Assessing physiological complexity
1 Department of Biological Sciences
2 Department of Mathematics, University of North Texas, Denton, TX 76203,
USA
* Author for correspondence (e-mail: burggren{at}unt.edu)
Accepted 21 June 2005
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Summary |
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Key words: physiology, complexity, experimental design, modeling, information theory, chaos
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Introduction: what is complexity? |
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Our historical progression in understanding of water flux in guts, kidneys, eyes and other organs exemplifies the fact that complexity riddles everything we do as physiologists. As physiologists, we may admire complexity, but we also fear it, because inherently complex systems are more difficult to study and often far less predictable. Moreover, few of us can actually offer any definition of this ubiquitous characteristic we call `complexity'. Just as we observe that Monet's water colours contain great beauty, but are at a complete loss to quantify the metrics we have used in making this observation, we acknowledge that physiological systems contain great complexity, yet we can't clearly express the metric we use to come to this conclusion. Even if physiologists piece together some definition of complexity involving `patterns of afferent pathways' or `numbers of possible target tissues for a hormone' or `elements of motor responses', we are typically unable to indicate quantitatively, or even qualitatively, how complexity changes as the number of afferents, target tissues or motor responses changes. Nor can we readily point to any applied mathematical or statistical tools to help us deal with this ill-defined complexity. Finally, few physiologists in any precise analytical way actually shape our experimental design specifically based on the perceived degree of complexity of the systems we work on.
We will argue in this essay that an appreciation and awareness of the
implications of complexity is essential for a deeper understanding of the
physiological systems we study. To achieve this deeper understanding, we feel
it is necessary to temporarily stand back and take a modestly philosophical
view of the field of physiological complexity. Existing paradigms have tended
to serve a relatively narrow physiological audience and are not readily
exported to other sub-disciplines. For example, there is considerable interest
in complexity as revealed in time series analysis of heart rates, endocrine
secretion and other physiological phenomena (e.g. Richman and Moore, 2000;
Meyer and Stiedl, 2003; Costa
et al., 2005). Yet, such non-linear dynamic analyses and related attempts to
define complexity provide little insight and even fewer tools to a
physiologist working on, for example, the complex interactions of multiple
hemoglobins on in vivo blood oxygen transport.
We also strongly advocate that additional interdisciplinary work involving mathematicians, physicists and physiologists (and, by extension, all biologists) is needed to increase our understanding and exploration of complex physiological systems. The first step in such collaboration is understanding each discipline's vocabulary. Indeed, even definitions are highly problematic, because common uses of words such as `complexity' and `chaos' are often at variance with the more precise and narrower definitions used by mathematicians. Thus, while the jargon appears the same, the ideas being discussed in disciplines may be quite different. For example, from a mathematical perspective, the behavior of a truly chaotic system cannot be precisely predicted in practice, whereas a system considered chaotic by a biologist may be viewed as predictable if only enough data are collected. A mathematician might then counter by saying that the biological system was not complex but merely complicated. While these semantic issues seem pedantic, they have presented substantial barriers to informed collaboration between disciplines. To assist this bridging process, let us now briefly explore some mathematical views of complex systems before moving on to practical implications for physiologists.
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A mathematician's view of complexity |
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Chaotic systems
A highly productive area in complex systems science is chaos theory.
Definitions of a chaotic system differ across disciplines, but two
characteristics occur in most descriptions. First, in chaotic dynamical
systems there are trajectories that do not converge to fixed points or become
periodic. (A trajectory in this context is the state of a system as a function
of time.) Rather, the trajectories exhibit aperiodic, highly irregular
behavior. Fig. 1 shows
trajectories (in this case, time series) for a set of hypothetical systems.
Fig. 1A shows a system that
converges to a fixed state; the system in
Fig. 1B is periodic; and
Fig. 1C gives the trajectory
for a chaotic system. Ventricular fibrillation is a commonly cited
physiological example of a chaotic trajectory.
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As early as 1890, Henri Poincare reported sensitive dependence while
investigating the classic `three-body problem'. He observed that small
differences in the initial state of the set of equations governing the
interactions between the earth, moon and sun produce large differences in the
subsequent time dynamics of this astronomical system. One way to characterize
this sensitive dependence is to determine the rate of separation of
trajectories starting out adjacent to one another. In chaotic systems,
trajectories separate at an exponential rate. Note that a large number of
system components is not necessary for sensitive dependence to exist
Poincare (1890) only needed
three. Moreover, sensitivity to initial conditions can arise even when the
system description is relatively straightforward (although some nonlinearity
needs to be present).
The link between sensitive dependence and the ability to predict future states of the system naturally suggests a connection between complexity and information theory.
Information theory
If a system does exhibit sensitivity to initial conditions, then imprecise
knowledge of those conditions leads to increased uncertainty in the future
states of the system. Another method for characterizing this sensitivity is to
quantify the information gained or uncertainty removed from observing the
system. To illustrate the basic idea, suppose that you knew a roulette wheel
was rigged to always deliver the number 17. No uncertainty on the outcome of a
spin of the wheel would be removed by going through the process of spinning
it. In this case, the entropy or amount of uncertainty about the outcome of a
spin would be a minimum of 0. On the other hand, if the wheel is balanced and
gives random numbers, then information is gained uncertainty is
removed by observing the outcome of a spin. Entropy is maximized when
no outcome is any more likely than any other (a fair wheel). Analogously, for
a simple (non-chaotic) dynamical system, little information is gained about a
trajectory from successive observations. If the initial position is known with
a certain degree of accuracy then relatively few observations are needed to
maintain approximately the same level of accuracy. To characterize the
difference between simple and chaotic systems, mathematicians and physicists
use a measure known as the KolmorgovSinai (KS) entropy. Intuitively,
the KS entropy measures the average information gained from successive
observations of a system. For simple systems, the KS entropy is 0. In chaotic
dynamic systems, the KS entropy is positive and is a fundamental property of
the system. Information is continually gained from successive observations of
chaotic systems. Thus, these systems exhibit behavior more characteristic of
random (stochastic) systems, even when the chaotic systems are completely
specified and deterministic. For chaotic systems, the challenge of predicting
long-term dynamics arises not from lack of knowledge about the system's
structure but from sensitive dependence and limited precision in measuring the
state of the system at any given time.
Modifications of KS entropy, as well as other metrics, have been used to
measure irregularity or lack of predictability of physiologically derived time
series (Pincus, 1991;
Richman and Moorman, 2000
;
Costa et al., 2002
). When
applied to biological data, the objective of these metrics is to quantify the
complexity of a time series in order to make inferences about the underlying
physiological system producing the series
(Pincus, 2001
). Some of the
literature goes further to equate the complexity of the system with the
complexity of the time series, as measured by the time series metric
(Costa et al., 2002
). However,
we argue that the primal definition needed is just `what is a complex system',
and it should be something more than a system that produces a complex time
series. Moreover, as mentioned above, solely focusing on a time series view of
complexity provides only limited insight to physiologists.
Emergent behavior
Emergent behavior is one of the most compelling but least well-defined
concepts in complex systems theory
(Morowitz, 2002). Emergent
behavior is also immediately relevant to animal physiology. The basic idea of
emergence is that, as a whole, a system may exhibit behavior that is
unexpected based just on descriptions of its components and their
interactions. Assertions about emergent properties of systems range from the
fairly innocuous `the behavior of the system is surprising given
the relatively simple description of the components' to the more
portentous `the rules governing the behavior of the system are
fundamentally different and independent from the rules governing the
components'. (See, for instance,
Mulhauser, 1998
.) Both the
former (limited) and latter (extensive) interpretations of emergent behavior
address questions of level, hierarchy or scale. The limited form takes the
approach that emergent behavior at the system level is logically dependent on
the rules at the component level, however surprising the higher-level
behavior. At the same time, the limited view acknowledges the advantage of
adapting descriptions of phenomena according to the level at which they
emerge. For example, descriptions of chemical processes generally exclude
references, without denying their relevance, to the laws of physics underlying
the processes.
The extensive view of emergence has a more fundamental implication: it is
not just that the higher-level behaviors were not predicted, rather they could
not have been deduced from the lower-level rules. A hierarchy of rules is
necessary not just useful for describing such systems. The
extensive perspective, while not explicitly stated, is often implied in
statements about the observance of emergent behaviors. Care must be taken in
evaluating such statements in the absence of a clear unambiguous definition of
emergence. Further caution should be exercised since what sometimes appears to
be an emergent property of a system may merely be an artifact of simulation
constraints (cf. Gray,
2003).
A fascinating aspect of emergent behavior is self-organization.
Self-organization addresses problems related to governance mechanisms for
physiological systems, how these systems develop and how they may have evolved
(see Gorshkov and Makar'eva,
2001; Burggren, in press
a
). Indeed, physiologists and cell and molecular biologists are
now using a self-organization construct to look at systems as diverse as
protein self-organization in E. coli
(Howard and Kruse, 2005
),
neural behavior in cortical minicolumns (Lucke et al., 2004), mesoderm
differentiation in the embryo (Green et
al., 2004
) and signal transduction in cardiac muscle stimulated by
epidermal growth factor receptor (Maly et
al., 2004
). Although an active area of investigation with
potentially deep implications to physiology, self-organization is beyond the
scope of this short review. However, an introduction into the literature can
be acquired from reviews such as Wolfram
(2002
), Morowitz
(2002
), Bak
(1996
) and Jensen
(1998
).
Working descriptions of complexity
Even with all of the deep, rich theory addressing complexity, mathematics
has yet to provide precise definitions that readily map onto the biological
world. However, as discussed above, there are central themes that allow us to
move beyond the colloquial use of terminology. In particular, complexity is
intimately related to the degree by which system dynamics or emergent behavior
can be predicted in practice. There must also be significant (e.g. nonlinear)
interaction between components. These themes are reflected in the system
descriptions we give below. We will consistently use these descriptions when
referring to types of systems. When the terms `complex' or `complexity' are
used without `system', a more colloquial use of these words may be assumed.
Note that our intent is not to provide the definition of `complex
systems'. Our purpose is merely to start the journey down the path towards a
common vocabulary between mathematicians, physicists, animal physiologists and
other biologists.
Simple systems
A simple system may have few components and little interaction between
components. System dynamics and any emergent behavior are straightforward and
easy to predict. A physiological example would be a simple nerve synapse in
which an action potential in the presynaptic neuron creates an action
potential in the postsynaptic neuron.
Complicated systems
A complicated system may have many components, however the interaction
between components does not introduce any insurmountable obstacles to
predicting the behavior of the system it may be difficult but it can
be done. The nerve network found in the sea slug Aplysia appears to
be a complicated system as opposed to complex. While the behaviors of
Aplysia may be manifold, they are understandable and can be
predicted.
Complex systems
A complex system is characterized by inherent limitations in the ability to
predict the long-term or emergent behavior of the system. It is not that
prediction is merely hard or that the system has not been completely
specified. Rather, the lack of predictability arises from the nature of the
interactions between system components and often from the inability to measure
the state of the system at any time with infinite precision. An obvious
candidate for such a system is the human brain.
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Seeking a complexity definition relevant to physiology |
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Summing structures and processes
A number of intuitive definitions of physiological complexity can be
offered, but each has considerable limitations. Rather straightforward is the
`sum of all parts' interpretation of complexity, described in the
`constructability theorem' of Nehaniv and Rhodes
(2000). Essentially, this
theorem holds that `a biological system is the sum of low-complexity,
interacting components' (see
Burggren, in press a
).
Simply counting parts or structures as a way of categorizing complexity is
a time-honored, anatomical approach. Consider nervous systems. From a
structural perspective, the simple nerve net of Aplysia is considered
less complex than the radially arranged nervous system of the echinoderm
Asterias, which in turn is viewed as less complex than the
bilaterally distributed, ganglion-based nervous system of decapod crustaceans
or vertebrates. There is an attendant assumption of progressing complexity
from sea slug to starfish to snake because of an anatomical progression, as
measured by numbers of structures, cell types, tissue types, etc. As
physiologists, we often fall into a similar trap. Instead of equating the
numbers of structures to complexity, we merely equate the number of processes
to complexity. Yet, neither a structure- nor processes-based view adequately
defines the true complexity of a nervous system. For example, the neural
network of Aplysia is relatively simple as defined by the numbers of
neurons and its repertoire of behaviors (see review by
Croll, 2003). Yet, this
`simple' neural system producing `simple' behaviors is capable of complex
information processing (Brembs,
2003
; Croll, 2003
)
and, as such, has become a contemporary model for investigating the role of
neural plasticity in non-associative and associative learning
(Cropper et al., 2004
;
Leonard and Edstrom, 2004
).
Indeed, Bullock (1993
,
1999
,
2003
) challenges us to expand
our view of nervous system complexity beyond structures and processes to
include the numbers of transactions, sensory discriminations and behavioral
alternatives. Such an approach begins to address the issue of the numbers of
possible interactions of components in addition to numbers of
components in complex systems.
Interactive approaches
If counting structures or processes yields the sum of the parts, then
examining the potential interactions between parts and processes describes `a
whole that exceeds the sum of the parts'. Indeed, this particular phrase,
although not particularly helpful in a quantitative sense, is appearing more
and more frequently in lay literature as symbolic of complexity and emergence
thinking (e.g. Morowitz, 2002;
Laughlin, 2005
). How do we
define the whole? Nehaniv and Rhodes
(2000
) have offered several
axioms for describing complexity in biological systems. Their `non-interaction
axiom' can be simply paraphrased as `complexity only increases if the
combined components actually interact'
(Burggren, in press a
).
Interactions among components are typically governed by a set of rules.
Consider again the nervous system, whose rules include one-way information
transmission across synapses and a fixed size of an action potential conducted
by any given neuron. Bullock
(1993
,
1999
,
2003
) has emphasized that the
measure of brain complexity is most accurately graded by what he refers to as
`connectivity' between neural components, which in turn leads to memory and
larger numbers of more complex behaviors.
If a view of physiological complexity based on interaction is to provide practical guidance in the design of physiological experiments, any definition of complexity used by physiologists has to account for at least three prominent attributes of complex physiological systems: (1) lack of high predictability of output; (2) sensitivity to initial conditions; and(3) non-linear interactions between structural components. Let us consider each in turn.
Even the best-understood physiological systems are not entirely
predictable. A tachycardia induced by decreased blood pressure is certainly an
anticipated response in most tetrapods, but physiologists don't expect the
magnitude of this chronotropic reflex to be the same each time a blood volume
or blood pressure drops due to the variability inherent in all cardiovascular
control systems (e.g. Ursino and Magosso,
2003). Indeed, as physiologists, we are suspicious of small
standard deviations (whereas a physicist, for example, might be suspicious of
large ones). The magnitude of uncertainty of output from a regulated
physiological system generally equates with the degree of complexity of the
system regulating it.
Complex physiological systems are sensitive to what mathematicians would call `initial conditions' that is, the values of the system variables at the point at which a series of measurements is made. Returning to the example of the interaction of blood pressure and heart rate in baroreflexes, the change in heart rate that one anticipates in response to a given reduction in blood volume will depend greatly upon the initial blood volume and initial blood pressure as the experiment begins.
Finally, when we consider interaction as a measure of complexity, we must
account for non-linear interactions between structural components. Putting it
differently, not all components in a complex system will interact equally or
identically. Nehaniv and Rhodes'
(2000) `bounded emergence
axiom' addresses this perspective thus: `interaction between components
increases complexity, but one-way interaction sets bounds on the possible
increase' (see Burggren, in press
a
). For a physiological example, consider respiratory development
in developing anuran amphibian larvae. Just prior to metamorphosis, many
anuran larvae use a combination of gills, skin and lungs (three components) to
breathe air and water (two processes). While respiratory complexity in these
intermediate developmental stages could be described as the sum (N=5)
of all the components (N=3) and all the processes (N=2), a
more meaningful complexity index of anuran respiratory development is compiled
from the product of all respiratory components (N=6) and all
respiratory process (Burggren, in press
a
, b
). However,
mindful of the bounded emergence axiom described above, not all respiratory
organs are involved in all processes in this example of anuran respiratory
development. For example, gills do not interact effectively with air, nor
lungs with water! Thus, while complexity certainly increases during
development, our description of changes in complexity during metamorphosis
must be tempered by the nature of actual interactions between the
various components. Moreover, complex dynamics can arise in systems with
relatively few components and straightforward interaction rules. Thus, a
corollary to Occam's razor appears to hold: complex behavior does not
necessarily imply a system with complicated sets of components and
interactions.
Types of physiological complexity: kinetic vs potential
The notion that true complexity depends on the actual pattern of
interaction between components leads to another perspective of complexity.
Many physiological regulatory systems have present or future
capability for complex actions. Must they actually be involved in
regulatory actions to confer complexity to the system? One might similarly ask
`is an automobile sitting silently in a garage only
"potentially" complex until its engine is started and it is driven
down the street?' Answering such a question may have more practical
implications than might at first be imagined. Consider how well the concept of
kinetic vs potential energy has served the physical sciences, dating
back beyond Ludwig Boltzman and James Maxwell to Rudolf Clausius and even back
to Robert Boyle. School children around the world are taught early on about
the potential energy stored in a stretched elastic material, only released as
kinetic energy performing work when the elastic material recoils. As an
example of applying this concept of potential vs kinetic energy to
biological complexity, consider physiological development. A fertilized egg
has all the `potential complexity' of the most complex period in that animal's
life cycle. The egg's `kinetic complexity' only becomes evident when it
develops physiological systems that are actually regulated (again underscoring
the importance of the non-interaction axiom, where complexity only increases
if components actually interact). As another example, consider a relaxed
muscle fiber loaded with ATP, and with actin and myosin poised for cross
bridge formation. As long as the fiber's membrane remains polarized, it
exhibits only potential complexity. Of course, with the release of
acetylcholine from a motor neuron onto the fiber's post-synaptic receptor, the
depolarization of the muscle membrane, and the accompanying Ca2+
stimulated actinmyosin cross bridge formation leading to fiber
shortening, the muscle fiber's kinetic complexity that was waiting in the
wings now becomes amply evident in muscle fiber contraction! To show how
potential and kinetic complexity can be nested, consider that while a relaxed
muscle might be considered to be in its state of greatest potential
complexity, this derives from the perspective of actin and myosin
cross-bridge formation. Yet, from the perspective of considering
regulatory proteins (troponin, tropomyosin), the kinetic complexity of these
proteins and their interactions with myosin might be at its greatest during
muscle relaxation. Thus, kinetic and potential complexity are highly context
dependent.
Do the concepts of potential and kinetic complexity help shape physiological experimentation and the interpretation of those experiments? If we fail to acknowledge the potential complexity of a poorly understood system, we then mistakenly view all physiological observations as reflecting the maximum possible complexity of that system. Not acknowledging the potential complexity of the system leads us to underestimate the complexity of its ultimate emergent behaviors. For example, a kidney processing urine in a human showing water and salt balance does not reveal its potential ability to secrete highly hypertonic urine. Only after the salt load of, for example, a typical fast-food meal does antidiuretic hormone regulation of collecting duct water permeability become evident, revealing a higher level of kinetic complexity of the kidney. Thus, while the complexity of well-understood systems seems obvious, how much potential complexity remains undiscovered until we make observations under new configurations of physiologically relevant conditions?
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Complexity and reductionism |
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Unfortunately, for reductionist proponents, theoretically `reassembled'
systems often do not perform as predicted by the reductionist-derived models
employing the system's components, in part because their interactions are
often not fully accounted for. Variation between predicted and actual behavior
is typically attributed to system noise. Indeed, system noise is often granted
some meta-physical identity of its own, averting the worrisome conclusion that
the real system may actually be more than the sum of its parts. However, this
very conclusion may be inescapable when the observed variability is large.
Interestingly, reductionism without more sophisticated attempts to reassemble
the whole appears to be increasingly viewed in retrospect as an important
stepping stone a step that was helpful along the way of understanding
the meaning of everything physiological but is no longer the sole pathway (or
even a desirable pathway). Advocacy for a balance between reductionism and
synthesis is waxing (for reviews, see
Rose, 1998;
Roenneberg and Merrow, 2001
;
Moalem and Percy, 2002
;
Van Regenmortel, 2002
;
Powell, 2004
;
Burggren and Warburton, 2005
).
Indeed, as Neugebauer et al.
(2001
) comment, `The part
is never the whole, and it is impossible to understand the whole through
limited dissections of its parts. The understanding of complex systems
requires approaches other than those of explanatory reductionism.'
Importantly, we are not advocating an abandonment of reductionism (as some
would) instead, we seek to stimulate a discussion regarding
alternative and/or complimentary approaches that physiologists can use to
study complex systems.
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The value of understanding physiological complexity |
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Choosing appropriate models
If we appreciate physiological complexity both potential and
kinetic we may be able to avoid choosing animal systems or animal
models that are unnecessarily complex, thus contributing to our near-term
understanding rather than confusion. The roundworm Caenorhabditis
elegans, with just under a thousand cells, is arguably one of the most
useful animal models to emerge in decades. Indeed, it is a prime example of
this approach of avoiding unnecessary complexity. Consider, for example, the
complexities of hypoxic tolerance in metazoans, which involves a huge array of
metabolic/biochemical responses, ranging from evolutionary adaptations such as
increased O2hemoglobin affinity to acute physiological
adjustments such as hyperventilation. Physiologists have long been interested
in hypoxia tolerance for a variety of reasons, spanning basic research in
understanding the evolution of air breathing in fishes
(Randall et al., 1981;
Little, 1983
;
Graham, 1997
) all the way to
treating ischemia and mycocardial infarctions in human patients
(James, 1997
;
Kloner and Rezkalla, 2004
;
Kolar and Ostadal, 2004
).
While the study of lungfish or mice, respectively, has certainly provided a
level of understanding of hypoxia tolerance in vertebrates, some of our most
exciting revelations have emerged from using the relatively simple (at least,
physiologically) C. elegans to investigate the biochemistry and
physiological genomics of hypoxic tolerance
(Nystul et al., 2003
;
Padilla et al., 2003
;
Treinin et al., 2003
).
Given the utility of the less complex C. elegans, should we direct all of our resources toward this model? Emphatically not! For all its strengths, C. elegans does not exhibit the behaviors of more complex metazoans it does not generate internal circulatory convection and does not actively ventilate dedicated respiratory organs. From an overarching integrative perspective, recognizing the kinetic physiological complexity of C. elegans allows us to predict more accurately the as yet unrevealed potential complexity of more derived animals.
Guiding data collection
Complex systems are often characterized by considerable dependence on
initial conditions (e.g. sensitivity of ventilation rate to initial states of
metabolism, body temperature, blood pH). Small changes in environmental
conditions may produce not only large but also unexpectedly large
subsequent variations in system performance over time. Thus, complex systems
require much more frequent monitoring with multiple observations over time to
be able to accurately forecast their near-future emergent behaviors. Whether
the system turns out to be complex or `merely complicated', near term
predictions are improved by a higher sampling frequency. As an example,
consider the different conclusions that might be drawn from differences in
heart rate sampling frequencies when cardiac patterns are very intricate, as
in the pupae of the moth Manduca sexta
(Fig. 2). The more elaborate
the observed heart rate pattern (or any other such physiological variable)
being measured, the greater is the sampling rate needed to reveal the overall
pattern.
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Improving interpretation of data from complex systems
The more we appreciate potential and kinetic complexity as it applies to
physiology, the less likely we are to misinterpret simple outputs as coming
from what we mistakenly think are simple physiological systems. To illustrate
this point of view, a mathematician tends to judge the complexity of a system
by the complexity of the system's emergent behavior or output. The more
complex the system, the more complex and unpredictable its output. Yet, very
complex physiological regulatory systems are often characterized by quite
simple and predictable emergent properties, in contrast to a mathematician's
expectations. Thus, for example, thermoregulation in a typical mammal results
in a simple emergent behavior a body temperature of 37°C
despite radiation, convection, diffusion and conduction resulting in a
variety of conditions and mechanisms for both heat gain and loss. Strictly on
the basis of its simple output then, a thermoregulatory system might be
misclassified as non-complex. Yet, this very intricate physiological
regulatory system (as evident from the number of parts and their interactions)
has evolved to be complex precisely so that its output is highly
predictable. In this respect, the complexity of the external environment
must be matched with an equally complex internal regulatory system, and the
result is a disarmingly simple behavior. As long as we appreciate
physiological complexity, even when masked by simple emergent behaviors, we
can guard against overly simple interpretations (recall how, until recently,
we thought that aquaporins described all aspects of transmembrane water
flux).
As physiologists, we have not yet defined complexity, but we have
nonetheless allowed the concept to influence our perceptions of the
progression of everything from evolution to development. Consider, for
example, the interpretation of data relating to complexity change during
ontogeny. Physiologists typically view complexity as increasing progressively
even linearly with development. Yet, a view of complexity
driven by an integrative view using anatomical components, physiological
processes and their interactions reveals prominent examples in vertebrate
development where physiological complexity actually peaks at some intermediate
point in the life cycle, with terminal, mature stages actually being less
complex (Burggren, 2005, in press
a, b
). In the
larvae of a terrestrial amphibian such as a terrestrial toad, for example,
early stages are characterized by water breathing with gills and skin. As the
larvae develops, however, air breathing with the lungs begins to occur, such
that the late larval stage is characterized by two respiratory processes
(water breathing, air breathing) and three sites of gas exchange (gills,
lungs, skin). Finally, with the advent of metamorphosis, the terrestrial toad
`reverts' to a simpler respiratory situation where it breathes air with lungs
(and marginally, with skin). Thus, in this amphibian, respiratory
physiological complexity builds during larval development to a peak just
before metamorphosis, then declines considerably in the terminal stage.
The progression of complexity during evolution of physiological systems
might be viewed similarly to that for development. A progressive increase in
complexity is seen as a hallmark of evolution of physiological processes (e.g.
Maina, 2002;
Morowitz, 2002
;
Battail, 2004
). Because we tend
to view the most derived (`highly evolved') forms as having the most complex
physiology, we can mistakenly overlook, or at least de-emphasize, some very
sophisticated physiology. An excellent example in this regard is the
cardiovascular physiology of reptiles. Some physiologists would view the
chelonian and squamate heart as a three-chambered heart essentially a
defective mammal heart desperately awaiting `evolutionary repair'. In fact,
the heart of turtles and snakes is a sophisticated blood delivery system
capable of responding to waxing and waning levels of oxygen in the lungs and
redistributing blood in a highly efficient manner to the oxygen-consuming
tissues during intermittent breathing (for reviews, see
Burggren et al., 1997
;
Axelsson, 2001
;
Hicks, 2002
). The heart of the
crocodile is even better adapted in this regard, operating as a dual-pressure
pump with separate pulmonary and systemic blood streams during lung
ventilation, but then being able to generate a progressively larger pulmonary
bypass during extensive periods of breath holding. The latter cardiovascular
system, by virtue of its more complex array of physiological responses, is
better suited to intermittent breathing and diving than the circulation of
diving mammals, which is actually constrained by having permanently divided
pulmonary and systemic circuits.
These examples show that developmental or evolutionary stages currently viewed as intermediate can be more, rather than less, complex than more mature or more evolved stages. We are especially likely to overlook complexity in developmentally or evolutionarily intermediate stages if emergent behaviors of physiological systems are simple on first examination. Clearly, we can meaningfully look for signs of complexity in places where it may have been formerly overlooked.
Modeling complicated physiological systems: focus on prediction
Unlike economists or astronomers, physiologists are typically more focused
on the `here and now' than the future. We make physiological measurements
(e.g. blood pressure, urine formation, neural discharge) and then interpret
what these data mean. If we want to know what happens in the future, we often
just wait until the future arrives, and then make the measurement! At the same
time, many physiologists are interested in modeling data, particularly in an
effort to understand complicated, if not complex, systems. If a model allows
prediction of complex behavior a short time into the future, then that model
is particularly robust, as it incorporates not only components and their
interactions but also how these interactions influence in the near term. As
physiologists develop more and more predictive models and as we come
to learn the impact of complexity on our models, then we can begin to use
models not just to affirm our understanding of the system but to predict
future behaviors of physiological systems. For example, physiologists may set
up experiments in which the desired behavior (e.g. molting, jumping, yawning,
feeding, sleeping, etc.) is aperiodic or has low predictability and then spend
inordinate amounts of either investigator time or hard disk space collecting
extraneous data while awaiting the occurrence of the actual behavior of
interest. By assessing the complexity of the behavior's pattern of appearance,
it may become possible to predict with a reasonable degree of accuracy both
the sampling frequency and the time period in which data collection is
actually necessary to capture that phenomenon
(Fig. 2).
![]() |
The future for physiological complexity studies |
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Future interdisciplinary collaborations between physiologists, mathematicians and physicists are vitally important on several fronts. Discourse with other quantitative scientists can stimulate physiologists to think about our experimental design in more rigorous ways and also interpret the data we produce with far greater insight. As physiologists, we can also help expand the view of mathematicians away from abstract descriptions of complexity into more applied avenues ripe for exploitation in the physiological sciences.
Collaborative efforts must recognize that semantics are hugely important and that they present a large but surmountable barrier to the interdisciplinary study of complexity. Consider how the very words `complex' and `complicated' are taken to mean different things by mathematicians, physicists and physiologists. It may sound disparaging to a physiologist who has been working for decades on an intricate system to hear the focus of their attention described by a mathematician as `merely complicated', but appreciating these seemingly subtle and technical semantic distinctions is important if we are to communicate effectively and stay engaged with our mathematical colleagues. (In fact, embarrassingly far into the writing of this essay, the physiologistmathematician author team was still struggling to calibrate their respective use of words that had both common English and technical definitions!) Thus, however tedious the process, stripping away jargon to reveal the common core ideas is of crucial importance for real conceptual advances in complexity studies.
Finally, efforts by physiologists to incorporate elements of complexity science into their research are highly likely to yield tangible results in the near future. To illustrate this point with an example used earlier, is water transport across biological membranes a complicated yet predictable process now known to involve a variety of mechanisms, including aquaporins and water pumps, or does it remain a complex and thus unpredictable mechanism with as yet undiscovered components? If, as physiologists, we learn the characteristics of complicated vs complex systems (e.g. greater predictability of the former), then we may be able to concentrate our studies on the interaction of a known, complete list of components of a complicated system, rather than searching for additional unknown components of a complex, unpredictable system.
If the reader of this essay had hoped for precise definitions of complexity, and clear pathways to improved experimental design, they have no doubt realized that they are not yet forthcoming. A great deal of interdisciplinary collaboration between physiologists and other quantitative scientists must first be realized to understand physiological complexity but appreciating physiological complexity is an important first step.
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Acknowledgments |
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