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Presenting models at both these levels emphasizes the relationshipbetween the whole animal level and the cellular level and assists readers togain an appreciation of the approximations u

22 Mathematical Modelling of Wool

Growth at the Cellular and Whole Animal Level

1CSIRO Livestock Industries, GPO Box 1600, Canberra, ACT 2601, Australia;

2CSIRO Plant Industry, GPO Box 1600, Canberra, ACT 2601, Australia

Introduction

Large variation exists both between and within sheep in the rate of growth,composition and physical characteristics of wool fibres The rate of clean woolgrowth can range from less than 1 to greater than 30 g per animal per day Themean diameter of fibres in the fleece from sheep of ultra-fine wool Merinostrains can be as low as 13mm whereas it is greater than 40 mm for some carpetwool breeds, and the diameter of individual fibres can range from less than

10mm to greater than 100 mm Diameter can also vary considerably along thelength of individual fibres reducing the strength of the wool, causing it to become

‘tender’ and decreasing the commercial value of the fleece Many fleece staplesare highly crimped whereas some have little or no crimp (Reis, 1992) Theamino acid composition of wool may also vary; in particular, the sulphur-containing amino acid cystine (usually quoted in units of half-cystine so that it

is equivalent to the amino acid cysteine) may vary considerably (Reis, 1979).This variation in wool characteristics is due to both genetic and environ-mental factors For each animal, the potential rate of wool growth and themorphology and chemical composition of wool fibres growing at their max-imum rate are controlled by several genetically determined factors and mech-anisms These were outlined in an earlier publication (Black and Nagorcka,1993) The actual rate of wool growth and the characteristics of the wool fibresare the result of the interaction between the genetic factors and the supply ofnutrients to the wool follicles (Black, 1987) The latter is influenced by thequantity and type of nutrients absorbed from the digestive tract and the com-petition for nutrients between wool growth and the growth of other bodytissues Thus, the stage of growth and the reproductive status of an animal,the amount and composition of the diet eaten, the climatic environment, thepresence of parasites and disease may all influence the amount and quality ofthe wool grown

ß CAB International 2005 Quantitative Aspects of Ruminant Digestion

and Metabolism, 2nd edition (eds J Dijkstra, J.M Forbes and J France) 583

In this chapter we describe our current capacity to quantitatively predictwool growth The mathematical models of wool growth presented here havebeen developed at two levels: for use in research to understand the factorscontrolling wool growth at a cellular level and for use by managers of woolproduction enterprises to optimize the quality and quantity of the wool pro-duced Presenting models at both these levels emphasizes the relationshipbetween the whole animal level and the cellular level and assists readers togain an appreciation of the approximations used at the higher level.

Equations Describing Fibre Growth in a Mature Wool Follicle

Cell division and differentiation in a mature wool follicle

Wool fibres are produced in primary and secondary wool follicles in the skin(Hardy and Lyne, 1956) Primary follicles (Fig 22.1) are so-called because theyare the earliest follicles to initiate in the skin during fetal development, and theydevelop with a sebaceous gland as well as an arrector pili musculature and asweat gland attached to them Secondary follicles initiate later in fetal develop-ment and only have a sebaceous gland attached to them Both primary and

Fig 22.1 A primary wool

follicle is illustrated showing the

arrector pili muscle, the sweat

gland and the sebaceous gland

attached to the follicle The cells

forming the fibre originate in the

follicle bulb and migrate up the

follicle towards the skin surface,

undergoing various changes that

are classified into the different

zones depicted here (Hardy and

Lyne, 1956; Chapman and Ward,

1979)

Epidermis Pilary canal

Zone of sloughing

Zone of final hardening

Keratogenous zone

Cell division

Dermal papilla

Fibre

Sebaceous gland

Sweat gland

Arrector pili muscle

Follicle bulb

secondary follicles normally produce only one fibre and this originates at thesite of highest mitotic activity in the follicle, i.e in the follicle bulb Cell division

is concentrated in the lower part of the follicle bulb (Fig 22.1) in a regionsurrounding the dermal papilla

It has been proposed (Nagorcka and Mooney, 1982; Nagorcka, 1984) thatepithelial stem cells (i.e epithelial cells that are totipotent and divide indefin-itely) are located in contact with the basement membrane that surrounds thefollicle and also separates the epithelium from the dermal papilla As the stemcells divide, a fraction of them are forced out of contact with the basement and

so become committed to a path of differentiation that terminates in cell death.Once committed, the cells may undergo a limited number of further celldivisions as they differentiate The age of a cell is defined to be the time sinceits commitment A scheme for the differentiation of these cells has beenproposed (Nagorcka, 1984) in which the path of differentiation chosen bycommitted cells depends on the concentration of two chemical factors thatthey experience at specific cellular ages as they migrate up and out of thefollicle bulb in response to the pressure in the follicle bulb One of the chem-icals, Z, is produced in the dermal papilla and diffuses radially away from thepapilla through the follicle bulb The second chemical factor is a component, X,

of a reaction–diffusion (RD) system which has been described by Nagorcka andMooney (1982)

It has been observed that initially cells migrate up from the basementmembrane at the base of the follicle bulb at different rates depending on theirdistance away from the dermal papilla (Fig 22.2) (Chapman et al., 1980).According to the differentiation scheme referenced above, cells at an early age,i.e while they are still low in the bulb, differentiate as presumptive fibre cells,inner root sheath (IRS) cells or outer root sheath (ORS) cells (Fig 22.2) At laterages and slightly higher in the bulb further differentiation occurs, which in thecase of the presumptive fibre cells leads to formation of a single cell layersurrounding the fibre cortex called the fibre cuticle The fibre cortex alsodifferentiates into orthocortical and paracortical cells (and under some circum-stances the cortex may also include mesocortical and/or metacortical cells)(Ahmad and Lang, 1957) In large diameter fibres, cells arising from the apex

of the dermal papilla may also differentiate to form medullary cells, which thenact as a central core to the fibre Once IRS and fibre cells reach the apex of thebulb they migrate up at the same rate Some migration of ORS cells also occursbut at a lower rate

The proteins that form the fibre and IRS are synthesized mainly in the zonejust above the apex of the dermal papilla called the keratogenous zone In thiszone macro- and microfibrils form in the cortical cells and are surrounded by aproteinaceous matrix that acts as a binding material Further up the follicle, thecells reach the zone of hardening where, catalysed by copper, the thiol residues

of cysteine undergo oxidative closure to form the hard disulphide linkages ofkeratin

The contents of IRS cells that migrate up the follicle are resorbed to someextent and the remains are sloughed into the pilary canal in the upper part ofthe follicle Wax and suint are also secreted into the pilary canal by the

sebaceous and sweat glands Finally the fibre emerges from the pilary canal atthe skin surface partially coated with ‘grease’ consisting of wax, suint and othercontents of the pilary canal.

Equations describing the cell dynamics in the follicle bulb

A number of researchers have studied the cell division rate in wool follicle bulbs(Fraser, 1965; Wilson and Short, 1979; Hynd, 1989; Hocking-Edwards andHynd, 1992) Their observations have recently been summarized and com-pared by Hynd and Masters (2002) At a maintenance level of nutrition in amedium-wool Merino a typical follicle bulb contains about 600 cells The bulbcells have a radius rcell 4 -5 mm and hence a cell volume of about 400 mm3 Itfollows that the volume of the follicle bulb is 2:3  105mm3 Assuming ahemispherical shape, the bulb has a radius RBulb 50 mm If the dermal papillahas cylindrical shape with a radius rDerpap Bulbthen the surface area ofthe membrane is approximately AMembrane¼ 2pR2

Bulbþ 2prDerpapRBulb¼

600 bulb cells If we regard the number of cells in contact with the membrane

Fig 22.2 A schematic diagram showing the

migration paths of cells out of the follicle bulb

According to the differentiation scheme of Nagorcka

and Mooney (1982) and Nagorcka (1984), cells aged

T1days that have reached the level in the bulb

indicated undergo the first stage of differentiation

becoming either presumptive fibre, inner root sheath

(IRS) or outer root sheath (ORS) cells According to

the scheme this is largely controlled by a chemical

factor produced in the dermal papilla that diffuses

radially away to produce a concentration gradient

shown here by the plot of [Z ] with distance from the

centre of the dermal papilla

Z

ORS

IRS FIBRE

T 1

IRS ORS

as stem cells, denoted here as NStem, then the stem cell density on the basementmembrane is given by dStem¼ NStem=AMembrane( 2).

The equation describing the rate of change in the number of stem cells onthe basement membrane in the follicle bulb is:

dNStem(t)

dt ¼ fStemDivNStem(t)
fCommitmentNStem(t) (22:1)where fCommitmentis the fraction of stem cells committed per day (i.e breakingattachment with and migrating away from the membrane) and fStemDiv is thefraction of stem cells dividing per day If the follicle is in equilibrium all rateequations are equal to zero As a first approximation both fStemDiv and

fCommitment are considered to be constants determined by genotype, i.e byfactors such as growth hormones with little dependence on diet fCommitment isset to a constant value of 1/7, i.e one in seven stem cells become detachedfrom the basement membrane per day (Potten and Lajtha, 1982) fStemDiv isgiven by:

fStemDiv¼ fCommitmentkStemDensity (22:2)where

0:016cells=mm2

Commitment of stem cells provides an input into the number of tiating cells in the follicle bulb, NDiff These cells are not attached to themembrane The number of committed or differentiating cells in the folliclebulb is assumed to divide at the fixed rate fDiffDiv If the number of differentiatingcells migrating out of the bulb per day is _NMig(t)¼ dNMig(t)=dt, then NDiff isgiven by:

differen-dNDiff(t)

dt ¼ fCommitmentNStem(t)þ fDiffDivPhoto(t)
_NNMig(t) (22:5)where fDiffDiv is considered to be a constant (i.e genetically determined andindependent of diet) and is set to a value of 1 (per day), i.e each cell undergoesone division per day on average _NMigis considered to be a proportion fMigBulb

of the unattached cells in the bulb, i.e

NMig(t)¼ fMigBulbNDiff(t) (22:6)

fMigBulbis defined below in Eq (22.7) Eq (22.5) includes an additional functionPhoto(t) multiplying the division rate of differentiating cells This is included torepresent the effect of photoperiod on the rate of wool growth, which isdiscussed in a later section (see Eqs (22.18) and (22.19)) Current evidencesuggests that photoperiod acts through the release of melatonin by the pinealgland, and influences the skin through prolactin (Lincoln et al., 1998) Prolac-tin and prolactin receptors have been found distributed in the dermal papilla,the wool follicle bulb and the ORS (Choy et al., 1997; Nixon et al., 2002) Weare assuming that prolactin regulates the division rate of the differentiating cells

in the follicle bulb If this is correct then the amplitude APhotoin Eqs (22.18) and(22.19) should be reduced by the order of a factor of 10 because of thefeedback occurring between the keratogenous zone and the follicle bulb, asdiscussed in relation to Figs 22.3 and 22.4

The number of cells migrating out of the follicle bulb, _NMig(t) (Eq (22.5)) isexpressed as a fraction, fMigBulb, of the number of differentiating cells in thebulb The fraction of cells migrating out of the bulb is expected to increase withthe pressure in the follicle bulb, PBulb, and to decrease as the resistance to flow

of cells up the follicle, RMig, increases fMigBulb is therefore defined by:

fMigBulb¼ f0

MigBulb

PBulb(t)

P0 Bulb

!

0 Mig

f0

MigBulb is considered to be genetically determined, i.e largely independent ofdiet, and is set to a constant value of 1 (per day)

The follicle, including the follicle bulb, is surrounded and contained by a net

of collagenous fibres so that the pressure in the follicle bulb will increase as thenumber of cells in the follicle bulb, and hence the volume of the bulb, VBulb,increases A functional form for this dependence has not been measured It isassumed here to be of the form

wherea is a constant

The resistance to cellular flow up the follicle is another aspect of folliclefunction that has never been studied experimentally In the upper three-fifths ofthe follicle, corresponding to the zone of final hardening (Fig 22.1), ‘degrad-ation of the IRS begins with presumed resorption of some cell contents’ (Chap-man and Ward, 1979) In fact, in the upper half of this region, corresponding to

the zone of sloughing and the pilary canal, the fibre becomes separatedfrom the IRS Therefore the main restriction to cellular flow occurs in thekeratogenous zone and it is assumed here to be dependent on the total volume,i.e the total mass of follicular material, MKer, in this zone defined by therelationship:

they migrate up the follicle through the keratogenous zone (Hynd, 1994) As afirst approximation these volumes are taken to reflect the changes in thecontents or mass of the cells.

Average rate of cell division in the wool follicle bulb

In the cellular model described above the average rate of cell division in the folliclebulb, CDiv, can be calculated by summing the cell division of both stem cells anddifferentiating cells and dividing it by the total number of cells in the bulb, i.e

CDiv(t)¼ ( fStemDivNStem(t)þ fDiffDivNDiff(t))=NBulb(t) (22:13)where

In equilibrium at a maintenance level of nutrition we can substitute

fStemDiv¼ 1=7, fDiffDiv¼ 1 and NStem=NBulb¼ NDiff=NBulb¼ 0:5 to obtain

CDiv¼ (1=7)  0:5 þ 1  0:5 0:57 consistent with observations at ‘medium’nutrition levels (Hynd and Masters, 2002)

Protein synthesis in the wool fibre

Variations in the amino acid composition of wool are known to occur betweenbreeds and between animals within a breed; variations are also known to occur inresponse to changes in nutrition (see reviews by Reis (1979), Black and Reis(1979), Rogers et al (1989) and Hynd and Masters (2002)) To characterizethese variations wool keratins are often classed into four groups Those in themain group are the low-sulphur (LS) keratins comprising about two-thirds of theproteins and providing the structural components of the microfibrils A secondgroup contains the high-sulphur (HS) proteins, which are rich in cystine, prolineand serine These proteins form the matrix surrounding the microfibrils Theproportion of the HS proteins in wool varies between 18% and 35% The ultra-high-sulphur (UHS) proteins in a third group are especially rich in cystine Theyare often considered as a sub-group of the HS proteins The fourth groupcontains the high-glycine/tyrosine (HGT) proteins that make up between 1%and 12% of the total The HGT proteins are found primarily in the matrix

A part of the observed amino acid variation in wool is due to variations incortical cell type determined in the follicle bulb For example, there is morematrix in paracortical cells than in orthocortical cells The scheme for cellulardifferentiation in the follicle bulb proposed by Nagorcka and Mooney (1982) andNagorcka (1984) produces a complicated relationship between follicle bulb sizeand shape, and the spatial pattern of cortical cell type in the fibre cross-section.Both genotype and nutrition determine the size and shape of the follicle bulb.Since the relationship is complex we will not attempt to describe it here but ratherdirect readers to an earlier review (Black and Nagorcka, 1993) The predominant

cortical cell pattern in the finer wool animals is expected to be bilateral, althoughthe proportions of ortho- and paracortex may still vary with follicle bulb size andshape It is emphasized that variations in composition caused by changes in thesize and shape of the follicle bulb are not considered in the following discussion.

A significant part of the variation in wool composition is also due tovariations in wool protein synthesis caused by changes in the amount andprofile of the amino acids digested and absorbed Some of the variation incomposition is, therefore, the result of competing biochemical reactions con-trolling the utilization of nutrients by wool follicles and other tissues One modelthat has explored the effect of competition for nutrients on wool competition isthat by Black and Reis (1979) (see also Black and Nagorcka (1993)), whodemonstrate that it is possible to use Michaelis–Menton kinetics to quantifythe rate of protein deposition, d Protj(t)=dt, in several protein groups in wooldenoted by j A similar approach is adopted here for each of the four proteingroups in wool (discussed above) specified by j ¼ LS, HS, UHS, HGT Theequation used here is given by:

d Protj(t)

i ¼1,n AA

d ~PProtij(t)dt

where i¼ 1, nAAspecifies a particular amino acid in a set of nAAamino acids

d ~PProtij(t)=dt is the calculated rate of synthesis of group j proteins determined

by the concentration, Ci, of amino acid i, and the concentration of able energy in plasma CME, given that the fraction of amino acid i in group jprotein is fij Each reaction rate d ~PProtij(t)=dt is characterized by a maximumvelocity Vijand a binding affinity Kij

metaboliz-Attempts to directly measure the size (i.e maximum diameter and length)

of cortical cells forming the mature fibre (Williams and Winston, 1987; Hynd,1994; Hynd and Masters, 2002) suggest that the size may remain unchangedeven in response to significant nutritional variation If this is true it implies thatcortical cells grow to synthesize approximately the same total weight of protein(keratins), ProtKer, so that a cell reaches a maximum volume ( 1500 mm3,Hynd, 1994) and weight MKerCell(t)¼ MBulbCell(t)þ ProtKer 1500 (mm3)

 density of wool(g=mm3) (Eq (22.9)) In fact, the total weight of proteinsynthesized in cortical cells, ProtCell is expressed as:

dt , if ProtCell (t )< ProtKer

0 if ProtCell (t ) ProtKer

(

(22:16)

Since each cortical cell grows to its maximum weight in the follicle, Eq.(22.16) is used only to calculate the protein composition of wool, and toestimate MKerCell(t) in Eq (22.10) In principle they are also required to calculatethe rate at which wool is produced in the follicle as measured at the skin surface

at time t Wool growth rate of the fibre, WGRFibre, is given by:

WGRFibre(t)¼ FFibreN_NMig(t
tFibre)MKerCell(t
tFibreþ 3) (22:17)

where tFibreis the time taken for the cells to migrate from just above the folliclebulb to the skin surface If it takes approximately 7 days for cells to migrate thefull length of the follicle (Downes and Sharry, 1971), then tFibre

days During the first 3 days of the migration the cells grow in size in thekeratogenous zone Observations to date (Hynd, 1994; Hynd and Masters,2002) appear to be consistent with MKerCell(t) remaining at or close to itsmaximum value as discussed above FFibreis the fraction of cells migrating out

of the bulb that form part of the fibre This fraction has been measured (Hynd,1989) and found to vary between sheep, but not to vary with the level ofnutrition FFibreis therefore considered to be genetically determined and set to

a fixed value; a typical value is FFibre¼ 0:25

The Effect of Photoperiod

It has been observed in experiments where sheep are fed a uniform diet at aconstant level of intake that the wool growth rate varies from a maximum insummer to a minimum in winter Although this was initially attributed totemperature, it has since been shown to be caused by photoperiod(Hart, 01955, 1961; Morris, 1961) Photoperiod appears to have a directeffect on the wool growth rate that in some breeds of sheep causes the fleece toshed In domestic breeds of sheep the annual rhythm of fleece shedding doesnot occur but a significant variation in the rate of wool growth remains

In a review of the observations of the effect of photoperiod on wool growthNagorcka (1979) showed that a sinusoidal function of the form:

wherev ¼ 2p=365, is sufficient to capture most of the variation in the growthrate of the fleece The amplitude of the variation, APhoto, is the differencebetween the maximum and the minimum growth rate expressed as a fraction

of the mean APhoto was found to vary between 0.15 and 0.70 depending onbreed Examples of values for APhotoare: Merinos 0.15; Southdown, Ryeland0.45; Corriedale, Romney 0.30; Dorset, Suffolk, Border Leicester 0.55; Bor-der Leicester  Merino 0.35 Eq (22.18) can also be expressed in terms ofdaylength, DL(t), as follows:

Photo(t)¼ 1 þ 0:1APhoto(DL(t)
12) (22:19)

Variability in Fibre Diameter and Length

Fibre diameter is a major factor determining the price of wool It has been wellestablished that there is a relationship between fibre diameter, DFibre, and thediameter of the wool follicle bulb (and dermal papilla) (Hynd, 1994), whichaccounts for most of the observed variability whether caused by nutrition orgenotype A linear relationship of the form:

DFibre(t)¼ D0

Fibreþ FBulbDBulb(t) (22:20)

is often used (e.g Henderson (1965)), where D0

Fibreand FBulbare constants, and

DBulb is the diameter of the follicle bulb Assuming the shape of the bulb ishemispherical:

LFibre(t)¼gWoolWGRFibre(t)

p(DFibre(t)=2)2 (22:22)given that the density of wool is gWool¼ 0:35  103kg=m3 Since WGRFibre iscalculated independently of DFibre, LFibre may vary at least to some extentindependently of DFibre

Staple Strength

To produce yarn, wool is processed through many stages, for example, ing, combing, carding and spinning Fibre breakages can occur during each ofthese stages of processing leading to losses of wool, called noil, and slowing ofthe rate of processing; both will cause the cost of fabric production to increase

wash-An objective measure called staple strength was introduced to help buyersassess the potential for fibre breakages Staple strength is second only tofibre diameter in determining the price of wool Factors that influence staplestrength have been reviewed by Reis (1992)

It is known that staple strength is dependent on both the coefficient ofvariation in fibre diameter between fibres in the staple, a characteristic that is

largely genetically determined, and on the variation in fibre diameter along thelength of the fibres, i.e DFibre, a characteristic that is largely determined byenvironmental factors (Petersen et al., 1998) It may be possible to use theexisting information to develop equations to account for the relationshipbetween staple strength and the variation in diameter along and between fibres.Unfortunately no satisfactory model for staple strength has yet been derivedfrom the observations A mathematical model incorporating all the majorfactors contributing to staple strength still remains a missing component ofour capacity to model wool growth.

Fibre Shape

Wool fibres have a characteristic shape referred to as crimp Crimp was originallyused as a visual indicator of the diameter of the fibre However, this has now beenreplaced by direct measurements of fibre diameter Recent research (MichaelHaigh and Gary Robinson, personal communication) has shown that crimpfrequency is still a factor in determining fabric attributes such as pilling andshrinkage, which are less with high-crimp frequency wools, and topmakingperformance, handle and softness, which are better with low-crimp frequencywools Therefore crimp is still a factor in assessing ‘wool quality’ and influences theprice of wool, but it is less important than either fibre diameter or staple strength

A mechanism explaining the formation of crimp which depends on themovement of cells out of the follicle bulb and on their migration up the folliclehas been proposed by Nagorcka (1981) This mechanism is based on thecapacity of the fibre to bend and twist while still in the follicle and the way inwhich this can affect the spatial distribution of cortical cell type within the fibrecross-section It is entirely complementary to the cellular kinetics described

in Eqs (22.1) to (22.22) The mechanism for crimp establishes a causalrelationship between crimp frequency and follicle length consistent with obser-vations (Nay and Johnson, 1967), and confirms that there is no direct relation-ship between crimp frequency and fibre diameter

Performance of the Model of Cell Dynamics in the Wool Follicle

Equations (22.1) to (22.22) describing cell division and fibre growth in a maturefollicle have been solved for a situation where the level of intake is doubled from

a maintenance level after 30 days The immediate effect is to cause proteinsynthesis in the keratogenous zone to increase The increased protein synthesisthen causes MKer (Eq (22.10)), the total cell mass in the keratogenous zone,

to increase steadily This also causes an increase in the resistance to cellmigration up the follicle As shown in Fig 22.3, the increased resistancecauses NDiff(the number of differentiating cells) and the pressure in the folliclebulb to increase, leading to an increase in the volume and surface area of thebulb so that NStem also increases An increase in NDiff and NStem causes anincrease in the mitotic activity in the follicle bulb and an increase in _N ,

leading to a further increase in MKer This causes another sequence ofchanges leading to a further increase in MKer This demonstrates that themechanisms now represented in Eqs (22.1) to (22.22) constitute a feedbackmechanism between the keratogenous zone and the follicle bulb The effect ofthe feedback mechanism is to cause increases in cell numbers in the follicle bulbthat are clearly lagged by approximately 20 days behind the changed level ofintake as can be seen in Fig 22.3 (a lag is defined as the time taken for aquantity to move two-thirds of the way towards its new equilibrium).

Such a lag in the response of cell number in the bulb is also seen in thenumber of cells migrating out of the bulb per day _NMigas is evident in the fibregrowth rate, WGRFibre(Fig 22.4, Eq (22.17)) Wool growth as observed at theskin surface WGRFibre(t
tFibre) lags even further behind any change in nutritionbecause of the time required, tFibre, for the fibre cells to migrate up the follicle tothe skin surface (Fig 22.4)

It has been known for some time that the rate of wool growth lags26 daysbehind any change in intake (Nagorcka, 1977) The model of fibre growth inEqs (22.1) to (22.22) is the first biological explanation for the occurrence of such

a substantial lag in the response of the wool growth rate to variations in nutrition.The response in changes of fibre diameter is also lagged (Fig 22.4), as is thelength growth rate (not shown)

The rate of protein synthesis into the four protein groups LS, HS, UHSand HGT is regulated by Eq (22.15) The most limiting amino acids in the case

of wool growth are normally the sulphur-containing amino acids (SAA) The

HS and UHS groups are much more sensitive to the availability of SAA thanare the LS and HGT groups, causing the proportions of HS and UHS groups to

be more variable This has been discussed by Black and Reis (1979) anddemonstrated by them using equations similar to those in Eq (22.15) Sincesimilar results are obtained here using Eqs (22.1) to (22.22) readers are referred

to Black and Reis (1979) and the review by Black and Nagorcka (1993) wherethese aspects of wool growth are discussed in detail

Equations Describing Wool Production in a Fleece

Wool follicle density and distribution

The fleece is made up of millions of fibres The actual number of fibres in afleece is dependent on breed For example, in Merinos this number has beenestimated to be between 40 and 80 million, although extremes of170 millionhave also been observed In coarser wool breeds, such as English longwools(e.g Lincoln), the number is more like 10 million

The millions of wool follicles in an animal that produces these fibres havebeen classified into a number of types depending on their position in theobserved time sequence of events seen in the initiation of these follicles (Carterand Hardy, 1947; Hardy and Lyne, 1956) Nagorcka and Mooney have used

a model based on a reaction–diffusion (RD) mechanism to predict a time

Time (days)

0 20 40 60 80 100 120

0.5 1.0 1.5 2.0

Number of stem cells

Fig 22.3 The response predicted in the number of differentiating cells in the follicle bulb, NDiff,and the number of stem cells in the follicle bulb, NStem, when the level of intake is doubled

at 30 days The predictions are made by solving Eqs (22.1) to (22.22) that define the cellularmodel

Time (days)

0 20 40 60 80 100 120

0.5 1.0 1.5 2.0

18 20 22 24 26 28 30 32

Fig 22.4 The response predicted in the fibre growth rate in the follicle, WGRFibre(tþ tFibre), and

at the skin surface, WGRFibre(t), as well as the fibre diameter when the level of intake is doubled

at 30 days The predictions are made by solving Eqs (22.1) to (22.22) that define the cellularmodel

sequence of spatial patterns to control follicle initiation and development(Mooney and Nagorcka, 1985; Nagorcka and Mooney, 1985; Nagorcka,1995a,b) The mechanism used is, in fact, basically the same as that used toaccount for many aspects of fibre formation in the follicle bulb (Nagorcka andMooney, 1982; Nagorcka, 1984) The follicle initiation model is important

in the context of modelling wool production in that it provides a causallink between the follicle size distribution and follicle density Such a causal linkappears to be consistent with the strong genetic correlation observed betweenmean fibre diameter and follicle density (Davis and McGuirk, 1987), and hencebetween the mean fibre diameter and the total follicle density of an animal Onthe basis of this causal link it is reasonable to characterize the fleece of an animal(or of a breed or strain) by the total skin surface area (containing follicles), ASur,the total follicle density, NFol, and a size distribution of the follicles The sizedistribution of the follicles may itself be characterized by the distribution of fibrediameters specified by the mean diameter, DFibre, and the coefficient of variation,

CVFibre, at a maintenance level of nutrition The specified or input value of DFibre

is required to initialize the fibre model defined above by Eqs (22.20) and (22.21)

in order to calculate WGRFibre(t) The expression for rate of wool growth in thefleece, WGRFleece, is then given by:

WGRFleece(t)¼ ASurNFolWGRFibre(t) (22:23)

Predictions of Wool Production using Current Models

Simplified models currently used in decision support tools

The most advanced model of wool growth currently used as a component of aruminant model to analyse the performance of wool production enterprises isavailable in a decision support tool calledGRASSGRO, designed for the strategicmanagement of grazing animals (Moore et al., 1997) The wool growthcomponent ofGRASSGROdoes not attempt to model growth at the level of thecell as in Eqs (22.1) to (22.22) Therefore it does not attempt to model cellkinetics in the follicle, or to relate fibre diameter to the changing follicle bulbsize, or to make wool growth directly dependent on the profile of amino acids

GRASSGROdoes, however, express the wool growth rate as a function of the totalamount of absorbed amino acids It also incorporates a lag in the wool growthrate, to represent the kinetics of cells migrating out of the follicle, and calculatesthe fibre diameter and length as functions of the wool growth rate

In GRASSGROthe growth of wool is predicted on a daily time step In theanimal model within this tool (Freer et al., 1997) intakes of digestible drymatter and crude protein by the sheep are predicted from the changing pattern

of available pasture (driven by daily climatic data) and from supplementary feedsthat may be offered to the animals From these intakes, the metabolizableenergy, ME (MJ), rumen-degraded protein, undegraded dietary true proteinand microbial true protein are computed The truly digestible fractions of the

last two components make up the digestible protein leaving the stomach(DPLS), which represents the total amount of amino acids available for syn-thetic processes No attempt is made to predict the proportions of individualamino acids in the DPLS, a large part of which is usually derived from themicrobial protein The genetic potential of the sheep with respect to the growthand diameter of the fibres is deduced from the animal specification provided bythe user: the standard reference weight, SRW (kg), being the weight of theshorn mature sheep in average body condition, the standard fleece weight,SFW (kg), being the average annual weight of greasy fleece and the averagediameter, Dmean(mm), of fibres in the fleece The yield, Y, of clean woolexpected from the greasy fleece must also be supplied by the user.

Daily wool growth in the fleece, WoolFleece(t) (g), is obtained by integratingthe wool growth rate of the fleece (Eq (22.24)) WGRFleece(t) estimated as a 25-day running mean (Eq (22.25)) to allow for the lag (25 days) discussed above (Figs22.3 and 22.4) The daily increment to this function, ProtWool(t) (g), (Eq (22.26))

is predicted either from the DPLS, DPLSWool(t) (g), that is available for woolproduction, i.e after deducting the needs for gestation or milk production (Eq.(22.28)) (see Corbett, 1979), or from the intake of ME, MEWool(t), similarlyadjusted (Eq (22.27)), whichever is limiting Protein that is mobilized frombody tissue in sheep that are losing weight contributes to the DPLS available forwool growth, an assumption supported by the recent work of Revell et al.(1999) The weight of protein, PG (g), mobilized per kg of loss of empty bodyweight in mature sheep is predicted from the relative body condition, BC¼W/SRW, where W is the current liveweight of the sheep, by the relationship

PG¼ 207
115BC, derived from the results of Wright and Russel (1984)with cattle In immature sheep, the protein content of weight loss is predicted

as a function of the degree of maturity of the animal (Freer et al., 1997)

where WLAG¼ 25 days

ProtWool(t)¼ min 10  0:116DPLSð Wool(t), 10 1:4MEWool(t)Þ

(22:28)and

FolDev(t)¼ 1
0:75 exp (
0:025Age(t)) (22:29)Hogan et al (1979) estimated that, for a wide range of Merino strains, themean gross efficiency of conversion to wool of amino acids absorbed fromroughage-based diets was 0.116, with most values lying between 0.103 and0.133 Data analysed by Kempton (1979) suggested that synthesis of wool islimited by DPLSWool(t) until the ratio of DPLSWool(t): MEWool(t) exceeds 12.Above this point, wool synthesis is limited to 0:116  12 g=MJ MEWool(t), i.e.

1:4 g=MJ MEWool(t) (Eq (22.26) and Fig 22.5) This efficiency of conversion ofDPLSWool(t) applies to mature Merinos in which the ratio of SFW to SRW isapproximately 0.1 (Hogan et al., 1979)

The ratio SFW:SRW scales ProtWool(t) and changes made by the user adjustthe efficiency of wool growth for other types of sheep or for other diets that areknown to provide absorbed protein with a higher proportion of sulphur-con-taining amino acids than would be expected from diets in which the DPLS isderived mainly from microbial crude protein

ProtWool(t) (Eq (22.26)) also includes a dependence on daylength, DL(t) (h)given by the function Photo(t) defined in Eq (22.19) Photo(t) describes theeffect of photoperiod on wool growth and is specific to the breed (Nagorcka,1979)

Secondary wool follicles are still developing during the first few months oflife and take some time to reach their full fibre-growing potential ConsequentlyProtWool(t) in Eq (22.26) includes the factor FolDev(t) (Eq (22.29)) thatquantifies the rate of maturation of secondary follicles with age, Age(t) (days)(Lyne, 1961)

No estimate is made of the number of cells in the follicle bulb, and hencethe volume of the bulb Therefore Eqs (22.20) to (22.22) cannot be used tocalculate the fibre diameter and the length growth rate Instead it is assumedhere that the ratio of the diameter of new wool to its length is constant(Downes, 1971; Reis, 1991), and the diameter of the day’s new growth,

DFib(t), is estimated (Eq (22.30)) as a proportion of the average fibre diameterspecified for the animal type, DMean This proportion is determined by the ratio

of predicted wool growth to the specified average daily growth of clean wool,WoolMean, adjusted for the age of the sheep

DFib(t)¼ DMean

WoolFleece(t)WoolMean(t)

1 =3

(22:30)where

The predicted value of fibre length growth rate, LFib(t) (cm) (Eq (22.32)) isderived from the day’s growth, assuming that mean follicle density is

NFol¼ 6  107=m2 over the predicted surface area of the sheep (Eq (22.33))

in Western Australia, a Mediterranean-like environment As the observed rates of wool growthare estimated as proportions of the total fleece weight at the second shearing, they cease at thisshearing The predictions are made using the simplified model defined by Eqs (22.23) to (22.35).

LFib(t)¼ 100 4WoolFleece(t)

pgWoolASurNFolð10
6DFib(t)Þ2 (22:32)where the surface area of the skin (m2) is given by:

To obtain the average fibre diameter of the whole fleece grown over a period

of 1 year, the measure used for commercial purposes, the fibre diameter isweighted by the length, according to Eq (22.34):

Predictions of seasonal variation in wool production in Western Australia

Schlink et al (1999) presented one of the few sets of data on seasonal variation

in wool growth rate and fibre diameter in grazing sheep These attributes weremeasured at 4-week intervals over 13 months in mid-side samples cut fromyoung Merino wethers grazing an annual pasture 60 km east of Perth, WesternAustralia, in a Mediterranean-like environment The sheep were also weighed

at 2-week intervals Ideally a full set of observations to test the predictions of thegrazing model would include weather data, soil data and observations of pas-ture availability, botanical composition and nutrient composition A completeset of observations is rarely collected, nevertheless the available informationwas used to simulate the grazing system, usingGRASSGRO

The comparison between observed and predicted values for the 13months from shearing on 29 September 1992 (Fig 22.5) shows reasonableagreement between observations and predictions of liveweight, wool growthrate and fibre diameter Significant discrepancies do occur at times of rapidchange in pasture growth There could be various reasons for these discrep-ancies, e.g incorrect predictions of pasture growth and/or quality in re-sponse to weather conditions, the need to account for variations in aminoacid availability and/or for variations in amino acid absorption by the ani-mals, or perhaps the need to account for variations in the ratio LFib(t)=DFib(t),which is assumed to be constant in GRASSGRO However, to examine these

possibilities and to provide an adequate test of the validity of the modelmuch more detailed measurements would be required at the site of a futureexperiment.

Summary and Discussion

The cellular model of fibre growth

It has been observed that sulphur amino-acids (SAAs) are frequently limiting therate of wool growth (reviewed by Reis, 1979) and that the mitotic activity in thefollicle bulb and the rate of wool growth increase when SAAs in the metabol-izable protein are increased However, when radioactively labelled SAAs areinfused into the abomasum the labelled SAAs are immediately and predomin-ately incorporated into the fibre in the keratogenous zone (Fratini et al., 1994),while the level of incorporation of SAAs into the follicle bulb remains compara-tively very low No explanation for the substantial effect of SAAs on mitoticactivity in the follicle bulb has been suggested The model of cellular dynamics inthe follicle not only provides an explanation for the effect of the rate of proteinsynthesis on mitotic activity and cell number in the follicle bulb, but also explainsthe existence of a substantial lag in the responses observed in the follicle bulb.The lag in the responses observed in cell dynamics in the follicle bulb isimportant in attempts to model wool growth because it also leads to a lag inthe response of fibre diameter and fibre length growth rate to changes innutrition

In terms of the cellular dynamics model of wool growth, fibre diameter isdependent on follicle bulb size and fibre length growth rate is dependent on thecell migration rate out of the follicle bulb as well as on follicle bulb size (throughfibre diameter) Fibre diameter and fibre length growth rate are thereforedetermined to some extent independently of one another in the cellularmodel Further work is required to examine the predicted variations in fibrediameter and length growth rate in the cellular model

The wool production model

Wool growth models at the level of the whole animal can avoid the need for amodel of the cellular dynamics in the follicle bulb:

1 Incorporating a 25-day lag in wool growth (Eq (22.25))

2 Incorporating the effect of photoperiod in the estimate of protein availablefor wool growth (Eq (22.26))

3 Assuming a fixed ratio of fibre length growth rate to fibre diameter andcalculating both fibre diameter and fibre length growth rate in terms of totalwool growth (Eqs (22.30) and (22.32)) As a consequence a lag is included inthe response of both fibre diameter and fibre length growth rate

4 Including equations similar to Eq (22.15) for protein synthesis.

TheGRASSGROmodel includes requirements (1) to (3) but does not consider the

AA profile of the metabolizable protein GRASSGRO does achieve reasonableagreement with observations as shown in Fig 22.5, but some discrepancies stilloccur and these indicate problems with using requirement (3) or not accountingfor the AA profile of metabolizable protein To incorporate (4) would requireinformation on AAs of both undigested feed protein and microbial proteinleaving the rumen The main concern with grazing models is, however, theircapacity to predict the amount and quality of the available pasture

Finally, equations or models are still required to predict staple strength interms of variations in fibre diameter along the fibre and the distribution of meanfibre diameters across fibres in the fleece Equations or models are also required

to predict crimp and the contribution made by crimp to wool quality as assessed

morph-Black, J.L and Nagorcka, B.N (1993) Wool growth In: Forbes, J.M and France,

J (eds) Quantitative Aspects of Ruminant Digestion and Metabolism CABInternational, Wallingford, UK, pp 453–478

Black, J.L and Reis, P.J (1979) Speculation on the control of nutrient partitionbetween wool growth and other body functions In: Black, J.L and Reis, P.J.(eds) Physiological and Environmental Limitations to Wool Growth University

of New England, Armidale, Australia, pp 223–242

Carter, H.B and Hardy, M.H (1947) Studies in the biology of the skin and fleece of sheep,I–III Council for Scientific and Industrial Research, Australia, Bulletin No 164.Chapman, R.E and Ward, K.A (1979) Histological and biochemical features of thewool fibre and follicle In: Black, J.L and Reis, P.J (eds) Physiological andEnvironmental Limitations to Wool Growth University of New England, Armi-dale, Australia, pp 193–208

Chapman, R.E., Downes, A.M and Wilson, P.A (1980) Migration and keratinization ofcells in wool follicles Australian Journal of Biological Sciences 33, 587–603.Choy, V.J., Nixon, A.J and Pearson, A.J (1997) Distribution of prolactin receptorimmunoreactivity in ovine skin and changes during the wool growth cycle Journal

of Endocrinology 155, 265–275

Corbett, J.L (1979) Variation in wool growth with physiological state In: Black, J.L.and Reis, P.J (eds) Physiological and Environmental Limitations to WoolGrowth University of New England, Armidale, Australia, pp 79–98.

Davis, G.P and McGuirk, B.J (1987) Genetic relationships between clean wool weight,its components and related skin characters In: McGuirk, B.J (ed.) Merino Im-provement Programs in Australia Australian Wool Corporation, Melbourne,Australia, pp 189–206

Downes, A.M (1971) Variations in wool length and diameter with sheep nutrition.Applied Polymer Symposium No.18, pp 895–904

Downes, A.M and Sharry, L.F (1971) Measurement of wool growth and itsresponse to nutritional changes Australian Journal of Biological Sciences 24,117–130

Fraser, I.E.B (1965) Cellular proliferation in the wool follicle bulb In: Lyne, A.G andShort, B.F (eds) Biology of Skin and Hair Growth Angus and Robertson,Sydney, Australia, pp 427–445

Fratini, A., Powell, B.C., Hynd, P.I., Keough, R.A and Rogers, G.E (1994) Dietarycysteine regulates the levels of mRNAs encoding a family of cysteine-rich proteins

of wool The Journal of Investigative Dermatology 102, 178–185

Freer, M., Moore, A.D and Donnelly, J.R (1997) GRAZPLAN: Decision supportsystems for Australian grazing enterprises II The animal biology model for feedintake, production and reproduction and the GrazFeed DSS Agricultural Systems

Henderson, A.E (1965) Relationship of wool follicle and wool fibre dimensions In:Lyne, A.G and Short, B.F (eds) Biology of Skin and Hair Growth Angus andRobertson, Sydney, Australia, pp 447–460

Hocking-Edwards, J.E and Hynd, P.I (1992) Cellular characteristics of wool folliclesand fibres in Finewool and Strongwool merinos Australian Journal of Agricul-tural Research 43, 355–365

Hogan, J.P., Elliott, N.M and Hughes, A.D (1979) Maximum wool growth ratesexpected from Australian Merino genotypes In: Black, J.L and Reis, P.J (eds)Physiological and Environmental Limitations to Wool Growth University ofNew England, Armidale, Australia, pp 43–59

Hynd, P.I (1989) Effects of nutrition on wool follicle cell kinetics in sheep differing inefficiency of wool production Australian Journal of Agricultural Research 40,409–417

Hynd, P.I (1994) Follicular determinants of the length and diameter of wool fibres I.Comparison of sheep differing in fibre length/diameter ratio at two levels ofnutrition Australian Journal of Agricultural Research 45, 1137–1147.Hynd, P.I and Masters, D.G (2002) Nutrition and wool growth In: Freer, M and Dove,

H (eds) Sheep Nutrition CAB International, Wallingford, UK, pp 165–187.Kempton, T.J (1979) Protein to energy ratio of absorbed nutrients in relation to woolgrowth In: Black, J.L and Reis, P.J (eds) Physiological and EnvironmentalLimitations to Wool Growth University of New England, Armidale, Australia,

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