Module 5: Reproduction & Genetics
Flowers are reproductive machines. This module derives the molecular genetics of self-recognition, the biophysics of pollen tube tip growth, the parental-conflict theory that explains imprinting in the endosperm, and the cellular biology of apomixis — clonal seed production that short-circuits sex itself.
1. Self-Incompatibility (SI)
Approximately 40% of all flowering plant species are self-incompatible, meaning they reject their own pollen (or the pollen of genetically similar relatives) before fertilization. SI is a recognition system encoded by a single, highly polymorphic locus called the S-locus, with two fundamentally different molecular architectures.
Gametophytic SI (GSI): S-RNase / F-box
Found in Solanaceae, Rosaceae, and Plantaginaceae, GSI recognises the haploid genotype of the pollen grain itself. The pistil expresses secreted S-RNases that enter all growing pollen tubes; the pollen expresses an SLF / SFB F-box protein that binds and ubiquitinates non-self RNases for degradation.
\(\text{SLF}_{S_i} \cdot \text{S-RNase}_{S_j \neq S_i} \longrightarrow \text{Skp1-Cul1-F-box} \longrightarrow \text{RNase degradation}\)
If the pollen SLF cannot target the pistil RNase (self-pair), the RNase degrades pollen rRNA and arrests the tube.
Sporophytic SI (SSI): SLG / SRK
Found in Brassicaceae (including Arabidopsis lyrata, cabbage, radish), SSI recognises the diploid genotype of the pollen-producing parent. The stigma expresses the membrane receptor kinase SRK and the soluble SLG; the pollen coat carries the ligand SCR/SP11. A matched SCR–SRK interaction triggers a kinase cascade that arrests hydration of the pollen grain on the stigmatic papilla within minutes.
Derivation: S-allele frequency dynamics
Consider a population with \(N\) S-alleles at frequencies \(p_1, \dots, p_N\)and assume random mating. An ovule of genotype \(S_i S_j\) is fertilizable by a pollen grain of genotype \(S_k\) only if \(S_k \neq S_i, S_j\). The expected siring success of allele \(S_k\) is
\( w(S_k) = \sum_{i \neq k}\sum_{j \neq k} p_i p_j = (1 - p_k)^2 \)
In the mean-field limit this becomes \(w(S_k) \approx 1 - 2 p_k\), i.e. rare alleles win.
At deterministic equilibrium, all \(N\) alleles must have equal fitness, which by symmetry requires \(p_k = 1/N\). This is the celebrated 1/N law of Wright (1939). Finite-population theory (Vekemans & Slatkin 1994) gives the expected allele number as a balance between mutation input and genetic drift:
\( \langle N \rangle \approx \sqrt{4 N_e \mu} \)
\(N_e\): effective population size, \(\mu\): rate of appearance of new specificities.
The S-locus — GSI vs SSI Architectures
2. Pollen Tube Growth as a Reaction-Diffusion System
The pollen tube is the fastest-growing cell known: lily pollen tubes extend at up to 1 cm per hour. Growth is strictly tip-focused: all cell-wall deposition occurs in a micron-scale apical dome driven by a steep tip-high Ca2+ gradient.
Pectin methylesterases and wall mechanics
Newly secreted pectin is highly methylesterified and viscoelastic. At the apex, PME demethylates the pectin, releasing protons and allowing Ca2+ to cross-link carboxyl groups into a rigid gel. The wall at the apex is therefore a self-stiffening material, and PMEI inhibitors maintain a soft window exactly at the tip where turgor pressure drives extension.
Derivation: tip growth as a reaction-diffusion system
Let \(C(x,t)\) be the cytosolic calcium concentration at arc length \(x\)from the tip. Calcium enters through apical stretch-activated channels with flux \(J_0\), diffuses with coefficient \(D\), and is pumped back at rate \(k\):
\( \dfrac{\partial C}{\partial t} = D\,\dfrac{\partial^2 C}{\partial x^2} - k\,C + J_0\,\delta(x) \)
At steady state, \(C(x) = (J_0 / \sqrt{4 D k})\, e^{-x \sqrt{k/D}}\) — an exponentially decaying tip gradient.
Growth rate \(v\) is coupled to apical Ca2+ and the PMEI/PME ratio:
\( v(t) = \phi\,\big(P_{\text{turgor}} - P_{\text{wall}}(t)\big)_+ \cdot \dfrac{[\text{PMEI}]}{[\text{PME}]} \)
\(\phi\): wall extensibility (Lockhart equation); \(()_+\) denotes positive part.
When the Ca2+ influx and efflux form a delayed negative feedback, the system exhibits sustained oscillations with a period of ~20 s. These oscillations have been measured directly in lily and tobacco (Holdaway-Clarke et al. 1997).
Tip-focused Growth: Vesicles, Ca2+ and Wall Mechanics
3. Double Fertilization & Parental Conflict
Angiosperms uniquely undergo double fertilization, discovered by Nawaschin (1898) and Guignard (1899). The pollen tube delivers two sperm cells into the embryo sac. One fuses with the egg to form the diploid zygote; the other fuses with the central cell (which already contains two polar maternal nuclei) to produce the triploid endosperm, a nutritive tissue that feeds the embryo.
Parental conflict theory of imprinting
The 2 maternal : 1 paternal genome dosage in the endosperm is intrinsically unfair, and many endosperm genes are subject to genomic imprinting — expression from only one parental allele. Haig & Westoby (1989) proposed that imprinting is the outcome of an evolutionary arms race over maternal resource allocation.
Let seed resource demand be the trait \(G\). Maternal fitness across a sibling cohort decreases with total demand (shared pool), whereas paternal fitness scales with per-seed success. The maternally-inherited allele’s inclusive fitness in a cohort of size \(n\) is
\( W_m(G) = \sum_{i=1}^{n} s(G_i) \quad\text{with}\quad \sum G_i \le R_{\text{tot}} \)
\(s\): concave survival function; \(R_{\text{tot}}\): fixed maternal budget.
The paternal allele, present only in this seed with probability 1 but in the next sibling with probability \(r < 1\) (mixed paternity), has fitness
\( W_p(G) = s(G) + r \sum_{j \neq i} s(G_j) \)
Setting \(\partial W_p / \partial G = 0\) gives a larger ESS seed size than \(\partial W_m/\partial G = 0\).
The prediction is therefore that paternally-expressed genes(PEGs) should promote endosperm growth (e.g., PHE1 in Arabidopsis), while maternally-expressed genes (MEGs, e.g., the Polycomb component MEA) should suppress it. Interploidy crosses spectacularly confirm this: a paternal excess (2x × 4x) produces oversized, lethal endosperm, whereas a maternal excess (4x × 2x) produces undersized seeds (Scott et al. 1998).
Double Fertilization — Nawaschin’s Discovery
4. Apomixis — Clonal Seeds
Apomixis is the asexual production of seeds: the embryo forms from an unreduced maternal cell and is therefore a genetic clone of the mother. It has evolved independently in over 400 angiosperm lineages (Asteraceae, Poaceae, Rosaceae) and is a central interest for plant breeders — it could fix hybrid vigour.
Three cytological routes
Apomixis combines three independently regulated steps: (i) apomeiosis, the production of an unreduced embryo sac; (ii) parthenogenesis, development of the embryo without fertilization; and (iii) functional endosperm, either pseudogamous (requiring pollination) or autonomous.
- Diplospory: the megaspore mother cell itself skips meiosis, as in Taraxacum (dandelion) and Tripsacum.
- Apospory: a somatic nucellar cell bypasses the MMC and forms an unreduced embryo sac, as in Hieracium (hawkweed) and Panicum.
- Adventitious embryony: embryos arise directly from somatic nucellar tissue (Citrus polyembryony).
Loss of AGO9 / RDR6 and mutations in meiotic recombination genes (SPO11, REC8, OSD1) cause apomixis-like phenotypes, and the MiMe triple mutant of Arabidopsis converts meiosis into a mitosis (d’Erfurth et al. 2009), a step toward synthetic apomixis in crops.
Simulation: S-Allele Frequency Dynamics
Negative frequency-dependent selection at the S-locus, Wright–Fisher simulation of allele trajectories, the \(\langle N \rangle \sim \sqrt{4 N_e \mu}\) scaling, and the bottleneck erosion of SI diversity that threatens endangered self-incompatible populations.
Click Run to execute the Python code
Code will be executed with Python 3 on the server
Simulation: Pollen Tube Ca2+ Oscillations
Apical Ca2+ oscillator coupled to PME / PMEI balance and the Lockhart growth law, reproducing ~20-second oscillations and the exponentially decaying tip gradient.
Click Run to execute the Python code
Code will be executed with Python 3 on the server
Simulation: Genomic Imprinting & Seed Size
The 2m:1p endosperm dosage, Haig’s parental-conflict ESS for seed size, and the bimodal seed-size distributions predicted under maternal-bias, paternal-bias, and symmetric regimes.
Click Run to execute the Python code
Code will be executed with Python 3 on the server
Key References
• Wright, S. (1939). “The distribution of self-sterility alleles in populations.” Genetics, 24, 538–552.
• Vekemans, X. & Slatkin, M. (1994). “Gene and allelic genealogies at a gametophytic self-incompatibility locus.” Genetics, 137, 1157–1165.
• Takayama, S. & Isogai, A. (2005). “Self-incompatibility in plants.” Annu. Rev. Plant Biol., 56, 467–489.
• Kao, T.-h. & Tsukamoto, T. (2004). “The molecular and genetic bases of S-RNase-based self-incompatibility.” Plant Cell, 16, S72–S83.
• Holdaway-Clarke, T. L. et al. (1997). “Pollen tube growth and the intracellular cytosolic calcium gradient oscillate in phase while extracellular calcium influx is delayed.” Plant Cell, 9, 1999–2010.
• Bosch, M. & Hepler, P. K. (2005). “Pectin methylesterases and pectin dynamics in pollen tubes.” Plant Cell, 17, 3219–3226.
• Haig, D. & Westoby, M. (1989). “Parent-specific gene expression and the triploid endosperm.” Am. Nat., 134, 147–155.
• Scott, R. J. et al. (1998). “Parent-of-origin effects on seed development in Arabidopsis thaliana.” Development, 125, 3329–3341.
• Köhler, C. et al. (2012). “Mechanisms and evolution of genomic imprinting in plants.” Heredity, 105, 57–63.
• d’Erfurth, I. et al. (2009). “Turning meiosis into mitosis.” PLoS Biology, 7, e1000124.
• Hand, M. L. & Koltunow, A. M. G. (2014). “The genetic control of apomixis: asexual seed formation.” Genetics, 197, 441–450.
• Nawaschin, S. (1898). “Resultate einer Revision der Befruchtungsvorgänge bei Lilium martagon und Fritillaria tenella.” Bull. Acad. Imp. Sci. St.-Pétersbourg, 9, 377–382.