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Module 1: Flower Development & the ABC Model

In 1991 Enrico Coen and Elliot Meyerowitz proposed a three-letter code for flower identity that still dominates the field. The ABC model - now expanded to ABCDE with the quartet hypothesis - explains why there are four concentric whorls, why homeotic mutants convert whole whorls into other organs, and why mutants in agamous produce indeterminate double flowers prized by horticulturists. This module develops the model rigorously, connects it to upstream meristem-identity genes (LEAFY, APETALA1), and then places flowering-time control (florigen, vernalization) upstream of the identity genes.

1. From Homeotic Mutants to the ABC Code

Three classes of homeotic mutations affect Arabidopsis thaliana flowers:

Class A mutants (e.g. apetala1, apetala2): whorl 1 becomes carpel-like, whorl 2 becomes stamen-like (i.e. whorls acquire whorl-4 and whorl-3 identity).
Class B mutants (e.g. apetala3, pistillata): whorl 2 becomes sepal, whorl 3 becomes carpel.
Class C mutants (e.g. agamous): whorl 3 becomes petal, whorl 4 becomes sepal, and the meristem is indeterminate - producing more whorls of petals (the "double flower" of roses and peonies).

The parsimonious interpretation: three gene activities A, B, C are expressed in overlapping domains along the radial axis, specifying:

\[ \text{Whorl 1: A} \rightarrow \text{sepal},\quad \text{Whorl 2: A+B} \rightarrow \text{petal} \]

\[ \text{Whorl 3: B+C} \rightarrow \text{stamen},\quad \text{Whorl 4: C} \rightarrow \text{carpel} \]

An additional rule: A and C are mutually antagonistic. If A is lost, C spreads into whorls 1-2; if C is lost, A spreads into whorls 3-4. This single constraint is sufficient to predict every homeotic phenotype above.

1.1 The ABC Diagram

Below, the three domains are drawn as overlapping rectangles across the four whorls, with the organ identity determined by which combination of letters is present.

2. The Quartet Model & MADS-Box TFs

All ABCDE genes except APETALA2 are MADS-boxtranscription factors. The acronym comes from the founding members - MCM1 (yeast), AGAMOUS (Arabidopsis), DEFICIENS (snapdragon), and SRF (humans). The MADS domain is a conserved ~60-residue N-terminal DNA-binding module that recognises a CArG box (CC(A/T)₆GG) as a dimer.

Theissen's quartet hypothesis (2001) posits that floral organ identity is specified not by pairs but by tetrameric protein complexes bound to two CArG boxes that loop chromatin. Each whorl has its own tetramer composition:

Sepal (W1)

(AP1)₂ (SEP)₂

Petal (W2)

AP1 AP3 PI SEP

Stamen (W3)

AP3 PI AG SEP

Carpel (W4)

(AG)₂ (SEP)₂

2.1 D-class (ovule identity)

SEEDSTICK (STK, formerly AGL11) and SHATTERPROOF (SHP1/2) are D-class MADS-box genes required specifically for ovule identity within the carpel. A quadruple stk shp1 shp2 ag mutant converts ovules into leaf-like organs.

2.2 A Quantitative Identity Rule

We can formalise the ABC logic as a majority-wins function on the tetramer composition. Let \(A, B, C, E \in [0,1]\) be the local expression levels. The organ identity score for each whorl type is:

\[ S_{\text{sepal}} = A E (1-B)(1-C), \quad S_{\text{petal}} = A B E (1-C) \]

\[ S_{\text{stamen}} = B C E (1-A), \quad S_{\text{carpel}} = C E (1-A)(1-B) \]

The predicted organ is the one with the highest score. The simulation below computes these scores, animates their emergence during development, and then reproduces the three canonical mutant phenotypes by setting A, B or C to zero.

Python

script.py135 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# ======================================================================
# ABC model (Coen & Meyerowitz 1991) in its quartet form
# ----------------------------------------------------------------------
# Floral organs are specified by combinatorial activity of MADS-box
# transcription factors:
#
#   Whorl 1 (sepals) : A alone
#   Whorl 2 (petals) : A + B
#   Whorl 3 (stamens): B + C
#   Whorl 4 (carpels): C alone
#
# A and C are mutually antagonistic -> loss of either expands the other
# Plus an E-class SEPALLATA in every whorl (quartet model).
#
# We compute gene expression domains across whorls x developmental time
# with a reaction-diffusion-like logistic model.
# ======================================================================

whorls = np.arange(1, 5)        # 1..4
t = np.linspace(0, 10, 200)     # developmental time (arb. units)

# Activation rates for each gene in each whorl
# A expressed in whorls 1-2, B in 2-3, C in 3-4, E everywhere
def logistic_rise(t, k=1.2, t0=2.0):
    return 1.0 / (1.0 + np.exp(-k*(t - t0)))

def profile():
    W, T = np.meshgrid(whorls, t, indexing='xy')
    A = np.where((W == 1) | (W == 2), 1.0, 0.0) * logistic_rise(T, 1.2, 2.0)
    B = np.where((W == 2) | (W == 3), 1.0, 0.0) * logistic_rise(T, 1.0, 3.5)
    C = np.where((W == 3) | (W == 4), 1.0, 0.0) * logistic_rise(T, 0.9, 4.0)
    E = np.ones_like(W, dtype=float)          * logistic_rise(T, 1.3, 1.5)
    return A, B, C, E

A, B, C, E = profile()

# Organ identity: majority quartet wins
# Sepal     = AE      Petal = ABE
# Stamen    = BCE     Carpel = CE
def organ_score():
    S_s = A * E * (1 - B) * (1 - C)
    S_p = A * B * E * (1 - C)
    S_st = B * C * E * (1 - A)
    S_c = C * E * (1 - B) * (1 - A)
    return S_s, S_p, S_st, S_c

Ss, Sp, Sst, Sc = organ_score()

fig = plt.figure(figsize=(14, 9))
fig.patch.set_facecolor('#0a0308')

# Panel 1: gene expression domains (whorl x gene) at maturity
ax1 = fig.add_subplot(2, 2, 1)
ax1.set_facecolor('#1a0612')
data_mature = np.array([A[-1,:], B[-1,:], C[-1,:], E[-1,:]])
im = ax1.imshow(data_mature, aspect='auto', cmap='RdPu',
                origin='lower', extent=[0.5, 4.5, 0, 4])
ax1.set_xticks([1,2,3,4]); ax1.set_xticklabels(['W1','W2','W3','W4'], color='white')
ax1.set_yticks([0.5,1.5,2.5,3.5]); ax1.set_yticklabels(['A','B','C','E'], color='white')
ax1.set_title('Gene expression at anthesis\n(rows: genes, columns: whorls)',
              color='#fbcfe8', fontsize=11)
for i in range(4):
    for j in range(4):
        ax1.text(j+1, i+0.5, f"{data_mature[i,j]:.2f}",
                 ha='center', va='center', color='white', fontsize=9)
plt.colorbar(im, ax=ax1).set_label('expression', color='white')

# Panel 2: developmental time courses, one line per gene x whorl
ax2 = fig.add_subplot(2, 2, 2)
ax2.set_facecolor('#1a0612')
for i, g_name, g in [(0,'A', A), (1,'B', B), (2,'C', C), (3,'E', E)]:
    col = ['#f472b6', '#fde68a', '#c084fc', '#93c5fd'][i]
    for w in range(4):
        ls = ['-','--',':','-.'][w]
        ax2.plot(t, g[:, w], color=col, linestyle=ls, alpha=0.7, linewidth=1.6,
                 label=f"{g_name} @ W{w+1}")
ax2.set_xlabel('Developmental time', color='white')
ax2.set_ylabel('Expression level', color='white')
ax2.set_title('Sequential onset of ABCE genes', color='#fbcfe8', fontsize=11)
ax2.legend(fontsize=7, ncol=2, facecolor='#1a0612', edgecolor='#f472b6', labelcolor='white')
ax2.grid(True, alpha=0.2, color='#f472b6')

# Panel 3: organ identity scores
ax3 = fig.add_subplot(2, 2, 3)
ax3.set_facecolor('#1a0612')
for w in range(4):
    scores = [Ss[-1,w], Sp[-1,w], Sst[-1,w], Sc[-1,w]]
    bars = ax3.bar(np.arange(4) + w*0.22, scores, width=0.2,
                   label=f"Whorl {w+1}",
                   color=['#65a30d','#f472b6','#fbbf24','#c084fc'][w])
ax3.set_xticks(np.arange(4)+0.3)
ax3.set_xticklabels(['Sepal','Petal','Stamen','Carpel'], color='white')
ax3.set_ylabel('Identity score', color='white')
ax3.set_title('Predicted organ identity per whorl (wild-type)',
              color='#fbcfe8', fontsize=11)
ax3.legend(fontsize=8, facecolor='#1a0612', edgecolor='#f472b6', labelcolor='white')

# Panel 4: Mutant simulations
ax4 = fig.add_subplot(2, 2, 4)
ax4.set_facecolor('#1a0612')
labels_m = ['wild-type','a mutant\n(apetala2)','b mutant\n(apetala3/pi)','c mutant\n(agamous)']
# In a mutant: no A -> C spreads everywhere -> all whorls = carpel or stamen
# In b mutant: no B -> petals = sepals, stamens = carpels
# In c mutant: no C -> stamens = petals, carpels = sepals, loss of determinacy
identities = {
    'wild-type': ['Sepal','Petal','Stamen','Carpel'],
    'a mutant\n(apetala2)': ['Carpel','Stamen','Stamen','Carpel'],
    'b mutant\n(apetala3/pi)': ['Sepal','Sepal','Carpel','Carpel'],
    'c mutant\n(agamous)': ['Sepal','Petal','Petal','Sepal'],
}
colors_o = {'Sepal':'#65a30d','Petal':'#f472b6','Stamen':'#fbbf24','Carpel':'#c084fc'}

y = np.arange(4)
for i, lab in enumerate(labels_m):
    for j, org in enumerate(identities[lab]):
        ax4.barh(i, 1, left=j, color=colors_o[org], edgecolor='#fbcfe8', linewidth=0.8)
        ax4.text(j+0.5, i, org, ha='center', va='center', fontsize=8, color='black')
ax4.set_yticks(y); ax4.set_yticklabels(labels_m, color='white', fontsize=8)
ax4.set_xticks([0.5,1.5,2.5,3.5])
ax4.set_xticklabels(['W1','W2','W3','W4'], color='white')
ax4.set_title('Homeotic mutants', color='#fbcfe8', fontsize=11)

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0308')

print("Organ identity scores (row=whorl, col=sepal petal stamen carpel):")
for w in range(4):
    print(f"  W{w+1}: {Ss[-1,w]:.2f}  {Sp[-1,w]:.2f}  {Sst[-1,w]:.2f}  {Sc[-1,w]:.2f}")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Note the elegance of the C-class loss-of-function simulation: because the A domain expands into whorls 3-4 (no antagonism), but B is unchanged, whorl 3 becomes A+B = petal and whorl 4 becomes A = sepal. Exactly the phenotype of agamous / double roses. The meristem also fails to terminate, explaining indeterminate growth of double flowers.

3. Meristem Identity: LEAFY & APETALA1

Before the ABC genes can act, a vegetative shoot apical meristem (SAM) must convert to an inflorescence/floral meristem. Two genes act at the top of this hierarchy:

LEAFY (LFY) - plant-specific transcription factor that integrates photoperiod, gibberellin and age cues. Mis-expression in vegetative tissue can transform leaf-axillary buds into terminal flowers.
APETALA1 (AP1) - class-A MADS-box but also a meristem-identity gene; LFY directly activates AP1, which in turn represses the inflorescence gene TERMINAL FLOWER 1 (TFL1).

The circuit is a classical mutual exclusion:

\[ \text{LFY} \rightarrow \text{AP1} \dashv \text{TFL1} \dashv \text{LFY,AP1} \]

TFL1 represses LFY/AP1 and keeps the apex inflorescence-like (indeterminate); when LFY/AP1 win, a terminal flower is specified and the meristem becomes determinate (except in agamous mutants, see above).

3.1 Two-Step Selector Logic

LFY activates the ABC genes region-specifically: in conjunction with WUSCHEL (WUS) it directly binds the AG locus (Lenhard 2001). In combination with UFO (UNUSUAL FLORAL ORGANS) it activates AP3 (class B). The system is a beautiful example of combinatorial gene regulation: the same LFY protein specifies different downstream targets depending on partner cofactors.

4. Flowering Time: Florigen & FLC

Grafting experiments in the 1930s (Chailakhyan) showed that a long-day plant, once induced, transmits a flowering signal through its phloem. This signal was christened florigen. Eighty years later it was identified: the FT protein, product of the FLOWERING LOCUS T gene.

4.1 Photoperiodic Induction

In long-day plants, CONSTANS (CO) mRNA accumulates at the end of the light period. CO is stabilised only in the presence of the blue-light photoreceptor CRY2 and the phytochrome PhyA. Stable CO activates FT transcription in the leaf vasculature. FT protein moves via phloem to the shoot apex where it binds FD (a bZIP TF) to activate AP1 and SOC1 - initiating the ABC cascade.

\[ \text{Light} \rightarrow \text{CO}_{\text{leaf}} \rightarrow \text{FT} \xrightarrow{\text{phloem}} \text{FT:FD}_{\text{apex}} \rightarrow \text{AP1, SOC1} \rightarrow \text{flower} \]

4.2 Vernalization: Winter Memory

Many biennials (Arabidopsis winter annuals, beets, winter wheat) must experience prolonged cold (weeks) before they can flower. The cold-repressed gene FLOWERING LOCUS C (FLC) is a MADS-box repressor of FT. Prolonged cold deposits repressive Polycomb\( \text{H3K27me3} \) marks at the FLC locus; silencing is cell-heritable and persists through warm spring, creating an epigenetic memory of winter.

The quantitative model (Angel et al. 2011) treats FLC silencing as a stochastic bistable switch: each cell's FLC flips OFF with rate \(k(T)\) depending on temperature, and the plant-level competence emerges from the fraction of silenced cells. We simulate a deterministic mean-field version below.

\[ \frac{\text{d FLC}}{\text{d}t} = -k(T)\,\text{FLC}, \qquad k(T) = k_{\max}\, e^{-(T-T_{\text{opt}})^2/\sigma^2} \]

Python

script.py94 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# ======================================================================
# Vernalization dose-response: FLC silencing by prolonged cold
# ----------------------------------------------------------------------
# Arabidopsis flowering is blocked by FLOWERING LOCUS C (FLC), a MADS-box
# repressor of FT (florigen). Cold exposure deposits H3K27me3 marks
# (Polycomb) on the FLC chromatin, progressively silencing it.
#
# Empirical model (Angel et al. 2011):
#   FLC(t) = FLC0 * exp(-t/tau(T))
#   tau(T) = tau_min + K*exp(-(T-Topt)^2/sigma^2)
# i.e. cold is most effective at ~5 degC, less so at 0 or 15 degC.
# ======================================================================

t = np.linspace(0, 100, 201)          # weeks of cold
temperatures = [0, 2, 5, 8, 12, 20]
colors = plt.cm.spring(np.linspace(0.1, 0.9, len(temperatures)))

def tau(T):
    tau_min = 200.0
    K       = 190.0                    # fastest silencing ~ 10 weeks at 5C
    Topt    = 5.0
    sigma   = 6.0
    return tau_min - K*np.exp(-(T-Topt)**2/sigma**2)

fig, axes = plt.subplots(1, 3, figsize=(16, 5))
fig.patch.set_facecolor('#0a0308')
fig.suptitle('Vernalization: chromatin silencing of FLC by prolonged cold',
             color='#fbcfe8', fontsize=14, fontweight='bold', y=1.02)

# Panel 1: FLC vs time, varying T
ax = axes[0]
ax.set_facecolor('#1a0612')
FLC0 = 1.0
for T, col in zip(temperatures, colors):
    FLC = FLC0 * np.exp(-t/tau(T))
    ax.plot(t, FLC, color=col, linewidth=2, label=f"{T}°C")
ax.axhline(0.3, color='white', linestyle=':', linewidth=1, alpha=0.5)
ax.text(5, 0.33, 'floral commitment threshold', color='white', fontsize=9)
ax.set_xlabel('Weeks of cold exposure', color='white')
ax.set_ylabel('Relative FLC expression', color='white')
ax.set_title('FLC decay (H3K27me3 accumulation)', color='#fbcfe8', fontsize=11)
ax.legend(fontsize=9, facecolor='#1a0612', edgecolor='#f472b6', labelcolor='white')
ax.grid(True, alpha=0.2, color='#f472b6')
ax.tick_params(colors='white')

# Panel 2: FT (florigen) induction = 1 - FLC (plus photoperiod gate)
ax = axes[1]
ax.set_facecolor('#1a0612')
for T, col in zip(temperatures, colors):
    FLC = FLC0 * np.exp(-t/tau(T))
    # FT accumulates if FLC < threshold AND photoperiod is long
    FT = np.maximum(0.0, 1.0 - FLC/0.3)
    ax.plot(t, FT, color=col, linewidth=2, label=f"{T}°C")
ax.set_xlabel('Weeks of cold exposure', color='white')
ax.set_ylabel('FT (florigen) competence', color='white')
ax.set_title('Emergent floral competence after warmth returns',
             color='#fbcfe8', fontsize=11)
ax.legend(fontsize=9, facecolor='#1a0612', edgecolor='#f472b6', labelcolor='white')
ax.grid(True, alpha=0.2, color='#f472b6')
ax.tick_params(colors='white')

# Panel 3: Time-to-flower as function of vernalization duration
ax = axes[2]
ax.set_facecolor('#1a0612')
T = 5.0
durations = np.linspace(0, 100, 200)
FLC_end = FLC0 * np.exp(-durations/tau(T))
# Time-to-flower = 20 weeks baseline, scaled by remaining FLC
TTF = 20.0 * (FLC_end + 0.1)
ax.plot(durations, TTF, color='#fbbf24', linewidth=3)
ax.fill_between(durations, 0, TTF, alpha=0.3, color='#f472b6')
ax.axhline(2.5, color='#93c5fd', linestyle='--', label='fully vernalised')
ax.set_xlabel('Weeks at 5°C', color='white')
ax.set_ylabel('Weeks to flower after warming', color='white')
ax.set_title('Vernalization dose-response curve', color='#fbcfe8', fontsize=11)
ax.legend(fontsize=9, facecolor='#1a0612', edgecolor='#f472b6', labelcolor='white')
ax.grid(True, alpha=0.2, color='#f472b6')
ax.tick_params(colors='white')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0308')

print("Time-to-flower for different vernalisation regimes (5 degC):")
for d in [0, 2, 4, 8, 12, 20]:
    flc = np.exp(-d/tau(5.0))
    ttf = 20.0 * (flc + 0.1)
    print(f"  {d:3d} weeks cold -> FLC={flc:.3f} -> {ttf:5.1f} weeks to flower")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Notice the bell-shaped temperature dependence of silencing rate: 5 °C is optimum, neither freezing nor warm spells help. This matches published data: winter-grown Arabidopsis at Haell (Sweden, ~4 °C mean) silences FLC more rapidly than plants grown at 10 °C.

4.3 Gibberellin Pathway

A fourth flowering pathway converges on SOC1: gibberellin biosynthesis increases LEAFY expression and overrides FLC in older plants. This is why biennials eventually flower without vernalization: endogenous GA accumulates with age, and GA-deficient mutants (ga1-3) stay vegetative forever under short days.

4.5 The Full Flowering Network

Integrating four pathways (photoperiod, vernalization, autonomous, gibberellin) the complete flowering-time circuit in Arabidopsis has more than 200 known genes. The core integrators - FT, SOC1, AP1, LFY - are the convergence points:

4.6 The MADS-Box Structure

The MADS-box is a ~60 amino-acid DNA-binding domain at the N-terminus. The canonical structure (Pellegrini et al. 1995) has a \(\beta\)-sheet lying in the DNA minor groove, followed by two \(\alpha\)-helices that dimerise via an antiparallel coiled-coil. The consensus CArG-box recognition sequence is\(\text{CC(A/T)}_6\text{GG}\). Downstream are the I (intervening), K (keratin-like coiled-coil, responsible for tetramerisation), and C (variable C-terminal) domains:

\[ \text{MADS-box TF: N-[MADS(60)]-[I(30)]-[K-domain(70)]-[C-term(variable)]-C} \]

Tetramerisation via the K domain is what allows quartet-model complexes to form: two MADS dimers each recognising one CArG box loop the DNA between them, contacting target promoters cooperatively.

5. Evolution of the ABC System

MADS-box genes predate angiosperms - they are present in mosses and ferns, where they control gametophyte development. The angiosperm innovation was to recruit paralogues into a strict spatial code across whorls. In basal angiosperms (Amborella, Nuphar) the boundaries between A, B, C are fuzzy - accounting for "undifferentiated" perianths of tepals. Eudicot and monocot core-eudicot lineages sharpen the boundaries by gene duplications: FUL (fruitful) is the euAPETALA1 sister gene.

The fading borders model (Buzgo et al. 2004) explains the continuous perianth of basal angiosperms without invoking failure of the ABC system: gradients of B-class expression yield gradual transitions from sepal to petal to stamen. In core eudicots the gradients have been replaced by sharp step functions.

6. Summary Table

ABC Model

Combinatorial code: A -> sepal, A+B -> petal, B+C -> stamen, C -> carpel

Antagonism

A and C mutually exclude; loss of A expands C and vice versa

Class A

APETALA1 (MADS-box), APETALA2 (AP2 domain, not MADS)

Class B

APETALA3 + PISTILLATA; obligate heterodimer

Class C

AGAMOUS; also provides determinacy - loss yields double flowers

Class D

SEEDSTICK, SHATTERPROOF 1/2 - ovule identity

Class E

SEPALLATA1-4; required in every whorl (quartet hypothesis)

Quartet Model

Tetrameric MADS complexes loop two CArG-box-containing enhancers

Meristem Identity

LEAFY -> APETALA1 -| TERMINAL FLOWER 1; converts SAM to floral meristem

Florigen

FT protein - moves from leaf phloem to apex, activates AP1/SOC1

Vernalization

Cold deposits H3K27me3 at FLC; silences MADS repressor; cell-heritable winter memory

Integration

FT + GA + LFY + (absence of FLC) converge on the floral transition

References

Coen, E. S. & Meyerowitz, E. M. (1991). The war of the whorls: genetic interactions controlling flower development. Nature, 353, 31-37.
Theissen, G. (2001). Development of floral organ identity: stories from the MADS house. Current Opinion in Plant Biology, 4, 75-85.
Pelaz, S., Ditta, G. S., Baumann, E., Wisman, E. & Yanofsky, M. F. (2000). B and C floral organ identity functions require SEPALLATA MADS-box genes. Nature, 405, 200-203.
Honma, T. & Goto, K. (2001). Complexes of MADS-box proteins are sufficient to convert leaves into floral organs. Nature, 409, 525-529.
Lenhard, M. et al. (2001). Termination of stem cell maintenance in Arabidopsis floral meristems by interactions between WUSCHEL and AGAMOUS. Cell, 105, 805-814.
Corbesier, L. et al. (2007). FT protein movement contributes to long-distance signaling in floral induction of Arabidopsis. Science, 316, 1030-1033.
Michaels, S. D. & Amasino, R. M. (1999). FLOWERING LOCUS C encodes a novel MADS domain protein that acts as a repressor of flowering. The Plant Cell, 11, 949-956.
Angel, A., Song, J., Dean, C. & Howard, M. (2011). A Polycomb-based switch underlying quantitative epigenetic memory. Nature, 476, 105-108.
Buzgo, M., Soltis, P. S. & Soltis, D. E. (2004). Floral developmental morphology of Amborella trichopoda. International Journal of Plant Sciences, 165, 925-947.
Theissen, G. & Saedler, H. (2001). Floral quartets. Nature, 409, 469-471.
Schmid, M. et al. (2003). Dissection of floral induction pathways using global expression analysis. Development, 130, 6001-6012.

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