence of the capture coefficient on the logarithm of Ca at various ratios of Cr to Ca, different double layer thicknesses and London wavelengths (see Hunter for a

detailed explanation27). Using this method they showed that in the absence of repulsive forces, the capture coefficient rapidly declined with increasing shear. However, at high

ratios of CJCa, the orthokinetic capture coefficient was shown to decline to zero and then increase from this mini mum as the shear rate was further increased. Duszyk and

Doroszewski"' confirmed van de Ven and Mason's findings67

where N, is the number concentration of particles at time t, No is the initial number concentration of particles, a,, is the orthokinetic capture coefficient, and ipo is the initial volume fraction of particles. This expression has been said to hold

for up to 80% reduction of paticle numbers20.

The orthokinetic capture coefficient is the most important variable in equation 3 as it is directly proportional to the flocculation tendency of a yeast strain in a given environment. The value of au is determined by the forces acting on the spheres or cells as they approach one another in shearing flow. The value of the capture coefficient is thus the key parameter in orthokinetic flocculation.

Essentially, two theories have been developed which esti mate the values of the capture coefficient. The first theory considers the attractive forces and double layer repulsive (DLVO) forces which act on the cells as they approach each other67 while the second considers the attractive effect of

lectin-like binding structures present on the cell wall5. Knowl

edge of the magnitude of this value at specific shear rates as well as its dependence on the rate of shear should allow one to determine whether brewing yeast flocculation is governed by DLVO interactions or lectin-mediated aggregation.

In first theory, presented by van de Ven and Mason67, the

orthokinetic capture coefficient was shown to be dependent on van der Waals attractive forces, electrostatic repulsive forces and highly dependent on the rate of shear. In this theory, two dimensionless numbers, Cu and Cr, (relating to the attractive forces and repulsive forces, respectively) were developed:

Cr = 2ee,,i/r/3Tj>'r:

(5)

where 17 is the viscosity of the medium. Thus, if values for

and recalculated capture coefficients at conditions encoun tered in the shearing flow of cellular suspensions. While there are a number of uncertainties in the values used in the preceding DLVO calculation of the capture coef ficient, the greatest uncertainty lies in assigning a value to the Hamaker function. The function is usually taken to be a

constant; however values varying from 10~w to almost 1O~24 J have been used. A summary of Hamaker values used in, or calculated from, cell flocculation studies is provided in

Table I. A second model for cell aggregation has been proposed by Bell5 who considered only the effect of antibody (or lectin) mediated bonding on the capture coefficient. In his model, the capture coefficient was shown to be dependent upon the number of cell wall receptors, their mobility and rate of bond formation. By use of typical cell antibody interaction parameters, he calculated capture coefficients at varying rates of shear using his theory. Bell's results showed that the capture coefficient declined rapidly with increasing shear rales5. He argued that the orthokinetic capture coefficient was dependent upon and proportional to y at low shear rates and y2 at high rates of shear. In an apparent contradiction to this theory, Duszyk and others17, measured the lectinmediated aggregation of thymus cells, and found that the orthokinetic capture coefficient was independent of the rate of shear at high lectin concentrations and dependent on shear rate at low lectin concentrations. The limited amount of aggregation data available at low lectin concentrations indi cate that under their experimental conditions, orthokinetic capture coefficients actually increased with increasing mean

shear rates. However, since their finding was based on measurements at only three mean shear rates, no firm con clusions can be drawn regarding the shear rate dependence of lectin-mediated cell flocculation.

As indicated previously in a companion review56, brewing

researchers have used only empirical means to determine the

rate of flocculation. While difficult, measurement of the decline of the total number of yeast floes with time (in a defined shear field) could provide estimates of the capture

coefficient values. Knowledge of these fundamental values would allow one to determine the applicability of either van

de Ven and Mason's DLVO model67 or Bell's antibody/lectin model5. Studies of this nature would help resolve the current Force (F) Velocity (AV)

Height (h)T/7

controversy over the mechanism of brewing yeast floccu lation.

Traditionally, brewing researchers have not controlled the rate of agitation (be it either turbulent or laminar flow) prior to and during flocculation assays. Only recently, has the effect of turbulent flow on yeast flocculation been considered

by Stratford and co-workers57-58-59-""-61-62-63. Research by

Speers52 and Speers and co-workers54 have described the flocculation rates of brewing yeasts subjected to laminar

Shear rate y = AV / h

shear. However, other cells such as sheep leucocytes,7" embryonic chicken cells''"1-2425, rat thymocytes16-17, and

Shear stress o»F/A

hybridoma cells3 have been subjected to steady shear and

Viscosity n =o/1

their flocculation rates adquately described by equation 3.

Fig. 3. Representation of a simple (laminar) shear field between two parallel planes.

In the flocculation experiments in laminar shear52-54 it was

concluded that the presence of the double layer could not


528

YEAST FLOCULATION TABLE I.

[J. Inst. Brew.

Values used for the Hamakcr function in studies from the literature'

System examined

Value of the Hamakcr function (J)

biological systems chick embryo cclls'Ca & Mg-frcc Hanks saline

biological cells/aqueous systems theoretical cell models

Reference

1-5

X

io-2'

Brooks el al.7

0.035-1.9

X

io-»

Hornby."

4

X

10 21

Visser,'1*

1-10

X

10-'

Nir.-W

biological cells

4-8

X

10"J1

Lips and Jcssup.1"

red blood cells/saline

5-8

X

1021

Parsegian and Gingcll,4"

red blood cells/saline

7

X

10"

Lerchc."

aqueous systems

4

X

10'v

Ho."

10-'"

Aunins and Wang,1

hybridoma cells

*A constant value for Hamaker function is normally employed by most researchers while recognizing this practice results in a first approximation of the Hamaker function only.

adequately explain the magnitude of the orthokinetic capture coefficient. However, due to the paucity of information regarding the density of lectins on the yeast cell wall it was not possible to either confirm or refute predictions of the magnitude of the orthokinetic capture coefficient derived

from BellV model.

2. Turbulent flow In the case of flocculation arising from turbulent flow,

Weber*4 and Camp and Stein" have proposed a modification

to the von Smoluchowski expression (Eq. 3) by including a term for an average shear rate (y):

(N,/No) = e-

(13)

where m is the consistency coefficient, y is the shear rate

and n is the flow behaviour index. Similarly, Rao and Hang42 reported that Candida utilis suspensions exhibited Newtonian flow at low concentrations but could be modelled according to the Casson model at solids concentrations of 29.2% at

25.8°C in the shear rate range of 5 to 50 s"1. Like the

Bingham and power-law models, the Casson model predicts a rapid decline in viscosity with increasing shear rates:

7j°s = (oy/y)a5 + tj," 5

(14)

Miyasaka and co-workers"* also employed the Casson model

to describe the flow behaviour of suspensions of temperature sensitive mutants of S. cerevisiae.

More recently, Lenoel et al.M in 1987 reported that suspen sions of brewing yeast (strain not specified) displayed New

tonian behaviour below a concentration of 40% (w[pressed

yeast]/v) and Bingham behaviour above those concentrations. The range of shear rates employed in their research was not specified but the viscometric measurements were carried out

at 0°C. These findings agree with that of Speers et al.52-

5-\ who employed the Bingham model to describe the flow behaviour of commercial ale and yeast suspensions. It is difficult if not impossible to quantitatively compare the viscosities reported in the above studies. Factors that


530

[J. Inst. Brew.

YEAST FLOCULATION

affect yeast suspension viscosity, as discussed earlier (see Fig. 4), varied in each of the previous studies. However, it is apparent that at higher volume concentrations the yeast sus pensions exhibited shear thinning behaviour. Since the fit of different flow models (i.e., Bingham, Casson and power-law) to the viscometric data of these suspensions was justified empirically rather than theoretically, caution should be used

in choosing the best model to predict the change in viscosity with shear rate. Only the Bingham model (Eq. 8) can be

applied to these suspensions with some theoretical justifi cation within the framework of Hunter's "elastic floe model" previously discussed. Hi. Effect of temperature on the flow behaviour of aqueous suspensions—The effect of temperature on the viscosity of

most fluids is often modelled developed by Arrhenius:

with an

v — A e'JE/"^

expression

dependent flow behaviour of various food fluids:

\og(v) = a - >t

(17)

In the case of flocculent cell suspensions, it may be possible to explain changes in viscosity with shearing time on a semitheoretical basis using the orthokinetic aggregation theory previously described. When dispersed cell suspensions are sheared at low rates of shear, one would expect singlet cells to aggregate according to equation 3. As these single cells form doublets, the energy required to maintain flow would increase, resulting in a higher apparent viscosity. If this energy requirement is primarily due to increases in floe vol

first

ume or doublet separation energy, it is possible to derive an expression relating the increase in viscosity to the capture coefficient, shear rate and volume fraction:

(15)

V, = (in-'?c)e(4a«>..'lr)1 + Vc

where A is the frequency factor, AE is the activation energy, R is the universal gas constant and T is the absolute tempera ture. This relationship has been successfully applied to a wide variety of simple fluids and complex dispersions over various temperature ranges. The viscosity of water is strongly depen

dent on temperature with an increase of one C° resulting in a 2.5% reduction of viscosity at 20°C. Since by definition water is the major constituent of aqueous suspensions, one would expect a decline in their apparent viscosity with increasing temperature. However, the opposite trend has been observed in some guar41 and xanthan gum" aqueous solutions. The measurement and examination of the acti vation energy can thus be a useful tool to help understand the extent of molecular associations within a fluid"5. To date, there have been only a few reports on the effect of temperature on the flow behaviour of brewing yeast sus pensions. In research by Speers et a/.55 it was found that temperature affected the flow behaviour of ale and lager suspensions differently. In the case of ale yeasts, increasing temperatures resulted in an increase in the Bingham yield

stress (cry—equation 8) while in lager strains the yield stress decreased with declining temperature. The increase in yield stress noted in the ale strains may indicate the involvement of hydrophobic forces in these cell-cell interactions. As only four temperatures (5, 15, 25 and 35°C) were examined, no attempt was made to fit the Arrhenius model to the data. These findings agreed with other literature reports that ale strains are more hydrophobic than lager strains2-22. iv. Time dependence of yeast suspension viscosity—When reviewing the effect of time on the Theological properties of colloidal suspensions, it is useful to distinguish between different types of time dependent behaviour and clarify a number of terms employed to describe these properties. The term thixotropy is applied to systems which exhibit a reversible decrease in shear stress or apparent viscosity at a constant shear rate and steady temperature. This decline in viscosity is believed to be due to a temporary breakdown in the structure of the fluid. Thixotropy is observed in many fluid food systems when subjected to shear after a period at rest. The phenomenon can also be observed when the shear rate of a system is suddenly increased to a higher rate. In both instances the decline in measured viscosity is due to a corresponding loss of structure in the fluid. An important feature of thixotropic systems is that they will completely recover their initial structure given sufficient resting times.

Modelling the change of viscosity of fluid materials with time has been caried out by a number of authors. For exam ple, Tung et al.M examined the time dependence of egg albumen using a power-law type function: -7j,.) = a-blog(t)

workers,12-13'14 used a similar model to examine the time

(16)

where i;e is the equilibrium apparent viscosity at a fixed rate of shear, a and b are constants and t is time. DeKee and co-

(18)

This semi-empirical expression was derived by Speers92 and assumed: (1) that viscosity increases could be attributed to single cells or floes forming doublets, (2) that (as assumed

by Hunter2") the high particle concentration did not seriously

affect the rate law, (3) that as the floe volume increased, shear forces caused floe breakup until an equilibrium was reached, and finally, (4) that the the rate constant for doublet formation was much larger than the rate constant for doublet breakup. In view of the uncertainties involved in the visco metric measurement of the orthokinetic capture coefficient, it was been termed the pseudo-capture coefficient. Values for the orthokinetic capture coefficient derived from viscometric data using this method have been reported

by Speers et a/.52-55 and agreed with the limited estimates of

the coefficient measured using light microscopy by the same researchers54. No other researchers have reported orthoki netic capture coefficients measured from brewing yeast experiments.

Summary This review has presented selected areas of colloid science which, while not traditionally considered by brewing scien tists, can be usefully applied to the study of brewing yeast flocculation. Application of such fundamental colloidal the ory and associated techniques may lead to the resolution of some of the present controversies concerning the mechanism of yeast flocculation. Use of these techniques may also permit quantification of intracellular forces involved in cell-cell flocculation, and may lead to a better understanding of brew ing yeast flocculation.

Acknowledgements. This study was funded by a grant from

Labatt Breweries of Canada and a scholarship from the British Society of Rheology (to R.A.S.) which is gratefully acknowledged. We would also like to thank Dr. D. Brooks and Dr. K. Pinder for their helpful advice.

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YEAST FLOCUI.AT1ON

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