ArticlePDF AvailableLiterature Review

Abstract and Figures

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.
(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 m M min -1 ), medium (M = 2.55 m M min -1 ) or high (H = 3.15 m M 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 .
… 
Content may be subject to copyright.
133
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
134
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
135
Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
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
.
136
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)
137
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.
REFERENCES
1. Nicolis, G. and Prigogine, I. (1977) Self-Organisation in Non-
Equilibrium Systems. Wiley-Interscience, London.
2. Haken, H. (1978) Synergetics. Springer-Verlag, Heidelberg.
3. Rosen, R. (1970) Dynamical System Theory in Biology. John
Wiley & Sons, New York.
4. Abraham, R.H. (1987) Dynamics and self-organisation. In Self-
Organising Systems. The Emergence of Order. Yates, F.E.,
Garfinke, A., Walter, D.O., and Yates, G.B., Eds. Plenum
Press, New York, pp. 599-613.
5. Glansdorff, P. and Prigogine, I. (1971) Thermodynamic Theory
of Structure, Stability and Fluctuations. Wiley, London.
6. Abraham, R.H. and Shaw, Ch.D. (1984) Dynamics - The Ge-
ometry of Behaviour. Part II: Chaotic Behaviour. Aerial Press,
Santa Cruz, CA.
7. Abraham, R.H. and Shaw, Ch.D. (1984) Dynamics - The Ge-
ometry of Behaviour. Part I: Periodic Behaviour. Aerial Press,
Santa Cruz, CA.
8. Lloyd, D. (1992) Intracellular time keeping: epigenetic oscil-
lations reveal the functions of an ultradian clock. In Ultradian
Rhythms in Life Processes. Lloyd, D. and Rossi, E.R., Eds.
Springer-Verlag, London, pp. 5-22.
9. Aon, M.A. and Cortassa, S. (1997) Dynamic Biological
Organisation: Fundamentals as Applied to Cellular Systems.
Chapman & Hall, London.
10. Kauffman, S. (1995) At Home in the Universe. The Search for the
Laws of Self-Organisation and Complexity. Oxford University
Press, New York.
11. Goodwin, B.C. (1998) Las Manchas del Leopardo. La Evolución
de la Complejidad. Tusquets Editores, Barcelona.
12. Lloyd, D. and Rossi, E.R. (1993) Biological rhythms as
organisation and information. Biol. Rev. 68: 563-577.
13. Aon, M.A., Cortassa, S., Gomez Casati, D.F., Iglesias, A.A.
(2000) Effects of stress on cellular infrastructure and meta-
bolic organisation in plant cells. Int. Rev. Cytol. 194, 239-273.
14. Hopkins, F.G. (1913) The dynamic side of biochemistry. Brit.
Med. J. 2, 13-24.
15. Bernard, C. (1927) Introduction à lEtude de la Medicine
Experimentale. Green, H.C. (transl.). McMillan, New York.
16. Cannon, W.B. (1932) The Wisdom of the Body. Norton, New
York.
17. Von Bertalanffy, L. (1950) The theory of open systems in phys-
ics and biology. Science 111, 23-29.
18. Burton, A.C. (1939) The properties of the steady state as com-
pared to those of equilibrium as shown in characteristic bio-
logical behaviour. Cell Comp. Physiol. 14, 327-330.
19. Hill, A.V. (1931) Adventures in Biophysics. University of Penn-
sylvania Press, Philadelphia.
20. Schoenheimer, R. (1942) The Dynamic State of Body Con-
stituents. Harvard University Press, Cambridge, MA.
21. Rittenberg, D. (1948) Turnover of proteins. J. Mount Sinai
Hosp. 14, 891-901.
22. Novick, A. and Szilard, L. (1950) Description of the chemostat.
Science 112, 715-716.
23. Monod, J. (1950) La technique de culture continue: théorie et
applications. Ann. Inst. Pasteur 79, 390-410.
24. Lloyd, D., Edwards, S.W., and Williams, J.L. (1981) Oscilla-
tory accumulation of total cell protein in synchronous cul-
tures of candida utilis. FEMS Microbiol Lett. 12, 295-298.
25. Lloyd, D., Edwards, S.W., and Fry J.C. (1982) Temperature
compensated oscillations in respiration and cellular protein
content in synchronous cultures of acanthahamoeba castellanii.
Proc. Natl. Acad. Sci. U.S.A. 79, 3785-3788.
26. Lloyd, D., Poole, R.K., and Edwards, S.W. (1982) The Cell Di-
vision Cycle: Temporal Organisation and Control of Cellular
Growth and Reproduction. Academic Press, London.
27. Luzikov, V.N. (1984) Mitochondrial Biogenesis and Breakdown.
Plenum Press, New York.
28. Wolf, D.H. (1980) Control of metabolism in yeast and the
lower eukaryotes through action of proteases. Adv. Microb.
Physiol. 21, 267-338.
29. Edwards, S.W. and Lloyd, D. (1980) Oscillations in protein
and RNA content during the synchronous growth
of Acanthamoeba castellanii: evidence for periodic turnover
of macromolecules during the cell cycle. FEBS Lett 109: 21-
26.
30. Wheatley, D.N., Grisolia, S., and Hernandez-Yago, J. (1982)
Significance of the rapid degradation of newly-synthesised
proteins in mammalian cells. J. Theor. Biol. 98, 283-300.
31. Mandelstam, J. (1960) The intracellular turnover of protein
and nucleic acids and its role in biochemical differentiation.
Bact. Rev. 24, 289-308.
32. Bartley, W. and Birt, I.M. (1970) Aspects of the turnover of
mitochondrial constituents. In Essays on Cell Metabolism.
Bartley, W., Kornberg, H.I., and Quayl, J.R., Eds. Wiley
Interscience, London, pp.1-44.
33. Yates, F.E. (1992) Outline of a physical theory of physiologi-
cal systems. J. Physiol. Pharmacol. 60, 217-248.
34. Lloyd, D. and Edwards, S.W. (1984) Epigenetic oscillations
during the cell cycles of lower eukaryotes: lifes slow dance
to the music of time. In Cell Cycle Clocks. Edwards, L.N., Jr.,
Ed. Marcel Dekker, New York, pp. 27-46.
35. Lloyd, D. and Edwards, S.W. (1986) Temperature-compen-
sated ultradian rhythms in lower eukaryotes: timers for cell
cycle and circadian events? Adv. Chronobiol. Vol. 1, Alan R.
Liss, New York.
36. Dysens, I.N.M. and Amesz, J. (1957) Fluorescence spectro-
photometry of reduced pyridine nucleotide in intact cells in
the near UV and visible region. Biochim.Biophys. Acta 24, 19-
26.
37. Ghosh, A. and Chance, B. (1984) Oscillations of glycolytic
intermediates in yeast cells. Biochem. Biophys. Res. Commun.
16, 174-181.
38. Higgins, J. (1967) The theory of oscillating reactions. Ind.
Engin. Chem. 59, 19-62.
39. Selkov, R.R. (1968) Self oscillations in glycolysis I. A simple
kinetic model. Eur. J. Biochem. 4, 79-86.
40. Goodwin, B.C. (1963) Temporal Organisation in Cells. Academic
Press, London.
144
Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
41. Panikov, NS. (1995) Microbial Growth Kinetics. Chapman &
Hall, London.
42. Nicolis, G. and Prigogine, I. (1989) Exploring Complexity. Free-
man, New York.
43. Glas, L. and Mackey, M.C. (1988) From Clocks to Chaos. The
Rhythms of Life. Princeton University Press, Princeton, NJ.
44. Aon, M.A., Cortassa, S., Westerhoff, H.V., Berden, J.A., van
Spronsen, E., and van Dam, K. (1991) Dynamic regulation of
yeast glycolytic oscillations by mitochondrial functions. J. Cell
Sci. 99, 325-334.
45. Cortassa, S. and Aon, M.A. (1994) Spatio-temporal regula-
tion of glycolysis and oxidative phosphorylation in vivo in
tumor and yeast cells. Cell. Biol. Int. 18, 687-713.
46. Lloyd, D. and Gilbert, D.A. (1998) Temporal organisation of
the cell division cycle in eukaryotic microbes. In Microbial
Responses to Light and Time. Caddick, M.X., Baumberg, S.,
Hodgson, D.A., and Phillips-Jones, M.K., Eds. Soc. Gen.
Microbiol. Symp. 56. Cambridge University Press.
47. Aon, M.A. and Cortassa, S. (1993) An allometric interpreta-
tion of the spatio-temporal organisation of molecular and cel-
lular processes. Mol. Cell. Biochem. 120, 1-14.
48. Lloyd, D. (1998) Circadian and ultradian clock-controlled
rhythms in unicellular microorganisms. Adv. Microb. Physiol.
39, 291-338.
49. Gomez Casati, D.F., Aon, M.A., and Iglesias, A.A. Ultra-
sensitive glycogen synthesis in cyanobacteria. FEBS Lett. 1999
446, 117-121.
50. Kirschner, M. and Mitchinson, T. (1986) Beyond self-assem-
bly: from microtubules to morphogenesis. Cell 45, 329-342.
51. Aon, M.A., Cortassa, S., and Cáceres, A. (1996) Models of
cytoplasmic structure and function. In Computation in Cellu-
lar and Molecular Biological Systems. Cuthbertson, R.,
Holcombe, M., and Paton, R., Eds. World Scientific, London,
pp.195-207.
52. Cortassa, S. and Aon, M.A. (1996) Entrainment of enzymatic
activity by the dynamics of cytoskeleton. In Biothermokinetics
of the Living Cell. Westerhoff, H.V. and Snoep, J., Eds.
Biothermokinetics, Amsterdam, pp. 337-342.
53. Aon, M.A and Cortassa, S. (1995) Cell growth and differen-
tiation from the perspective of dynamical organisation of cel-
lular and subcellular processes. Prog. Biophys. Mol. Biol. 64,
55-79.
54. Cortassa, S., Aon, J.C., Aon, M.A., and Spencer, J.FT. (2000)
Dynamics of cellular energetics and metabolism and their
interactions with the gene regulatory circuitry during sporu-
lation in Saccharomyces cerevisiae. Adv. Microb Physiol. 43, 75-
115.
55. Aon, J.C. and Cortassa, S. (2001) Involvement of nitrogen me-
tabolism in the triggering of ethanol fermentation in aerobic
chemostat cultures of Saccharomyces cerevisiae. Metab. Eng. (in
press).
56. Peng, B., Petrov, V., and Showalter, K. (1991) Controlling
chemical chaos. J. Phys Chem. 95, 4957-4959.
57. Shinbrot, T., Grebogi, C., Ott, E., and Yorke, J.A. (1993) Us-
ing small perturbations to control chaos. Nature 363, 411-417.
58.Lloyd, A.L. and Lloyd, D. (1993) Hypothesis: the central
oscillator of the circadian clock is a controlled chaotic
attractor. BioSystems 29, 77-85.
59. Lloyd, A.L. and Lloyd, D. (1995) Chaos: its significance and
detection in biology. Biol. Rhythm Res. 26, 233-252.
60. Edwards, S.W., Evans, J.B., and Lloyd, D. (1981) Oscillatory
accumulation of catalase during the cell cycle of Acanthamoeba
castellanii. J. Gen. Microbiol. 125, 459-462.
61. Edwards, S.W., Evans, J.B., Williams, J.L., and Lloyd, D.
(1982) Mitochondrial ATPase of Acanthamoeba castellanii: os-
cillating accumulation of enzyme activity, enzyme protein
and F1-inhibitor during the cell cycle. Biochem. J. 202, 453-
458.
62. Lloyd, D. and Volkov, E.I. (1990) Quantized cell cycle times:
interaction between a relaxation oscillator and ultradian clock
pulses. BioSystems 23, 305-310.
63. Tyson, J.J. (1991) Modeling of the cell division cycle: cdc2
and cyclin interactions. Proc. Natl. Acad. Sci. U.S.A. 88, 7328-
7332.
64. Novak, B. and Tyson, J.J. (1993) Numerical analysis of a com-
prehensive model of M-phase control in Xenopus oocyte ex-
tracts and intact embryos. J. Cell Sci. 106, 1153-1168.
65. Balzer, I., Neuhauss-Steinmetz, V., and Hardeland, R. (1989)
Temperature compensation in an ultradian rhythm of ty-
rosine aminotransferase activity in Euglena gracilis Klebs.
Experientia 45, 476-477.
66. Gerisch, G. and Hess, B. (1974) Cyclic AMP controlled oscil-
lations in suspended Dictyostelium cells. Their relation to mor-
phogenetic cell interactions. Proc. Natl. Acad. Sci. U.S.A. 71,
2118-2122.
67. Slater, M.L., Sharrow, S.O., and Gart, J.J. (1977) Cell cycle of
Saccharomyces cerevisiae in populations growing at different
rates. Proc. Natl. Acad. Sci. U.S.A. 74, 3850-3854.
68. Hildebrandt, G. (1988) Temporal order of ultradian rhythms
in man. In Trends in Chronobiology. Hekkens, W.T.J.M.,
Kerkhof, G.A., and Rietveld, W.J., Eds. Pergamon Press, Ox-
ford, pp. 107-122.
69. Nijhuis, J.G., Precht, H.F.R., Martin, C.B., Jr., and Bots,
R.S.G.M. (1982) Are there behavioural states in the human
fetus? Early Hum. Dev. 6, 177-195.
70. Visser, G., Reinten, C., Coplan, P., Gilbert, D.A., and
Hammond, K.D. (1990) Oscillations in cell morphology and
redox state. Biophys. Chem. 37, 383-394.
71. Edwards, C., Statham, M., and Lloyd, D. (1975) The prepara-
tion of large-scale synchronous cultures of the pry-
panosomatid Crithidia fasciculata by cell size selection: changes
in respiration and adenylate charge through the cell-cycle. J.
Gen. Microbiol. 88, 141-152.
72. Brandenberger, G. (1992) Endocrine ultradian rhythms dur-
ing sleep and wakefulness. In Ultradian Rhythms in Life Pro-
cesses. Lloyd, D., Rossi, E.R., Eds. Springer-Verlag, London,
pp. 123-138.
73. Glass, L., Guevara, M.R., Belair, J., and Shrier, A. (1984) Glo-
bal bifurcations of a periodically forced biological oscillator.
Phys. Rev. 29, 1348-1357.
145
Lloyd, et al.: Why Homeodynamics, Not Homeostasis? TheScientificWorld (2001) 1, 133145
74. Kyriacou, C.P. and Hall, J.C. (1980) Circadian rhythm
mutations in Drosophila affect short-term fluctuations in the
males courtship song. Proc. Natl. Acad. Sci. U.S.A. 77, 6929-
6933.
75. Lloyd, D. and Kippert, F. (1987) A temperature-compensated
ultradian clock explains temperature-dependents quantal cell
cycle times In Temperature and Animal Cells. Bowler, K. and
Fuller, B.J., Eds. Symp. Soc. Exp. Biol. 41, Cambridge Uni-
versity Press, Cambridge, pp. 135-155.
76. Dowse, H.B. and Ringo, J.M. (1992) Do ultradian oscillators
underlie the circadian clock in Drosophila? In Ultradian
Rhythms in Life Processes. Lloyd, D. and Rossi, E.R., Eds.
Springer-Verlag, London, pp. 105-117.
77. Churchland, P.S. (1989) Neurophilosophy. Toward a Unified Sci-
ence of the Mind/Brain. MIT Press, Cambridge, MA.
78. Jalife, J. and Moe, G.K. (1976) Effect of electrotonic potential
on pacemaker activity of canine Purkinje fibers in relation to
parasystole. Circ. Res. 39, 801-808.
79. Jenkins, H., Griffiths, A.J., and Lloyd, D. (1990) Selection
synchronized Chlamydomonas reinhardtii display ultradian
but not circadian rhythms. J. Interdiscipl. Cycle Res. 21, 75-
80.
80. Aon, M.A., Cortassa, S., and Lloyd, D. (2000) Chaotic dy-
namics and fractal space in biochemistry: Simplicity under-
lies complexity. Cell Biol. Int. 24, 581-587.
81. Cortassa, S., Cáceres, A., and Aon, M.A. (1994) Microtubular
protein in its polymerized or non-polymerized states differ-
entially modulates in vitro and intracellular fluxes catalyzed
by enzymes related to carbon metabolism. J. Cell Biochem. 55,
120-132.
82. Cortassa, S. and Aon, M.A. (1994) Metabolic control analysis
of glycolysis and branching to ethanol production in
chemostat cultures of Saccharomyces cerevisiae under carbon,
nitrogen, or phosphate limitations. Enz. Microb. Technol. 16,
761-770.
83. Cortassa, S. and Aon, M.A. (1997) Distributed control of the
glycolytic flux in wild-type cells and catabolite repression mu-
tants of Saccharomyces cerevisiae growing in carbon-limited
chemostat cultures. Enz. Microb. Technol. 21, 596-602.
84. Edmunds, L.N., Jr. (1988) Cellular and Molecular Bases of Bio-
logical Clocks. Models and Mechanisms for Circadian Timekeep-
ing. Springer-Verlag, New York.
85. Kondo, T. and Ishiura, M. (2000) The circadian clock of
cyanobacteria. BioEssays 22, 10-15.
86. Edwards, S.W. and Lloyd, D. (1978) Oscillations of respira-
tion and adenine nucleotides in synchronous cultures of
Acanthamoeba castellanii: mitochondrial respiratory control
invivo. J. Gen. Microbiol. 108, 197-204.
87. Aon, M.A. (2000) Mechanisms of spatio-temporal coherence
and transduction in cellular cytoplasm. The role of cytoskel-
eton organization and geometry. Available at: Center
for Computational Medicine and Biology, John Hopkins
University, http://www.bme.jhu.edu/news/seminars/
archive.html (November 21).
88. Aon, M.A. and Cortassa, S. (2001) Global, robust and coher-
ent modulation of a metabolic network by cytoskeleton or-
ganization and dynamics (submitted).
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
... whereas it is a dynamic mechanism [31]. This of course also applies to allostasis where allodynamics is a more appropriate term [32]. ...
... Sutherland's observation that a human being is a system with different rhythms is confirmed by science [33,35,36,]. Synchronization takes place between these rhythms, where the microlevel (cell) influences the macro-level (brain) and vice versa [31,35,40]. When the patient is laid down relaxed on the treatment table, the osteopath perceives the Primary Respiratory Mechanism (PRM). ...
... Life is not static but dynamic like Sutherland wrote and maintaining health is a dynamic process so it is better to speak about homeodynamics and no about homeostasis [31]. There is not one control centre in the human body, it is the whole that does the regulation. ...
Article
Full-text available
A proposition is made for scientific substantiation of “Primary respiration” and related concepts, including suggestions for future research. For research and support, the field of mathematics, artificial intelligence, chaos theory and complex systems thinking can be of fundamental and essential value.
... From this perspective, every human body is believed to have multiple automatic inhibitory mechanisms that suppress disquieting influences, whether those disruptions are generated by the environment external to the body or by malfunctioning internal systems. This particular notion has recently been replaced by homeodynamics, with the recognition that life is a non-equilibrium process and therefore requires rich dynamics to maintain stability [3,4]. ...
... This notion of homeodynamics offered a radically new concept departing from the traditional homeostatic idea that emphasizes the stability of the internal dynamics with respect to perturbation. Indeed, Lloyd et al. [4] argue in their review that biological systems are homeodynamic as a manifestation of a network's ability to self-organize at behavior bifurcation points where they lose stability and restabilize in a new state. As a result of this self-organization, living systems displays complex behaviors with a spectrum of emergent characteristics, including bistable switches, thresholds, mutual entrainment, and periodic as well as chaotic behavior. ...
Article
Full-text available
This is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars. In prequel II, the network effect was introduced to explain how the collective dynamics of a complex network can transform a many-body non-linear dynamical system modeled using the integer calculus (IC) into a single-body fractional stochastic rate equation. Note that these essays are about biomedical phenomena that have historically been improperly modeled using the IC and how fractional calculus (FC) models better explain experimental results. This essay presents the biomedical entailment of the FC, but it is not a mathematical discussion in the sense that we are not concerned with the formal infrastucture, which is cited, but we are concerned with what that infrastructure entails. For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies. Physiologic time series that have explicitly related pathology to a narrowing of multifractal time series include but are not limited to heart rate variability (HRV), stride rate variability (SRV) and breath rate variability (BRV). The efficiency of the transfer of information due to the interaction between two such complex networks is determined by their relative spectral width, with information being transferred from the network with the broader to that with the narrower width. A fractional-order differential equation, whose order is random, is shown to generate a multifractal time series, thereby providing a FC model of the information exchange between complex networks. This equivalence between random fractional derivatives and multifractality has not received the recognition in the bioapplications literature we believe it warrants.
... Constant intracellular surveillance is vital for maintaining redox homeostasis, termed "homeodynamics" due to its dynamic property. 4 Recent studies on redox biology have indicated a relatively complete redox architecture that is closely linked to physiological function, 5 with a set of intricate mechanisms denoted as the "redox code." 6 H 2 O 2 as a key second messenger is central to the redox code, contributing to cell fate decisions. ...
Article
Full-text available
Redox biology is at the core of life sciences, accompanied by the close correlation of redox processes with biological activities. Redox homeostasis is a prerequisite for human health, in which the physiological levels of nonradical reactive oxygen species (ROS) function as the primary second messengers to modulate physiological redox signaling by orchestrating multiple redox sensors. However, excessive ROS accumulation, termed oxidative stress (OS), leads to biomolecule damage and subsequent occurrence of various diseases such as type 2 diabetes, atherosclerosis, and cancer. Herein, starting with the evolution of redox biology, we reveal the roles of ROS as multifaceted physiological modulators to mediate redox signaling and sustain redox homeostasis. In addition, we also emphasize the detailed OS mechanisms involved in the initiation and development of several important diseases. ROS as a double‐edged sword in disease progression suggest two different therapeutic strategies to treat redox‐relevant diseases, in which targeting ROS sources and redox‐related effectors to manipulate redox homeostasis will largely promote precision medicine. Therefore, a comprehensive understanding of the redox signaling networks under physiological and pathological conditions will facilitate the development of redox medicine and benefit patients with redox‐relevant diseases. Redox homeostasis is essential for human health, supported by multiple functional signaling pathways including the Keap1‐Nrf2, FOXO, HIF and NF‐κB pathways. However, redox imbalance causes multiple serious diseases such as type 2 diabetes, atherosclerosis, chronic obstructive pulmonary disease, Alzheimer's disease, cancer, and aging. Our review emphasizes the significance of redox manipulation in clinical therapeutics and points out the existing challenges involved in this field.
... They can adapt to changes in the environment and are a real mechanism of homeostasis. The very concept of homeostasis began to be supplemented or even replaced by the concept of homeodynamics (Yates, 1994;Lloyd et al., 2001). In several models and real observations, it has been shown that circadian and ultradian rhythms interact, and that ultradian oscillations modify the daily cycle. ...
Book
Full-text available
This is a translation of my book published in Russian a year earlier. Some changes have been made. The data on ultradian (circahoralian) rhythms are summarized: their distribution, nature, importance in biochemistry and physiology. Such rhythms of protein synthesis and cell mass, enzyme activity, ATP and cAMP concentration, pH, and cellular respiration are considered with examples from bacteria, protists, and mammalian cells, as well as integral rhythms of human respiration, pulse, and behavior. The fractal nature of ultradian rhythms is established as one of the intrinsic properties of the cell. Using ultradian rhythms in cell cultures, a model is created for studying the mechanisms of direct intercellular interactions. Signaling factors have been found − gangliosides, blood neurotransmitters and some peptides. The processes in the cytoplasm triggered by them, leading to synchronization of cell and organ functions as a result of interactions of cells in the population, are determined. The section of the book "Biomedical Supplements" analyzing the kinetics of the processes and their signaling factors contains new ideas about the origin of multicellularity, the possibility of compensation of some senile disorders, the diagnosis and prognosis of heart and intestinal diseases, the rhythms of mobility and behavior of animals and humans, previously unknown properties of drugs.
... At the turn of the 20th century the foundation of biology started moving from the concept of homeostasis, which is compatible with the physical notion of regression to equilibrium, to the concept of homeodynamics, which involves periodicity (Lloyd et al., 2001;Tu and McKnight, 2006), chaos and complexity (Guzm´an et al., 2017). As far as the important biological role of periodicity is concerned, we invite the readers to consult the excellent review paper of Strogatz (Strogatz, 2000), which reveals a connection between homeodynamics and neurophysiology. ...
Article
Full-text available
This is an essay advocating the efficacy of using the (noninteger) fractional calculus (FC) for the modeling of complex dynamical systems, specifically those pertaining to biomedical phenomena in general and oncological phenomena in particular. Herein we describe how the integer calculus (IC) is often incapable of describing what were historically thought to be simple linear phenomena such as Newton’s law of cooling and Brownian motion. We demonstrate that even linear dynamical systems may be more accurately described by fractional rate equations (FREs) when the experimental datasets are inconsistent with models based on the IC. The Network Effect is introduced to explain how the collective dynamics of a complex network can transform a many-body noninear dynamical system modeled using the IC into a set of independent single-body fractional stochastic rate equations (FSREs). Note that this is not a mathematics paper, but rather a discussion focusing on the kinds of phenomena that have historically been approximately and improperly modeled using the IC and how a FC replacement of the model better explains the experimental results. This may be due to hidden effects that were not anticapated in the IC model, or to an effect that was acknowledged as possibly significant, but beyond the mathematical skills of the investigator to Incorporate into the original model. Whatever the reason we introduce the FRE used to describe mathematical oncology (MO) and review the quality of fit of such models to tumor growth data. The analytic results entailed in MO using ordinary diffusion as well as fractional diffusion are also briefly discussed. A connection is made between a time-dependent fractional-order derivative, technically called a distributed-order parameter, and the multifractality of time series, such that an observed multifractal time series can be modeled using a FRE with a distributed fractional-order derivative. This equivalence between multifractality and distributed fractional derivatives has not received the recognition in the applications literature we believe it warrants.
... However, the functions of adult stem cells decline with age and a breakdown in stem cell homeostasis jeopardizes the regulatory mechanisms that act against age associated disorders [18]. The onset and the rate of aging process differ with individuals based on their adaptability to maintain physiological balance through various homeodynamic mechanisms [19] that mediate DNA repair, host immunity, clearance of damaged/dysfunctional proteins and organelles and synthesis and regulation of proteins and lipids [20]. Expression of anti-aging proteins and suppression of aging markers in MSCs are crucial for their maintenance and function and therefore they serve as effective targets for aging drugs [17,18]. ...
Article
Common characteristics of aging include reduced somatic stem cell number, susceptibility to cardiac injuries, metabolic imbalances and increased risk for oncogenesis. In this study, Pleiotropic anti-aging effects of a decoction Jing Si herbal drink (JS) containing eight Traditional Chinese Medicine based herbs, with known effects against aging related disorders was evaluated. Adipose derived mesenchymal stem cells (ADMSCs) from 16 week old adult and 24 month old aging WKY rats were evaluated for the age-related changes in stem cell homeostasis. Effects of JS on self-renewal, klotho and Telomerase Reverse Transcriptase expression DNA damage response were determined by immunofluorescence staining. The effects were confirmed in senescence induced human ADMSCs and in addition, the potential of JS to maintain telomere length was evaluated by qPCR analysis in ADMSCs challenged for long term with doxorubicin. Further, the effects of JS on doxorubicin-induced hypertrophic effect and DNA damage in H9c2 cardiac cells; MPP+-induced damages in SH-SY5Y neuron cells were investigated. In addition, effects of JS in maintaining metabolic regulation, in terms of blood glucose regulation in type-II diabetes mice model, and their potential to suppress malignancy in different cancer cells were ascertained. The results show that JS maintains stem cell homeostasis and provides cytoprotection. In addition JS regulates blood glucose metabolism, enhances autophagic clearances in neurons and suppresses cancer growth and migration. The results show that JS acts on multiple targets and provides a cumulative protective effect against various age-associated disorders and therefore it is a candidate pleiotropic agent for healthy aging.
... "Biological systems are homeodynamic because intracellular processes through their dynamic self-organization may exhibit not only monotonic states, but also a capacity for bistable switching threshold phenomena, waves, gradients, mutual entrainment, and periodic as well as chaotic behavior." [7] The Two-Process Model of circadian and homeodynamic processes, in sleep-wake states, is the currently accepted model. It also applies to many other human physiological processes. ...
Chapter
The temporal dynamics in biological systems displays a wide range of behaviors, from periodic oscillations, as in rhythms, bursts, long-range (fractal) correlations, chaotic dynamics up to brown and white noise. Herein, we propose a comprehensive analytical strategy for identifying, representing, and analyzing biological time series, focusing on two strongly linked dynamics: periodic (oscillatory) rhythms and chaos. Understanding the underlying temporal dynamics of a system is of fundamental importance; however, it presents methodological challenges due to intrinsic characteristics, among them the presence of noise or trends, and distinct dynamics at different time scales given by molecular, dcellular, organ, and organism levels of organization. For example, in locomotion circadian and ultradian rhythms coexist with fractal dynamics at faster time scales. We propose and describe the use of a combined approach employing different analytical methodologies to synergize their strengths and mitigate their weaknesses. Specifically, we describe advantages and caveats to consider for applying probability distribution, autocorrelation analysis, phase space reconstruction, Lyapunov exponent estimation as well as different analyses such as harmonic, namely, power spectrum; continuous wavelet transforms; synchrosqueezing transform; and wavelet coherence. Computational harmonic analysis is proposed as an analytical framework for using different types of wavelet analyses. We show that when the correct wavelet analysis is applied, the complexity in the statistical properties, including temporal scales, present in time series of signals, can be unveiled and modeled. Our chapter showcase two specific examples where an in-depth analysis of rhythms and chaos is performed: (1) locomotor and food intake rhythms over a 42-day period of mice subjected to different feeding regimes; and (2) chaotic calcium dynamics in a computational model of mitochondrial function.
Article
Full-text available
This review focuses on the added value provided by a research strategy applying metabolomics analyses to assess phenotypic flexibility in response to different nutritional challenge tests in the framework of metabolic clinical studies. We discuss findings related to the Oral Glucose Tolerance Test (OGTT) and to mixed meals with varying fat contents and food matrix complexities. Overall, the use of challenge tests combined with metabolomics revealed subtle metabolic dysregulations exacerbated during the postprandial period when comparing healthy and at cardiometabolic risk subjects. In healthy subjects, consistent postprandial metabolic shifts driven by insulin action were reported (e.g., a switch from lipid to glucose oxidation for energy fueling) with similarities between OGTT and mixed meals, especially during the first hours following meal ingestion while differences appeared in a wider timeframe. In populations with expected reduced phenotypic flexibility, often associated with increased cardiometabolic risk, a blunted response on most key postprandial pathways was reported. We also discuss the most suitable statistical tools to analyze the dynamic alterations of the postprandial metabolome while accounting for complexity in study designs and data structure. Overall, the in-depth characterization of the postprandial metabolism and associated phenotypic flexibility appears highly promising for a better understanding of the onset of cardiometabolic diseases.
Chapter
Publications abound on the physiology, biochemistry and molecular biology of “anaerobic” protozoal parasites as usually grown under “anaerobic” culture conditions. The media routinely used are poised at low redox potentials using techniques that remove O2 to “undetectable” levels in sealed containers. However there is growing understanding that these culture conditions do not faithfully resemble the O2 environments these organisms inhabit. Here we review for protists lacking oxidative energy metabolism, the oxygen cascade from atmospheric to intracellular concentrations and relevant methods of measurements of O2, some well-studied parasitic or symbiotic protozoan lifestyles, their homeodynamic metabolic and redox balances, organism-drug-oxygen interactions, and the present and future prospects for improved drugs and treatment regimes.
Chapter
Episodic hormone secretion appears to be a common characteristic of several endocrine systems, including the hypothalamic-pituitary axis, adrenal glands, gonads and the pancreas. Alterations in episodic secretion are associated with the pathophysiology of certain diseases. Correction of these pulsatile disorders with exogenous hormonal replacement therapy frequently cures the defect, the most notable examples of this phenomenon being the hypogonadotrophic disorders. While there is substantial evidence indicating that the central nervous system is at the origin of hormone pulsatility, the organization of the corresponding pacemaker structures remains to be elucidated. In particular, the question of unity versus multiplicity of pacemakers responsible for the ultradian rhythms in the 80–120-min range is debated (Lavie and Kripke 1981). In humans, included in this range is the time of recurrence of the episodic pulses of many hormones as well as a number of rhythms of apparently unrelated physiological and behavioural processes, such as the rate of urine flow, gastric motility and cognitive variables. One of the most prominent ultradian rhythms is the alternation of rapid eye movement (REM) and non(N)REM stages of sleep, which is accompanied by similar cycles of dreaming, penile erection and cardiac variability. Kleitman proposed the concept of a basic rest-activity cycle (BRAC), suggesting that the periodic recurrence of REM sleep reflects a fundamental physiological periodicity which also modulates brain functions during wakefulness (Kleitman 1963, 1982).
Chapter
Ultradian rhythms are being discovered to be nearly as ubiquitous as circadian rhythms. Here, we define ultradian periods as the range between about 1 h and 18 h. Oscillations faster than that reflect metabolic processes (Lloyd and Edwards 1984; Edmunds 1988), and 18 h is an hour less than the mean period of the shortest clearly circadian clock mutant in Drosophila melanogaster (hereafter simply Drosophila: Konopka and Benzer 1971; Hall and Kyriacou 1990). Ultradian oscillations have been found in organisms as disparate as unicells (Lloyd et al. 1982; Michel and Hardeland 1985) and mammals (Daan and Aschoff 1981). They occur in both the presence and the absence of normal circadian rhythms, and now are found also in animals that lack circadian rhythms but do exhibit tidal or lunar periodicity (Dowse and Palmer 1990, 1992).
Chapter
Unless special constraining elements are built in, any complex system will have a natural tendency to exhibit oscillatory behaviour; the more complex the system, the greater the possibilities for outputs of various frequencies and amplitudes. We see this for atomic motions within molecules, current flow in electronic circuits, concentrations of chemical reactants in the test tube or in the universe, and in mechanical structures (e.g. bridges and boats). Living organisms are extremely complex systems (>109 bits of information for a bacterium, >1028 bits for a human being), and the dynamics of their subsystems span a wide range of time scales (Lloyd 1987; Fig. 1.1). The potential usefulness of periodic behaviour has not been overlooked in biological evolution (Lloyd and Volkov 1991; Table 1.1), and has resulted in an astonishing richness of dynamic behaviour. Detailed description of this panoply is only in its infancy, and our appreciation of most of its functional significance is even more rudimentary. Compared with the intensely studied and elaborately elucidated structural hierarchy of cellular components and constituents, the documentation of time structure is rather meagre; some parts of the frequency range are much better documented than others, but none is completely understood (Lloyd et al. 1982b).
Chapter
Several approaches to elucidate the nature of biological clocks, particularly circadian oscillators, have emerged over the years (Hastings and Schweiger 1976; Edmunds 1988). These include the attempt to locate the anatomical loci responsible for generating these periodicities, efforts to trace the entrainment pathway for light signals (and other zeitgebers) from the photoreceptor(s) to the clock itself, the experimental dissection of the clock using chemicals and metabolic inhibitors and employing the exciting new techniques of molecular genetics, and the characterization of the coupling pathways and the transducing mechanisms between the clock(s) and the overt rhythmicities (hands) it drives. The results obtained by these experimental lines of attack, in turn, have provided the grist for several classes of biochemical and molecular model for autonomous circadian oscillators (COs).