Why Homeodynamics, Not Homeostasis?

Abstract

Ideas of homeostasis derive from the concept of the organism as an open system. These ideas can be traced back to Heraclitus. Hopkins, Bernard, Hill, Cannon, Weiner and von Bertalanffy developed further the mechanistic basis of turnover of biological components, and Schoenheimer and Rittenberg were pioneers of experimental approaches to the problems of measuring pool sizes and dynamic fluxes. From the second half of the twentieth century, a biophysical theory mainly founded on self-organisation and Dynamic Systems Theory allowed us to approach the quantitative and qualitative analysis of the organised complexity that characterises living systems. This combination of theoretical framework and more refined experimental techniques revealed that feedback control of steady states is a mode of operation that, although providing stability, is only one of many modes and may be the exception rather than the rule. The concept of homeodynamics that we introduce here offers a radically new and all-embracing concept that departs from the classical homeostatic idea that emphasises the stability of the internal milieu toward perturbation. Indeed, biological systems are homeodynamic because of their ability to dynamically self-organise at bifurcation points of their behaviour where they lose stability. Consequently, they exhibit diverse behaviour; in addition to monotonic stationary states, living systems display complex behaviour with all its emergent characteristics, i.e., bistable switches, thresholds, waves, gradients, mutual entrainment, and periodic as well as chaotic behaviour, as evidenced in cellular phenomena such as dynamic (supra)molecular organisation and flux coordination. These processes may proceed on different spatial scales, as well as across time scales, from the very rapid processes within and between molecules in membranes to the slow time scales of evolutionary change. It is dynamic organisation under homeodynamic conditions that make possible the organised complexity of life.

Full text

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Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
* Corresponding Author: Miguel A. Aon, INTECH, C.C. 164, 7130-
Chascomús, Buenos Aires, ARGENTINA; e-mails: maaon@criba.edu.ar
(Aon & Cortassa); LloydD@Cardiff.ac.uk (Lloyd)
© 2001 with author.
Review Article
TheScientificWorld (2001) 1, 133145
ISSN 1532-2246; DOI 10.1100/tsw.2001.20
Ideas of homeostasis derive from the concept of the
organism as an open system. These ideas can be traced
back to Heraclitus. Hopkins, Bernard, Hill, Cannon,
Weiner and von Bertalanffy developed further the mecha-
nistic basis of turnover of biological components, and
Schoenheimer and Rittenberg were pioneers of experi-
mental approaches to the problems of measuring pool
sizes and dynamic fluxes. From the second half of the
twentieth century, a biophysical theory mainly founded
on self-organisation and Dynamic Systems Theory al-
lowed us to approach the quantitative and qualitative
analysis of the organised complexity that characterises
living systems. This combination of theoretical frame-
work and more refined experimental techniques revealed
that feedback control of steady states is a mode of op-
eration that, although providing stability, is only one of
many modes and may be the exception rather than the
rule. The concept of homeodynamics that we introduce
here offers a radically new and all-embracing concept
that departs from the classical homeostatic idea that
emphasises the stability of the internal milieu toward
perturbation. Indeed, biological systems are homeody-
namic because of their ability to dynamically self-
organise at bifurcation points of their behaviour where
they lose stability. Consequently, they exhibit diverse
behaviour; in addition to monotonic stationary states,
living systems display complex behaviour with all its
emergent characteristics, i.e., bistable switches, thresh-
olds, waves, gradients, mutual entrainment, and peri-
odic as well as chaotic behaviour, as evidenced in cel-
lular phenomena such as dynamic (supra)molecular
organisation and flux coordination. These processes
may proceed on different spatial scales, as well as
across time scales, from the very rapid processes within
and between molecules in membranes to the slow time
scales of evolutionary change. It is dynamic organisation
under homeodynamic conditions that make possible the
organised complexity of life.
KEY WORDS: organised complexity, dynamic organisation,
homeodynamics, coherence, ultradian and circadian clocks,
cytoskeleton, metabolic fluxes
DOMAINS: microbiology, organisms; bioenergetics, metabo-
lism, signalling, intracellular communication; cell cycle (mi-
tosis), differentiation & determination; biomathematics,
structural biology, biochemistry, biophysics, gene expres-
sion, cell biology, physiology, modelling; information data-
bases
TABLE OF CONTENTS
Introduction ............................................................... 134
The Steady State ....................................................... 134
The Oscillatory States in Biological
Systems ..................................................................... 135
Dynamic Organisation under
Homeodynamic Conditions ...................................... 136
A Geometric Interpretation of
Homeodynamics ....................................................... 136
Coherence.................................................................. 136
Mechanisms of Coherence....................................... 138
Bottom-up Mechanisms ........................................... 138
Top-Bottom Mechanisms ......................................... 140
Conclusions and Outlook ......................................... 140
References ................................................................. 143
Why Homeodynamics, Not Homeostasis?
David Lloyd
1
, Miguel A. Aon
2,
*, and Sonia Cortassa
2
1
Microbiology (BIOSI), Cardiff University, P.O. Box 915, Cardiff, CF10 3TL,
Wales, U.K.
2
Instituto Tecnológico de Chascomús (INTECH/CONICET),
Casilla de Correo 164, 7130- Chascomús, Buenos Aires, Argentina

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Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
INTRODUCTION
In the second half of the last century, fundamental informa-
tion about the spatio-temporal organisation in living sys-
tems became established. For the first time, we have at hand
a biophysical theory to approach the quantitative and quali-
tative analyses of the organised complexity that characterise
living systems.
Two main foundations of this biophysical theory are self-
organisation
1,2
, and Dynamic Systems Theory
3,4
. Self-
organisation is deeply rooted in nonequilibrium thermo-
dynamics
5
and the kinetics of nonlinear systems whereas
Dynamic Systems Theory lies within the geometric theory
of dynamical systems created by Poincaré
6,7
.
By applying this biophysical theory of biological
organisation to successively more complicated systems (i.e.,
artificial, artificial-biological-oriented, or biological),
8,9
it be-
came clear that self-organisation is a fundamental and nec-
essary property of living systems. Conditions under which
self-organisation appears are
9
 openness to fluxes of energy and matter;
 the operation of coupled processes through some
common intermediate; and
 the occurrence of at least one process that exhibits a
kinetic nonlinearity.
The mainstream of biological thought is only slowly
recognising the dynamic nature of living systems. A main
reason is that dynamics is a property of the whole system,
integrated by manifold interactions in the form of parallel,
sequential, and branched pathways of chemical reactions
involving mass, energy, and information transfer. The type
(i.e., negative or positive) and number of feedbacks nested
in these mass-energy-information-carrying networks deter-
mine the dynamic behaviour of living systems by provid-
ing the necessary nonlinearities and coupling between
processes. Emergent properties are accounted for in those
interlinked circuits with autocatalytic potential
5,9,10,11
. These
emergent properties are crucial in the transfer and process-
ing of information in biochemical as well as cellular net-
works
12,13
that may be modulated either by genetic or
epigenetic mechanisms.
THE STEADY STATE
Hopkins
14
description of life as the expression of a dynamic
equilibrium in a polyphasic system provided several gen-
erations of biochemists with a model for thinking about
mechanisms whereby stability can be achieved by balanc-
ing supply to demand. The constancy of the internal en-
vironment had already become an all-pervading concept in
physiology ever since its introduction by Claude Bernard in
1865; this work has been translated
15
. Cannon
16
stressed that
no organism can be considered in isolation from its environ-
ment and that because organisms exchange matter and en-
ergy with their surroundings, the process of homeostasis,
whereby steady states are obstinately preserved and re-es-
tablished, does not imply something set and immobile. The
ideas of the organism as an open system were further devel-
oped into a general systems theory by von Bertalanffy from
1932
17
who built on the classical fascination of Heraclitus with
the idea that life processes have features in common with a
flowing stream, and of Roux, that a candle flame with its fluxes
of matter and energy may also serve as an analogue. The ther-
modynamics of living organisms became of great interest in
mainstream physiology in the 1930s and produced work of
fundamental significance
18, 19
.
Measurement of turnover rates of proteins had to await
the discovery of deuterium and the heavy isotope of nitro-
gen. With these new metabolic labels, Schoenheimer
20
was
able to show that the apparent stability of essential constitu-
ents belies an extremely dynamic reality. Post-war availabil-
ity of radioisotopic carbon-containing compounds made
these studies more easily feasible. Rittenberg
21
was able to
show that the apparent overall absence of reactions in living
cells simply indicates a balance that is subtly attained and
maintained. It became clearly evident for the first time that
the approach to equilibrium is a sign of death.
The introduction of continuous culture techniques by
Novic and Szilard
22
and by Monod
23
further entrenched these
ways of thinking about the living state and led to the rather
simplistic concept of balanced growth.
Even in the late 1970s, there was an almost universal
tendency among biochemists to overlook the growing evi-
dence for the truly astonishing dynamic nature of life pro-
cesses. For instance, at that time there was a great resistance
to the idea that protein turnover is, for the most part, ex-
tremely rapid, and that even newly synthesised proteins are
unstable and are, to a surprising degree, susceptible to
degradative hydrolysis
24,25,26,27
.
More recently, the essential roles of proteolytic systems
in cellular economy
28
have become recognised to be so all-
embracing that it has become evident that degradation is
central, even to biological growth processes
26
. Turnover times
in vivo, never easily measured, must be on a time scale of
minutes and hours
29,30
, rather than days, as formerly
thought
31,32
. Even so, homeostasis is even now regarded as
an universal principle; however, it becomes increasingly
evident that maintaining the status quo cannot explain
biological complexity and the long sequence of evolution-
ary changes that have led to its development.
10,11,33

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THE OSCILLATORY STATES IN BIOLOGICAL
SYSTEMS
In any system built without specially designed constraints,
it is to be expected that oscillations will occur. This is true of
mechanical, electrical, optical, and chemical systems. Thus
it is so for the motions of boats and bridges, of electrons in
circuits, of photons in lasers, and of molecules in test-tube
mixtures. The more complex the system, the greater the num-
bers of degrees of freedom, and the greater the likelihood of
outputs of varied frequencies and amplitudes. Processes that
occur in nanoseconds are characteristic of the very small (e.g.,
vibrational events in molecules), whereas those that are slow,
for instance, those that take billions of years (e.g., geological
changes), are also on a giant scale. Time structure of living
organisms also spans many scales (Fig. 1), from those oc-
curring within single molecules and on membranes (mea-
sured in femtoseconds) to the slow evolutionary changes
that require thousands of generations. Periodic processes can
occur on all these time scales (Fig. 1).
The natural environment also has an obvious time struc-
ture that is generated by the geophysical cycles. Finely honed
to optimise performance, organisms have evolved in peri-
odic surroundingsthe ebb and flow of the tides and the
certainty that night will follow day, under the lunar cycle,
throughout the seasons and the years. The matching of or-
ganism with environment has generated one of lifes most
fundamental characteristics: its rhythmic nature. The com-
plex and varied time structure stems from this. Oscillations
have been harnessed to provide rhythms, and where these
rhythms become embedded so as to become heritable and
to provide anticipatory advantages, they become biological
clocks
34,35
.
Although the existence of an endogenous clock has been
recognised since de Mairans observations in 1728 of the daily
leaf movements in plants, the elements that comprise the
time frame for living organisms have only slowly been dis-
covered.
In biochemical systems, the oscillatory state was not
observed until 1957, when Dysens and Amesz
36
showed os-
FIGURE 1. Periodic phenomena across several temporal scales. Ultradian clocks in the temporal domain between half to one hour with several intracellular
outputs, coordinate (top-bottom) cell function and circadian, clock-type, behaviour. This coordination is an expression of dynamic organisation under
homeodynamic conditions, according to the graphic visualisation depicted in Figures 2 and 3. The x-axis displays the period (in seconds) of the oscillatory
phenomena, plotted in a logarithmic scale. The phenomena range from milliseconds (action potential in neurons) to a month (the female menstrual cycle).
Numbers indicate references as follows: 1
44
, 2
65
, 3
66
, 4
67
, 5
68
, 6
69
, 7
70
, 8
71
, 9
72,
10
73
, 11
74
, 12
75
, 13
76
, 14
77
, 15
78
, 16
79
, and 17
8
.

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Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
cillations in nicotinamide nucleotide levels in intact cells. The
discovery of oscillations in glycolysis in yeast
37
led to an ex-
plosion of interest in the mechanism of control of glycolysis:
This area has produced a wealth of data, even if the func-
tions of this mode of metabolic operation are still not defi-
nitely understood. Fundamental theoretical treatments of
observed kinetic data
38,39
established the importance of feed-
back inhibition and feedforward activation in the genera-
tion of oscillatory behaviour in the glycolytic pathway. The
prediction of oscillatory dynamics in biosynthetic pathways
40
clearly demonstrated in synchronous cultures
29
was a fur-
ther prescient step forward in the series of advances that
concluded with a burgeoning recognition that complex dy-
namics is an integral property of life. Biophysical and bio-
chemical oscillators are part of the spectrum of biological
periodicities that even extend into geological time
8,9,41
.
DYNAMIC ORGANISATION UNDER
HOMEODYNAMIC CONDITIONS
The concept of dynamic organisation has been introduced to
describe function in cellular, or even supracellular, systems
that arises as the spatio-temporal coherence of events result-
ing from the intrinsic, autonomous, dynamics of biological
processes
9
.The concept of homeostasis refers to the relative
constancy, i.e., stable steady states, of the internal milieus
physiological status. The resistance to change by a homeo-
static state is given by its stability to perturbations, i.e., given
a stimulus and a transient response, it returns to its pre-
stimulation state. In this sense, the concept of homeodynamics
that we introduce here offers a radically new departing con-
cept. Biological systems are homeodynamic because intrac-
ellular processes through their dynamic self-organisation
may exhibit not only monotonic states (fixed points), but
also a capacity for bistable switching threshold phenomena,
waves, gradients, mutual entrainment, and periodic as
well as chaotic behaviour. This complex behaviour is also
evidenced in cellular phenomena such as dynamic (supra)
molecular organisation and flux coordination (Fig. 2, 3).
At bifurcation points, a dynamic system loses stability
and behavioural changes occur
1,42
.These may be quantita-
tive, qualitative, or both (Fig. 3). Quantitatively, it may hap-
pen that the system dynamics moves at limit points, to a
different branch of steady-state behaviour (lower or higher),
e.g., as in bistability. Under these conditions, the system does
not change its qualitative behaviour, i.e., it continues to be
at a point attractor, either a stable node or a focus. However,
at some bifurcation points, drastic qualitative changes oc-
cur; the system evolves from a monotonic operation mode
toward periodic (Hopf bifurcation) or chaotic motions (Fig.
3)
4,6,7,9,42,43,44,45
.Thus, dynamically organised phenomena are
homeodynamic (Fig. 2, 3), and visualised as demonstrating
spatio-temporal coherence.
A GEOMETRIC INTERPRETATION OF
HOMEODYNAMICS
Homeodynamics refers to the continuous transformation of
one dynamical system into another through instabilities at
bifurcation points (Fig. 3). Generically, the state space is an
n-dimensional space representing the set of all possible states
of the system (n is the number of variables). The phase space
is a two-dimensional state space which, filled with trajecto-
ries, constitutes the phase portrait of the system whose mo-
tion may be seen as a fluid flowing around itself (Fig. 3).
When all the trajectories settle or approach a restricted re-
gion of the phase space, that region is called an attractor. An
attractor has a basin to which a large number of trajectories
tend over time (i.e., the dynamics tends to this attractor as
time approaches infinity). Since various initial conditions are
implicated, the set of points whose probability is given by
its relative area or volume is called the basin of attraction
(Fig. 3). A system has a set of basins of attraction and
attractors that represents the integrated dynamic behaviour
of the variables in the system as they mutually influence
one another.
A dynamic system usually has basins with one attractor
in each. Considering that the state space is decomposed into
a set of basins, the systems motion may flow between
attractors. The continuous motion of the systems dynamics
and its potentiality for shifting between attractors at bifur-
cation points, based on its intrinsic dynamic properties, is
what we call homeodynamics (Fig. 3). The latter is given by
the general tendency of the system to self-organise and, in
particular, because of nonlinear kinetic mechanisms as well
as the dynamic coupling between processes (see above and
Fig. 4). Thus, under homeodynamic conditions, a dynamic
system may shift between attractors.
Dynamic systems that exhibit large attractors are more
likely to behave homeodynamically than those with small
attractors. In large attractors, essential variables are likely
to be subjected to a large range of variation, rather than re-
maining clamped to small variations as in the case of small
attractors (see below). Thus, we regard homeodynamics as
a more general, all-embracing concept from which homeo-
stasis becomes a special case.
COHERENCE
Under homeodynamic conditions a system (e.g., network of
reactions or cells) may exhibit emergent spatio-temporal
coherence, i.e., dynamic organisation (Fig. 2, 4). Coherence
may be understood as the synchronisation in space and time
of molecules, or the architecture of supramolecular or su-
pracellular structures, through self-organisation, in an ap-
parent, purposeful, functional way. Under coherent
behavioural conditions, spatially distant (e.g., cytoplasmic)

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Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
FIGURE 2. A graphic analogy of the concept of dynamic organisation under homeodynamic conditions. Dynamic organisation in, e.g., cells or tissues, is an
emergent property arising from transitions between levels of organisation at bifurcation points in the dynamics of biological processes. The different
landscapes represent the dynamic trajectories of (sub)cellular processes (e.g., enzyme activity, synthesis of macromolecules, cell division; indicated as
spheres in the plot), resulting from the functioning of those processes at different spatio-temporal scales (levels of organisation). The dotted lines that link
the spheres (different (sub)cellular processes) indicate the coupling between them. The coupling between processes that function simultaneously on
different spatio-temporal scales homeodynamically modifies the system trajectories (the landscapes shapes), as represented by the motion of the spheres
through peaks, slopes, and valleys. The sphere on the landscape on top symbolises a process occurring at a higher level of organisation (higher spatial
dimensions and lower relaxation times), i.e., a macroscopic one belonging to spatial structures (waves, macromolecular networks, subcellular organelles,
etc.). Indeed, the functioning of the system is coordinated and coupling occurs top-bottom as well as bottom-up. The interdependent and coupled cross-
talk between both flows of information trans-influences levels of organisation, i.e., beyond but through each level.

138
Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
regions function simultaneously and coordinately, spanning
spatial coordinates higher than the molecular or supramo-
lecular realms, and temporal relaxations slower than the
molecular or supramolecular levels of organisation. The
major functional consequence of this is that the qualitative
behaviour of the system changes through the scaling of its
spatio-temporal coordinates
9
.
The statement made by von Bertalanffy
17
(quoted in
Lloyd and Gilbert
46
) that what are called structures are slow
processes of long duration, functions are quick processes of
short duration is explained when one considers the func-
tioning of cells or tissues at several simultaneous levels of
organisation each one with characteristics space, E
c
, and re-
laxation time, T
r
. From distinct levels of organisation in-
volved in microbial and plant cell growth, solute transport,
energy transduction, neuron firing, and enzyme activity, E
c
and T
r
range from 10
-11
to 10
4
s and from 10
-10
to 10
-1
m
9,47
.We
have shown that E
c
and T
r
scale as a function of the level of
organisation according to an allometric law, implying that
both quantities grow exponentially. The exponent of the al-
lometric relationship depicts the sensitivity of E
c
and T
r
, char-
acteristic of variations in the level of organisation. At lower
levels of organisation, i.e., before the transition point (de-
fined as the drastic change in slope of the allometric equa-
tion at spatial and temporal dimensions of micrometers and
a few minutes), changes in the dynamics of processes given
by their relaxation toward fluctuations are roughly three-
fold higher than the changes in spatial dimensions. Other-
wise stated, temporal changes are more conspicuous than
spatial changes. Further from this transition point, where
the system moves from microscopic to macroscopic order,
the drastic increase in the slope of the allometric law sug-
gests that structural patterns whose existence involve emer-
gent macroscopic coherence imply that essential dynamic
variables remain bounded or that attractors reduce to small
ones. This behaviour clamps variables to a bounded (small)
range of variation
9
.
MECHANISMS OF COHERENCE
Bottom-Up Mechanisms
Most of the main functional properties of cells, such as en-
ergy transduction, solute transport, action potentials in neu-
rons, macromolecules poly-merisation, and cell growth and
division, are placed in T
r
ranges of 1 to 3 (seconds to several
minutes on a logarithmic scale) and E
c
of -7 to -6 (around
FIGURE 3. A geometric interpretation of homeodynamics. Several types of attractors with their corresponding basins of attraction are represented. The
putative trajectories followed by systems dynamics, are emphasised by arrows as well as the separatrices between basins. The homeodynamic condition
implies that the systems dynamics, visualised as a fluid flowing around itself, may shift between attractors at bifurcation points where stability is lost.
Thereby, the systems dynamics, following a perturbation, flies away toward another attractor exhibiting either qualitative or quantitative changes in its
behaviour. The upper left three-dimensional (3D) plot shows saddle and fixed points; the latter with different values, each one representing a different
branch of steady states. Alternative occupancies of these states, following the change of a bifurcation parameter, give a bistable switch with memory-like
features. Also stable and unstable foci are depicted in the upper left 3D plot. The lower right 3D plot, shows a limit cycle with its basin of attraction that
may be attained through an unstable focus, characteristic of oscillatory behaviour (self-sustained or damped oscillations, respectively). The middle 3D
plot depicts an attractor with three orbits embedded in it, with the potential for chaotic behaviour.

139
Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
FIGURE 4. (Supra)molecularly organised environments may exert global modulation of metabolic networks. Cellular systems are able to show coherent
as well as emergent properties that arise from dynamic organisation under homeodynamic conditions. Two important characteristics of microtubular
networks make them likely candidates for the coherent synchronisation of intracellular dynamics
9,13,45,80,87
: 1) their nonlinear dynamics which, at some
nonequilibrium state, might give rise to self-organisation and macroscopic structuring, and 2) their fractal or self-similar nature over a range of spatial
length scales
9
. The figure shows the sensitivity of two coupled enzymatic reactions (pyruvate kinase/lactate dehydrogenase [PK/LDH], panel A and
hexokinase/glucose-6-phosphate-dehydrogenase [HK/G6PDH], panel B) to the intracellular polymeric status of microtubules in permeabilized
Saccharomyces cerevisiae cells in the presence of stabilizing (taxol) or depolymerizing (nocodazole) agents
81
. Plotted curves represent the best fit to the
experimental data. Previous experimental analysis in vitro of coupled enzymatic reactions (PK/LDH, HK/G6PDH) in the presence of polymerised or
nonpolymerised microtubular protein (MTP) showed that global activation of the flux may be achieved
81
. Another important piece of evidence showed
that changes in the dynamics of tubulin assembly-disassembly may entrain the dynamics of enzymatic reactions
9,52
. The in situ kinetic parameters of PK or
G6PDH (A, B) and their dependence on microtubules were taken into account in a mathematical model. This couples the dynamics of assembly-disassembly
of microtubular protein (MTP) to the glycolytic pathway and branching to the tricarboxylic acid (TCA) cycle, ethanolic fermentation
82,83
, and the pentose
phosphate cycle (central scheme, green arrows). The mathematical model comprises 11 ordinary differential equations; 8 of them represent the intermediate
concentration levels, whereas the other 3 describe the concentration of polymerised or nonpolymerised (GTP-bound) MTP and the oligomeric status of
PK
9,51,81,82,83
. The polymeric status of MTP may globally modulate the glycolytic flux in a coherent manner (panels C, D). Indeed, the main results obtained
show that the steady state glycolytic flux was globally increased under conditions in which 100% of the MTP was polymerised at either low (L = 1.93 mM
min
-1
), medium (M = 2.55 mM min
-1
) or high (H = 3.15 mM min
-1
) cellular glucose uptake rate (panel C). On the contrary, the flux through glycolysis was
decreased when the bulk of MTP was depolymerised. Intermediary, although nonproportional, results were achieved when 50% of MTP was polymerised
(panel C). In the presence of high or low levels of polymerised MTP the main rate-controlling steps of the glycolytic flux are the glucose uptake (positive),
HK (positive), and the branch toward the pentose phosphate (PP) cycle (negative). Apparently, the negative control exerted by the PP pathway was less
important at high than at low levels of polymerised MTP, in this way explaining the higher glycolytic fluxes attained
87
. Concomitantly with the global flux
modulation, the steady-state values of metabolites also changed systemically (panel D). The fact that the alterations induced by the polymeric status of
MTP on the metabolic network were properties of the integrated system was confirmed by varying individual kinetic parameters of enzymes (e.g., PK)
coupled to MTP dynamics. In the latter case, only local changes in the level of metabolites (i.e., PEP) affected by the enzyme activity were observed
87,88
.
micrometers)
9
. The temporal span corresponds to metabolic
and epigenetic domains
8,46,48
. Molecular properties involved
in those processes span T
r
s of -6 to -10 (ms to ps) and E
c
s of -
8 to -10 (nanometers to angstroms). These are wide spatio-
temporal spans. On these grounds, we have proposed that
for molecular properties to extend their range of action to
higher spatio-temporal dimensions, organising principles
implying coherence in space and time must be invoked
9
.
Relevant to the functional behaviour of cells or tissues
are the mechanisms through which dynamic organisation
is achieved under homeodynamic conditions. We have pre-
viously suggested that dynamically organised phenomena
are visualised as being spatio-temporally coherent. Several
mechanisms underlie this bottom-up coherence, that we

140
Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
briefly describe. Thus, for example, waves of second mes-
sengers or ions may arise through a combination of amplifi-
cation in biochemical reaction networks and spreading
through diffusion or percolation. Amplification may arise
at instabilities in the dynamics of biochemical reactions by
autocatalysis through allosteric or ultrasensitive mecha-
nisms
13,49
. Under these conditions, transduction (sensitivity
amplification) and coherence (spatio-temporal waves) mu-
tually cooperate.
Dynamic supramolecular organisation of components
of the cytoskeleton gives rise to sophisticated spatial
organisation and intricate fractal geometry in cells. The cel-
lular cytoskeleton fulfills all the requirements for self-
organisation, i.e., they are open to fluxes of matter (proteins)
and energy (GTP), and non-linearity is provided by autoca-
talysis during polymerisation. Similar considerations apply
to the so-called dynamic instability that results in the cata-
strophic depolymerisation of microtubules
50
. We have
offered an interpretation of microtubular dynamic instabil-
ity in terms of an irreversible bistable transition. Thus, the
dynamic coupling between changes in cytoskeleton
organisation and of enzymatic reactions taking place con-
comitantly produces entrainment of one system by the other,
in a global bistable switch (Fig. 4)
51,52,87
.
Biochemically and thermodynamically, cellular metabo-
lism may be represented as a set of catabolic and anabolic
fluxes coupled to each other through energy-transducing
events. In this framework, pathway stoichiometry consti-
tutes a built-in autocatalytic source of nonlinear kinetics able
to give rise to homeodynamic behaviour, i.e., both mono-
tonic and periodic. Thus, the coordination of metabolic fluxes
is an expression of the cells dynamic organisation. Flux co-
ordination is, in turn, involved in the regulation of cell
growth. We have studied the processes of growth, division
and sporulation in S. cerevisiae; subcellular structural remod-
elling can be related in this system to the degree of coupling
between carbon and energy fluxes
9,53,54,55
.
The ability of biological systems, either unicellular or
multicellular, to exhibit rhythmic behaviour in the ultradian
domain is a fundamental property because of its potential
role as an inducer of bottom-up coherence, e.g., entrainment
of cell division
8
, or coordination of intracellular functions
(top-bottom coherence: see below). In systems exhibiting
chaos, many possible motions are simultaneously present.
In fact, since the dynamics of a chaotic system traces a strange
attractor in the phase space, in principle a great number of
unstable limit cycles are embedded therein; each of these is
characterised by a distinct number of oscillations per pe-
riod
56,57
. Within the perspective of homeodynamics, biologi-
cal systems exhibiting chaotic dynamics need only small
perturbations of their parameters in order to select stable
periodic outputs
58,59
. This characteristic facilitates dynamic
motion of the system between attractors, i.e., homeodynamics
(Fig. 3).
Top-Bottom Mechanisms: Ultradian and
Circadian Clocks
Recently, it has become evident that the circadian clock-con-
trol dominates the entire functioning of the organism in
slowly growing lower eukaryotes as well as in some prokary-
otes
48
. Circadian gating of the cell division cycle under daily
alternation of light and dark, for example (Fig. 5), is well
documented
46,48,84
. Circadian control of gene expression in
the cyanobacteria Synechococcus has been reported
85
.
It has been proposed that the ultradian clock has timing
functions providing a time base for intracellular coordi-
nation
8
. In the latter sense, ultradian oscillations are, po-
tentially, a coherence-inducer of the top-bottom type. The
ultradian clock has multiple outputs, e.g., rhythms of res-
piration, adenine nucleotides, accumulating protein, en-
zyme concentration and activity, and it provides a
time-frame for cell division (Fig. 6)
48,86
. Cycles of activity
of energy-yielding processes are the consequences of
timer-controlled alternating phases of high and low bio-
synthetic energy need
29,60,61
. Epigenetic ultradian oscilla-
tions with periods that range between 30 min and 4 h
have been identified as playing a central timekeeping role
in embryos and in lower eukaryotes under conditions of
rapid growth (see ref. 46 for a review). Thus, in rapidly di-
viding organisms, the organisation of central metabolic pro-
cesses (energy generation and biosynthetic pathways)
requires a time-base given by phase-locking to the ultradian
clock
48
. Limitation of the respiratory rate by ADP levels and
their phase relationship take part of the ultradian clock
mechanism (Fig. 6). Mitochondrial activities are determined
by energy requirement on an epigenetic time scale rather
than on a faster metabolic dynamic
8
.
The ultradian clock has been interpreted as a forcing
function in the differential equation for the slow variable in
a mathematical model that basically represents a cell divi-
sion cycle oscillator with a slow and a fast component
8,62
.
The short-period (ultradian) clock exerts a dominant con-
trol of the cell division time, in both lower eukaryotes and
in higher animal cells in culture
46
.
Another model of the cell division cycle takes into ac-
count the coordination of macromolecular synthesis by
cyclin-dependent kinases whose active forms are a complex
of at least a kinase and a cyclin called maturation promot-
ing factor (MPF)
48,63,64
. The latter models homeodynamic
behaviour shows three modes: as a steady state with high
MPF activity, as a spontaneous oscillator, or as an excitable
switch
63,64
.
CONCLUSIONS AND OUTLOOK
Dynamic systems exhibit different types of attractors either
large or small. Large attractors are more likely to behave

141
Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
homeodynamically with respect to small attractors, because
essential variables are likely to be subjected to a large range
of variation rather than remaining clamped to small varia-
tions. Thus, we suggest, homeodynamics as a more general
and all-embracing concept of which homeostasis becomes a
special case, is better suited for describing the temporal struc-
ture of living systems. Under homeodynamic conditions,
living systems spatio-temporally coordinate their function-
ing by essentially top-bottom or bottom-up mechanisms. The
former are represented by circadian and ultradian rhythms
with clock characteristics, whereas the latter emerge from
the intrinsic, autonomous dynamics of the integrated mass-
energy-information carrying networks that represent living
systems.
FIGURE 5. Circadian clock control of the cell division cycle in the algal flagellate Euglena. Entrainability is a key property of circadian rhythms according
to which circadian rhythmicities can be synchronized by imposed diurnal light or temperature cycles to precise 24-h periods and can be predictably
phase-shifted by single light and temperature signals.
26,35,48,84
The figure illustrates the entrainment of the cell division rhythm in populations of Euglena
gracilis batch cultured photoautotrophically at 25°C by a full-photoperiod, diurnal light-dark (LD) cycle: 10, 14 light cycle. Step sizes (ss, ratio of number
of cells per milliliter after a division burst to that just before the onsets of divisions) are given for successive steps; the estimated period (t) of each
oscillation (intervals between successive onsets of divisions) is indicated by the encircled numbers (hours). The average period (t) of the rhythm in the
culture was almost identical to that (T) of the synchronizing LD cycle. Divisions were confined primarily to the main dark intervals, commencing at their
onsets. A doubling cell number (ss @ 2.00) usually occurred every 24 h in this full-photoperiod LD cycle. (Reproduced from Edmunds, 1988, by permission
of Springer-Verlag, New York.)

142
Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
FIGURE 6. Cell-cycle-ultradian clock interactions in Acanthamoeba castellanii. In rapidly dividing organisms the organization of central metabolic processes
(energy generation and biosynthetic pathways) requires a time-base, and the processes are phase-locked to a central oscillator, in this case the ultradian
clock.
48
The figure shows changes in adenine nucleotide pool levels and adenylate charge values in a synchronously dividing culture of A. castellanii
(τ=69 min at 30°C).
86
The synchronous culture contained 10% of the exponentially growing population. Adenine nucleotides were measured in 1 ml
samples withdrawn at 15 min intervals. (a) Cell numbers and synchrony index, F. Adenylate concentrations are expressed as nmol mL
-1
culture. (Reproduced
from Edwards and Lloyd, 1978, by permission of The Society for General Microbiology.)

143
Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
Globally organised complexity is brought forth by the
cross-talk between these two opposing, but complementary,
flows of information. In this realm, gaps in our knowledge
are still large, but pointing to where the trend of our efforts
should be directed.
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This article should be referenced as follows:
Lloyd, D., Aon, M.A., and Cortassa S. (2001) Why homeodynamics,
not homeostasis? TheScientificWorld 1, 133145.
Published: April 4, 2001