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First published online September 5, 2008
doi: 10.1242/10.1242/dev.018697
Hypothesis |
1 Laboratory for Development and Evolution, University Museum of Zoology,
Department of Zoology, University of Cambridge, Cambridge CB2 3EJ, UK.
2 School of Medicine, University of Sheffield, Sheffield S10 2JF, UK.
3 School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD,
UK.
Author for correspondence (e-mail:
jj231{at}cam.ac.uk)
SUMMARY
Positional specification by morphogen gradients is traditionally viewed as a two-step process. A gradient is formed and then interpreted, providing a spatial metric independent of the target tissue, similar to the concept of space in classical mechanics. However, the formation and interpretation of gradients are coupled, dynamic processes. We introduce a conceptual framework for positional specification in which cellular activity feeds back on positional information encoded by gradients, analogous to the feedback between mass-energy distribution and the geometry of space-time in Einstein's general theory of relativity. We discuss how such general relativistic positional information (GRPI) can guide systems-level approaches to pattern formation.
Introduction
Ever since Hans Driesch's famous experiments on sea urchin embryos, it has
been evident that developmental processes are capable of global regulation
(Driesch, 1892
). A small part
of an embryo, such as a single totipotent cell, can regenerate a whole intact
embryo. Driesch was so baffled by his results that he rejected a materialist
explanation for this phenomenon and turned to vitalism instead
(Driesch, 1914). The problem
of embryonic regulation essentially reduces to the problem of regulative
positional specification: how do cells adopt a state that is appropriate to
their relative position within a developing embryo?
Classical embryology introduced the notion of a morphogenetic field to
explain global regulatory capacities (reviewed by
Gilbert et al., 1996). The
morphogenetic field aims to capture the ability of the cells in a developing
tissue to establish a pervasive influence that imparts information about the
state of the whole tissue. Local interactions within the field then allow
cells to access global information, and, in principle, to adopt states that
lead to appropriate patterning of the tissue or embryo as a whole. However,
owing to the lack of molecular evidence, the mechanistic basis of such fields
has remained obscure.
Lewis Wolpert sought to address the issue of the missing mechanistic basis
of embryonic regulation and developmental fields in 1968, when he proposed his
French flag model to illustrate the concept of positional information
(Fig. 1)
(Wolpert, 1968). At the time,
gene expression in development was largely considered to be a problem of
temporal regulation based on the paradigm established by Jacob and Monod from
their work on the lac operon of Escherichia coli
(Jacob and Monod, 1961;
Monod and Jacob, 1962). To
shift focus back to the spatial aspects of pattern formation, Wolpert argued
that cells must have some means of determining their relative position in a
developing field (Wolpert,
1969). In contrast to the concept of the morphogenetic field,
Wolpert suggested that this happens by a mechanism imposed on, instead of
arising from within, the field. According to this view, embryonic fields are
defined by their boundaries (Irvine and
Rauskolb, 2001), and positional information provides a mechanism
by which cells can measure their distance from these boundaries. Signalling
from field boundaries specifies a positional value for each cell in the field.
Interpretation of the positional value by a cell (that is, its adoption of a
particular fate based on its positional value) is then thought to occur
autonomously, according to each cell's particular developmental history.
This view implies that positional specification is a two-step process, where the establishment and interpretation of positional values are independent of each other (Fig. 1). In other words, positional specification is essentially a hierarchical, feed-forward process in which cells within a developmental field play a passive, `interpretative' role. We refer to this as the `classical' theory of positional information.
The most common way in which positional information is thought to be
implemented is by morphogen gradients
(Wolpert, 1968;
Crick, 1970) (reviewed by
Slack, 1987;
Gurdon and Bourillot, 2001;
Tabata and Takei, 2004;
Ashe and Briscoe, 2006;
Lander, 2007). The term
`morphogen' was introduced by Alan Turing
(Turing, 1952) to denote any
kind of form-giving or pattern-forming substance. In its more restricted,
modern definition, a morphogen acts across several cell diameters to induce at
least three different states of gene expression in its target cells in a
concentration-dependent manner (Gurdon and
Bourillot, 2001). Specific threshold concentrations in the
gradient correspond exactly to the positions of boundaries of target gene
expression, which in turn determine the developmental fate adopted by cells
within the tissue (Fig. 1). In
this way, the concept of classical positional information suggests that
positional values correspond to a simple biochemical variable (morphogen
concentration) that is measurable by responding cells. As the morphogen
gradient is itself not influenced by the response of cells within the tissue,
the specified positional values are independent of subsequent processes
operating within the developmental field.
Classical positional information and the modern (restricted) definition of
the morphogen concept fail to capture important aspects of positional
specification. Some recent criticisms of these concepts focus on temporal
aspects, i.e. the duration and timing, of morphogen signalling
(Pagès and Kerridge,
2000), or on processes involved in the interpretation of the
signal (Ashe and Briscoe, 2006;
Jaeger and Reinitz, 2006;
Lander, 2007). More generally,
there are two main problems with the classical theory of positional
information: it cannot account convincingly either for size regulation (the
ability of the pattern of cell fates in a developing tissue to scale with the
overall size of the tissue) or for the observed precision of patterning in the
presence of perturbations or fluctuations (robustness). Wolpert's purely
geometrical argument on size regulation in the French flag model
(Wolpert, 1968;
Wolpert, 1969) depends
crucially on the assumption of a linear gradient profile, and breaks down if
more realistic exponential gradients are considered
(Slack, 1987). Furthermore,
classical positional information requires precise interpretation of the
gradient, which renders it very sensitive to fluctuations in morphogen
concentration [see appendix of Wolpert
(Wolpert, 1989)].
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), and the target
tissue they act upon. Data-driven computational modelling approaches,
complementing the powerful tools of modern genetics, now allow such feedback
to be studied quantitatively and in unprecedented detail. However, a suitable
conceptual framework to guide such investigations is only slowly emerging, and
many recent studies still rely (at least implicitly) on the classical
conceptual framework of positional information. Here, we introduce a revised and extended framework for positional specification within developing tissues that places a central emphasis on dynamics and regulative feedback. This is in contrast to the traditional concepts of positional information from which it is derived, as these are of a strictly feed-forward and static nature. Our proposed framework has interesting parallels with the concepts of physical space and time introduced by Einstein in his general theory of relativity (see Box 1). In the following sections, we present a number of examples that provide evidence in support of our revised conceptual framework, which we then describe in detail.
Regulative feedback and dynamic positional information
The classical concept of positional information has proven invaluable for
guiding experimental research on pattern formation in developing fields.
Although rarely acknowledged explicitly, Wolpert's ideas have inspired
developmental biologists to search for and identify a number of candidate
morphogen gradients and their respective regulatory targets (e.g.
Green, 2002;
Ephrussi and St Johnston,
2004; Tabata and Takei,
2004). However, a rapidly growing body of experimental evidence
suggests that classical positional information is insufficient to account for
the observed dynamics and regulative capabilities of gradient-based
morphogenetic fields. Instead, the establishment of morphogen gradients turns
out to be tightly coupled to their interpretation in a dynamic process, often
involving multiple layers of regulatory feedback and interactions with the
target tissue. In the following sections, we present a number of key examples
that illustrate various levels of regulatory feedback involved in pattern
specification. For more comprehensive reviews on feedback in signalling and
patterning processes, see Freeman or Perrimon and McMahon
(Freeman, 2000;
Perrimon and McMahon,
1999).
Shifting gap domains in the Drosophila embryo
Regulative feedback can operate at many different levels. Our first example
illustrates a `semi-classical' case, where feedback occurs only between target
genes and does not affect the concentration profile of the upstream morphogen
Bicoid (Bcd; Fig. 2A,
Fig. 3B). Bcd is a
transcription factor that is encoded by a maternal gene. It is distributed as
an exponential gradient emanating from the anterior pole of the early
syncytial blastoderm embryo of Drosophila melanogaster
(Driever and Nüsslein-Volhard,
1988). Its nuclear concentration profile remains constant
throughout the period during which it initiates localised expression of its
primary downstream targets, the zygotic gap genes, in broad overlapping
domains (Tautz, 1988;
Kraut and Levine, 1991a;
Kraut and Levine, 1991b;
Rivera-Pomar et al., 1995;
Gregor et al., 2007a;
Surkova et al., 2008). These
domains are then stabilised and their boundaries sharpened by cross-repressive
interactions between the gap genes
(Jäckle et al., 1986;
Eldon and Pirrotta, 1991;
Kraut and Levine, 1991b;
Clyde et al., 2003).
Traditionally, it has been thought that boundary refinement through
cross-regulation does not alter the position of gap gene expression domain
boundaries, and, therefore, that the gap genes provide an excellent example of
a `French flag' encoded by a maternal gradient
(Wolpert, 1989;
Wolpert, 1996).
However, a quantitative network-level analysis of the gap gene system
revealed that gap domain boundaries in the posterior part of the embryo
undergo significant positional shifts towards the central region
(Jaeger et al., 2004a;
Jaeger et al., 2004b;
Surkova et al., 2008). These
shifts do not depend on concentration changes in maternal gradients, such as
Bcd, and do not rely on gap protein diffusion. Instead, they are caused by
asymmetries in gap gene cross-repression with posterior dominance occurring
between gap genes that have overlapping expression domains
(Fig. 2A). This means that each
posterior neighbour represses its anterior neighbour more strongly than the
other way around, leading to a cascade of asymmetric feedback. Because more
anterior domains shift less than posterior ones, the entire gap gene
expression pattern becomes compressed and sharpened towards the middle of the
embryo, similar to the compaction of an accordion
(Jaeger et al., 2004a;
Jaeger and Reinitz, 2006).
The shift of domain boundaries as a result of target gene cross-regulation
implies that there is no one-to-one correspondence between concentration
thresholds in the maternal gradient and the positions of target domain
boundaries over time. Thus, the static nuclear Bcd gradient does not impose
positional information on its target tissue. Rather, Bcd provides only an
initial bias towards the expression of certain target genes, whereas
positional information in the Drosophila blastoderm is encoded
dynamically by the positions of expression boundaries of zygotic downstream
factors. As these boundaries constantly shift, positional information needs to
be seen as a dynamic process rather than a static metric. Moreover, it does
not simply correspond to the concentration of Bcd (or any other morphogen),
but rather consists of changing combinations of maternal and zygotic
transcription factors expressed in a given nucleus over time. This example
shows that even `semi-classical' positional information cannot be simply
equated to a specific chemical entity, such as a morphogen gradient, but is
combinatorial and dynamic in nature
(Jaeger and Reinitz,
2006).
Box 1. Metrics, and dynamic feedback in general relativity
The dynamics of material systems depend explicitly on the relative spatial locations of their components. Distances between components are determined by a function called a metric, which encodes the geometry of the space; in a `flat' Cartesian space, the separation of two points is given by Pythagoras' theorem, whereas curved spaces (such as the surface of a sphere) require different metrics. Classical mechanics presumes the existence of an inert spatial metric that acts as a passive `arena'. Although the forces acting on bodies depend on their spatial separation, the metric is itself unaffected by material systems. A principal motivation for the development of general relativity was Einstein's dissatisfaction with this immutability of the metric:
"... it is contrary to the mode of thinking in science to
conceive of a thing (the space-time continuum) which acts itself, but which
cannot be acted upon"
(Einstein, 1967 General relativity denies this immutability, providing a description of gravity radically different to that of classical physics. Rather than generating a gravitational field in a fixed spatial geometry, matter generates a dynamic space-time metric. In turn, the geometry specified by this metric determines the dynamics of the material systems within it (illustrated schematically in A by a ball rolling down, and at the same time altering the slope of, a `valley' in a two-dimensional space). The transition from an immutable to a dynamically responsive metric inextricably links the dynamics of material systems and the metric (see B).
|
Hedgehog, Wingless and Decapentaplegic in the Drosophila wing imaginal disc
More generally, the dynamic response of cells to a morphogen can provide
feedback onto the shape of the morphogen gradient itself
(Fig. 3C). In the
Drosophila wing imaginal disc, the secreted proteins Hedgehog (Hh),
Wingless (Wg) and Decapentaplegic (Dpp) form spatial gradients over several
cell diameters to regulate global aspects of wing development, including size,
shape and vein positioning (reviewed by
Crozatier et al., 2004;
Tabata and Takei, 2004). They
act as morphogens by inducing the expression of target genes in a
concentration-dependent fashion. Wg and Dpp emanate from, and form gradients
centred on, the dorsoventral (DV) and anteroposterior (AP) compartment
boundaries of the disc, respectively; hh is expressed in all
posterior cells and the Hh protein forms a gradient in the neighbouring
anterior compartment. In each case, a key feature of the signalling response
in target cells is the control of receptor expression, which in turn alters
the morphogen profile (Fig.
2B).
In the case of Hh, signalling activity upregulates the expression of its
receptor Patched (Ptc), which antagonises signal transduction by inhibiting
the co-receptor Smoothened (Smo) and which restricts the movement of
extracellular Hh ligand across the tissue by sequestering it
(Fig. 2B)
(Chen and Struhl, 1996).
Furthermore, the upregulation of Ptc changes the ratio of bound to unbound Ptc
receptor, which alters morphogen read-out as bound Hh-Ptc complexes can
titrate the repressive effect of unbound Ptc receptor
(Casali and Struhl, 2004).
This feedback increases the amount of Hh that is bound, internalised and
degraded close to the AP boundary, resulting in a net sharpening and
steepening of the gradient (Eldar et al.,
2003). In addition, this feedback is predicted to enhance
robustness against fluctuations in Hh production, as an increase in morphogen
production is counteracted by an increase in Ptc receptor levels
(Eldar et al., 2003). An
analogous negative-feedback loop has been found in vertebrate embryos
(Goodrich et al., 1996;
Marigo et al., 1996;
Marigo and Tabin, 1996).
By contrast, Wg signalling activity downregulates its receptor, Frizzled2
(Fz2), leading to reduced levels of receptor close to the Wg source at the DV
boundary of the wing disc (Fig.
2B) (Cadigan et al.,
1998). High Fz2 levels have been shown to increase Wg protein
stability away from the source (Fig.
2B) (Cadigan et al.,
1998). Conversely, Fz2 has also been shown to cooperate with a
second receptor, Arrow, to internalise and degrade Wg
(Piddini et al., 2005),
suggesting that the interaction between Wg and Fz2 acts to differentially
regulate Wg stability across the disc in a complex manner. As with Hh,
feedback regulation of receptor levels is predicted to sharpen the morphogen
gradient and to increase the robustness of the signalling system against
fluctuations in the morphogen source
(Eldar et al., 2003).
Feedback also plays an important role in the formation and interpretation
of the Dpp gradient. dpp expression is localised to cells at the AP
boundary of the wing disc, from where it establishes protein gradients in both
the A and P compartments. The response of cells to these concentration
gradients, mediated through the receptor Thickveins (Tkv), patterns the
surrounding wing disc tissue (reviewed by
Affolter and Basler, 2007). Tkv
is downregulated by Dpp signalling activity, although indirectly and in
cooperation with Hh, affecting both the read-out and the shape of the Dpp
gradient (Fig. 2B)
(Lecuit and Cohen, 1998;
Funakoshi et al., 2001;
del Alamo Rodriguez et al.,
2004). As in the case of Ptc and Hh, Tkv inhibits Dpp movement
through the tissue, and increased levels of Tkv far from the source sensitise
target cells to the Dpp signal (Fig.
2B) (Lecuit and Cohen,
1998).
Wg and Dpp also play a role in cell proliferation, providing evidence for
an additional layer of feedback between the shape of the gradient and the size
of the target tissue (Rogulja and Irvine,
2005; Baena-Lopez and
García-Bellido, 2006). Moreover, the levels of the Dpp
receptor Tkv have been shown to be important for size regulation in the wing
and haltere (Crickmore and Mann,
2006). Overexpression of tkv leads to wing discs of
reduced size, whereas decreasing Tkv levels in the (much smaller) haltere disc
increases its size.
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Sonic Hedgehog in the vertebrate neural tube
An excellent example of how complex regulative feedback occurring at
multiple levels is integrated to lead to a coherent spatial and temporal
response in the target tissue is provided by the patterning of the vertebrate
neural tube by Sonic Hedgehog (Shh) (reviewed by
Ingham and Placzek, 2006;
Dessaud et al., 2008). Shh, a
vertebrate homologue of Drosophila Hh, is secreted from the notochord
and the ventral neural tube, and diffuses to form a ventral-to-dorsal gradient
that is required for specifying discrete progenitor domains from which
different neural subtypes derive (Briscoe
et al., 2000). The mechanisms underlying this process show
striking similarities to both the gap gene network and the wing disc gradients
discussed above.
As with Bcd and the gap gene network, cross-repressive interactions amongst
target genes play an integral part in interpreting the Shh gradient, affecting
the final positions of the different progenitor domains
(Fig. 2C)
(Briscoe et al., 2000;
Vallstedt et al., 2001;
Pachikara et al., 2007).
Primarily, cross-repressive interactions exist between two main classes of
transcription factors, one of which is activated (or de-repressed) at low
levels of Shh signalling and the other at high levels. In addition, repressive
interactions among genes of each target class further refine the borders
between progenitor domains, leading to substantial shifts in domain boundaries
over time. Overall, the Shh gradient provides a bias for localised target gene
expression, which is then refined by cross-regulatory interactions between
downstream targets that lead to dynamic shifts in their respective expression
domains. For instance, a recent study by Dessaud et al.
(Dessaud et al., 2007)
demonstrated that the expression domain of the Olig2 gene first
expands and then contracts once levels of the transcription factor Nkx2.2
build up in the ventral-most part of the neural tube
(Fig. 2C). In addition, the
final pattern of cellular responses in this system depends on both the
strength and duration of exposure to the Shh morphogen, exemplified by the
finding that Olig2 expression requires merely a brief exposure to Shh
signalling, whereas Nkx2.2 becomes activated only after sustained
exposure (Dessaud et al.,
2007).
As in the Drosophila wing disc, feedback between cellular response
and the morphogen gradient is important in this system. In fact, such feedback
is required for the temporal integration of the signalling response described
above. Target cells become desensitised to the Shh signal over time as a
consequence of Ptc1 upregulation (Marigo
and Tabin, 1996; Dessaud et
al., 2007), which leads to increased levels of unbound receptor
that inhibit signalling activity by repressing Smo
(Fig. 2C). Such temporal
modulation of the Shh signal is by no means unique to the neural tube. For
example, during mouse limb and zebrafish muscle development, the level and
duration of Shh exposure is essential for determining cellular response
(Wolff et al., 2003;
Ahn and Joyner, 2004). In
addition, the Ptc1 upregulation is likely to limit the spread of Shh in a
manner analogous to the Hh-Ptc interaction in the wing imaginal disc. Shh
upregulates an additional antagonist of its own signal, Hip1
(Chuang and McMahon, 1999;
Goodrich et al., 1999). Hip1
binds Shh at the cell surface, and can therefore limit the movement of Shh
across the tissue. Finally, these different forms of feedback can also
regulate cell proliferation, with the neural tube becoming overgrown in
Ptc1 Hhip1 double mutants (Jeong
and McMahon, 2005).
In summary, regulatory feedback in this system occurs at four different
levels. First, upregulation of Ptc affects the shape of the gradient itself.
Second, upregulation of Ptc leads to the desensitisation of cells experiencing
low levels of, and a short exposure to, the Shh signal. Third, regulatory
feedback between target genes leads to temporal shifts in boundary positions.
Lastly, morphogen signalling affects cell proliferation. All of these feedback
interactions are crucial for determining the correct size and position of each
neuronal progenitor domain. If any of these forms of feedback fail, the range
and strength of Shh signalling is significantly expanded
(Jeong and McMahon, 2005;
Dessaud et al., 2007). This
implies that the establishment and the interpretation of the Shh gradient rely
on a complex interplay between signal strength, signal duration, cell
proliferation, and interactions involving Shh receptors and target genes.
Dorsoventral patterning in Drosophila and vertebrates
In the above examples, morphogens are produced in a `signalling centre'
that acts as a boundary; the morphogens then establish gradients that pattern
the surrounding tissue. However, it is also possible for positional
information to be specified by broadly expressed proteins that are then
localised through feedback-regulated transport. One such example is involved
in DV patterning during early Drosophila embryogenesis (reviewed by
O'Connor et al., 2006). It
illustrates that positional specification that is driven by feedback is a very
general phenomenon and that it is not limited to gradient-based fields.
In Drosophila, dpp is initially expressed uniformly in the
dorsal-most 40% of the embryo. Subsequently, Dpp protein is shuttled to the
dorsal midline of the embryo, establishing a steep concentration gradient that
specifies the extraembryonic amnioserosa and dorsal ectoderm
(Fig. 2D)
(Dorfman and Shilo, 2001).
This gradient is achieved by dorsal diffusion of Dpp and its paralogue Screw
(Scw) in complex with the Twisted Gastrulation (Tsg) and Short Gastrulation
(Sog) proteins, the latter of which is expressed in (and diffuses from) the
ventral domain (Holley et al.,
1995; Marques et al.,
1997; Ross et al.,
2001; Shimmi et al.,
2005). This process gives rise first to a shallow dorsal gradient,
which subsequently matures into a narrow distribution of Dpp with very steep
boundaries around the dorsal midline. This refinement involves positive
feedback between the complexed ligand heterodimers and an, as yet,
unidentified surface bound ligand-binding protein (SBP), which increases
ligand concentration locally (Fig.
2D) (Wang and Ferguson,
2005). An analogous refinement is involved in the positioning of
cross-veins during Drosophila wing development by Dpp and its
paralogue Glass bottom boat (Gbb), with the secreted Crossveinless2 protein
identified as the upregulated SBP (Serpe
et al., 2008).
Modelling results confirm that positive feedback can account for the
observed sharpening of the gradient as it creates a spatially bistable
response, where the fate of each cell is determined by both the strength and
duration of Dpp/Scw signalling (Umulis et
al., 2006). Moreover, these studies suggest that this system is
robust to changes in the gene dosage of scw and sog, and of
the receptor tkv, and that it exhibits scale invariance across
changes in embryo size of up to 40%
(Shimmi et al., 2005;
Umulis et al., 2006).
A slightly different type of regulative feedback leads to size regulation
during DV patterning in Xenopus laevis embryos
(Ben-Zvi et al., 2008).
Analogous to Drosophila, the vertebrate BMP ligand homologues of Dpp
and Scw are shuttled to the ventral pole of the embryo by chordin, a
vertebrate homologue of Sog, which is released by the organiser tissue at the
dorsal blastopore lip. In addition, vertebrates have a BMP ligand called
anti-dorsalising morphogenetic protein (ADMP), which is co-expressed with
chordin in the organiser. ADMP is negatively regulated by BMP signalling.
Because of this, the system reaches steady state when ADMP accumulates at
sufficient levels to repress its own expression dorsally. Modelling studies of
this feedback mechanism have shown that it can lead to a gradient of BMP
signalling, the range of which scales perfectly with embryo size and thus
explains size regulation in isolated dorsal halves of Xenopus
embryos, which develop into small but complete tadpole larvae
(Ben-Zvi et al., 2008).
General relativistic positional information
In Wolpert's original conception, the field of positional information
produced by a localised source of morphogen is read and interpreted by
responding cells without the information in the field being changed
significantly. In this sense, it resembles the logical structure of classical
or Newtonian mechanics in physics, where the relative positions of bodies are
determined with reference to the static geometry of space that is itself
unaffected by any objects or processes that are referred to it. This view
depends on making a well-defined distinction between an imposed field (the
morphogen gradient specified by the boundaries of the developing tissue) and
an interpretation system (which resides within the responding cells;
Fig. 1)
(Wolpert, 1969), and implies
that there is a unidirectional transfer of information from the field to the
responding cells (Fig. 3D).
However, the specific examples that we have described show that positional
specification by a wide range of different morphogens depends on regulative
feedback from responding cells (Fig.
2, Fig. 3D). Such
feedback from the cellular response system, which we believe to be of central
importance in positional specification, does not fit into the traditional
framework of positional information.
The field of positional information specifies a spatial metric (see Box 1) that is used by responsive cells to determine their relative position in the developmental field. In the examples discussed above, the form of this metric is dynamic and is determined in part by feedback from responding cells. Interestingly, the transition from classical positional information, in which the form of the metric is independent of the response system, to this new framework has parallels with the change in the status of the space-time metric in the transition from classical mechanics to general relativity (compare B in Box 1 with Fig. 3D). In classical mechanics, the spatial metric specifies a passive `arena' in which physical processes take place; although the form of the metric affects the dynamics of physical processes, the metric is independent of objects and processes within it. Therefore, the logical structure is strictly feed-forward, just as in classical positional information. By contrast, in general relativity, the geometry of space-time (encoded by the metric) is dynamic and depends on feedback from the mass-energy distribution within it. For this reason, we refer to our revised concept as general relativistic positional information (GRPI).
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An important aspect of GRPI is that there is no longer any simple correspondence between positional value and any specific biochemical variable, such as the concentration of a morphogen. In other words, GRPI is not a `thing' but a dynamic state of the system that implements a kind of biological space and time within developing fields. It can consist of rapidly changing combinations of factors, such as signalling and transcription factor levels, and can incorporate non-genetic elements, such as ionic potentials and mechanical stress. This implies that it is no longer sufficient to measure single biochemical variables of a system as proxies for positional value, or to study regulatory interactions between isolated genes. Instead, our notion of GRPI requires characterisation of the dynamic state of an entire developing system in order to understand how position is specified.
One possible response to the discovery of dynamic feedback is to state that
any split of the positional specification system into two distinct conceptual
components, a metric-generator and a response system, is artificial and should
be avoided. Rather, developing fields have to be understood in terms of the
regulative dynamics of the entire spatially distributed system. Although this
approach is consistent, we believe that there is value in maintaining a
conceptual framework that preserves the notions of metric-generating and
response systems while incorporating a two-way interaction between them. One
major advantage of such a framework is that it puts an explicit emphasis on
the spatial aspects of development, which, as stated above, was Wolpert's
original (and still very much valid) motivation for introducing the concept of
positional information (Wolpert,
1969).
In the case of gradients established by the movement of morphogens away
from a localised source or boundary, these sources can often be considered as
`organisers' for a tissue. The GRPI formalism preserves the valuable concept
of organisers, while elevating the status of the remainder of the tissue from
passive `organisee' to that of an active participant in the process of
organisation. Indeed, organisers can themselves be dynamic emergent features
of the organisation process, residing in a particular (relative) position in a
tissue, rather than in a fixed population of cells
(Joubin and Stern, 1999).
A similar conceptual split is often useful in analysing the dynamics of
physical systems. Several different conceptual approaches to understanding the
nature and consequences of the feedback between matter and space-time can be
adopted (Friedman, 1983;
Monk, 1997). A formalism that
emphasises the dynamic interaction between a `quasi-static' space-time metric
and material bodies can yield valuable conceptual insight into the
consequences of feedback. For example, in studying the dynamics of the solar
system, the dominant contributor to the overall gravitational field is the
sun, and the motion of the planets can be approximated by considering them as
small `test particles' that are affected by the field generated by the sun
without themselves affecting this field. This view provides a framework in
which the specific effects of feedback onto the field (the metric) can be
studied in detail as perturbations to the strictly feed-forward dynamics. An
early triumph of general relativity was that it provided an explanation for
the anomalous precession of the perihelion of Mercury's orbit in terms of a
small perturbation to its classically predicted orbit caused by feedback onto
the space-time metric (Einstein,
1916).
Despite the strong conceptual parallels between Einstein's theory of general relativity and GRPI, there are some notable differences as well. First, although gravitational fields are governed by known general laws, relatively little is understood about the laws that govern morphogenetic fields. In fact, it seems unlikely that any such general laws exist. Moreover, there is conservation of mass-energy in physics, whereas it is highly improbable that any such conservation applies to the activities of cells, as they are open thermodynamic systems. This suggests that there is no finite, well-defined set of rules that govern developmental processes. It also implies that while physicists can deduce specific cases from general laws, biologists will have to study as many particular examples of developmental systems as they can in order to learn what generalisations can usefully be made about them.
Conclusions
The data we review demonstrate that positional specification is a dynamic
process that is driven by feedback. This basic insight is not new. In fact, it
formed the foundation for the fundamental concept of classical embryology, the
morphogenetic field, a concept that has been eclipsed by the reduction of
embryology to molecular genetics (reviewed by
Gilbert et al., 1996) (see
also Jaeger and Reinitz,
2006). Classical positional information was an attempt to redefine
the developmental field concept based on specific molecular mechanisms
(morphogen gradients), while retaining a focus on regulative spatial
patterning (Wolpert, 1968;
Wolpert, 1969;
Wolpert, 1989;
Wolpert, 1996). The concept of
positional information is still useful for making explicit the spatial nature
of positional specification. However, Wolpert's definition of a field loses
much of the explanatory power of the original morphogenetic field concept
through its neglect of regulative feedback
(Jaeger and Reinitz,
2006).
Here, we attempt, in a similar spirit to Wolpert's original efforts, to reconcile the old phenomenological concepts of classic embryology with positional information. The main purpose of our effort is to shift our focus back to the intrinsically dynamic and regulative nature of positional specification, while maintaining Wolpert's mechanistic rigour.
The advantages of regulatory feedback are obvious. Since its early days,
positional information has been criticised for its lack of robustness and its
heavy reliance on the precise interpretation of minute differences in
morphogen concentration [see appendix of Wolpert
(Wolpert, 1989)].
Feedback-based systems, by contrast, allow for increased stability against
expression noise, mutation or fluctuations in the environment. This is
substantiated by the fact that mathematical models incorporating three of the
previously described feedback interactions, Hh-Ptc, Wg-Fz2 and Dpp/Scw-SBP,
show significant robustness to changes in the levels of signalling factors
(Eldar et al., 2003;
Shimmi et al., 2005;
Umulis et al., 2006).
A key challenge that must be met by conceptual frameworks for positional
specification is to provide a mechanism for size regulation (e.g.
Gregor et al., 2005;
Lott et al., 2007;
Gregor et al., 2008).
Classical positional information is severely limited in this regard, as a
morphogen gradient only encodes information about the boundaries of the
developmental field. By incorporating local feedback from dynamic cell states
onto the morphogen gradient itself, GRPI provides an explicit mechanism for
achieving locally encoded global regulation (e.g.
Ben-Zvi et al., 2008). This was
one of the main strengths of the original concept of the morphogenetic field,
which was lost in the transition to Wolpert's fields, whose definition relies
entirely on their boundaries without considering processes within the field
(Jaeger and Reinitz,
2006).
Note that feedback and long-range signalling need not be entirely chemical,
as the mechanical properties of tissues can play a central role in these
processes (Forgacs and Newman,
2005). For example, it has been proposed that local mechanical
feedback in response to tissue compression or stress can lead to global growth
regulation under the control of the Dpp gradient in the wing imaginal disc
(Shraiman, 2005;
Hufnagel et al., 2007;
Aegerter-Wilmsen et al., 2007).
Once the size of the disk exceeds a certain limit, cells on the margin no
longer receive enough morphogen to proliferate and therefore constrain the
space available to those cells still dividing in the centre, halting growth
throughout the disk. The morphogen gradient is both affected by and affects
growth patterns in the tissue. Such interaction between patterning and tissue
growth appears to be a very widespread phenomenon in developmental
systems.
It is important to stress again that positional specification relies not on a static `thing' (such as a chemical gradient), but on a complex process involving the target tissue. This implies that downstream factors and their interactions need to be considered when analyzing positional specification by morphogen gradients. The following example illustrates how ignoring such interactions can lead to results that are inconclusive and difficult to interpret.
A recent, quantitative study in Drosophila concluded that
precision in the positioning of an expression domain boundary of the gap gene
hunchback (hb) is due exclusively to high precision in the
Bcd gradient (Gregor et al.,
2007b). The authors measured the transcriptional response of
hb with respect to Bcd concentration without considering the known
gap-gap cross-repressive interactions. Sensitivity analysis of this
interaction showed that the time required to obtain the measured hb
precision exceeds the age of the embryo at the relevant developmental stage.
This led the authors to propose that precision was based on spatial
integration of signal interpretation across neighbouring nuclei
(Gregor et al., 2007b). It
remains unclear how such spatial integration could be achieved. In addition,
closer scrutiny of the fluctuation levels in Bcd and hb reveals that
positioning of the target gene expression boundary is still more precise than
fluctuation levels in the gradient
(Reinitz, 2007), and that the
spatial distributions of positional errors in gradient and downstream
expression boundaries become increasingly uncorrelated over time
(Holloway et al., 2006). In
light of the above, it remains plausible that regulatory feedback among target
genes contributes to the observed levels of precision, and that no spatial
integration of signal is required. It seems that this possibility was not even
considered by Gregor et al. (Gregor et
al., 2007b) because we are used to equating positional information
with concentration levels of morphogen gradients. By contrast, the authors of
a recent study of the Dpp gradient in Drosophila wing discs, although
focussing exclusively on direct, instructive interactions of the gradient with
its target genes as well, suggested that the lack of achievable precision by
morphogen signalling alone indicates a role for downstream regulation in the
patterning process (Bollenbach et al.,
2008).
The above example illustrates that classical positional information still
influences current experimental design and can lead to complications in the
interpretation of experimental evidence. GRPI is intended to clarify these
issues, as it shifts the emphasis away from the notion of morphogen gradients
as simple biochemical coordinate systems, on to a dynamic metric that allows
cells to measure their relative position within a developing field that itself
changes in response to the activity of those cells. The underlying biochemical
mechanisms are likely to be diverse and change rapidly over time, involving a
range of regulatory feedbacks on multiple levels. Mechanisms of this type are
the focus of the emerging paradigm of systems biology, which shifts the
emphasis of experimental approaches away from individual biochemical findings
to dynamic regulatory principles that integrate biochemical processes. The
study of such principles requires researchers to keep track of many
simultaneous interactions. This is impossible without the help of
computational models and their analysis using the methods and concepts of
dynamical systems theory (Strogatz,
2001). Most developmental biologists today are not yet familiar
with these methods and concepts. GRPI illustrates why we need to understand
the dynamic behaviour of complex systems to understand positional
specification, and provides a guiding metaphor that will be useful in
focussing integrative studies of the complex feedback systems that underlie
regulative spatial patterning in development.
ACKNOWLEDGMENTS
We thank Tanya Whitfield, Manu, John Reinitz, Michael and Thomas Akam for comments on the manuscript. J.J. and N.M. are funded by the Biotechnology and Biological Sciences Research Council, and D.I. and N.M. by the Engineering and Physical Sciences Research Council.
Footnotes
* All three authors contributed equally to this article 
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