Molecular structure and biochemical properties of lignins
in relation to possible self-organization of lignin networks
B. Monties
Laboratoire de Chimie
Biologique,
INRA (CBAI), Institut National AgronomiqueParis-Grignon,
Centre de Grignon, 78850
Thiverval-Grignon,
FranceIntroduction
This review
briefly
recalls chemical data related to the variations in the molecular structure oflignin
andmainly
discussesthe biochemical
heterogeneity
and occur-rence of associations between
lignins
andother cell wall
components.
In anattempt
to relate the formation of such
lignin
net-works to
possible
functions oflignins,
anew
hypothesis
on theself-organization properties
oflignin
ispresented.
From a biochemical
point
ofview, lignins
are
particularly complex polymers
whosechemical structure
changes
withinplant species,
organs,tissues,
cells and evencell fractions. Furthermore, from a
physio- logical point
ofview, lignin biosynthesis
isunusual in that the final
polymerization step
isonly enzymatically
initiated and israndom
chemically
directed. Occurrence of such randomsynthesis
raises the cen-tral
question
of theorigin
of thebiological
fitness of
lignification
to the lifecycle
ofplants.
Thisquestion
is relevant notonly
for the formation of ’abnormal
lignins’
and’lignin-like compounds’
in reactionwoods,
and wounded and diseased tissues but also in the case of ’normal’
lignin
in woodxylem.
Such randompolymerization
may also be relevant in relation to the evolution of thequality
of thelignocellulosic
pro-ducts,
such asduring
heartwood forma-tion, drying
oflogs
andsawings,
and hard-board and paper
manufacture,
as sug-gested, respectively,
forexample by
Sar-kanen
(1971;!,
Northcote(1972), Fry (1986),
Back(1987),
Jouin et al..(1988),
and Horn and
Setterholm (1988).
This review focuses thus on
self-organi-
zation and recalls
only briefly
the chemicaland biochemical
properties
oflignin
inrelation to other
plant
cell wall compo- nents. Due to edition constraints,only
main relevant references are cited.
Molecular structure of
lignin
In vitro model studies and in vivo
experi-
ments
(Freudenberg
andNeish,
1968;Higuchi, 1985;!
have shown that the gen- eral molecular structure oflignin
can beexplained by
one-electron oxidation of cin-namyl
alcohols followedby non-enzymatic polymerization
of thecorresponding
mesomeric free radicals.
Fig.
1 shows thephenylpropane (C
6 -C 3
)
skeleton of thelignin
monomers(M)
and the structure of 4 of the mostcommon
linkages
found inlignins.
Thesestructures have been established
by
invitro
peroxidase
oxidation ofmainly
coni-feryl
alcohol((a
=Fig. 1 followed by
iso-lation of dimers
(dilignols), oligomers (oli-
i-golignols)
anddehydropolymers (DHP model).
Modelpolymerization
studieshave also shown that the relative
frequen-
cy of these intermonomeric
linkages and, thus,
thecorresponding
macromolecular structure of DHPchanges according
topolymerization
conditions(Sarkanen, 1971), such
as, the concentrations and the rate of addition of thereagents,
thepolarity
of the medium orsolvents,
the electronic and steric effects of the substi- tuents in the aromaticcycle, according
tothe various substitution
patterns
of thelignin
monomeric units: H,G,
S(Table I).
Formation of para- and
ortho-quinone
methide has also been
suggested during
the dimerization of mesomeric
oligolignols
or monomeric units and
during
chemicaloxidation of
simple phenolic
model com-pounds (Harkin, 1966).
Intermediateoligo- lignol-p-quinone
methides areimplicated
in the formation of
lignin
networks. Ac-cording
to in vitroexperiments,
such struc-tures are involved in the
growth
of thelignin polymer through copolymerization,
but also
through heteropolymerization
withother
macromolecules,
such aspolysac-
charides
(Sarkanen,
1971;Higuchi, 1985).
Fig.
1 shows the addition reaction bet-ween a
compound
A-B and a terminal p-methylene quinone
unit(a’: Fig. 1 Addi-
tion of A-B led to the formation of the
corresponding A,B-(a)
substituted hex-alignol (a-f: Fig. 1). Depending
upon the structure of A-B and when A ishydrogen,
the aromatic character of the a-monomeric unit is recovered with reformation of a
phenolic
group. Thisphenolic
unit mayfurther
polymerize, leading
to a trisub-stituted monomeric unit or ’branch
point’
ofthe
lignin
network(Pla
and Yan,1984).
Such a reticulation process with reforma- tion of a
phenolic
group could be asignifi-
cant
self-organization property
oflignin (see below). Depending
upon the A-B structure, the addition reaction shown inFig.
1 may also beimportant
and thusexplain
certain macromolecularregulari-
ties in
lignin
structure. Asearly
as in1968, Freudenberg
and Neish stressed that &dquo;the sequence of the individual(monomeric)
units in
lignin
isfortuitous,
forthey
are notmoulded like
proteins
on atemplate.
Thisdoes not exclude the occurrence of a cer-
tain
regularity
in the distribution of weak andstrong
bonds between the units. As arough estimate,
7 to 9 weak bonds arerandomly
distributed among 100units,
’gluing’ together
more resistantclusters,
ofan average, 14 units.&dquo; Such ’clusters’ or
’primary
chains’ of about 18strongly
link-ed monomeric units have been
reported
after
delignification experiments by
Bolkerand Brener
(1971)
andby
Yan et aL(1984). According
to theseauthors,
theweak-bonds
suggested by Freudenberg
and Neish are
mainly a-aryl
ether link- ages,respectively,
intermolecular(Ca !B
bond in a-unit:Fig. 1)
and intra- molecular(C a -04
bond in b-unit:Fig. 1 ).
Confirming
theimportance
of addition reactions withp-methylene quinone,
sucha weak
a-aryl
ether bond maycorrespond
to a
Ca !B linkage (a
=Fig. 1 )
where Bis a
phenoxy
substituentcorresponding
tothe addition of a BA
phenolic
terminalmonomeric unit.
Summarizing
the mostcharacteristic chemical
properties, lignin
does not appear to be a defined chemical
compound
but a group ofhigh
molecularweight polymers
whose random structure, which is related to theirchemically
drivenpolymerization,
does not exclude theappearance of certain
regularities
in the 3dimensional network.
Biochemical
properties
Biochemical
heterogeneity
orinhomoge- neity (Monties, 1985)
is the second main feature oflignin.
Characteristic variations inlignin
structure and monomeric com-position
have indeed been found and confirmed betweenplant species (Logan
and Thomas,
1985),
betweenplant
organs and tissues grown either in vitro or in vivo and also betvveen cell wall fractions(Hoff-
man et
al., 1985;
Sorvari etaL, 1986;
Saka etal.,
1 !)88;
Erikssonet al., 1988).
Inagreement
with thesedata,
which cannotbe discussed here in
detail, heterogeneity
in
lignin
formation and molecular structure,has been demonstrated in the case of gymnosperms
(Terashima
and Fukushi- ma,1988)
and in the case ofangiosperms (Higuchi, 19135; Monties,
1985;Lapierre, 1986;
Tollier etal., 1988;
Terashima andFukushima, 1988).
From a biochemicalpoint
ofview, lignin
thus appears to be non-randomheterogeneous copolymers
enriched
by
eithernon-methoxylated (p-
hydroxyphemyl
=H), monomethoxylated
(guaiacyl
=G)
anddimethoxylated (syrin-
gyl
=S)
monomeric units(Fig. 1 These
copolymers
areunequally
distributedamongst
cells and subcellularlayers,
intissues
according
topatterns changing
with
species.
Thebiosynthesis
of the pre-cursors and the
regulation
oflignification
most
likely
occurs within individual cells and variations are observedaccording
tothe
type
and the age of cells(Wardrop, 1976),
as in the case ofsecondary
me-tabolism
(Terashima
andFukushima, 1988).
Molecular associations and cell wall
lignification
Formation of molecular associations with other cell wall
components
is the third main feature oflignins.
Indirect evidence of the occurrence of suchheteropolymers, mainly
based onextractability
orliquid chromatographic experiments,
has beenreported
in the case ofpolysaccharides, phenolic
acids andproteins,
tannins andsome other
simple compounds.
Thetypes
of chemical bonds involved in these asso-ciations have been established
only
forpolysaccharides, phenolic
acids and pro-teins, mainly
based on modelexperiments
of addition to
p-methylenequinone
dis-cussed
previously.
The most
frequently suggested types
oflignin-carbohydrate complex (LCC)
link-ages are a
benzyl
ester bond with theC 6 - carboxyl
group of uronicacids,
abenzyl
ether bond with the
hydroxyl
of theprimary
alcohol of hexose or
pentose,
aglycosidic
bond with either the
C 4 -phenolic hydroxyl
or the
Cy-primary
alcohol ofphenylpro-
pane units
(M
=Fig. 1 The synthesis
ofLCC model
compounds,
theirreactivity
and their chemical or
enzymatic stability
have been
compared
to those of woodLCC
(Higuchi, 1983; Minor, 1982;
Enokiet
al., 1983). Recently, using
a selectivedepolymerization procedure,
Takahashiand
Koshijima (1988)
have concluded thatxylose participates
inlignin-carbohydrate linkages through benzyl
ether bonds in LCC fromangiosperm (Fagus sp.)
andgymnosperm
(Pinus sp.)
woods. Macro- molecular differences werereported by
these authors: in
Fagus,
thelignin moiety
of LCC would consist of a small number of
extremely large
molecularfractions,
whilepine
would haverelatively
smaller andmore numerous
fractions, confirming
thehypothesis
of biochemicalheterogeneity
oflignins.
Phenolic acids are known to be bound to
lignin, especially
in the cases of mono-cotyledons (grasses
andbamboos)
andSalicaceae
(poplars).
Ester bonds ofphe-
nolic acids to
C a
andCy-hydroxyls
ofmonomeric propane
chains (Fig. 1 C5-
carbon-carbon bonds and ether bonds at
C 4
-phenolic
oxygen of aromaticcycles (Fig. 1 )
have beenreported
in the cases ofmodel DHP
(Higuchi, 1980)
and gra- mineaelignins
from wheat(Scalbert
etal., 1985)
andreed,
Arundo sp.(Tai ef aL, 1987).
Etherlinkages
ofphenolic
acidshave been
tentatively implicated
in thecharacteristic alkali
solubility
of grasslignins; however,
freephenolic hydroxyl
groups would also
participate
in thissolubility (Lapierre et aL, 1989).
Lignin-protein complexes
in the cell wall ofpine (Pinus sp.)
callus culture have beenreported:
covalentbonds,
formedpreferentially
withhydroxyproline,
havebeen
suggested
on the basis of selective extractionexperiments
and of the reactivi-ty
of model DHPscontaining hydroxypro- line,
which were more stable to acidhydrolysis
thancarbohydrate-DHP
com-plexes (Whitmore, 1982).
Chemical bonds betweenlignin
andprotein
have also beenrecently
indicatedduring
the differentiation ofxylem
in birchwood,
Betula sp.(Eom
et al.,1987).
Agradual
decrease inphe-
nolic
hydroxyl
group content andchanges
in molecular
weight
distributionduring
thelignification
have also been shownby
these authors. These variations were
explained
in terms ofchanges
inlignin
structure in relation to variations in concentrations of available monomers and effects of the conditions of
polymerization
as discussed above .
Possible associations with other
pheno- lics,
such as condensed andhydrolyzable
tannins have also been
suggested
in rela-tion to the difficulties in
completely
remov-ing tannins,
after solvent and mild chemi- cal extractions of woodsand,
also in rela-tion to
coprecipitation,
such as sulfuricacid-insoluble
lignin
fractions. Mecha- nisms ofrandom, i.e., chemically-driven polymerization
of tannins with cell wallcomponents,
have been discussed recent-ly (Haslam
andLilley, 1985;
Jouin eta/., 1987). However,
no evidence of chemical bonds between tannins andlignins
wasgiven.
Network formation and
self-organiza-
tion
properties
Formation of molecular associations be- tween
lignins
and cell wallcomponents
sheds
light
on theimportance
of thephe-
nolic
group’s reactivity,
such as the addi-tion to
methylene quinone
withphenolic
group reformation
(Fig. 1 in
the reticula- tion of theplant
cell wall. Suchreactivity
isnot
unique,
sincephenol dimerization, by
formation of
diphenyl
and ofdiarylether
bonds, has also beenreported
fortyrosine during
cell wallcross-linking
processes(Fry, 1986). Recently,
similar reactions have also beensuggested
fortyramine
inthe
phenolic
fraction associated with su-berin
(Borg-Olivier
andMonties, 1989).
Asvery
clearly
stressedby
Northcote asearly
as
1972,
with reference tosynthetic
fibrous
composite,
the formation of such cross-linkedphenolic polymers
may besignificant
inregard
to the structure andfunctions of
plant
cell walls. Reticulation may be ofimportance
indurability
andmechanical
properties,
asrecently
dis-cussed in the case of cell wall
proteins by
Cassab and Warner
(1988). Furthermore,
in the case of
lignins,
thiscross-linking phenomenon
may be of much more gen- eral interest. Forexample,
the formation of chemical bonds in the residuallignin
net-work of thermomechanical
pulps
has beenimplicated
in theautocross-linking
of thesecellulosic fibers
during
theproduction
ofpaper and hardboard in the so called
’press-drying’
process(Back,
1987; Hornand Setterholm, 1988).
In order to
try
to understand thegeneral
formation of
phenolic
networksby
non-enzymatic pol’ymerization
processes, self-organizing properties
oflignin
can be sug-gested.
Theself-organization concept
comes from the
general theory
ofsystems.
Self-organization
accounts for the mannerin which
complex systems adapt
to andincrease their
organization
under the sti-mulation of random environmental factors.
This
theory
has beenapplied extensively
to the
growth
oforganisms
and transmis-sion of information
(Atlan, 1972).
Self-organization
also seems relevant in thecase of
lignin,
sincelignin
is a non-enzy- maticpolymerized macromolecule,
itsstructure
changes
as a function of random external environmental factors, it rear- rangesduring maturation, ageing
or tech-nological
transformationsand, finally,
these
changes provide
a better fitness of cell wallfunctions,
such as resistanceagainst
biotic and abiotic factors.According
to Atlan(1974),
aself-orga- nizing system
is acomplex system
in whichchanges
inorganization
occur withincreasing efficiency
inspite
of the fact thatthey
are inducedby
random environ- mental factors;changes
are not directedby
atemplate. Self-organization capacity
can be
expressed
as a function of 2 mainparameters: redundancy
andreliability.
When the
organization
is defined as ’varie-ty
andinhomogeneity’
of thesystem, redundancy
is viewed as’regularity
ororder as
repetitive
order’ andreliability
expresses the
system’s
’inertiaopposed
torandom
perturbation’. According
to thesedefinitions,
the information content,i.e.,
the
organization
of asystem,
can beexpressed
as a function ofredundancy
and of time
(see Annex).
Evolution of theorganization
as a function of time can thus be calculatedshowing
differenttypes
oforganization.
Thus,
aself-organizing system
is char- acterizedby
a defined maximumorganiza-
tion
resulting
from an initial increase ininhomogeneity
associated with a contin-uous decrease in
redundancy
under theeffect of random environmental factors. At the other extreme, a
non-self-organizing system
shows a continuous decrease oforganization, mainly
due to a low initialredundancy. Furthermore,
intermediatecases have also been described
by
Atlan(1972, 1974) corresponding
torelatively
very
high
or very lowreliability
and lead-ing, respectively,
to a verylong
or a very short duration of the initialphase
of in-crease in
organization. According
to Atlan(1974), crystals
can be viewed as a non-self-organizing system
because of low in- itialreliability
inspite
of theirlarge
redun-dancy.
At the other extreme, lessrepetitive
and more flexible structures, such as macromolecular
systems,
can be self-organizing.
In
agreement
with thismodel,
it is sug-gested
thatlignin
networks be consideredas
self-organizing systems,
thus ex-plaining
the formation of molecular com-plexes by
auto- andheteropolymerization
in
plant
cell walls with an increase oflignin
functional
properties.
The
high frequency
ofrelatively
labileintermonomeric
linkages,
such as/3-
andmainly
a-etherbonds,
and also ofeasily
activated groups, such as free
phenolic
terminal units
(Fig. 1),
may allow rear-rangement
reactionsand, thus,
easy evo- lution of thesystem
as a function of ran-dom environmental factors. Occurrence of chemical and biochemical
regularities, previously
discussed, may, inaddition, provide enough
initialredundancy. Finally,
a
high reliability, i.e.,
inertia toperturba- tion,
may result from theability
to reformphenolic
groupsafter,
forexample,
anaddition reaction as shown in
Fig.
1, butalso from the release of reactive
phenolic
and/or
benzylic
groups after/3-
andmainly
a-ether
cleavage.
In
conclusion,
even whenlignin
forma-tion appears as an
enzyme-initiated
andchemically
driven process, structural stu- dies haveprovided
evidence ofregulari-
ties in chemical and biochemical proper- ties in
lignin
networks. Suchregularities
may allow
self-organizing properties
oflignin macromolecules, explaining
theirfunctional fitness and the
biological signifi-
cance of the ’random
process’
oflignifica-
tion. However, until now, this
theory
suf-fers from 2 main drawbacks: a lack of
quantitative
evaluation and a definite account of thephylogenic
andontogenic significance
of the substitutionpattern
ofthe
lignin
monomeric units.Acknowledgments
Thanks are due to Drs. Catherine
Lapierre,
C.Costes and E. Odier for critical assessment of the
manuscript
and to Kate Herve du Penhoat forlinguistic
revisions.References
Atlan H. (1972) In:
L’organisation biologique
etla theorie de I’information. Hermann, Paris, pp.
229
Atlan H.
(1974)
On a formal definition oforgani-
zation. J. Theor. Biol. 45, 295-304
Back E.I.
(1987)
Thebonding
mechanism inhardboard manufacture.
Holzforschung
41,247-258
Bolker H.I. & Brener H.S. (1971) Polymeric
structure of spruce lignin. Science 170, 173-176 Borg-Olivier O. & Monties B. (1989) Characteri- zation of
lignins,
phenolic acids and tyramine inthe suberized tissues of natural and wound- induced potatoe
periderm.
C.R. Acad. Sci. Ser.111308, 141-147
Cassab G.I. & Varner J.E. (1988) Cell wall pro- teins. Annu. Rev. Plant PhysioL 39, 321-353 Enoki A., Yaku F. &
Koshijima
T. (1983)Synthe-
sis of LCC model
compounds
and their chemi-cal and
enzymatic
stabilities.Holzforschung
37,135-141
Eom T.J., Meshitsuka G., Ishizu A. & Nakano T.
(1987) Chemical characteristics of
lignin
in dif- ferentiating xylem of a hardwood III. Mokuzai Gakkaishi 33, 716-723Eriksson I., Lindbrandt O. & Westermark U.
(1988) Lignin
distribution in birch(Betula
veru- cosa) as determinedby
mercurization with SEM- and TEM-EDXA. Wood Sci. Technol. 22,251-257
Freudenberg K. & Neish A.C. (1968) In:
Constitution and
Biosynthesis
of Lignin.Sprin- ger-Verlag,
Berlin, pp. 129Fry
S.C.(1986) Cross-linking
of matrixpoly-
mers in the
growing
cell walls ofangiosperms.
Annu. Rev. Plant Physiol. 37, 165-186
Harkin J.M. (1966) O-Quinonemethide as tenta- tive structural elements in
lignin.
Adv. Chem.Ser. 59, 65-75
Haslam E. &
Lilley
T.H. (1985) Newpolyphenols
from old tannins. In: The
Biochemistry
of PlantPhenolics. Annu. Proc.
Phytochem.
Soc. Eur.(van
Sumere C.F. & Lea P.J.,eds.),
25, 237-256Higuchi
T. (1983)Biochemistry
oflignification.
Wood Res. 66, 1-16 6
Higuchi
T. (1985)Biosynthesis
oflignin.
In:Biosynthesis
andBiodegradation
of WoodComponents. (Higuchi
T, ed), Academic Press,Orlando, pp.
141-160Hoffman A. Sr., Miller R.A. &
Pengelly
W.L.(1985) Characterizations of
polyphenols
in cellwalls of cultured Populus
trichocarpa
tissues.Phytochemistry 24,
2685-2687Horn R.A. & Setterholm V. (1988) Press drying:
a way to use hardwood CTMP for
high-strength paperboard.
TAPPI 71, 143-146Jouin D., Tollier M.T. & Monties B. (1988)
Ligni-
fication of oak wood:
lignin
determinations insapwood
and heartwood. Cell. Chem. Technol.22, 231-243
Lapierre C. (1986) H6t6rog6n6it6 des lignines
de
peuplier:
mise en evidence syst6matique.Ph.D. Thesis, Universit6 d’Orsay, France Lapierre C., Jouin D. & Monties B.
(1989)
Onthe molecular
origin
of the alkali solubility of gramineae lignins.Phytochemistry
28, 1401-1403
Logan
K.J. & Thomas B.A. (1985) Distribution oflignin
derivatives inplants.
NewPhytol.
99,571-585
Minor J.L.
(1982)
Chemicallinkage
ofpine poly-
saccharide to
lignin.
J. Wood Chem. TechnoL 2, 1-16 6Monties B. (1985) Recent advances in
lignin inhomogeneity.
In: TheBiochemistry
of PlantPhenolics. Annu. Proc.
Phytochem.
Soc. Eur.(van Sumere C.F. & Lea P.J.,
eds.),
25, 161-181 Northcote D.H.(1972) Chemistry
ofplant
cellwall. Annu. Rev. Plant
Physiol.
23, 113-132 Pla F. & Yan Y.F. (1984)Branching
and func-tionality
oflignin
molecules. J. Wood Chem.Technol. 4, 285-299
Saka S.,
Hosoya
S. & Goring D.A.I. (1988) A comparison of bromination ofsyringyl
andguaiacyl
typelignins. Holzforschung
42, 79-83 Sarkanen K.V.( 1971 )
Precursors and theirpoly-
merization. In:
I.ignins:
Occurrence, Formation, Structure and Reactions. (Sarkanen K.V. & Lud-wig
C.H., eds.),Wiley
Interscience, New York, pp. 138-156Scalbert A., Monties B., Lalemand J.Y., Guittet E. & Rolando C.
(1985)
Etherlinkage
betweenphenolic
acids andlignin
fractions from wheat straw.Phytochemistry 24, 1359-1362
Sorvari J.,
Sjostrom
E., Klemola A. & Laine J.E.(1986) Chemical characterization of wood constituents
especially lignin
in fractions sepa- rated from midd’le lamella andsecondary
wall of Norway spruce (Picea abies). Wood Sci. Tech- nol. 20, 35-51Tai D., Cho W. & Ji W. (1987) Studies on Arun-
do donax
lignins.
Proc. Fourth Int.Symp.
Wood
Pulping
Cnem. 2, C.T.P., Grenoble, pp.13-17 7
Takahashi &
Koshijima
(1988) Molecular prop- erties oflignin--carbohydrate complexes
frombeech
(Fagus
c:renata) andpine (Pinus
densi- flora) woods. Waod Sci. Technol. 22, 177-189 Tanahashi M., Takeuchi H. & Higuchi T. (1976)Dehydrogenative
polymerization of 3,5-disubsti- tutedp!oumaryl
alcohols. Wood Res. 61, 44- 53Terashima N. & Fukushima K. (1988) Heteroge- neity in formation of
lignin: autoradiographic
study of formation ofguaiacyl
andsyringyl lignin
in
Mangnolia
Icobus D.C. Holzforschung 40suppl., 101-105
Tollier M.T., Monties B. & Lapierre C. (1988)
Heterogeneity
inangiosperm lignins.
Holzfor-schung,
40suppl.,
75-79Wardrop A.B. (1976)
Lignification
in plant cellwall.
Appl. Pofyin. Symp.
28, 1041-1063 Whitmore F.A.(1982) Lignin-protein complex
incell walls of Pinus elliottii: amino acid consti- tuents.
Phytochl!mistry 21,
315-318 8Yan J.F., Pla F., Kondo R., Dolk M. &
McCarthy
J.L. (1984)
Lignin:
21:depolymerization by
bond
d eavagfi
reactions anddegelation.
Macrofno/ecu/es 17, 2137-2142
Annex
According
to Atlan’sproposal, organiza-
tion should
correspond
to anoptimum
compromise
between maximum informa-tion content
(Hm!)
andredundancy (R)
both considered as a function of time.
Starting
from Shannon’s definition:H=
t &dquo; t max (1-R )
and
differentiating
H versustime,
with theassumption
that time means accumulated randomperturbation
from the environ- ment, onegets:
dMt)f
(1 -R)(dNm!ldt)
+H m ax
(-dH/dQ(1 )
As
perturbations
decrease bothH m ax
andR,
the first term on theright
side of eqn. 1 isnegative
and thus showsdisorganiza-
tion effects due to random
perturbations.
The second term,
however,
ispositive explaining
apossible
increase inorganiza-
tion and thus
self-organization
under theeffect of random
perturbations.
A self-organizing system
appears,thus,
to be redundantenough
to sustain a continuousprocess of
disorganization,
first term,constantly
associated withreorganization
and increased
efficiency
of thesystem
dueto its
reliability, i.e.,
its inertiaopposed
torandom