Graduate Research Course
Tree Biophysics & Biochemistry
From quantum-scale proton transfers in chloroplasts to the macroscopic mechanics of hydraulic failure — the physics and chemistry of arboreal life.
Key Equations of Tree Biophysics
Water Potential
\( \Psi_w = \Psi_s + \Psi_p + \Psi_g + \Psi_m \)
Hagen-Poiseuille Flow
\( Q = \frac{\pi r^4}{8\eta}\frac{\Delta P}{\ell} \)
Farquhar Photosynthesis
\( A_c = V_{c,\max}\frac{C_i - \Gamma^*}{C_i + K_c(1+O/K_o)} \)
Lockhart Growth
\( \frac{1}{V}\frac{dV}{dt} = \phi(\Psi_p - Y) \)
Penman-Monteith
\( \lambda E = \frac{\Delta(R_n-G)+\rho_a c_p(e_s-e_a)/r_a}{\Delta+\gamma(1+r_s/r_a)} \)
WBE Scaling
\( B = B_0 M^{3/4} \)
About This Course
Trees are the largest and longest-lived organisms on Earth. A 100-meter redwood lifts water against gravity using nothing but the tensile strength of liquid water and nanoscale capillary forces. Its chloroplasts capture photons with near-unity quantum yield. Its cambium builds wood — a composite material of cellulose, hemicellulose, and lignin — that rivals engineered materials in specific strength.
This course integrates biophysics (hydraulics, mechanics, quantum biology, scaling laws) with biochemistry (photosynthesis, secondary metabolism, hormone signaling, defense chemistry) to explain how trees work from the molecular to the whole-organism scale.
Every module includes detailed MathJax derivations, SVG diagrams of transport systems and metabolic pathways, and Python simulations of hydraulic conductance, photosynthetic models, and scaling relationships. Cross-links to our Plant Biochemistry course for shared pathway content.
Nine Modules
M0
Mathematical & Physical Foundations
Irreversible thermodynamics, Onsager reciprocal relations, Fick's laws, continuum mechanics for wood, reaction-diffusion systems, dimensional analysis.
M1
Water Transport & Xylem Hydraulics
Cohesion-tension theory, cavitation dynamics, Hagen-Poiseuille flow, vulnerability curves, stomatal biophysics, Penman-Monteith transpiration.
M2
Photosynthesis: Quantum to Calvin
LHCII quantum coherence, Förster energy transfer, Z-scheme, Mn₄CaO₅ water splitting, Farquhar-von Caemmerer-Berry model, photorespiration.
M3
Phloem Transport & Carbon Allocation
Münch pressure-flow hypothesis, sucrose loading (apoplastic/symplastic), sink-source dynamics, pipe model theory, NSC dynamics.
M4
Wood Formation & Cell Wall Mechanics
Cambial activity, xylogenesis, cellulose microfibril architecture, lignin polymerization (H/G/S units), Lockhart growth equation, viscoelastic wood mechanics.
M5
Root Biochemistry & Rhizosphere
Ion channel biophysics (GHK equation), mycorrhizal symbiosis, root exudate chemistry, Frankia nitrogen fixation, rhizosphere microbiome.
M6
Secondary Metabolites & Chemical Defense
Phenylpropanoid pathway, terpenoid biosynthesis (MVA/MEP), conifer oleoresin defense, VOC emissions (Guenther algorithm), bark tannins.
M7
Stress Biophysics: Drought, Cold & Pathogens
ABA signaling (PYR/PYL-PP2C-SnRK2), osmotic adjustment, freeze-thaw embolism physics, SAR (systemic acquired resistance), cold acclimation.
M8
Whole-Tree Integration & Scaling
West-Brown-Enquist vascular scaling, Kleiber's law (B = B₀ M¾), Cowan-Farquhar stomatal optimization, FSPM models, climate change impacts.
Core References
- [1] Tyree, M.T. & Zimmermann, M.H. (2002). Xylem Structure and the Ascent of Sap, 2nd ed. Springer.
- [2] Farquhar, G.D. et al. (1980). A biochemical model of photosynthetic CO₂ assimilation. Planta, 149(1), 78–90.
- [3] Fleming, G.R. et al. (2007). Quantum coherence in photosynthesis. Nature, 446, 782–786.
- [4] Sperry, J.S. & Tyree, M.T. (1988). Mechanism of water stress-induced xylem embolism. Plant Physiology, 88(3), 581–587.
- [5] West, G.B. et al. (1999). A general model for the structure and allometry of plant vascular systems. Nature, 400, 664–667.
- [6] Lockhart, J.A. (1965). An analysis of irreversible plant cell elongation. J. Theor. Biol., 8(2), 264–275.
- [7] Cosgrove, D.J. (2005). Growth of the plant cell wall. Nature Rev. Mol. Cell Biol., 6(11), 850–861.
- [8] Jones, J.D.G. & Dangl, J.L. (2006). The plant immune system. Nature, 444, 323–329.