Trends in Genetics Feb
-
Upload
lehel-beni -
Category
Documents
-
view
218 -
download
0
Transcript of Trends in Genetics Feb
-
8/12/2019 Trends in Genetics Feb
1/46
-
8/12/2019 Trends in Genetics Feb
2/46
Editor
Rhiannon Macrae
Portfolio Manager
Milka Kostic
Journal Manager
Basil Nyaku
Journal Administrators
Ria Otten and Patrick Scheffmann
Advisory Editorial Board
K.V. Anderson, New York, USA
A. Clark, Ithaca, USA
G. Fink, Cambridge, USA
S. Gasser,Geneva, Switzerland
D. Goldstein, Durham, USAL. Guarente, Cambridge, USA
Y. Hayashizaki, Yokohama, Japan
S. Henikoff, Seattle, USA
H.R. Horvitz, Cambridge, USA
L. Hurst, Bath, UK
E. Koonin, Bethesda, USA
E. Meyerowitz, Pasadena, USA
S. Moreno, Salamanca, Spain
A. Nieto, Alicante,Spain
C. Ponting, Oxford, UK
C. Scazzocchio, Orsay, France
and London, UK
D. Tautz, Pln, Germany
O. Voinnet, Strasburg, France
J. Wysocka,Stanford,California
Editorial EnquiriesTrends in Genetics
Cell Press
600 Technology Square, 5th floorCambridge MA 02139, USATel: +1 617 397 2818Fax: +1 617 397 2810E-mail: [email protected]
Cover:The apple is one of the most famous cultural symbols, from the Bible to iPhones. It is also one of the most important
fruit crops in the world. The origin of the apple as we know it today, however, is not entirely clear, and the genetic makeup
of the apples we eat is only just now beginning to be understood. On pages 5765 of this issue of Trends in Genetics,
Amandine Cornille and colleagues discuss genomic data that has illuminated the domestication of the apple and discuss
the genetic history of this common fruit. Cover image from iStock/Sieboldianus.
February 2014 Volume 30, Number 2 pp. 4184
Reviews
Amandine Cornille, Tatiana Giraud,
Marinus J.M. Smulders,
Isabel Roldn-Ruiz, and Pierre Gladieux
Kristin C. Scott and Beth A. Sullivan
Clare Stirzaker, Phillippa C. Taberlay,
Aaron L. Statham, and Susan J. Clark
57 The domestication and evolutionary ecology
of apples
66 Neocentromeres: a place for everything and
everything in its place
75 Mining cancer methylomes: prospects and
challenges
41 Canalization: what the flux?
49 Particle genetics: treating every cell as
unique
Tom Bennett, Genevive Hines, and
Ottoline Leyser
Gal Yvert
Opinions
-
8/12/2019 Trends in Genetics Feb
3/46
Canalization: what the flux?Tom Bennett, Genevie`ve Hines, and Ottoline Leyser
Sainsbury Laboratory, University of Cambridge, Bateman Street, Cambridge, CB2 1LR, UK
Polarized transport of the hormone auxin plays crucial
roles in many processes in plant development. A self-
organizing pattern of auxin transport canalization is
thought to be responsible for vascular patterning and
shoot branching regulation in flowering plants. Mathe-
matical modeling has demonstrated that membrane
localization of PIN-FORMED (PIN)-family auxin efflux
carriers in proportion to net auxin flux can plausibly
explain canalization and possibly other auxin transport
phenomena. Other plausible models have also been
proposed, and there has recently been much interest
in producing a unified model of all auxin transport phe-nomena. However, it is our opinion that lacunae in our
understanding of auxin transport biology are now limit-
ing progress in developing the next generation of mod-
els. Here we examine several key areas where significant
experimental advances are necessary to address both
biological and theoretical aspects of auxin transport,
including the possibility of a unified transport model.
Auxin and self-organization in plant development
The hormone auxin (see Glossary) regulates almost every
aspect of plantdevelopment, and thedirectionalmovement
of auxin by a specialized transport system (polar auxin
transport, PAT) is crucial for many of these processes (Box
1, Figure 1A) [1]. In simple cases, fine-scale redistribution
of auxin allows for differential responses in different cells,
driving patterning and specification events. However, in
many cases patterns are generated not simply by auxin
redistribution but emerge as a property of the system of
feedback between the tissue, auxin, and auxin transport. It
is widely supposed that these developmental systems, and
the auxin transport patterns that drive them, are self-
organizing that is, little or no pre-pattern is needed
[2]. Understanding these apparently self-organising phe-
nomenahas long been an area of interest, as exemplified by
research on phyllotaxis the pattern of leaf initiation at
the shoot meristem (Figure1B) and thevascularpatterns
of leaves (Figure 1C).Because of their self-organizing properties, intuitive
understanding of these systems is difficult and there has
therefore been considerable interest in mathematically
modeling these phenomena [3]. Vascular patterning and
phyllotaxis have primarily been simulated using two fun-
damentally different (but non-exclusive) auxin transport
heuristics, often respectively referred to as with-the-flux
(WTF) and up-the-gradient (UTG) (Box 2). Although these
models have been immensely useful in demonstrating the
plausibility of self-organizing transport as a developmen-
tal mechanism, neither type of model is explicit about their
biological basis, and they include parameters that are not
based in current mechanistic understanding, such as as-
sessment of auxin concentration in neighboring cells. Fur-
thermore, it is probable that neither heuristic is inherently
capable of capturing the full range of self-organizing auxintransport [3]. To understand better the role of self-orga-
nizing auxin transport in plant development, a new gener-
ation of models that are more deeply rooted in a
mechanistic understanding of auxin biology is needed.
However, our understanding of the biology of canalization
and related phenomena has been somewhat outstripped by
theoretical work on these problems, and now represents a
limiting factor for modeling. The purpose of this article is
thusnot topropose anext-generationmodel but to examine
the areas in which we need to improve our understanding
of auxin transport and discuss how current models can be
used to prioritize these experiments. We primarily discuss
WTF
models,
particularly
in
the
context
of
the
canalizationhypothesis, vascular patterning, and shoot branching.
There has recently been considerable interest in attempt-
ing to unify models of auxin transport, and we also assess
prospects for achieving this goal.
The canalization hypothesis of vascular patterning
Vascular patterning in plants is complex but orderly [4]
it is not hardwired but clearly proceeds according to firm
principles such that the same general vascular topology is
reproduced in almost every individual in a species
(Figure 1C). Local auxin application induces vascular dif-
ferentiation in plant tissue, but in narrow strands running
away from the application site, rather than in wide fields of
cells [5]. These observations led to the singular and pio-
neering contributions of Tsvi Sachs, whose elegant experi-
ments are still central to the field [4,68]. Sachs proposed
that as auxin flows through tissues it upregulates and
polarizes its own transport,which gradually becomes chan-
neled or canalized into files of cells with very high
auxin flux away from auxin sources (Figure 1D); these cell
files can then differentiate to form vasculature (Figure 2)
[7,8]. Sachs also demonstrated that new vasculature usu-
ally develops towards and unites with existingvasculature
strands, leading to a connectedvascularnetwork (Figure 2)
[4,7,8]. However, he also demonstrated that existing vas-
culature could be hyper-canalized by the addition of
Opinion
0168-9525/$ see front matter
2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tig.2013.11.001
Corresponding author: Leyser, O. ([email protected]).
Keywords: auxin; auxin transport; self-organization; canalization; mathematical
modeling.
Trends in Genetics, February 2014, Vol. 30, No. 2 41
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://dx.doi.org/10.1016/j.tig.2013.11.001mailto:[email protected]:[email protected]://crossmark.crossref.org/dialog/?doi=10.1016/j.tig.2013.11.001&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.tig.2013.11.001&domain=pdfhttp://dx.doi.org/10.1016/j.tig.2013.11.001http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?- -
8/12/2019 Trends in Genetics Feb
4/46
auxin, in which case developingvasculature could not find
and unite with it (Figure 2) [7].
The work of Sachs pre-dated the advent of molecular
genetics, and he therefore needed to infer upstream events
based largely on terminal vascular differentiation patterns.
Remarkably, recent investigations have supported his hy-
potheses at a molecular level including the central canali-
zation concept that, from an initially broad domain of cells
with low auxin flux, a subset of cells become progressively
morepolarizedandcompetent to transport auxinandhave
shown that canalization is an important component ofvas-
cular patterning [911]. It should be emphasized that,
although some
auxin
flows
do
undoubtedly
canalize, notall auxin transport phenomena involve canalization. For
instance, initiation of leaf primordia in angiosperm shoot
meristems(Figure 1C) requiresformation ofan auxin maxi-
mum by a focused pattern of transport (maximization)
(Figure 1D) [12]. Canalization has generally been explored
throughWTFmodels (Box 2) which canaccurately simulate
patterns of auxin transport in a number of developmental
processes, includingvascular formation in stems and leaves
[1315]. Canalization of auxin transport has also been
recently modeled as an explanation for the inhibition of
bud outgrowth by actively growing shoots, a scenario in
which thedevelopment ofvasculature isnot directly consid-
ered, although it is an important additional outcome of the
bud activation process [16]. Auxin transport canalizationthus has the potential to explain multiple developmental
phenomena in plants.
What is the flux?
All current models of canalization are based on a large
corpus of research into polar auxin transport, and in
particular the behavior of PIN-family auxin efflux carriers
(Box 1). Examination of phyllotaxis andvein formation has
shownvery distinctive patterns of PIN protein localization
consistent with canalization and maximization [9,12,17].
Almost all modern models of auxin transport therefore
explicitly simulate membrane-localized PIN proteins that
directly
influence
the
amount
and
direction
of
auxin
trans-port. The main difference between the WTF and UTG
models, based on the experimental observations of PIN
protein localization in different scenarios, relates to the
rules for allocating PIN proteins to membranes (Box 2). In
WTF models PIN proteins are allocated to each membrane
in a cell inproportion to flux, thenetquantity of auxin that
exits the cell across that membrane. Net flux efficiently
couples cells together (because high net flux from cell i!jtends to prevent high flux from j!i), allowing cells tocouple to larger-scale patterns of flux and speeding the
emergence of global WTF patterns in the overall direction
i!j (Box 2). Although mathematically this is a very neatsolution, as a concept it is likely to be unrealistic because it
requires a cell to calculate the net exchange of auxin across
its membranes (including passive uptake). There is no
known biological mechanism that achieves this, which is
a common criticism of flux-based models [18]. Neverthe-
less, it is clear that cells in real systems do canalize auxin
transport, and do so by allocating PIN proteins apparently
in proportion to net auxin flux. It is thus the absolute crux
of canalization research to establish how cells are able to
localize PIN proteins in relation to larger-scale patterns in
a self-organizing manner.
The most plausible explanation for the apparent ability
of cells to calculate net flux is that cells measure one or
more other variables, the combined effect of which is
Glossary
Angiosperms: floweringplants.By farthe largest major groupingof plants and
also the most recently evolved. Includes almost all crop species and model
species such as Arabidopsis thaliana.
Apoplast: the space between plant cells, occupied by thick cellulosic walls
(Figure 1A). There is a significant pH difference between the apoplast (pH 5.5)
and cytoplasm (pH 7), and this directly affects auxin transport in accordance
with the chemiosmotic hypothesis.
Arabidopsis thaliana: a principal plantmodel species,particularly formolecular
genetic studies, due to its small size, small genome, andshort life-cycle. Its smallsize, however, means that it is not ideally suited to canalization research.
Auxin, auxin transport: auxin (indole-3-acetic acid, IAA) is a low molecular
weight, long-distance signal with many functions in plant development.
Specific, polar auxin transport (PAT) through tissues seems to be an ancient
characteristic of land plants.
Canalization: an apparently self-organizing pattern of auxin transport in which
an initially broaddomain ofauxin-transporting cells is reduced to a narrow canal.
This is thought to occur by auxin upregulating and polarizing its own transport.
Charophyte algae: a group of green algae that constitute the sister taxon of
land plants.
Chemiosmotic hypothesis: see Box 1.
Gymnosperms: a diverse group of plants, including conifers, that produce
seeds butnot flowers. Togetherwith angiosperms theymake up the seed-plant
(spermatophyte) clade.
Lycophytes: an ancient group of vascular plants; sister taxon to the clade
containing ferns and seed plants.
Maximization: an apparently self-organizing pattern of auxin transport in
which auxin is transported towards cells containing higher concentrations ofauxin, leading to the formation of an auxin maximum.
Meristem: a specialized region of cell division in plants. Shoot meristems in
angiospermsandgymnosperms combinecelldivisionwiththe productionofnew
organs, either leaves or reproductive structures. Shootmeristems in otherplants
are generally simpler in structure and contain far fewer cells. Rootmeristemsare
only present in vascular plants and do not directly produce new lateral organs.
Phyllotaxis: an apparently self-organizing developmental pattern describing
the position of organs (e.g., leaves) along and around the stem. Different
phyllotactic patterns occur in different species. Phyllotaxis in angiosperms
results primarily from the positioning of neworgan primordia on the flanks of
the multicellular shoot meristem, and is established by maximization-like
patterns of auxin transport in the meristem.
PIN auxin efflux carriers (PINs): a family of proteins that are general ly
accepted to be auxin efflux carriers. Canonical PIN proteins have plasma
membrane localizations, often polarized, and are thought to be the principal
determinants of the direction of auxin efflux, in line with the chemiosmotic
hypothesis. Named after a founding member, PIN-FORMED1 (PIN1), in turn
named for its mutant phenotype involving impaired organ initiation at theshoot meristem a result of aberrantmaximization.
PINOID-family kinases: a small family of serine/threonine kinases that
phosphorylate the intracellular loop of canonical PIN proteins, thereby
controlling their localization. Named after the founding member, PINOID, in
turn named for the resemblance of its mutant phenotype to pin1.
Super-linear: a mathematical relationship in which one variable is influenced
by another with a greater than linear effect; examples include quadratic
(y = a x 2), cubic (y = ax3), and exponential (y = ax) functions.
Up-the-gradient (UTG): a modeling heuristic widely used to simulate
maximization-like patterns of auxin transport (Box 2), in which PIN proteins
are allocated to the plasma membrane in proportion to the concentration of
auxin in cells neighboring that membrane.
Vascular patterning: an apparently self-organizing developmental phenomen-
on in which the position of future veins is established by canalization-like
patterns of polar auxin transport through a tissue.
Vascular plants: the plant clade containing angiosperms,gymnosperms, ferns,
and lycophytes. Defined by the presence of a differentiated vascular network.
Non-vascularplantssuchasmosses lackspecialized tissues forwater transportand are limited in their size as a result.
Vasculature/veins: the vascular network in plants plays analogous roles to the
vascular system in animals. I t consists of two paral le l systems, xylem
(primarily water-conducting) and phloem (primarily sugar-conducting), that
generally develop in association with each other.
With-the-flux (WTF): a modelingheuristic widely usedto simulate canalization-
like patterns of auxin transport (Box 2) in which PIN proteins are allocated to
the plasma membrane in proportion to the net flux of auxin through that
membrane.
Opinion Trends in Genetics February 2014, Vol. 30, No. 2
42
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?- -
8/12/2019 Trends in Genetics Feb
5/46
proportional to net flux. It is not even necessary for these
measurements to include any component of flux, but an
attractive hypothesis is that cells canmeasure transport-
er-mediated efflux of auxin across a givenmembrane, and
combine this with other information to regulate PIN
protein allocation. For instance, it is possible that, as
PIN proteins transport molecules of auxin, they (or a
protein partner) produce a positive-feedback signal that
reduces the removal of those PIN proteins from the
membrane. This alone would be sufficient to maintain
WTF patterns of PIN protein localization, but not to
generate them in the first place, because this mechanism
would not specifically orient PINs on the membrane
opposite an auxin source. To achieve this aspect of PIN
localization presumably requires at least some informa-
tion from outside the cell. It is therefore likely that the
canalization mechanism has at least two components,
and these might include measurement of auxin concen-
trations on either (or both) sides of cell membranes, as for
instance proposed in a recent model of auxin transport in
which extracellular auxin concentration is the major
determinant of PIN allocation [19]. A recently proposed
framework for cell coupling,unrelated to concentration or
flux-based models, but operating through bidirectional
exchange of information across the apoplast, would also
theoretically be able to generate large-scale patterns of
PIN localization [20].
The first step towards testing these ideas must be to
probe the genetic basis of the canalization feedback mech-
anism, using the well-established toolkit inArabidopsis, a
goal distinct from understanding how PIN proteins are
polarized in general [10] or providing descriptive analyses
of the
process
of
canalization
[9,10,21].
A
pure
canaliza-tion system must be established in Arabidopsis, compara-
ble to the original experiments of Sachs even though its
diminutive size makes this difficult but with the addition
of reporter lines such that the early stages of canalization
can be visualized. By using this system to test the canali-
zation response in mutants or under pharmacological
treatments that impair known auxin-sensing, auxin trans-
port, and PIN polarity-generating mechanisms, the role of
those factors in the canalization process can be examined,
helping to narrow down the mechanisms involved. Of
course, as yet undiscovered factors might be central to
the canalization mechanism, in which case screening for
canalization-deficient mutants may be a sensible ap-
proach. The vascular patterning defects seen in pin1pin6 doublemutants [11] provide a possible reference point
for screening for developmental phenotypes, but another
approach to screening may be to look for mutants in which
initially well-established but broad transport domains
(visualized by reporter genes) fail to narrow down, the
hallmark of canalization. Distinguishing potential canali-
zation mutants from generalized auxin transport mutants
will be important, and a sensitized genetic background
might be preferable to help pick out otherwise relatively
subtle phenotypes.
This top-down approach to canalization should be ac-
companied by general research to allow improved param-
eterization
of
auxin
transport
models.
Trying
to
quantify,for example, the amounts of auxin and PIN protein in
different parts of each cell, or the cycling rates for PIN
proteins, will be fiendishly difficult, but even establishing a
loose range would be an improvement over the current
absence of data. Other important questions to address
include whether the relationship between flux (or equiva-
lent) and PIN allocation is linear or super-linear, whether
there is a saturation point for flux-correlated PIN-alloca-
tion, and whether the pool of PIN proteins is quasi-infinite
and freely allocated or limited and proportionately (re-
)allocated according to flux, all aspects that current models
have shown to be potentially important in pattern emer-
gence [3,18,22]. Cell culture-based systems may prove
useful in addressing these questions, as they have been
in dissecting the action of auxin transporters and mecha-
nisms of auxin homeostasis [23,24].
Increased understanding of PIN protein behavior will
aid modeling of auxin transport,
The experiments described above would be well-comple-
mented by bottom-up approaches to improve understand-
ing of the behavior of PIN proteins. There is a significant
body of work relating to the localization of PIN proteins,
and it is known that in some cell types they can cycle
rapidly between the plasma membrane and endosomal
compartments [25]. It is this system that presumably
Box 1. Auxin transport
Auxin is transported in a polar manner through many tissues, and
the canalization theory of Sachs [7,8] is framed in the context of
PAT. Long-distance PAT has often been theorized as connecting
auxin sources (regions of highauxin concentration or production)
to sinks (regions of lowauxin concentration or high turnover) [6].
In most canalizing systems, developing tissue (leaves, buds, etc.)
acts as an auxin source and established vasculature acts as a sink
(Figure 2). More recent work
has shown that vasculature generallyhas high auxin concentrations [45], and therefore sink strength in
this system is probably determined by auxin flux rapidly carrying
auxin away from the source. Subsequent to Sachs initial canaliza-
tion work, a mechanistic basis for PAT was proposed in the
chemiosmotic hypothesis. Central to this is the weakly-acidic
nature of auxin (pKa 4.75), which means that a significant fraction
of auxin molecules in the apoplast (pH 5.5) are protonated and
neutrally charged, and can passively enter cells through the lipid
membrane; however, the largely deprotonated auxin in the
cytoplasm (pH 7) cannot passively exit cells (Figure 1A). Specific
efflux carriers are therefore required to mobilize auxin from cells,
and it wasproposed that polar localization of these proteinswould
explain theoverall polarityof auxin transport [46,47]. Thediscovery
of PIN-family auxin efflux carriers, transmembrane proteins which
often have polar localization [44,48], confirmed the validity of the
chemiosmotic
hypothesis, and it
is generally
accepted that PINproteins are the major determinants of the directionality of local
auxin flux (Figure 1A) [28]. Members of the large ABC family of
auxin transporters seem to act as non-polar auxin efflux carriers
[49], andthere arealsoauxin influxcarriers of theAUX1/LAXfamily
[50] (Figure 1A). Auxin regulates its own transport, andin particular
PIN protein abundance and localization, at multiple levels, both
transcriptional and post-transcriptional [1,51]. For instance, intra-
cellular auxin levels can regulate transcription of PIN genes
through canonical auxin signaling [52], whereas apoplastic auxin
can inhibit PIN endocytosis though the ABP1 receptor [53]. Work in
thi s area has been greatly a facil itated by l ive imaging of
transporters fused to fluorescent proteins [54], and by proxy live-
imaging of intracellularauxin based on fluorescent reporters of the
activity of various components of the transcriptional auxin signal-
ing pathway [55,56].
Opinion Trends in Genetics February 2014, Vol. 30, No. 2
43
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?- -
8/12/2019 Trends in Genetics Feb
6/46
allows for the dynamic changes in PIN protein localization
necessary for both WTF and UTG patterns to emerge.
However, the mechanisms that determine how PIN pro-
teins are allocated to different membranes in different
situations are poorly understood, despite observations of
the resultant patterns. PIN protein localization can be
influenced by regulatory proteins such as PINOID-family
protein kinases,which phosphorylate the long intracellular
(A) (B)
(C)
(D)
I1
P1
P8
P3
P6
P1
P9P4P7
P2
P10
P5 I1
I2
P11
IAA
IAA
IAA
Cytoplasmp
H7
ApoplastpH5.5
TRENDS in Genetics
Figure 1. Auxin transport, plant development, and self-organization. (A) Schematic illustrating the chemiosmotic mechanism of polar auxin transport. Protonated auxin
(indole-3-acetic acid, IAA) inthe cell wall space theapoplast (green) canmovepassivelyinto cells throughplasmamembranes(black arrows). Influxmayalsobe assisted
by influxcarriers (yellow circles). Deprotonated auxin(IAA) inthecytoplasm canonlymove out ofcells bytheactionof efflux carriers (redcircles), andpolarlocalization of these
carriers (such as PINproteins) generatesoverall polarity in auxin transport. (B) Schematic showing the phyllotactic pattern of organ initiation atArabidopsisshootmeristems
(top-down view).New organsareproduced in a stable spiral pattern, withapproximately 1378 separating eachnew organ. I1 and I2mark theposition of the next twoinitiating
organ primordia to form. P1 (youngest)P11 (oldest) are existing organ primordia. Phyllotaxis is an apparently self-organizing developmental process that involves auxin
maximization, and has primarily been modeled using an up-the-gradient (UTG) heuristic. (C) Schematic showing vascular patterning in an Arabidopsis leaf. The midvein
(purple) forms first and joins the leaf to the main vascular bundles in the stem. First-order veins (dark blue) directly connect to themidvein andareassociatedwithlocal auxin
maximaat theedgeof theleaf. Themajorauxinmaxima associatedwith lobes/serrations areshown in red, others areomitted forclarity. Lower-order veins (light blue) connect
first-orderveinstogetherto form ahighlyconnective reticulatenetworkthatveryefficientlyservesthewholeorgan.Thevascularnetwork is specified byauxintransportthrough
the leafblade, towards themidvein andultimately the stem. Vascular patterning is an apparently self-organizing developmental process that involves auxin canalization, and
has primarily been modeled using a with-the-flux (WTF) heuristic. (D) Schematic cross-section through an Arabidopsisshoot meristem showing organ initiation events at I1
andP1. Auxin in themeristem is transported (blue arrows) towards thesite of I1 by PINproteins (greenbars),resultingin the formationof an auxinmaximum (redshading). At
P1 thepatternof auxin transport is partially reversed,withauxinbeing transported away from themaximum in a down-the-gradient pattern. Only a thin fileof cells transports
auxin,thus showing a canalizedpattern of transport;thesecellswill become themidveinof theneworgan.Organinitiation thus involvesauxin canalizationandmaximizationin
tight spatiotemporal cooperation. Neither WTF nor UTGmodels of auxin transport have yet convincingly captured this complete range of behavior.
Opinion Trends in Genetics February 2014, Vol. 30, No. 2
44
-
8/12/2019 Trends in Genetics Feb
7/46
loop domain of particular PIN proteins [26,27]. This loop
domain shows extensive variation in structure between
different types of PIN protein (Bennettet al., unpublished),
meaning that each type of PIN protein could have an
inherently different potential for localization; for instance,
disruption of specific loop domains can result in different
localizations within the same cell type [28]. Ultimately,
canalization-like patterns are mediated through specific
regulation of a subset of PIN proteins. A deep structure
function analysis of PIN proteins would therefore delineate
howeachpartof theloopcontributes toPIN localization, and
how each PIN protein behaves under different circum-
stances. Indeed, it is possible that part of the loop in some
PIN proteins is a specific regulatory element for flux-based
feedback, mediating canalization-like behavior of the pro-
tein in effect, a canalization motif. In Arabidopsis PIN1
plays major roles inbothcanalizationand maximization, but
in other species including grasses these two processes may
bemediatedby structurally-distinctPINproteins(OConnor
et al., unpublished). Investigating the possible evolution of
PIN protein structures specialized for canalization may
therefore also provide an entry point for dissecting how
canalization is regulated at a molecular level. Cell type-
specific factors [29], external stimuli including light [30]
and long-distance signals such as cytokinins and strigolac-
tones [31,32] can all influence the localization of PIN pro-
teins, and it is thereforealso important tocontinueassessing
how different combinations of these proximal factors might
contribute in large-scale self-organizing PIN behavior.
The role of the apoplast in auxin transport
A frequent simplifying assumption in modeling auxin
transport is to ignore the apoplast and assume that auxin
is transported directly from one cell to the next. Given the
chemiosmotic basis of auxin transport (Box 1) thismay be a
dangerous omission because apoplastic conditions are
interconnected with auxin transport in multiple ways
[33].For instance, low extracellular pH results in increased
passive movement of auxin into cells (Figure 1A), and
auxin ion export through PIN proteins is likely to be
energized by the proton motive force across the plasma
membrane. Furthermore, a long-established activity of
Box 2. Auxin transport models
Most mathematical models so far published have generally taken a
major experimental observation regarding auxin transport (e.g., PIN
localization towards an auxin maximum), and abstracted it into a
singlemathematical concept (basicmodeling terminology is summar-
ized in Figure I). These observation-based models can be broadly
allocated to two classes flux-based or concentration-based
depending on the primary source of information they use to allocate
PIN proteins to plasma-membranes. In practice all flux-based modelsare explicitly of a WTF subset, and almost all concentration-based
models are UTG. Within each broad class, the exact set of parameters
and level of abstraction varies between models. These models are not
mutually exclusive (mathematically they could be combined), but so
far have been considered separately. A small number of mechan-
istically more explicit models have been proposed, for example one
that proposes that auxin concentration in neighboring cells is
measured via its effects on cell wall stress(alsobased on experimental
observation) [57], although purely theoretical models, for example
based on apoplastic transcriptional auxin gradients, have also been
proposed [19].
WTF PIN allocation
In WTF models a positive feedback loop increases PIN insertion rate
(or decreases PIN removal) in a given cell membrane when there is
increased flux f the net quantity of auxin exported through thatmembrane, per unit time and per unit area.
Mathematically, a general formulation for the dynamics of PIN
concentration ( p) in the membrane section of a cell i facing
neighboring cell j (ij) includes PIN insertion, both at a basal rate (r0)
and at an increased rate given by the auxin flux feedback [f(fij)] and
PIN removal (m).
d pi j
dt
f fij r0 mpi j; x>0r0 mpi j; x 0
The exact feedback relationship between flux and PIN allocation has
important ramifications for model function. Several different and
purely theoretical relationships have been explored in models,
including a simple linear relationship, f(f)= af [40], quadratic,
f(f)= af2 [15], or a Hil l function ff afn/Kfn[16].
UTG PIN allocation
In UTG models, PIN insertion rate is increased in membrane sectionsaccording to the auxin concentrations in cells neighboring those
membranes. PIN proteins in cell i are preferentially inserted in the
section of membrane that faces the neighboring cell jwith the highest
auxin concentration, at the expense of other membranes. This
increases the auxin concentration in j, thus driving positive feedback
of PIN allocation.
Although some models [39,41] explicitly include PIN cycling
between an intracellular pool of non-allocated PINs ( pi) and mem-
brane-bound PINs (pij), the more streamlined model proposed in [38]
assumes that all PINs (pi) are instantly and competitively allocated
between the different membrane sections proportionally to concen-
tration. The sets of equations below describe the two situations; inboth cases, ai is the auxin concentration in cell i and aj is the auxin
concentration in cell jwhich is adjacent to cell ialong the membrane
section ij. The set of cells kadjacent to cell iis the set of neighbors N(i).
d pi j
dt aaj; pi pi v pi j
d pidt
gai; pi m piX
k 2 Ni
aaj; pi pi v pij
8>>>:
39;41
pij aajP
k 2 Niaakpi
d pidt
gai; pi mpi
8>>>:
38
Cell i Cell j
ajai
pij
0
ij
TRENDS in Genetics
Figure I. Basic modeling terminology. Schematic illustrating some of the major
terms used in mathematical modeling of auxin transport, and their interrelation.
The cell i faces its neighborjat themembrane ij. The basal concentration of PIN
protein (pij) in the membrane ij (indicated by a green bar) is determined by the
relative rates of insertion (r0) from an intracellular pool (indicated by a greencircle) and recycl ing from the membrane to the intracellular pool (m). PIN
allocation to the membrane can be increased by positive feedback relating the
either fluxthroughfij (indicated by a blue arrow)or theauxin concentration in cell
j (aj).
Opinion Trends in Genetics February 2014, Vol. 30, No. 2
45
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?- -
8/12/2019 Trends in Genetics Feb
8/46
intracellular auxin is to stimulate proton-pumping
ATPases, thereby further acidifying the cell wall [34]. This
gives rise to a potential positive feedback loop in which
increased intracellular auxin in one cell, acting through
apoplastic acidification, drives increased auxin uptake in
neighboring cells and increased activity of its in situ PIN
proteins. This mechanism can therefore contribute to the
generation
of
net
flux
between
cells,
particularly
at
highauxin concentrations, and might have important ramifica-
tions in the switching behavior seen during organ initia-
tion (Figure 1D) where auxin accumulation in the
epidermis is associated with internalization and canaliza-
tion of auxin flow. The apoplast is the central focus of a
recently proposed model [19] which invokes a polarity-
generating mechanism that is neither WTF nor UTG,
but instead relies on gradients of auxin across the cell wall
partitioning an extracellular receptor to generate PIN
polarization in the adjoining cells.The apoplast is certainly
a potential source of information for polarization mecha-
nisms but there is little biological evidence to support this
model, which requires steep gradients of auxin in the tiny
apoplastic space to make it work [3,19]. It will certainly be
interesting to test the effect of apoplastic auxin and pH
dynamics in both WTF and UTG models. However, al-
though there are now a range of approaches for assessing
intracellular auxin concentrations (albeit indirectly), there
is currently no way to quantify apoplastic auxin, and tools
to do so should be a priority for the field.
Unification of auxin transport models
The integration of modeling and molecular genetics has
demonstrated that auxin transport dynamics provide a
plausible explanation for vascular patterning and shoot
branching regulation via canalization [9,15,16,18] and for
phyllotaxis via maximization [35,36]. Subsequently, there
has been considerable interest in producing a unifying
model of auxin transport that is capable of reproducing
both canalization and maximization patterns with a single
heuristic and set of parameters. Published models of this
type have mostly been extensions of previous models with
either purely WTF mechanisms [37] or purely UTG mech-
anisms
[38], but
cannot
straightforwardly
reproduce
bothbehaviors because they require significantly altering
parameters in different parts of the simulation, making
biologically improbable assumptions, or ignoring wet lab
data [3]. It is fair to say that the consensus in the field,
supported by reanalysis of current models [3], is that no
satisfactory unifying model has been developed yet per-
haps not surprisingly given the current gaps in our under-
standing. From a biological perspective, an interesting
question is not whether the models can be mathematically
unified after all, with enough parameters one could
model anything [39,40] but whether they should be
unified. Are canalization and maximization really flip-
sides of the same coin or are they fundamentally different
processes using different mechanisms in different tissues?
There are also other auxin transport patterns, particularly
in the root, that do not resemble either canalization or
maximization are all these phenomena essentially the
same process or are they divergent mechanisms that share
only some basic aspects?
This question is particularly intriguing from an evolu-
tionary perspective because PAT is present throughout
land plants and in at least some charophyte algae [41].
However, there is currently little evidence for the specific
phenomena of canalization or maximization outside
angiosperms. Given its importance in vascular develop-
ment, it seems a reasonable hypothesis that canalization
(A) (B) (C) (D) (E)
TRENDS in Genetics
Figure2 . Canalization phenomena. Schematics based on the classic experiments of Sachs on excised pea epicotyls (juvenile stems). Green cylinders indicate naive non-
vascular tissue; gray cylinders indicate vascular bundles. Red semicircles indicate addition of exogenous auxin. Blue lines indicate newly induced vascular strands. (A)
Simple demonstration of canalization: lateral auxin application induces vascular connection with the main vascular bundle. (B,C) Sourcesink relationships in induced
vascular strands. Thevascularbundle is surgically removed and two sources of auxin areadded to the apicalend of theepicotyl. If added simultaneously(B) twonew sets
of vasculature are formed. In both cases canalization occurs towards the site of the former vascular bundle, indicating that it is still a strong sink for auxin. If one auxin
sourceis added subsequent to theother (C), canalization now occursfrom that sourcetowards thenew vascular tissueformed by thefirstsource, indicating that it is now a
stronger sink. (D) Sink-finding in canalization. A cut in the epicotyl does not prevent canalization occurring between an exogenous auxin source and the existing vascular
bundle. (E) Hyper-canalization. Addition of a strong auxin source to the existing vascular bundle now prevents sink-finding by an exogenous auxin source. However,
canalizationand vascular formation fromthe auxin source can stilloccur in a non-connective fashion.Dotted bluelines indicate the discontinuation of the vascularstrands.
Opinion Trends in Genetics February 2014, Vol. 30, No. 2
46
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?- -
8/12/2019 Trends in Genetics Feb
9/46
evolved early in the vascular plant clade and is present
throughout it. PAT is present in the lycophyte Selaginella
kraussiana and plays a role in vascular development, but
whether this is canalization-driven is currently unclear
[42]. Lycophytes and ferns have meristems with single
apical cells, and initiate organs in a fundamentally differ-
ent manner to seed plants. This suggests that auxin max-
imization
in
meristems
arose
specifically
in
the
largemeristems of the seed-plant lineage although this does
not necessarily preclude maximization-type phenomena in
ferns and lycophytes. If generalized PAT, canalization, and
maximization did evolve at different points in the evolu-
tionary history of plants then sequential innovations could
have generated novel auxin transport phenomena. In turn,
this would suggest that these phenomena are not equal or
equivalent, but require process-specific genetic compo-
nents, which could have included changes in the structure
of the PIN proteins themselves; however, more work is
necessary to establish the exact evolutionary history of
auxin transport. In angiosperms, different PINs are prob-
ably specialized for, or act preferentially in, particular
processes; for instance, the primary (but not sole) functionof PIN2 in Arabidopsis is to control a specific shootward
auxin flux in the root meristem [43,44]. Further investiga-
tion of auxin transport phenomena and PIN protein sub-
functionalization outside angiosperms will not only be
illuminating with regard to the evolution of development
in land plants but will also help in dissecting the nature of
auxin transport itself.
Even though canalization and maximization both in-
volve PIN1 inArabidopsis, there is some molecular genetic
evidence to suggest that they might not be identical pro-
cesses; for instance, PINOID plays a crucial role in maxi-
mization but is less central to canalization [29]. This has
led
to
suggestions
that
there
is
tissue-
or
context-specificswitching between modes of auxin transport, an approach
used in another model [17] in which maximization and
canalization are effectively modeled separately. However,
as with so much in biology, it is likely that the reality will
be more nuanced, especially because we do not yet under-
stand the mechanisms of either canalization or maximiza-
tion. It is plausible that there is a core machinery for
allocating PIN proteins to membranes that, given the in-
herent differences between contexts, is capable of generat-
ing both canalization and maximization and possibly all
auxin transport phenomena. For example, if PIN allocation
is achieved by the combined assessment of two or more
factors inside and outside cells (as discussed above), then
perhaps both patterns can be generated depending on the
weightings given to those different factors in different con-
texts.This coremachinery couldhave beenelaboratedupon
during plant evolution to generate new patterns of auxin
transport, butremainthesame fundamental unifiedmech-
anism.Ultimately, althoughcomputational work can tellus
that themodelsareunifiable,wewillonlyfindoutforsureby
pushing forward our biological understanding of auxin
transport across the whole plant kingdom.
Concluding remarks
The impressive progress of theoretical research into auxin
transport phenomena has outstripped advances in our
biological understanding of these processes, particularly
in the case of canalization, which has only received limited
experimental attention in the recent molecular genetic era
ofplantdevelopment [911,21].Further experiments along
the lines proposed here are now required to gain a deeper
understanding of the canalization mechanism, and must
aim to unite physiological and genetic approaches in a
single
species.
These
will
not
only
be
relevant
to
canaliza-tion itself but also to the auxin transport field more gener-
ally, allowing construction of a new generation of models to
examine self-organizing plant development.
Acknowledgments
Our research is funded by the Gatsby Foundation and the European
Research Council (Project 294514 EnCoDe). We would like to thank
Graeme Mitchison for critical reading of the manuscript.
References1 Benjamins, R. and Scheres, B. (2008) Auxin: the looping star in plant
development. Annu. Rev. Plant Biol. 59, 443465
2 Leyser, O. (2011) Auxin, self-organisation, and the colonial nature of
plants. Curr. Biol. 21, R331R337
3 van Berkel, K. et al. (2013) Polar auxin transport: models and
mechanisms. Development 140, 22532268
4 Sachs, T. (1968)On the determinationof the pattern of vascular tissue
in peas. Ann. Bot. 32, 781790
5 Jacobs, W.P. (1952) The role of auxin in the differentiation of xylem
around a wound. Am. J. Bot. 39, 301309
6 Sachs, T. (1968) The role of the root in the induction of xylem
differentiation in peas. Ann. Bot. 32, 391399
7 Sachs, T. (1969) Polarity and the induction of organized vascular
tissues. Ann. Bot. 33, 263275
8 Sachs, T. (1981)The control of thepatterned differentiationof vascular
tissues. Adv. Bot. Res. 9, 151162
9 Scarpella, E. et al. (2006) Control of leaf vascular patterning by polar
auxin transport. Genes Dev. 20, 10151027
10 Sauer, M. et al. (2006) Canalization of auxin flow by Aux/IAAARF-
dependent feedback regulation of PIN polarity. Genes Dev. 20, 2902
291111 Sawchuk, M.G. et al. (2013) Patterning of leaf vein networks by
convergent auxin transport pathways. PLoS Genet. 9, e1003294
12 Reinhardt, D. et al. (2003) Regulation of phyllotaxis by polar auxin
transport. Nature 426, 255260
13 Mitchision, G.J. (1980) The dynamics of auxin transport. Proc. R. Soc.
Lond. B: Biol. Sci. 209, 489511
14 Mitchison, G.J. et al. (1981) The polar transport of auxin and vein
patternsin plants.Philos.Trans. R. Soc.Lond.B: Biol.Sci.295,461471
15 Rolland-Lagan,A.G.andPrusinkiewicz, P. (2005) Reviewingmodels of
auxin canalization in the context of leaf vein pattern formation in
Arabidopsis. Plant J. 44, 854865
16 Prusinkiewicz, P. et al. (2009) Control of bud activation by an auxin
transport switch. Proc. Natl. Acad. Sci. U.S.A. 106, 1743117436
17 Bayer, E.M. et al. (2009) Integration of transport-based models for
phyllotaxis and midvein formation. Genes Dev. 23, 373384
18 Krupinski, P. and Jonsson, H. (2010) Modeling auxin-regulateddevelopment. Cold Spring Harb. Perspect. Biol. 2, a001560
19 Wabnik,K. et al. (2010)Emergence oftissuepolarizationfrom synergy
of intracellular and extracellular auxin signaling.Mol. Syst. Biol. 6,
447
20 Abley, K. et al. (2013) An intracellular partitioning-based framework
for tissue cell polarity in plants and animals.Development 140, 2061
2074
21 Balla, J. et al. (2011) Competitive canalization of PIN-dependent
auxin flow from axillary buds controls pea bud outgrowth. Plant J.
65, 571577
22 Feugier, F.G. et al. (2005) Self-organization of the vascular systemin
plant leaves: inter-dependent dynamics of auxin flux and carrier
proteins. J. Theor. Biol. 236, 366375
23 Barbez, E. et al. (2013) Single-cell-based system to monitor carrier
driven cellular auxin homeostasis. BMC Plant Biol. 13, 20
Opinion Trends in Genetics February 2014, Vol. 30, No. 2
47
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0005http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0005http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0005http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0005http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0010http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0010http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0010http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0010http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0015http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0015http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0015http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0015http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0015http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0015http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0020http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0020http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0020http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0020http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0025http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0025http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0025http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0025http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0030http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0030http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0030http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0030http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0035http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0035http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0035http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0035http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0040http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0040http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0040http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0040http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0045http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0045http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0045http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0045http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0045http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0045http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0055http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0055http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0055http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0055http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0055http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0055http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0060http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0060http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0060http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0060http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0060http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0060http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0065http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0065http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0065http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0065http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0075http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0075http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0075http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0075http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0075http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0075http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0080http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0080http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0080http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0080http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0080http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0080http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0085http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0085http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0085http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0085http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0085http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0085http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0115http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0115http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0115http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0115http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0115http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0115http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0115http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0115http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0110http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0105http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0100http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0095http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0090http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0085http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0085http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0080http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0080http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0075http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0075http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0075http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0070http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0065http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0065http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0060http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0060http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0055http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0055http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0050http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0045http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0045http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0040http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0040http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0035http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0035http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0030http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0030http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0025http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0025http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0020http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0020http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0015http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0015http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0010http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0010http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0005http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0005http://-/?-http://-/?-http://-/?-http://-/?-http://-/?- -
8/12/2019 Trends in Genetics Feb
10/46
24 Petrasek, J.et al. (2006) PINproteins perform a rate-limiting function
in cellular auxin efflux. Science 312, 914918
25 Geldner, N.et al. (2001)Auxin transport inhibitors block PIN1 cycling
and vesicle trafficking. Nature 413, 425428
26 Huang, F.et al. (2010) Phosphorylation of conservedPINmotifs directs
ArabidopsisPIN1polarityand auxintransport.PlantCell22,11291142
27 Dhonukshe, P. et al. (2010) Plasma membrane-bound AGC3 kinases
phosphorylate PIN auxin carriers at TPRXS(N/S) motifs to direct
apical PIN recycling.Development 137, 32453255
28 Wisniewska, J.et al. (2006) Polar PIN localizationdirects auxin flowinplants. Science 312, 883
29 Friml, J. et al. (2004) A PINOID-dependent binary switch in apical-
basal PIN polar targeting directs auxin efflux. Science 306, 862865
30 Ding, Z. et al. (2011) Light-mediated polarization of the PIN3 auxin
transporter for the phototropic response inArabidopsis.Nat. Cell Biol.
13, 447452
31 Shinohara, N. et al. (2013) Strigolactone can promote or inhibit shoot
branching by triggering rapid depletion of the auxin efflux protein
PIN1 from the plasma membrane.PLoS Biol. 11, e1001474
32 Marhavy , P. et al. (2011) Cytokinin modulates endocytic trafficking of
PIN1 auxin efflux carrier to control plant organogenesis. Dev. Cell 21,
796804
33 Steinacher, A. et al. (2012) A computational model of auxin and pH
dynamics in a single plant cell. J. Theor. Biol. 296, 8494
34 Hager, A. (2003) Role of the plasma membrane H+-ATPase in auxin-
induced elongation growth: historical and new aspects. J. Plant Res.116, 483505
35 Smith, R.S. et al. (2006) A plausible model of phyllotaxis. Proc. Natl.
Acad. Sci. U.S.A. 103, 13011306
36 Jonsson, H.et al. (2006)An auxin-driven polarized transportmodel for
phyllotaxis. Proc. Natl. Acad. Sci. U.S.A. 103, 16331638
37 Stoma, S. et al. (2008) Flux-based transport enhancement as a
plausible unifying mechanism for auxin transport in meristem
development. PLoS Comput. Biol. 4, e1000207
38 Merks,R.M.et al. (2007)Canalizationwithout flux sensors: a traveling-
wave hypothesis. Trends Plant Sci. 12, 384390
39 Dyson, F. (2004) A meeting with Enrico Fermi. Nature 427, 297
40 Brown, K.S. andSethna, J.P. (2003) Statisticalmechanicalapproaches
to models with many poorly known parameters. Phys. Rev. E: Stat.
Nonlin. Soft Matter Phys. 68, 021904
41 Boot, K.J. et al. (2012) Polar auxin transport: an early invention. J.
Exp. Bot. 63, 42134218
42 Sanders, H.L. and Langdale, J.A. (2013) Conserved transport
mechanisms but distinct auxin responses govern shoot patterning in
Selaginella kraussiana. New Phytol. 198, 419428
43 Luschnig, C.et al. (1998)EIR1,a root-specific protein involved in auxin
transport, is required for gravitropism in Arabidopsis thaliana. Genes
Dev. 12, 21752187
44 Mu ller, A. et al. (1998) AtPIN2 defines a locus ofArabidopsis for root
gravitropism control. EMBO J. 17, 69036911
45 Avsian-Kretchmeret al. (2002) Indoleacetic aciddistribution coincides
withvascular differentiationpattern duringArabidopsis leafontogeny.Plant Physiol 130, 199209
46 Rubery, P.H. and Sheldrake, A.R. (1974) Carrier-mediated auxin
transport. Planta 118, 101121
47 Raven, J.A. (1975) Transport of indoleacetic acid in plant cells in
relation to pH and electrical potential gradients, and its significance
for polar IAA transport. New Phytol. 74, 163172
48 Galweiler, L. et al. (1998) Regulation of polar auxin transport by
AtPIN1 in Arabidopsis vascular tissue. Science 282, 22262230
49 Geisler, M. and Murphy, A.S. (2006) The ABC of auxin transport:
the role of p-glycoproteins in plant development. FEBS Lett. 580,
10941102
50 Peret, B. et al. (2012) AUX/LAX genes encode a family of auxin influx
transporters that perform distinct functions during Arabidopsis
development. Plant Cell 24, 28742885
51 Leyser, O. (2010) The power of auxin in plants. Plant Physiol. 154,
50150552 Vieten, A. et al. (2005) Functional redundancy of PIN proteins is
accompanied by auxin-dependent cross-regulation of PIN expression.
Development 132, 45214531
53 Robert, S. et al. (2010) ABP1 mediates auxin inhibition of clathrin-
dependent endocytosis in Arabidopsis. Cell 143, 111121
54 Blilou, I.et al. (2005)ThePINauxin efflux facilitator network controls
growth and patterning in Arabidopsis roots. Nature 433, 3944
55 Benkova, E. et al. (2003) Local, efflux-dependent auxin gradients as a
common module for plant organ formation. Cell 115, 591602
56 Brunoud, G. et al. (2012) A novel sensor to map auxin response
and distribution at high spatio-temporal resolution. Nature 482,
103106
57 Heisler, M.G. et al. (2010) Alignment between PIN1 polarity and
microtubule orientation in the shoot apical meristem reveals a tight
coupling between morphogenesis and auxin transport. PLoS Biol. 8,
e1000516
Opinion Trends in Genetics February 2014, Vol. 30, No. 2
48
http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0120http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0120http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0120http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0120http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0120http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0120http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0120http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0120http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0125http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0125http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0125http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0125http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0125http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0125http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0130http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0135http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0135http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0135http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0135http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0135http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0135http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0135http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0140http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0140http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0140http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0140http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0140http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0140http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0145http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0145http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0145http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0145http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0145http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0145http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0150http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0150http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0150http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0150http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0150http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0150http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0150http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0150http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0150http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0155http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0155http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0155http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0155http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0155http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0155http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0155http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0160http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0165http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0165http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0165http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0165http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0165http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0165http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0170http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0170http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0170http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0170http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0170http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0175http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0175http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0175http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0175http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0175http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0175http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0190http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0190http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0190http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0190http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0190http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0190http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0195http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0195http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0195http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0200http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0200http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0200http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0200http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0200http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0205http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0205http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0205http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0205http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0205http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0205http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0210http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0210http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0210http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0210http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0210http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref9225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref9225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref9225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref9225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0230http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0230http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0230http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0230http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0230http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0255http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0255http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0255http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0255http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0255http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0255http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0280http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0275http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0270http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0265http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0260http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0255http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0255http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0255http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0250http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0245http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0240http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0235http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0230http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0230http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0230http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref9225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref9225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0225http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0220http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0215http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0210http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0210http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0210http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0205http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0205http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0200http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0200http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0200http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0195http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0190http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0190http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0185http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0180http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0175http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0175http://refhub.elsevier.com/S0168-9525(13)00192-3/sbref0170http://refhub.elsevier.com/S0168-