Systems Biology Approaches To Development Beyond Bioinformatics: Nonlinear Mechanistic Models Using Plant Systems
Systems Biology Approaches To Development Beyond Bioinformatics: Nonlinear Mechanistic Models Using Plant Systems
Systems Biology Approaches To Development Beyond Bioinformatics: Nonlinear Mechanistic Models Using Plant Systems
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Keywords: gene regulatory networks, genotype–phenotype map, epigenetic landscape, systems developmental biology, nonlinear stochastic modeling
BioScience XX: 1–13. © The Author(s) 2016. Published by Oxford University Press on behalf of the American Institute of Biological Sciences. All rights
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doi:10.1093/biosci/biw027 Advance Access publication XX XXXX, XXXX
regulated is very useful, but on its own, it does not explain previously by pioneer theoretical biologists (Kauffman 1993,
how a cell type is specified, an organ is formed, or a disease Goodwin 1994, Solé and Goodwin 2008, Waddington 1957).
is developed. Even if we study the so-called master genes,
we are not able to understand the systems-level underlying Nonlinearity in genotype to phenotype maps
mechanisms implied in its prominent role. The systems- Despite the fact that nonlinearity is intrinsic to biological
biology approach that implies the proposal of mechanistic, and biochemical systems, reasoning in biology has tra-
dynamic models to uncover G–P mapping algorithms is ditionally followed a remarkably and instrumental linear
referred to as the bottom-up approach, and it has been cause–effect paradigm for particular components. This latter
mostly applied to well-curated regulatory modules with approach does not consider explicitly the conditional role of
clear phenotypical consequences. each part on others or the direct and indirect interactions
The top-down and the bottom-up approaches comple- among components that altogether constitute the system.
ment each other and are increasing the explanatory and pre- In a cause–effect framework, which avoids the consider-
dictive power of systems biology (Bruggeman et al. 2007). A ation of interactions and feedback loops, linear schemes of
key aspect of the bottom-up mechanistic approach is that it causation are frequently invoked (see, e.g., discussions in
considers nonlinear dynamical mapping models at different Huang 2011). The latter approach, which assumes that the
levels of organization (e.g., gene interactions and circuits, behavior of a whole system can be understood on the basis
networks, cells, tissues, organs), incorporating both molecu- of the behavior of its isolated components or their added
Multistability is the property of a given GRN of attaining inside: sepals, petals, stamens, and carpels (see, e.g., Alvarez-
more than one of these attractor states. In systems-biology Buylla et al. 2010a,b). Such a conserved pattern suggested
literature, multistability is generally accepted as the for- an underlying robust mechanism that evolved before the
mal dynamic mechanism explaining cellular differentiation, origin of the flowering plant species. We aimed at discover-
reprogramming, and dedifferentiation (Kauffman 1969, ing such a robust regulatory core. To this end, we proposed
Mendoza and Alvarez-Buylla 1998, Laurent and Kellershohn a GRN model grounded on experimental data to test, for
1999). Importantly, multistable systems are necessarily non- the first time, that a multistable GRN could partition the
linear (Ellner and Guckenheimer 2011). space of possible configurations of gene expression states
in a manner consistent with that seen in the different cell
Floral organ primordial cell-fate specification. As a first example types of the floral meristem. This model demonstrated that
of the nonlinear perspective to plant development, we have in a real biological case, cellular phenotypes could indeed
developed a cellular level model of cell-fate determination correspond to different attractors or stable configurations of
during floral-organ specification in Arabidopsis thaliana (see gene expression states (Mendoza and Alvarez-Buylla 1998).
figures 1 and 2; Mendoza and Alvarez-Buylla 1998, Espinosa- This GRN was first published on the basis of limited avail-
Soto et al. 2004, Alvarez-Buylla et al. 2010a, Azpeitia et al. able experimental data; however, since then, it has been
2014). Most flowers have four types of floral organs that are updated to incorporate additional data as they become avail-
formed with a stereotypical pattern from the outside to the able (Espinosa-Soto et al. 2004, Alvarez-Buylla et al. 2010a).
is further elaborated below, using other examples at higher Further simulation studies were performed to postulate
levels of organization. novel missing interactions (Azpeitia et al. 2013). Some of the
interactions were later corroborated by independent experi-
Root stem-cell differentiation and spatial patterning. Stem-cell mental studies (Azpeitia et al. 2013), once again document-
niches (SCN) are fundamental for multicellularity; they ing the predictive power of GRN models. In this case, the
include proliferation and differentiation capabilities at the spatial arrangement of each gene-expression configuration
same time and in restricted spatial domains. These cel- associated with each type of stem cell was also recovered
lular structures have generic traits of cellular organization by incorporating the patterns of intercellular movements
conserved in plants and animals, suggesting underlying bio- for some of the SCN–GRN components (Azpeitia et al.
generic mechanisms (Sablowski 2004, Azpeitia and Álvarez- 2011). Interestingly, the network of networks that followed
Buylla 2012). Conserved patterns include the position of the the intracellular configuration for each cell at each spatial
organizer cells at the center of the SCN that have very low location (40 nodes) converged to a single robust attractor
rates of proliferation. These cells are surrounded by stem that mimicked the spatial arrangement of different gene-
cells with slightly higher proliferation rates that first transit expression configurations observed in the actual Arabidopsis
to a domain of active proliferation, then to one of elonga- root SCN. Ongoing research is explicitly incorporating into
tion, and later on to one of differentiation. Plant SCNs are this model hormone signaling, cell proliferation, and other
more amenable to in vivo experimental studies than those components to understand how SCN size is established and
on animals. Therefore, they may be useful for uncovering spatiotemporally maintained during development.
such biogeneric mechanisms. We have used the root SCN The results of all these models for single cells and static
for integrating a dynamic GRN model based on available spatial domains have been useful to support the hypothesis
data. We used the model to test the sufficiency of uncovered that cell types emerge naturally as self-organized properties
pathways and then proposed a regulatory module able to of the underlying molecular regulatory network, as well as
recover the gene-expression configurations characteristic additional restrictions that couple GRN dynamics, such as
of the four precursor stem cell types or initial cells: vascu- cell–cell movement of some of the networks components or
lar initials, cortex–endodermis initials, quiescent center, cell geometry (figures 1 and 2).
and columella—that is, epidermis-lateral root cap initials The detailed analysis of the proposed models through
(figure 2; for details, see Azpeitia et al. 2010). This study virtual mutation experiments provides insights into the
showed that the two pathways that had been thought to be impact on pattern formation that the different genes within
both necessary and sufficient to recover the cell types and the GRN can have. Importantly, it demonstrates that such
their spatial patterns within the root SCN are not sufficient. effects depend on the whole regulatory system rather than
on individual genes or molecular components. Certain genes influence, a noise effect that varies randomly each time.
reach the master title when their strong effect on the phe- Introducing stochasticity into nonlinear dynamical models
notype is described experimentally in developmental func- has provided interesting results, suggesting, for example,
tional genetic studies (see, e.g., Williams and Fletcher 2005). that noise may play a constructive role in biology and that
Dynamical GRN models enable a system-level mechanistic present-day biological networks might have evolved in noisy
interpretation to their apparent “more relevant” role in conditions (Álvarez-Buylla et al. 2008, Tawfik 2010). In order
development—relative to the other genes without the title— to explore this possibility in a plant developmental process,
when their altered expression causes the GRN to attain we studied the role of stochastic perturbations on the GRN
altered stable configurations or attractors. An important underlying floral-organ primordial cell fates. We addressed
contribution of nonlinearity in this respect is the realization, whether such stochastic GRN recovered, in addition to the
through dynamical modeling, of the fact that the quality that observed cell states, the robust temporal morphogenetic pat-
gives their higher rank to master genes is indeed a systemic tern with which such states are attained during early flower
property emerging from the joint effect of the gene in ques- development (Álvarez-Buylla et al. 2008).
tion and its interacting partners and not from itself: Out of In flowering plants, a floral meristem is sequentially
justice to the collaborating genes, perhaps the master title partitioned into four regions from which the floral-organ
should refer to a core regulatory module rather than to a primordia are formed and sequentially give rise to sepals in
gene alone. For example, in the floral-organ specification the outermost whorl; petals in the second; stamens in the
Figure 5. A schematic representation of the epigenetic landscape associated with the GRN for flower development and
uncovered by a stochastic exploration. Cell gene-expression configurations corresponding to the attractors are represented
in the bottom of each basin (in this case, associated with the cell states characteristic of four inflorescence cell types and
four floral organ primordial cell types: sepals, petals, stamens, and carpels). Noise (randomness represented by dice)
or stochastic modeling is used in order to uncover the structure of the landscape, the latter being manifested by the
differential likelihood of cell-state transitions (here represented with arrows).
nodes. Such alterations can result from perturbations in sig- ethylene in the root (figure 2) and can now be integrated
nal transduction pathways or to the physicochemical fields with GRN models and EL reconfiguration analyses.
connected to the GRN under analysis. Models to study how An additional application of EL formalisms to under-
such signaling pathways process information and filter noise standing Arabidopsis developmental mechanisms concerns
(Díaz and Álvarez-Buylla 2009) have been proposed for the GRN that underlies the transition from vegetative
(VM) to inflorescence meristem (IM) and then into flower frameworks that consider various levels of organization and
meristems (FM) at the shoot apical meristem (SAM; morphogenetic patterning.
figure 2; Pérez -Ruiz et al. 2015). In this study, experiments Key to these multilevel models is to postulate processes
on the role of a MADS-box gene, AGAMOUS LIKE14 that generate the cells’ positional information at all times
(AGL12)/XANTAAL2(XAL2), yielded apparently contra- and which produce changes in the operation of the invari-
dictory data. The overexpression lines of this gene pro- ant underlying GRN accordingly. Such models can be used
duced early flowering and at the same time caused a loss to address issues concerning the regulation of the size and
of determinacy in flowers, especially under short days. We dimension of tissues, as well as the relative position of organs
put forward a multistable GRN module that incorporates a (Alvarez-Buylla et al. 2007, Swat et al. 2015). Concordantly,
set of XAL2 interactions able to recover the observed gene we have started to put forward dynamic spatiotemporal
expression profiles in different SAM stages for the main models that consider GRNs in cellularized domains and that
regulators discovered up to now to be involved in such encompass the aforementioned sources of extrinsic con-
developmental processes. We used this model to reconcile straint from fields of mechanic-elastic forces or hormones
and to provide an explanation for the two apparently con- (Alvarez-Buylla et al. 2007, Barrio et al. 2010, 2013).
tradictory phenotypes of the 35S::XAL2 lines. An EL model In addition to understanding how mechanics, geometry,
for the proposed XAL2 GRN module showed that overex- and growth contribute to the formation of functional and
pression of this gene, in the context of the GRN module robust structures (Mirabet et al. 2011), we must consider
Mechanical forces provide cues for heterogeneous cellular Given the nongenetic character of developmental dynam-
behaviors by establishing sources of positional informa- ics, phenotypic variation to a great extent has been neglected
tion, thereby contributing to the regulation of morphogen- in the study of evolution. A deviation from a linear causation
esis (Wolpert 1969, Meinhardt 1982, Alvarez-Buylla et al. view of development would potentially affect the rate and
2007, Barrio et al. 2008, Hamant et al. 2010, Barrio et al. direction of evolution, however (see, e.g., Alvarez-Buylla
2013). Recent work has started to uncover the molecular et al. 2007b, Jaeger et al. 2012). Empirical evidence of
mechanisms by which mechanic-elastic forces are sensed by the evolutionary relevance of network structure and gene
intracellular GRNs (Ning et al. 2009), as well as the role of interaction—and therefore nonlinearity—on evolutionary
myosin, actin, and tubulin fibers in cell structuring and in dynamics at the molecular level is starting to emerge (Balleza
the transduction of changes in mechanical and elastic forces et al. 2008). Evolutionary forces, functional constraints, and
into GRN signals (Hamant et al. 2010, Mammoto et al. 2012, molecular interactions are conditionally dependent on the
Romero et al. 2015). systems level and ensure that small changes within the
GRN can yield large phenotypical alterations (Kauffman
Organogenesis: The cooperative dynamics of 1993, Purugganan 2004, Álvarez-Buylla et al. 2010a, Davila-
physicochemical fields and cell proliferation Velderrain et al. 2014 and references therein). In addition,
in the root the origin of novel core GRNs may underly the emergence
In line with our view on cooperative dynamics, we devel- of evolutionary innovations (Wagner 2015).
impacts of small genetic alterations (see Alvarez-Buylla et al. chemical and physical extrinsic conditions are the focus
2010a). The question of how such critical networks evolved of ongoing research. The possibility of actually accounting
is under active investigation in several research groups (see, experimentally for these physical processes—in an attempt
e.g., Torres-Sosa et al. 2012). It is important to note that the to understand how cellular decisions occur during tissue
dynamical analysis of network models is particularly help- patterning—will go beyond cell culture studies. Multilevel
ful to uncovering the evolutionary relevance of nonlinear approaches, grounded in experimental data, will yield more
regulatory systems. Network dynamics approximate phe- accurate models of morphogenesis during normal devel-
notypical, functional behaviors not directly accessible for opment and also under altered conditions, such as those
the structural properties of gene sequences or static wiring experienced in cancerous growths in humans. Plant systems
diagrams alone. The examples above show how dynamics are promising experimental models to propose and test such
and conventional molecular evolutionary analyses can be models and will continue to illuminate the biogeneric mech-
integrated. anisms at play during both plant and animal development.
Finally, we postulate that the consideration of complex The merging of conceptually clear theories, computa-
networks that incorporate both intracellular, genetic, and tional-mathematical tools, and molecular–genomic data
external components as well as models of cooperative into coherent frameworks is at the basis of a much-needed
physicochemical, cell proliferation, and regulatory dynam- nonlinear, dynamic, system-level explanatory and predic-
ics (Barrio et al. 2013) may also contribute to understand- tive approach to development and to evolution. Once again,
Azpeitia E, Benítez M, Vega I, Villarreal C, Álvarez-Buylla ER. 2010. Single- Goodwin BC. 1994. How the Leopard Changed Its Spots: The Evolution of
cell and coupled GRN models of cell patterning in the Arabidopsis Complexity. Princeton University Press.
thaliana root stem cell niche. BMC Systems Biology 4 (art. 134). Flintoft L. 2005. From genotype to phenotype: A shortcut through the
Azpeitia E, Weinstein N, Benítez M, Mendoza L, Alvarez-Buylla ER. 2013. library. Nature Reviews Genetics 6 (art. 520).
Finding missing interactions of the Arabidopsis thaliana root stem cell Hamant O, Traas J, Boudaoud A. 2010. Regulation of shape and patterning
niche gene regulatory network. Frontiers in Plant Science 4 (art. 110). in plant development. Current Opinion in Genetics and Development,
Azpeitia E, Davila-Velderrain J, Villarreal C, Álvarez-Buylla ER. 2014. Gene 20: 454–459.
regulatory network models for floral organ determination. Pages 441– Huang S, Eichler G, Bar-Yam Y, Ingber DE. 2005. Cell fates as high-dimen-
469 in Riechmann JL, Wellmer F, eds. Flower Development: Methods sional attractor states of a complex gene regulatory network. Physical
and Protocols. Methods in Molecular Biology, vol. 1110. Springer. Review Letters 94 (art. 128701).
Barrio RA, Hernandez-Machado A, Varea C, Romero-Arias JR, Álvarez- Huang S. 2011. Systems biology of stem cells: Three useful perspectives
Buylla ER. 2010. Flower development as an interplay between dynami- to help overcome the paradigm of linear pathways. Philosophical
cal physical fields and genetic networks. PLOS ONE 5 (art. e13523). Transactions of the Royal Society B 366: 2247–2259.
Barrio RA, Romero-Arias JR, Noguez MA, Azpeitia E, Ortiz-Gutiérrez E, Hui KR, Zheng X, Huang L, SchiefelbeinJ. 2013. Computational modeling
Hernández-Hernández, V, Cortes-Poza Y, Álvarez-Buylla ER. 2013. Cell of epidermal cell fate determination systems. Current Opinion in Plant
patterns emerge from coupled chemical and physical fields with cell Biology 16: 5–10.
proliferation dynamics: The Arabidopsis thaliana root as a study system. Jaeger J, Irons D, Monk N. 2012. The inheritance of process: A dynamical
PLOS Computational Biology 9 (art. e1003026). systems approach. Journal of Experimental Zoology B: Molecular and
Benítez M, Espinosa-Soto C, Padilla-Longoria P, Díaz J, Álvarez-Buylla Developmental Evolution 318: 591–612.
ER. 2007. Equivalent genetic regulatory networks in different con- Kaneko K. 2006. Life: An Introduction to Complex Systems Biology.
Rogers ED, Jackson T, Moussaieff A, Aharoni A, Benfey PN. 2012. Cell Wang J, Zhang K, Xu L, Wang E. 2011. Quantifying the Waddington
type-specific transcriptional profiling: Implications for metabolite pro- landscape and biological paths for development and differ-
filing. Plant Journal 70: 5–17. entiation. Proceedings of the National Academy of Sciences 108:
Sablowski R. 2004. Plant and animal stem cells: Conceptually similar, 8257–8262.
molecularly distinct? Trends in Cell Biology 14: 605–611. Wilkins AS. 2008. Waddington’s unfinished critique of neo-Darwinian
Sawyer JM, Harrell JR, Shemer G, Sullivan-Brown J, Roh-Johnson M, genetics: Then and now. Biological Theory 3: 224–232.
Goldstein B. 2010. Apical constriction: A cell shape change that can Williams L, Fletcher JC. 2005. Stem cell regulation in the Arabidopsis shoot
drive morphogenesis. Developmental Biology 341: 5–19.
apical meristem. Current Opinion in Plant Biology 8: 582–586.
Selker JM, Steucek GL, Green PB. 1992. Biophysical mechanisms for morpho- Wolpert L. 1969. Positional information and the spatial pattern of cellular
genetic progressions at the shoot apex. Developmental Biology 153: 29–43. differentiation. Journal of Theoretical Biology 25: 1–47.
Schiefelbein J. 2003. Cell-fate specification in the epidermis: A common Zernicka-Goetz M, Huang S. 2010. Stochasticity versus determinism
patterning mechanism in the root and shoot. Current Opinion in Plant in development: A false dichotomy? Nature Reviews Genetics 11:
Biology 6: 74–78. 743–744.
Sick S, Reinker S, Timmer J, Schlake T. 2006. WNT and DKK determine Zhou JX, Aliyu MDS, Aurell E, Huang S. 2012. Quasi-potential landscape
hair follicle spacing through a reaction–diffusion mechanism. Science in complex multi-stable systems. Journal of the Royal Society Interface
314: 1447–1450. 9: 3539–3553.
Shmulevich I, Kauffman SA, Aldana M. 2005. Eukaryotic cells are dynami-
cally ordered or critical but not chaotic. Proceedings of the National
Academy of Sciences 102: 13439–13444. Elena R. Alvarez-Buylla (ERAB) (eabuylla@gmail.com) is a professor at the
Solé R, Goodwin B. 2008. Signs Of Life How Complexity Pervades Biology: Universidad Nacional Autonoma de Mexico (UNAM), Jose Davila-Velderrain