The transition from the vegetative to reproductive development is a critical event in the plant life cycle. The accurate prediction of flowering time in elite germplasm is important for decisions in maize breeding programs and best agronomic practices. The understanding of the genetic control of flowering time in maize has significantly advanced in the past decade. Through comparative genomics, mutant analysis, genetic analysis and QTL cloning, and transgenic approaches, more than 30 flowering time candidate genes in maize have been revealed and the relationships among these genes have been partially uncovered. Based on the knowledge of the flowering time candidate genes, a conceptual gene regulatory network model for the genetic control of flowering time in maize is proposed. To demonstrate the potential of the proposed gene regulatory network model, a first attempt was made to develop a dynamic gene network model to predict flowering time of maize genotypes varying for specific genes. The dynamic gene network model is composed of four genes and was built on the basis of gene expression dynamics of the two late flowering id1 and dlf1 mutants, the early flowering landrace Gaspe Flint and the temperate inbred B73. The model was evaluated against the phenotypic data of the id1 dlf1 double mutant and the ZMM4 overexpressed transgenic lines. The model provides a working example that leverages knowledge from model organisms for the utilization of maize genomic information to predict a whole plant trait phenotype, flowering time, of maize genotypes.
Citation: Dong Z, Danilevskaya O, Abadie T, Messina C, Coles N, Cooper M (2012) A Gene Regulatory Network Model for Floral Transition of the Shoot Apex in Maize and Its Dynamic Modeling. PLoS ONE 7(8): e43450. https://doi.org/10.1371/journal.pone.0043450
Editor: Frank G. Harmon, USDA-ARS, United States of America
Received: December 27, 2011; Accepted: July 20, 2012; Published: August 17, 2012
Copyright: © Dong et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The authors have no support or funding to report.
Competing interests: The authors have read the journal's policy and have the following conflicts. All the authors are employed by Pioneer Hi-Bred International. There are no patents, products in development or marketed products to declare. This does not alter the authors' adherence to all the PLOS ONE policies on sharing data and materials, as detailed online in the guide for authors.
Flowering time is a major adaptive trait in plants and an important selection criterion in plant breeding . Because this trait is the single most important control of the plant demand for resources and the determinant of the plant's ability to capture resources for growth, understanding the underlying genetic controls is of importance to determine efficient molecular selection strategies. Shoot apical meristem transition from the vegetative to the reproductive stage is controlled by a genetic program that is regulated by environmental and endogenous factors , . Major components of the genetic control system for the flowering time in Arabidopsis thaliana have been defined in the past decades. Genetic Regulatory Network (GRN) models for flowering time control in Arabidopsis have been developed and often presented in graphical form –. Studies in other species –, including maize (Zea mays L.) –, suggest that the basic genetic components of the GRN controlling the floral transition from the vegetative to the reproductive stage are largely conserved.
The understanding of the genetic control of flowering time in maize has advanced significantly in recent years, especially after the completion of the maize genome sequence ,–. Many of the flowering time pathways and genetic elements in these pathways discovered in Arabidopsis and rice (Oriza sativa L.) are conserved in maize. Through comparative genomics, mutant analysis, genetic analysis and Quantitative Trait Locus (QTL) mapping and cloning, and transgenic approaches, more than 30 flowering time candidate genes have been identified in maize. Despite these advances in molecular mechanisms, a synthesis in the form of a GRN in maize is lacking.
The limited understanding of the genetic controls of flowering time in maize in the past decades led to the development of quantitative empirical models that use environmental and genotypic rather than genomic information to predict the floral transition and the timing of pollen shedding and silking in maize. Heat units or growing degree days to shedding and to silking are examples of empirical models widely used to synchronize shedding and silking events in seed production –. When these models were embedded within comprehensive physiological frameworks such as CERES  and APSIM  they were applied to understand the physiological basis of maize adaptation in different environment types, construct trait performance landscapes, and predict responses to trait selection in breeding programs .
Empirical models such as the heat unit model have limitations to predict flowering time for novel genotypes. The advancement in the understanding of the genetic control of flowering time in maize, the availability of GRNs for model organisms, and the conservation of the main components of these GRNs across species suggest the opportunity to build upon models developed for Arabidopsis and rice – to predict flowering time in maize for existing and novel genotypes in diverse environments.
The purpose of this paper is to develop a simple model that will serve as a foundation for Dynamic Gene Network (DGN) modeling of the vegetative to reproductive transition in maize. The overall objectives of this study are: (1) to develop a conceptual model in the form of a GRN of flowering time control in maize, (2) to translate the conceptual GRN model into a quantitative DGN model, and (3) to demonstrate and evaluate the prediction of flowering time of maize genotypes varying for specific genes. First, a GRN is proposed based on a synthesis of the literature for flowering time candidate genes and their interactions. Second, a quantitative DGN model is described. Third, the DGN model is evaluated against field experimental data for flowering time of novel genotypes created from allelic variation for specific genes and from expression of transgenes.
Materials and Methods
Plant materials and trait phenotypes
A segregating population (id1/+ dlf1/+) for dlf1 and id1 mutant alleles was constructed by crossing the heterozygous dlf1/+ plants to the heterozygous id1-m1/+ plants in the B73 genetic background. Heterozygous plants were identified by the PCR genotyping method  and self pollinated for generating the homozygous id1 and dlf1 single mutants and the id1 dlf1 double mutant. Leaf tissues of the offspring plants were taken around the V8–V10 stage for genotyping. The genotypes of individual plants were confirmed by PCR genotyping. Construction of the ZMM4 transgenic lines in the B73, the dlf1 and id1 single mutant genetic backgrounds was described in detail by Danilevskaya et al. .
In order to obtain total leaf number (TLN) observations, plants of different genotypes grown in field conditions at the Pioneer Johnston research farm were tagged. The fifth leaf and the tenth leaf, and sometimes the fifteenth leaf, of the tagged plants were identified by cutting the respective leaf tips during the first half of the growing season. TLN observations of all tagged plants were obtained at or after flowering. TLN data for plants with the same genetic composition were combined and the mean and standard error statistics were estimated.
Tissue sampling and mRNA expression measurement
Plants of the id1 and dlf1 mutants, the Gaspe Flint landrace, and the B73 inbred for tissue sampling were grown in a greenhouse at 25°C under 16-h day length. The V-stages were determined based on the topmost liguled leaf. Tissue samples of shoot apices were taken from the emergence stage for the Gaspe Flint landrace or the V1–V3 stage for the mutants and the B73 inbred until about one week after flowering. The intervals between two sampling times and the total number of sampling times were determined by genotypes and developmental stages. Total RNA was isolated with TRIzol Reagent in combination with Phase Lock gel. The ZMM4 mRNA expression levels were measured by the GenomeLab GeXP analysis system at Althea Technologies. The raw RNA expression data were normalized against α-tubulin as the internal control within the same reaction. More details were described in Danilevskaya et al. .
Construction of the Conceptual Gene Regulatory Network
A large number of QTL mapping studies for maize flowering time have demonstrated the complexity of the genetic architecture of this trait ,–. In contrast to Arabidopsis, for which more than 100 flowering time genes were characterized ,, only a few QTLs and mutants have been cloned in maize, and a number of homologs from other species have been identified through comparative genomics. This limited knowledge constrains our ability to fully define the topology of a GRN for flowering time in maize. The consensus GRN for Arabidopsis , could be used as a scaffold to organize the limited knowledge in maize into a first logical synthesis. Using the framework provided by the Arabidopsis GRN, maize flowering time candidate genes were organized by pathways (Table 1) and discussed below.
Light is an important environmental signal implicated in the regulation of flowering time of plants. In maize, early flowering of many temperate inbred lines is associated with reduced response to light . Phytochromes are the primary red/far-red photoreceptors, with three pairs discovered in maize, PHYA1/2, PHYB1/2, and PHYC1/2 . phyB mutants flower earlier than lines that carry functional copies of PHYB1 and PHYB2. PHYB genes were implicated in the perception and transduction of photoperiod, thus playing a role in the delay of floral transition and flowering time under long day conditions . The gene ZmHY2 (Table 1), homologous to the Arabidopsis HY2 gene, encodes a phytochromobilin synthase . A point mutation in this gene, i.e., elongated mesocotyl1 mutant, prevents synthesis of the phytochrome chromophore and is light insensitive and exhibits early flowering .
Many physiological processes in plants are regulated to match daily and seasonal external changes through the endogenous timekeeper known as the circadian clock ,. The molecular mechanism of the circadian clock is largely preserved across plant species ,–. Because of a recent polyploidization event that resulted in duplications of a large number of maize genomic segments , there are multiple copies of homologues of the Arabidopsis circadian clock core genes in the maize genome. Studies show that 10–23% of expressed transcripts in maize exhibit diurnal oscillations ,. The maize circadian clock regulates genetic networks controlling key physiological processes, such as carbon fixation, cell wall synthesis, phytohormone biosynthesis, flowering time, and phototropism .
Candidate genes in the core oscillator of the maize circadian clock include ZmCCA1, ZmLHY, ZmTOC1a, ZmTOC1b, ZmPRR73, ZmPRR37, ZmPRR59, GIGZ1a, GIGZ1b, ZmFKF1a and ZmFKF1b, which are homologous to their counterparts in Arabidopsis and rice (Table 1). The diurnal expression patterns of these key components at the mRNA and protein levels are largely conserved across plant species . A detailed study of ZmCCA1 and ZmTOC1 confirmed that they are the key components in the maize circadian clock .
Photoperiod transduction pathway
To date, a few candidate genes involved in the photoperiod transduction pathway of maize have been published. They are CONZ1 (also known as ZmCO1), ZmCCT and ZCN8 (Table 1) ,,. CONZ1 and its upstream genes GIGZ1a and GIGZ1b exhibit diurnal expression patterns similar to their homologues in Arabidopsis and rice. Maize is able to perceive the differences in photoperiod through the distinct expression patterns of CONZ1 in long and short days . ZmCCT is homologous to the rice photoperiod response regulator Ghd7 and plays a critical role in maize photoperiod response . Teosinte ZmCCT alleles are consistently expressed at higher level and confer later flowering than temperate maize alleles under long day condition. ZCN8 is homologous to Arabidopsis FT and rice Hd3a and RFT1 and may function as the florigen in maize . The mRNA transcript of the maize ZCN8 exhibits strongly up-regulated diurnal oscillation in leaves under inductive short days in photoperiod-sensitive tropical lines and a weak diurnal pattern in day-neutral temperate lines. Lines of evidence suggest that ZCN8 protein moves through the phloem to the shoot apical meristem to induce transition from the vegetative to the reproductive development. Transgenic plants carrying an overexpressed ZCN8 gene flower earlier than the wild type. Down-regulation of ZCN8 via artificial microRNA induces a late flowering phenotype. ZCN8 was placed downstream of ID1 and upstream of DLF1 .
The regulatory relationship between CONZ1 and ZCN8 in maize is unknown. Deciphering the similarity with that observed between Hd1 and Hd3a in rice will help frame the flowering response to photoperiod observed in maize within the context of the external and internal coincidence models. The underlying molecular mechanism inside the external and internal coincidence models consists in the form of blue-light dependent FKF1 and GI protein complex, which regulates the timing of CO expression (internal coincidence) and stabilization and activation of the CO protein by light (external coincidence) –. The Arabidopsis CO-FT module is conserved in long-day plants, such as barley (Hordeum vulgare), wheat (Triticum aestivum) and poplar (Populus alba) , while the module is altered or missing in short-day plants, such as rice , and Pharbitis nil .
The maize genes ID1 and ZmLD have been cloned and characterized at the molecular level, and may function in the autonomous pathway to positively regulate flowering time.
ID1 (Table 1), a zinc finger transcription factor, is only expressed in immature leaves. It is believed to be unique in cereal crops because its homologous counterparts are only found in rice and other grass species – but not in Arabidopsis. Loss-of-function id1 mutant produces more leaves and flowers much later with aberrant floral organs . Because ID1 expression is not altered by photoperiod and is developmentally regulated it is plausible that ID1 works through the autonomous pathway to regulate flowering time . The downstream targets of the ID1 gene may play a role in facilitating the movement of the ZCN8 protein through the phloem to the shoot apical meristem . Alternatively, ID1 may function in the floral induction through a CO/FT independent pathway .
ZmLD (Table 1), homologous to an autonomous gene LD in Arabidopsis, is expressed in the shoot apex and developing inflorescences in maize . It may function in the autonomous pathway through some unknown mechanism in maize because there is no maize homolog of the Arabidopsis FLC gene, which integrates signals from the autonomous and vernalization pathways in Arabidopsis .
Higher plants experience a series of phase transitions during their life cycle. At early stages of development the transition from the juvenile phase to the adult phase is the most significant developmental event. During this transition period a plant becomes competent for reproductive development . In maize, the transition from the juvenile phase to the adult phase has a significant impact on the total leaf number, which is tightly associated with flowering time –. The genetic module in Arabidopsis that governs this phase transition was named the aging pathway . There are two key miRNA gene families in this pathway, namely miR156 for suppression of and miR172 for promotion of the phase change ,. The expression of the two miRNA families is negatively correlated, that is, miR156 expression is higher in younger tissues while miR172 expression is higher in adult tissues .
miR156 (Table 1), as a juvenile gene, regulates the transition from the juvenile phase to the adult phase through repression of SQUAMOSA PROMOTER BINDING PROTEIN LIKE (SPL) gene expression . Expression of specific members of the miR156 gene family is repressed by a developmental regulation factor produced in leaf primordia . In contrast, miR172 (Table 1) promotes the transitions between developmental phases and is involved in specifying floral organ identity by downregulating AP2-like target genes, such as GLOSSY15 (GL15)  and ZmRAP2.7 –.
Gibberellin (GA) is an endogenous plant growth regulator that affects both growth and development. DWARF8 and DWARF9 (Table 1) encode proteins with SH2-like domain and DELLA domain , and are homologous to the Arabidopsis gene GIBBERELLIC ACID INSENSITIVE (GAI) gene. Studies show that DWARF8 is associated with the variation in flowering time in temperate inbred lines , and is involved in maize climatic adaptation through selection for flowering time . A gain-of-function dwarf9-1 mutant exhibits a late flowering phenotype in maize while the same allele in transgenic Arabidopsis lines causes the opposite phenotype . Another transcription factor gene KNOTTED1 (KN1, Table 1) negatively modulates the accumulation of gibberellins through regulating the gene GA2ox1, which encodes for an enzyme that inactivates GA .
A group of genes are responsible for the integration of all floral inductive or repressive signals and for the activation of floral organ identity genes, such as LFY and AP1 in Arabidopsis –. Candidate genes in maize implicated in integrating floral signals from different pathways include DLF1, ZMM4, ZmRAP2.7, ZFL1, ZCN2, and ZAP1 (Table 1) ,,,–.
DLF1 (Table 1), homologous to FLOWERING LOCUS D (FD) in Arabidopsis, encodes a bZIP protein that mediates floral inductive signals at the shoot apical meristem in maize. Loss-of-function dlf1 mutant flowers late, indicating that DLF1 promotes the floral transition. Gene transcript expression analysis reveals that DLF1 transcript increases and peaks at the floral transition, which indicates that DLF1 is involved in a positive feedback loop to promote the floral transition . In the shoot apical meristem, the DLF1 and ZCN8 proteins may form a complex, which is comparable to the FD and FT protein complex in Arabidopsis, to activate downstream floral organ identity genes, such as ZMM4 ,.
ZMM4 (Table 1) is a maize MADS-box gene in the FUL1 family that regulates floral transition in temperate cereals . Through double mutant analysis, ZMM4 is positioned functionally downstream of the flowering time genes DLF1 and ID1. Analysis of overexpressed transgenic lines indicates that ZMM4 promotes floral transition and inflorescence development in maize . Its mRNA expression initiates in leaf primordia of the vegetative shoot apices, increases during the elongation of the shoot apical meristem, peaks around the time of the spikelet branch meristem initiation, and then declines as inflorescence development progresses . The precise regulatory mechanism of the ZMM4 gene expression is still elusive. It could involve positive and negative feedback loops, which may be comparable to the feedback loops among the LFY, AP1/FUL1 and CAL genes in Arabidopsis ,,.
ZCN2 (Table 1), homologous to the Arabidopsis TFL1, is a member of the maize PEBP gene family . It acts as a maintainer of meristem indeterminacy. Overexpression of ZCN2 causes delayed flowering and altered inflorescence architecture .
ZmRAP2.7 (Table 1), homologous to the Arabidopsis TARGET OF EAT1 (TOE1), is a negative regulator of flowering time in maize ,[77,93]. The flowering time QTL VGT1 functions as a cis-regulatory element of the ZmRAP2.7 gene by down-regulating its mRNA transcript abundance . VGT1 is mapped to chromosome arm 8L in the cross of the Gaspe Flint landrace and the N28 inbred. The Gaspe Flint allele reduces the flowering time, number of leaves, and plant height in the N28 background .
ZFL1 and ZFL2 (Table 1) affects the floral transition time and development in maize in a similar manner to their homolog LEAFY found in Arabidopsis . Double mutant analysis shows that ZFL1 and ZFL2 act as upstream regulators of the ABC floral organ identity genes . Association mapping results show that ZFL1 is strongly associated with flowering time .
ZAP1a (Table 1) is homologous to the floral homeotic gene AP1 in Arabidopsis  and ZAP1b (known as ZmMADS3, Table 1) is orthologous to ZAP1a . The ZAP1 expression pattern is restricted to terminal and axillary inflorescences and it is consistent with that observed for Arabidopsis AP1 . Studies show their functions in floral organ identity and development ,. Overexpression of ZAP1b reduces the total leaf number and plant height .
A conceptual gene regulatory network model for flowering time control in maize
A conceptual GRN model for flowering time control in maize is proposed as a first synthesis of our current knowledge (Figure 1). Candidate genes are grouped into multiple pathways as described above (Table 1) based on their confirmed relationships and hypothetical relationships derived from Arabidopsis and rice through comparative genomics. Genes with unclear regulatory relationships are placed into the boxes without any input and output.
The GRN model is divided into two components: leaf and shoot apical meristem (SAM). It includes several pathways: light transduction, circadian clock, photoperiod, autonomous, aging, GA pathways and pathway integration. Thick lines are confirmed by genetic analysis. Thin lines are based on comparative genomics. Arrows between genes stand for promotion or activation. T bars between genes stand for inhibition or suppression. Dashed lines stand for putative relationships derived through comparative genomics. Genes highlighted in yellow background are selected for the DGN modeling.
Upstream pathways include receptors that sense environmental cues and usually operate in leaves. Signals from the photoperiod and autonomous pathway are physically transduced from leaves to the shoot apical meristem by ZCN8 protein via movement through the phloem. Accumulation of a threshold amount of ZCN8 protein triggers the reprogramming in the shoot apical meristem which stops producing leaves and initiates the tassel development. Known key integrator genes in maize are DLF1 and ZMM4.
Dynamic Gene Network Modeling
Discrete and/or continuous DGN modeling approaches can contribute to solve the genome-to-phenome prediction problem –. Boolean networks, one form of a discrete DGN model, have been extensively applied to GRN models –. In Boolean networks, each node denotes a gene. All nodes have binary values, 0 or 1, that represent the active or inactive state of a gene. The linkages between nodes represent regulatory relationships of a gene with other genes within a given GRN. In continuous DGN modeling, a system of ordinary differential equations is employed to describe the behavior of a GRN and predict phenotypes based on the expression level of genes at the convergent point. The two approaches were combined to model gene networks around the promoter of the endo 16 gene in the sea urchin . Simple algorithms that combine logic and algebraic functions can capture major features of this promoter's behavior ,. The methodology that combines logic and algebraic functions was adapted and applied to the prediction of flowering time of maize genotypes in this study.
A dynamic gene network model to predict floral transition time in maize
Based on the regulatory relationships shown in the simplified GRN for maize (Figure 2), four key components of the network (ID1, DLF1, VGT1 and ZMM4) were selected to develop a DGN model to predict the floral transition time in maize. The proposed DGN model includes an ordinary differential equation and can simulate the ZMM4 mRNA expression pattern, which in turn is associated with the floral transition time of maize genotypes varying for specific genes.
The simplified GRN model includes the confirmed relationships through genetic analysis, putative relationships derived through comparative genomics, and the proposed ZMM4 positive feedback loop. Arrows between genes stand for promotion or activation. T bars between genes stand for inhibition or suppression. Solid lines stand for confirmed relationships while dashed lines stand for putative relationships. Genes highlighted in yellow background are included in the DGN model.
The terms used to construct the differential equation model are justified here. The gene ID1 regulates ZMM4 expression through two paths: 1) the DLF1-dependent path via regulation of the ZCN8 protein movement through the phloem and 2) the direct autonomous path. Because the ZCN8 and DLF1 proteins combine to form a protein complex to regulate the ZMM4 expression, the interaction between ZCN8 and ID1 can be substituted by a term that represents the interaction between ID1 and DLF1. The model includes two regulatory terms to account for the effect of ID1 alone on flowering time and the combined effect that results from the interaction between ID1 and DLF1. The regulatory relationship between VGT1 and ZMM4 is through ZmRap2.7. The double suppression relationship can be substituted by a positive term only involving VGT1. As discussed earlier, there is plausible positive feedback mechanism that governs the regulation of the ZMM4 gene expression before the floral transition and generates the exponential ZMM4 mRNA expression pattern. A feedback term involving ZMM4 mRNA expression is included in the model as a parsimonious approach to describe the observed growth pattern of the ZMM4 mRNA transcript. Because all the regulatory relationships shown in the GRN (Figure 2) independently converge at the ZMM4 node, all the terms can be added for mathematical convenience.
The presence of a gene in regulatory relationships can be expressed as a continuous quantity or as discrete binary values based on the nature of the gene and related relationships. In this study, discrete binary values, 0 and 1, for ID1, DLF1 and VGT1 were used (see detail in Table 2).
The peak of the ZMM4 mRNA expression in shoot apices synchronizes well with the floral transition and is consistent across the genotypes (Figure 3). Therefore, the ZMM4 gene will be used as a marker to indicate the floral transition and further to associate its expression level with the whole plant trait phenotype, days to floral transition or tassel initiation (DTI). In the final form of the DGN model, the ZMM4 mRNA expression level (mZMM4) was directly associated with the floral transition status (FTS) of the genotypes under investigation as follows.(1)where, mZMM4 stands for the mRNA expression level of the ZMM4 gene. ID1, DLF1, and VGT1 stand for allele status of the ID1, DLF1, and VGT1 genetic elements (Table 2). FTS stands for the floral transition status; 0 indicates the floral transition has not occurred while 1 indicates the floral transition has been reached. The floral transition time or DTI is the number of days from planting to when FTS equals 1. The coefficients, α1, α2, α3, β, and ω, are parameters in the model, which represents the strength or weight of the gene effects or the ZMM4 feedback effect.
Scaled ZMM4 mRNA expression levels in shoot apices before and around the floral transition in four genotypes (the Gaspe Flint landrace, the dlf1 mutant, the B73 inbred, and the id1 mutant) were plotted against days after planting. Filled squares are the observed mRNA expression levels whereas open circles are the predicted mRNA expression levels. The time to the floral transition of each genotype is indicated by arrows.
Parameterization of the dynamic gene network model
Four genotypes with contrasting flowering time phenotypes were chosen to parameterize the model. They are the extreme early flowering landrace Gaspe Flint, which carries the early flowering allele of the QTL VGT1, the temperate inbred line B73 and the late flowering homozygous id1 and dlf1 mutants.
Levels of the ZMM4 gene expression were scaled to a range of 0.0 to 1.0 across all genotypes before and at the floral transition. The ZMM4 expression levels and DTI were used to parameterize the DGN model in Eq. 1. The multi-target objective function used in the optimization is shown in the Eq.2.(2)where, RNApg,i and RNAog,i stand for predicted and observed ZMM4 mRNA expression levels at the ith sampling time for the gth genotype; DTIpg and DTIog stand for predicted and observed DTI for the gth genotype; g is a loop variable for genotypes and its value ranges from 1 to 4; i is a loop variable for the sample time (ng) of each genotype; SSEg, SSEp, and SSE stand for sum of squared errors for gene expression data, phenotypic data, and the sum of both, respectively. The Euler integration method was employed to numerically integrate the differential equation model in Eq. 1. The time step used in the numerical integration was 0.01 d. The mZMM4 initial value was set to zero to reflect the negligible size of the plant at t = 0.0 d. The Nelder-Mead downhill simplex method , was used to estimate the model parameters.
Table 3 lists the estimated parameter values. The coefficient of ID1 is assumed to be 1, the parameter α2 stands for the impact of ID1 and DLF1 combination while the parameter α3 stands for the impact of VGT1 alone. The parameter β is considered as the basal synthesis rate of the ZMM4 gene. By comparing the values of the coefficients, it is evident there is a large impact of VGT1 relative to the impact of DLF1 and ID1 combination and the impact of ID1 alone. The parameter ω has a positive value that indicates a positive feedback loop reinforced by other integrators at a switching point before the floral transition. The parameter α1 is a scaling factor that influences the size of the gene effects, including the basal synthesis of the ZMM4 gene, relative to the effect of the positive feedback loop. Thus, the smaller value of the parameter α1 relative to that of the parameter ω indicates the strong effect of the positive feedback loop.
Evaluation of the dynamic gene network model
Novel genotypes, defined here as genotypes not used to parameterize the model, were utilized to evaluate the capacity of the DGN model to predict floral transition. Although the DGN model was developed to predict the time of transition of the shoot apical meristem from the vegetative to the reproductive stage, the model was evaluated based on observations on TLN. The rationale for this is that TLN is easier to measure and a more stable measurement across environments than DTI . The process that links these two phenotypes is the rate of the leaf differentiation within the shoot apical meristem prior to the transition to the reproductive stage. Thus, the number of leaves present in the mature plants provides an accurate quantitative measurement of the time to floral transition. Phenotypic data for TLN were collected for the id1 dlf1 double mutant created in the B73 genetic background, single mutants alone, the wild type, and the PROUBI:ZMM4 overexpressed lines in the B73, dlf1 and id1 mutant genetic backgrounds (Figure 4). All data were collected in the same field conditions at a single location .
Different shapes represent different genotypes: open diamonds for the Gaspe Flint landrace, filled diamonds for the id1 dlf1 double mutant, open triangles for the B73 inbred line, filled triangles for the PROubi:ZMM4 B73 transgenic line, open squares for the dlf1 mutant, filled squares for the PROubi:ZMM4 dlf1 transgenic line, open circles for the id1 mutant, and filled circles for the PROubi:ZMM4 id1 transgenic line. The vertical bar of each point represents the standard error of the observations for a given genotype. The straight line represents the best linear fit between the observed TLN and the predicted DTI.
Predictions for all genotypes except for the PROUBI:ZMM4 transgenic lines were made by using the DGN model (Eq. 1) as parameterized above. Because the PROUBI:ZMM4 transgenic lines overexpressed ZMM4 cDNA by means of the maize constitutive ubiquitin promoter, significantly higher levels of the ZMM4 mRNA transcript are expected than in non-transgenic lines. To accommodate the constitutive expression of the transgenic ZMM4 gene, a conservative assumption was made to predict DTI for the PROUBI:ZMM4 transgenic lines. The coefficient β, the ZMM4 basal synthesis rate (Eq.1), was multiplied by 2 to represent the expression of two copies of the ZMM4 gene, the native and the transgenic copies.
The correlation between the predicted DTI and the observed TLN (R2 = 0.86, Figure 4) is comparable to what Russell and Stuber observed in the field for a diverse set of maize genotypes (R2 = 0.87) . The DGN model derived from a data set of single mutants can predict the trait phenotype of novel genotypes, such as the double mutant and the overexpressed transgenic lines. This result is encouraging but limited to the prediction of effects of the selected genes.
Assuming that the ZMM4 gene regulates the floral transition through the timing of the transition but not the rate of the leaf initiation, the predicted DTI of the PROUBI:ZMM4 transgenic lines should randomly scatter around the fitted line in Figure 4. However, all but one predicted DTI of the PROUBI:ZMM4 transgenic lines are under the fitted line. This implies the model overestimated DTI for the PROUBI:ZMM4 transgenic lines. We attribute this less accurate predicted result to an inadequate assumption about the expression level of the transgenic ZMM4 gene under the maize ubiquitin promoter. Multiplying the coefficient β by 2 most likely underestimated the expression level of the transgenic ZMM4 gene in the transgenic plants thus increasing the predicted DTI (Figure 4). Additional terms to accommodate effects of different promoters on gene expression could be formalized within the DGN models.
This paper proposes a synthesis of our current knowledge of genetic determinants of flowering time in maize in the form of a GRN. This model can serve as a foundation to build upon as new genetic knowledge becomes available and to guide future studies. The process of model building demonstrated a realized opportunity that leveraged learning and networks created for Arabidopsis to organize knowledge and thoughts in a crop species such as maize. Despite different biological processes among species and processes being missing altogether in maize, the network topology identified in Arabidopsis provided fundamental insights to organize the knowledge created for maize. The conceptual GRN model provides the basic knowledge to conduct a rudimentary quantitative modeling exercise. The resulting DGN model is a step forward relative to current empirical models utilized to predict flowering time in maize. The performance of the simple model is encouraging and suggests there is an opportunity to develop quantitative models that transparently map genes and their effects to whole plant phenotypes. Numerous paths could be foreseen to advance this quantitative model with disparate objectives: from simply advancing our understanding of flowering time in maize, to the study of the emergent properties of GRN models, to facilitation of gene discovery, maize breeding and transgenic product development.
Conceived and designed the experiments: ZD OD TA MC. Performed the experiments: ZD OD TA. Analyzed the data: ZD OD. Contributed reagents/materials/analysis tools: ZD OD. Wrote the paper: ZD OD MC TA CM NC.
- 1. Jung C, Müller A (2009) Flowering time control and applications in plant breeding. Trends in Plant Science 14: 563–573. Available:http://www.ncbi.nlm.nih.gov/pubmed/19716745. Accessed 4 January 2011.
- 2. Simpson G, Dean C (2002) Arabidopsis, the Rosetta stone of flowering time? Science 296: 285–289 doi:10.1126/science.296.5566.285.
- 3. Westerman J, Lawrence M (1970) Genotype-environment interaction and developmental regulation in Arabidopsis thaliana I. Inbred lines; Analysis. Heredity 25: 609–627. Available:http://www.nature.com/doifinder/10.1038/hdy.1971.9.
- 4. Blázquez M (2000) Flower development pathways. Journal of Cell Science 113: 3547–3548.
- 5. Ehrenreich I, Hanzawa Y, Chou L, Roe J, Kover P, et al. (2009) Candidate gene association mapping of Arabidopsis flowering time. Genetics 183: 325–335 doi:10.1534/genetics.109.105189.
- 6. Fornara F, De Montaigu A, Coupland G (2010) SnapShot: control of flowering in Arabidopsis. Cell 141: 550–550.e2.
- 7. Liu C, Thong Z, Yu H (2009) Coming into bloom: the specification of floral meristems. Development 136: 3379–3391. Available:http://www.ncbi.nlm.nih.gov/pubmed/19783733. Accessed 11 January 2011.
- 8. Song Y, Ito S, Imaizumi T (2010) Similarities in the circadian clock and photoperiodism in plants. Current Opinion in Plant Biology 13: 594–603. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2965781&tool=pmcentrez&rendertype=abstract. Accessed 10 January 2011.
- 9. Izawa T, Takahashi Y, Yano M (2003) Comparative biology comes into bloom: genomic and genetic comparison of flowering pathways in rice and Arabidopsis. Current Opinion in Plant Biology 6: 113–120 doi:10.1016/S1369-5266(03)00014-1.
- 10. Tsuji H, Tamaki S, Komiya R, Shimamoto K (2008) Florigen and the photoperiodic control of flowering in rice. Rice 1: 25–35. Available:http://www.springerlink.com/index/10.1007/s12284-008-9005-8. Accessed 9 March 2011.
- 11. Kong F, Liu B, Xia Z, Sato S, Kim BM, et al.. (2010) Two coordinately regulated homologs of FLOWERING LOCUS T are involved in the control of photoperiodic flowering in soybean. Plant physiology 154: 1220–1231. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2971601&tool=pmcentrez&rendertype=abstract. Accessed 24 March 2011.
- 12. Andersen C, Jensen C, Petersen K (2004) Similar genetic switch systems might integrate the floral inductive pathways in dicots and monocots. Trends in Plant Science 9: 105–107 doi:10.1016/j.tplants.2004.01.002.
- 13. Cockram J, Jones H, Leigh F, O'Sullivan D, Powell W, et al.. (2007) Control of flowering time in temperate cereals: genes, domestication, and sustainable productivity. Journal of Experimental Botany 58: 1231–1244. Available:http://www.ncbi.nlm.nih.gov/pubmed/17420173.
- 14. Colasanti J, Coneva V (2009) Mechanisms of floral induction in grasses: something borrowed, something new. Plant Physiology 149: 56–62. Available:http://www.ncbi.nlm.nih.gov/pubmed/19126695.
- 15. Greenup A, Peacock W, Dennis E, Trevaskis B (2009) The molecular biology of seasonal flowering-responses in Arabidopsis and the cereals. Annals of Botany 103: 1165–1172. Available:http://www.ncbi.nlm.nih.gov/pubmed/19304997.
- 16. Lagercrantz U (2009) At the end of the day: a common molecular mechanism for photoperiod responses in plants? Journal of Experimental Botany 60: 2501–2515.
- 17. Colasanti J, Muszynski M (2009) The maize floral transition. In: Bennetzen JL, Hake SC, editors. Handbook of Maize: Its Biology. New York, NY: Springer New York. 41–55. Available:http://www.springerlink.com/index/10.1007/978-0-387-79418-1. Accessed 20 January 2011.
- 18. McSteen P, Laudencia-Chingcuanco D, Colasanti J (2000) A floret by any other name: control of meristem identity in maize. Trends in Plant Science 5: 61–66 doi:10.1016/S1360-1385(99)01541-1.
- 19. Meng X, Muszynski M, Danilevskaya O (2011) The FT-like ZCN8 gene functions as a floral activator and is involved in photoperiod sensitivity in maize. The Plant Cell 23: 942–960 doi:10.1105/tpc.110.081406.
- 20. Buckler E, Holland J, Bradbury P, Acharya C, Brown P, et al. (2009) The genetic architecture of maize flowering time. Science 325: 714–718.
- 21. Schnable P, Ware D, Fulton R, Stein J, Wei F, et al. (2009) The B73 maize genome: complexity, diversity, and dynamics. Science 326: 1112–1115.
- 22. Bonhomme R, Derieux M, Edmeades G (1994) Flowering of diverse maize cultivars in relation to temperature and photoperiod in multilocation field trials. Crop Science 34: 156–164.
- 23. Dijkhuis F (1956) Computation of heat unit accumulations in maize for practical application. Euphytica 5: 267–275.
- 24. Ferwerda F (1953) Methods to synchronize the flowering time of the components in crossing plots for the production of hybrid seed corn. Euphytica 2: 127–134.
- 25. Ritchie JT (1986) The CERES-Maize model. In: Jones CA, Kiniry JR, editors. CERES Maize: A simulation model of maize growth and development. Texas A&M Univ. Press, College Station, TX. 1–6.
- 26. Hammer GL, van Oosterom E, McLean G, Chapman SC, Broad I, et al.. (2010) Adapting APSIM to model the physiology and genetics of complex adaptive traits in field crops. Journal of experimental botany 61: 2185–2202. Available:http://www.ncbi.nlm.nih.gov/pubmed/20400531. Accessed 9 March 2011.
- 27. Messina CD, Podlich D, Dong Z, Samples M, Cooper M (2010) Yield-trait performance landscapes: from theory to application in breeding maize for drought tolerance. Journal of Experimental Botany 62: 855–868. Available:http://www.ncbi.nlm.nih.gov/pubmed/21041371. Accessed 18 November 2010.
- 28. Welch SM, Dong Z, Roe J, Das S (2005) Flowering time control: gene network modelling and the link to quantitative genetics. Australian Journal of Agricultural Research 56: 919–936. Available:http://www.publish.csiro.au/?paper=AR05155.
- 29. Koduru P, Dong Z, Das S, Welch SM, Roe J, et al.. (2008) A multiobjective evolutionary-simplex hybrid approach for the optimization of differential equation models of gene networks. IEEE Transactions on Evolutionary Computation 12: 572–590. Available:http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4469887.
- 30. Wilczek A, Roe J, Knapp M, Cooper M, Lopez-Gallego C, et al. (2009) Effects of genetic perturbation on seasonal life history plasticity. Science 323: 930–934.
- 31. Muszynski M, Dam T, Li B, Shirbroun D, Hou Z, et al. (2006) delayed flowering1 encodes a basic leucine zipper protein that mediates floral inductive signals at the shoot apex in maize. Plant Physiology 142: 1523–1536.
- 32. Danilevskaya O, Meng X, Selinger D, Deschamps S, Hermon P, et al.. (2008) Involvement of the MADS-box gene ZMM4 in floral induction and inflorescence development in maize. Plant Physiology 147: 2054–2069. Available:http://www.plantphysiol.org/cgi/content/abstract/147/4/2054. Accessed 23 March 2011.
- 33. Chardon F, Virlon B, Moreau L, Falque M, Joets J, et al.. (2004) Genetic architecture of flowering time in maize as inferred from quantitative trait loci meta-analysis and synteny conservation with the rice genome. Genetics 168: 2169–2185. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1448716&tool=pmcentrez&rendertype=abstract. Accessed 25 January 2011.
- 34. Coles N, McMullen M, Balint-Kurti P, Pratt R, Holland J (2010) Genetic control of photoperiod sensitivity in maize revealed by joint multiple population analysis. Genetics 184: 799–812. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2845347&tool=pmcentrez&rendertype=abstract. Accessed 21 July 2010.
- 35. Salvi S, Castelletti S, Tuberosa R (2009) An updated consensus map for flowering time QTLs in maize. Maydica 54: 501–512.
- 36. Markelz N, Costich D, Brutnell T (2003) Photomorphogenic responses in maize seedling development. Plant Physiology 133: 1578–1591 doi:10.1104/pp.103.029694.quality.
- 37. Sheehan M, Farmer P, Brutnell T (2004) Structure and expression of maize phytochrome family homeologs. Genetics 167: 1395–1405. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1470959&tool=pmcentrez&rendertype=abstract. Accessed 4 September 2010.
- 38. Sheehan M, Kennedy L, Costich D, Brutnell T (2007) Subfunctionalization of PhyB1 and PhyB2 in the control of seedling and mature plant traits in maize. The Plant Journal 49: 338–353. Available:http://www.ncbi.nlm.nih.gov/pubmed/17181778. Accessed 9 September 2010.
- 39. Sawers RJH, Linley PJ, Gutierrez-marcos JF, Delli-bovi T, Farmer PR, et al. (2004) The Elm1 ( ZmHy2 ) gene of maize encodes a phytochromobilin synthase. Plant Physiology 136: 2771–2781 doi:10.1104/pp.104.046417.1.
- 40. Sawers RJH, Linley PJ, Farmer PR, Hanley NP, Costich DE, et al. (2002) elongated mesocotyl1, a phytochrome-deficient mutant of maize. Plant Physiology 130: 155–163 doi:10.1104/pp.006411.1.
- 41. Harmer SL, Hogenesch JB, Straume M, Chang HS, Han B, et al. (2000) 37. 2000. Orchestrated transcription of key pathways in Arabidopsis by the circadian clock. Science 290, 2110–2113. Science 290: 2110–2113.
- 42. McClung C (2010) A modern circadian clock in the common angiosperm ancestor of monocots and eudicots. BMC Biology 8: 55. Available:http://www.biomedcentral.com/1741-7007/8/55.
- 43. Hayes K, Beatty M, Meng X, Simmons C, Habben J, et al.. (2010) Maize global transcriptomics reveals pervasive leaf diurnal rhythms but rhythms in developing ears are largely limited to the core oscillator. PloS ONE 5: e12887. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2944807&tool=pmcentrez&rendertype=abstract. Accessed 9 March 2011.
- 44. Khan S, Rowe S, Harmon F (2010) Coordination of the maize transcriptome by a conserved circadian clock. BMC Plant Biology 10: 126. Available:http://www.ncbi.nlm.nih.gov/pubmed/20576144.
- 45. Murakami M, Tago Y, Yamashino T, Mizuno T (2007) Comparative overviews of clock-associated genes of Arabidopsis thaliana and Oryza sativa. Plant Cell Physiology 48: 110–121.
- 46. Takata N, Saito S, Saito C, Uemura M (2010) Phylogenetic footprint of the plant clock system in angiosperms: evolutionary processes of pseudo-response regulators. BMC Evolutionary Biology 10: 126. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2887406&tool=pmcentrez&rendertype=abstract.
- 47. Gaut B, Doebley J (1997) DNA sequence evidence for the segmental allotetraploid origin of maize. PNAS 94: 6809–6814. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=21240&tool=pmcentrez&rendertype=abstract.
- 48. Wang X, Wu L, Zhang S, Wu L, Ku L, et al.. (2011) Robust expression and association of ZmCCA1 with circadian rhythms in maize. Plant Cell Reports 30: 1261–1272. Available:http://www.ncbi.nlm.nih.gov/pubmed/21327386. Accessed 9 March 2011.
- 49. Miller T, Muslin E, Dorweiler J (2008) A maize CONSTANS-like gene, conz1, exhibits distinct diurnal expression patterns in varied photoperiods. Planta 227: 1377–1388.
- 50. Hung H-Y, Shannon LM, Tian F, Bradbury PJ, Chen C, et al.. (2012) ZmCCT and the genetic basis of day-length adaptation underlying the postdomestication spread of maize. Proceedings of the National Academy of Sciences: 1–9. Available:http://www.pnas.org/cgi/doi/10.1073/pnas.1203189109. Accessed 19 June 2012.
- 51. Samach A, Coupland G (2000) Time measurement and the control of flowering in plants. BioEssays 22: 38–47.
- 52. Sawa M, Nusinow DA, Kay SA, Imaizumi T (2007) FKF1 and GIGANTEA complex formation is required for daylength measurement in Arabidopsis. Science: 261–265.
- 53. Sawa M, Kay SA, Imaizumi T (2008) Photoperiodic flowering occurs under internal and external coincidence. Plant Signal Behavior 3: 269–271.
- 54. Turner A, Beales J, Faure S, Dunford R, Laurie D (2005) The pseudo-response regulator Ppd-H1 provides adaptation to photoperiod in barley. Science 310: 1031–1034. Available:http://www.ncbi.nlm.nih.gov/pubmed/16284181. Accessed 23 March 2011.
- 55. Izawa T, Oikawa T, Sugiyama N, Tanisaka T, Yano M, et al. (2002) Phytochrome mediates the external light signal to repress FT orthologs in photoperiodic flowering of rice. Genes & Development 16: 2006–2020.
- 56. Hayama R, Yokoi S, Tamaki S, Yano M, Shimamoto K (2003) Adaptation of photoperiodic control pathways produces short-day flowering in rice. Nature 422: 719–722. Available:http://www.ncbi.nlm.nih.gov/pubmed/12700762.
- 57. Hayama R, Agashe B, Luley E, King R, Coupland G (2007) A circadian rhythm set by dusk determines the expression of FT homologs and the short-day photoperiodic flowering response in Pharbitis. Plant cell 19: 2988–3000. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2174708&tool=pmcentrez&rendertype=abstract. Accessed 7 August 2010.
- 58. Wu C, You C, Li C, Long T, Chen G, et al. (2008) RID1, encoding a Cys2/His2-type zinc finger transcription factor, acts as a master switch from vegetative to floral development in rice. PNAS 105: 12915–12920.
- 59. Park SJ, Kim S, Lee S, Je B, Piao H, et al.. (2008) Rice Indeterminate 1 (OsId1) is necessary for the expression of Ehd1 (Early heading date 1) regardless of photoperiod. The Plant Journal 56: 1018–1029. Available:http://www.ncbi.nlm.nih.gov/pubmed/18774969. Accessed 18 December 2010.
- 60. Matsubara K, Yamanouchi U, Wang Z-X, Minobe Y, Izawa T, et al.. (2008) Ehd2, a rice ortholog of the maize INDETERMINATE1 gene, promotes flowering by up-regulating Ehd1. Plant Physiology 148: 1425–1435. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2577255&tool=pmcentrez&rendertype=abstract. Accessed 9 March 2011.
- 61. Higgins JA, Bailey PC, Laurie DA (2010) Comparative genomics of flowering time pathways using Brachypodium distachyon as a model for the temperate grasses. PloS one 5: e10065. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2856676&tool=pmcentrez&rendertype=abstract. Accessed 15 August 2010.
- 62. Colasanti J, Yuan Z, Sundaresan V (1998) The indeterminate gene encodes a zinc finger protein and regulates a leaf-generated signal required for the transition to flowering in maize. Cell 93: 593–603. Available:http://www.ncbi.nlm.nih.gov/pubmed/9604934.
- 63. Wong A, Colasanti J (2007) Maize floral regulator protein INDETERMINATE1 is localized to developing leaves and is not altered by light or the sink/source transition. Journal of Experimental Botany 58: 403–414. Available:http://www.ncbi.nlm.nih.gov/pubmed/17307745. Accessed 9 March 2011.
- 64. Coneva V, Zhu T, Colasanti J (2007) Expression differences between normal and indeterminate1 maize suggest downstream targets of ID1, a floral transition regulator in maize. Journal of Experimental Botany 58: 3679–3693. Available:http://www.ncbi.nlm.nih.gov/pubmed/17928372. Accessed 9 March 2011.
- 65. van Nocker S, Muszynski M, Briggs K, Amasino R (2000) Characterization of a gene from Zea mays related to the Arabidopsis flowering-time gene LUMINIDEPENDENS. Plant Molecular Biology 44: 107–122. Available:http://www.ncbi.nlm.nih.gov/pubmed/11094985.
- 66. Lee I, Aukerman M, Gore S, Lohman K, Michaels S, et al. (1994) Isolation of LUMINIDEPENDENS: a gene involved in the control of flowering time in Arabidopsis. Plant Cell 6: 75–83.
- 67. Strable J, Borsuk L, Nettleton D, Schnable P, Irish E (2008) Microarray analysis of vegetative phase change in maize. The Plant Journal 56: 1045–1057 doi:10.1111/j.1365-313X.2008.03661.x.
- 68. Kiniry JR, Rosenthal WD, Jackson BS, Hoogenboom G (1991) Predicting leaf development of crop plants. In: Hodges T, editor. Predicting crop phenology. Boca Raton, Florida: CRC Press. 29–42.
- 69. van Esbroeck GA, Ruiz Corral JA, Sanchez Gonzalez JJ, Holland JB (2008) A comparison of leaf appearance rates among teosinte, maize landraces and modern maize. Maydica 53: 117–123.
- 70. Lauter N, Kampani A, Carlson S, Goebel M, Moose S (2005) microRNA172 down-regulates glossy15 to promote vegetative phase change in maize. PNAS 102: 9412–9417.
- 71. Amasino R, Michaels S (2010) The timing of flowering. Plant Physiology 154: 516–520. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2948982&tool=pmcentrez&rendertype=abstract. Accessed 9 March 2011.
- 72. Poethig R (2010) The past, present, and future of vegetative phase change. Plant Physiology 154: 541–544. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2949024&tool=pmcentrez&rendertype=abstract. Accessed 4 February 2011.
- 73. Zhang L, Chia J-M, Kumari S, Stein J, Liu Z, et al.. (2009) A genome-wide characterization of microRNA genes in maize. PLoS Genetics 5: e1000716. Available:http://www.ncbi.nlm.nih.gov/pubmed/19936050.
- 74. Wu G, Poethig R (2006) Temporal regulation of shoot development in Arabidopsis thaliana by miR156 and its target SPL3. Development 133: 3539–3547. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1610107&tool=pmcentrez&rendertype=abstract. Accessed 17 January 2011.
- 75. Yang L, Conway S, Poethig R (2011) Vegetative phase change is mediated by a leaf-derived signal that represses the transcription of miR156. Development 138: 245–249. Available:http://www.ncbi.nlm.nih.gov/pubmed/21148189. Accessed 15 December 2010.
- 76. Aukerman M, Sakai H (2003) Regulation of flowering time and floral organ identity by a microRNA and its APETALA2 -Like target genes. Plant Cell 15: 2730–2741 doi:10.1105/tpc.016238.pression.
- 77. Salvi S, Sponza G, Morgante M, Tomes D, Niu X, et al. (2007) Conserved noncoding genomic sequences associated with a flowering-time quantitative trait locus in maize. PNAS 104: 11376–11381.
- 78. Zhu Q-H, Helliwell C (2011) Regulation of flowering time and floral patterning by miR172. Journal of Experimental Botany 62: 487–495. Available:http://www.ncbi.nlm.nih.gov/pubmed/20952628. Accessed 14 December 2010.
- 79. Peng J, Richards D, Hartley N, Murphy G, Devos K, et al.. (1999) “Green revolution" genes encode mutant gibberellin response modulators. Nature 400: 256–261. Available:http://www.ncbi.nlm.nih.gov/pubmed/10421366.
- 80. Lawit SJ, Wych HM, Xu D, Kundu S, Tomes DT (2010) Maize DELLA proteins dwarf plant8 and dwarf plant9 as modulators of plant development. Plant & Cell Physiology 51: 1854–1868. Available:http://www.ncbi.nlm.nih.gov/pubmed/20937610. Accessed 4 January 2011.
- 81. Andersen J, Schrag T, Melchinger A, Zein I, Lubberstedt T (2005) Validation of Dwarf8 polymorphisms associated with flowering time in elite European inbred lines of maize (Zea mays L.). Theoretical and Applied Genetics 111: 206–217.
- 82. Thornsberry J, Goodman M, Doebley J, Kresovich S, Nielsen D, et al.. (2001) Dwarf8 polymorphisms associate with variation in flowering time. Nature Genetics 28: 286–289. Available:http://www.ncbi.nlm.nih.gov/pubmed/19952783.
- 83. Camus-Kulandaivelu L, Veyrieras J, Madur D, Combes V, Fourmann M, et al.. (2006) Maize adaptation to temperate climate: relationship between population structure and polymorphism in the Dwarf8 gene. Genetics 172: 2449–2463. Available:http://www.ncbi.nlm.nih.gov/pubmed/16415370.
- 84. Bolduc N, Hake S (2009) The maize transcription factor KNOTTED1 directly regulates the gibberellin catabolism gene ga2ox1. Plant Cell 21: 1647–1658. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2714931&tool=pmcentrez&rendertype=abstract. Accessed 23 June 2010.
- 85. Bomblies K, Wang R, Ambrose B, Schmidt R, Meeley R, et al.. (2003) Duplicate FLORICAULA/LEAFY homologs zfl1 and zfl2 control inflorescence architecture and flower patterning in maize. Development 130: 2385–2395. Available:http://dev.biologists.org/cgi/doi/10.1242/dev.00457. Accessed 12 February 2011.
- 86. Danilevskaya O, Meng X, Ananiev E (2010) Concerted modification of flowering time and inflorescence architecture by ectopic expression of TFL1-Like genes in maize. Plant Physiology 153: 238–251 doi:10.1104/pp.110.154211.
- 87. Heuer S, Hansen S, Bantin J, Brettschneider R, Kranz E, et al.. (2001) The maize MADS box gene ZmMADS3 affects node number and spikelet development and is co-expressed with ZmMADS1 during flower development, in egg cells, and early embryogenesis. Plant Physiology 127: 33–45. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=117960&tool=pmcentrez&rendertype=abstract.
- 88. Wigge P, Kim M, Jaeger K, Busch W, Schmid M, et al.. (2005) Integration of spatial and temporal information during floral induction in Arabidopsis. Science 309: 1056–1059. Available:http://www.ncbi.nlm.nih.gov/pubmed/16099980.
- 89. Malcomber S, Preston J, Reinheimer R, Kossuth J, Kellogg E (2006) Developmental Gene Evolution and the Origin of Grass Inflorescence Diversity. Advances in Botanical Research 44: 425–481. Available:http://linkinghub.elsevier.com/retrieve/pii/S0065229606440118. Accessed 15 March 2012.
- 90. Pastore JJ, Limpuangthip A, Yamaguchi N, Wu M-F, Sang Y, et al.. (2011) LATE MERISTEM IDENTITY2 acts together with LEAFY to activate APETALA1. Development 138: 3189–3198. Available:http://dev.biologists.org/cgi/doi/10.1242/dev.063073. Accessed 13 July 2011.
- 91. Liljegren SJ, Gustafson-Brown C, Pinyopich a, Ditta GS, Yanofsky MF (1999) Interactions among APETALA1, LEAFY, and TERMINAL FLOWER1 specify meristem fate. The Plant cell 11: 1007–1018. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=144247&tool=pmcentrez&rendertype=abstract.
- 92. Danilevskaya O, Meng X, Hou Z, Ananiev E, Simmons C (2008) A genomic and expression compendium of the expanded PEBP gene family from maize. Plant Physiology 146: 250–264. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2230559&tool=pmcentrez&rendertype=abstract. Accessed 9 September 2010.
- 93. Salvi S, Tuberosa R, Chiapparino E, Maccaferri M, Veillet S, et al. (2002) Toward positional cloning of Vgt1, a QTL controlling the transition from the vegetative to the reproductive phase in maize. Plant Molecular Biology 48: 601–613.
- 94. Vlăduţu C, McLaughlin J, Phillips R (1999) Fine mapping and characterization of linked quantitative trait loci involved in the transition of the maize apical meristem from vegetative to generative structures. Genetics 153: 993–1007. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1460787&tool=pmcentrez&rendertype=abstract.
- 95. Bomblies K, Doebley J (2006) Pleiotropic effects of the duplicate maize FLORICAULA/LEAFY genes zfl1 and zfl2 on traits under selection during maize domestication. Genetics 172: 519–531. Available:http://www.ncbi.nlm.nih.gov/pubmed/16204211.
- 96. Mena M, Mandel M, Lerner D, Yanofsky M, Schmidt R (1995) A characterization of the MADS-box gene family in maize. The Plant Journal 8: 845–854. Available:http://onlinelibrary.wiley.com/doi/10.1046/j.1365-313X.1995.8060845.x/abstract. Accessed 23 March 2011.
- 97. Cooper M, Chapman S, Podlich D, Hammer G (2002) The GP problem: Quantifying gene-to-phenotype relationships. In Silico Biology 2: 151–164.
- 98. Hammer GL, Cooper M, Tardieu F, Welch S, Walch B, et al. (2006) Models for navigating biological complexity in breeding improved crop plants. Trends in Plant Science 11: 587–593.
- 99. Benfey P, Mitchell-Olds T (2008) From genotype to phenotype: systems biology meets natural variation. Science 320: 495–497.
- 100. Yin X, Struik P (2010) Modelling the crop: from system dynamics to systems biology. Journal of Experimental Botany 61: 2171–2183. Available:http://www.ncbi.nlm.nih.gov/pubmed/20051352. Accessed 15 September 2010.
- 101. Kauffman SA (1993) The Origins of Order: Self-Organization and Selection in Evolution. New York, USA: Oxford University Press. 734.
- 102. Mendoza L, Alvarez-Buylla E (1998) Dynamics of the genetic regulatory network for Arabidopsis thaliana flower morphogenesis. Journal of Theoretical Biology 193: 307–319.
- 103. Akutsu T, Miyano S, Kuhara S (1999) Identification of genetic networks from a small number of gene expression patterns under the Boolean network model. Pacific Symposium on Biocomputing 4: 17–28.
- 104. Genoud T, Métraux J (1999) Crosstalk in plant cell signaling: structure and function of the genetic network. Trends in Plant Science 4: 503–507.
- 105. Di-Paolo E (2001) Rhythmic and non-rhythmic attractors in asynchronous random Boolean networks. BioSystems 59: 185–195.
- 106. Genoud T, Trevino-Santa-Cruz M, Métraux J (2001) Numeric simulation of plant signaling networks. Plant Physiology 126: 1430–1437.
- 107. Alvarez-Buylla E, Benítez M, Dávila E, Chaos A, Espinosa-Soto C, et al.. (2007) Gene regulatory network models for plant development. Current Opinion in Plant Biology 10: 83–91. Available:http://www.ncbi.nlm.nih.gov/pubmed/17142086.
- 108. Yuh C, Bolouri H, Davidson E (2001) Cis-regulatory logic in the endo16 gene: switching from a specification to a differentiation mode of control. Development 128: 617–629. Available:http://www.ncbi.nlm.nih.gov/pubmed/11171388.
- 109. Yuh C, Bolouri H, Davidson E (1998) cis-regulatory logic in the endo 16 gene: Experimental and computational analysis of a sea urchin gene. Science 279: 1896–1902.
- 110. Davidson E, Rast J, Oliveri P, Ransick A, Calestani C, et al. (2002) A genomic regulatory network for development. Science 295: 1670–1678.
- 111. Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical recipes in C: the art of scientific computing. Cambridge: Cambridge University Press. 933.
- 112. Nelder J, Mead R (1965) A simplex method for function minimization. Computer Journal 7: 308–313.
- 113. Russell W, Stuber C (1982) Effects of photoperiod and temperatures on the duration of vegetative growth in maize. Crop Science 23: 847–850.
- 114. Morishige D, Childs K, Moore L, Mullet J (2002) Targeted analysis of orthologous phytochrome A regions of the sorghum, maize, and rice genomes using comparative gene-island sequencing. Plant Physiology 130: 1614–1625.
- 115. Ku L, Li S, Chen X, Wu L, Wang X, et al.. (2011) Cloning and Characterization of Putative Hd6 Ortholog Associated with Zea mays L. Photoperiod Sensitivity. Agricultural Sciences in China 10: 18–27. Available:http://linkinghub.elsevier.com/retrieve/pii/S1671292711603039. Accessed 5 April 2011.
- 116. Moose SP, Sisco PH (1994) Glossy15 Controls the Epidermal Juvenile-to-Adult Phase Transition in Maize. Plant Cell 6: 1343–1355. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=160525&tool=pmcentrez&rendertype=abstract.
- 117. Jung J-H, Seo Y-H, Seo P, Reyes J, Yun J, et al.. (2007) The GIGANTEA-regulated microRNA172 mediates photoperiodic flowering independent of CONSTANS in Arabidopsis. Plant cell 19: 2736–2748. Available:http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2048707&tool=pmcentrez&rendertype=abstract. Accessed 12 January 2011.
- 118. Tadege M, Sheldon C, Helliwell C, Upadhyaya N, Dennis E, et al.. (2003) Reciprocal control of flowering time by OsSOC1 in transgenic Arabidopsis and by FLC in transgenic rice. Plant Biotechnology Journal 1: 361–369. Available:http://www.ncbi.nlm.nih.gov/pubmed/17166135.