explain mass flow in phloem sieve tubes down a hydrostatic pressure gradient from source to sink

Transport Mechanisms – Mass Flow in Phloem Sieve Tubes

Learning Objective

Explain how soluble assimilates are transported in the phloem by mass flow down a hydrostatic (turgor) pressure gradient from a source to a sink, and be able to use the quantitative relationships to predict the effect of different factors on the flow rate.

What you need to be able to do (Syllabus 7.2‑4)

• Interpret the Hagen–Poiseuille equation for phloem flow and the osmotic pressure equation ΔP = RT ΔC.
• Carry out a simple calculation of volumetric flow rate Q for given values of tube radius, sap viscosity, pathway length and pressure difference.
• Predict qualitatively how a change in each of the factors listed in the “Factors influencing flow” table will affect Q and justify the prediction.

Key Definitions (Syllabus 7.2‑1)

• Source: Tissue that produces or releases soluble sugars (e.g. sucrose), amino acids, hormones etc., and therefore supplies the phloem with material to be distributed. In most plants the main source is a mature, photosynthetically active leaf.
• Sink: Tissue that consumes, stores or uses those assimilates (e.g. growing root tip, developing fruit, tuber, bud).
• Hydrostatic (turgor) pressure gradient: A difference in internal pressure between source and sink that drives bulk flow of phloem sap.

Structure of Phloem Transport Cells (Syllabus 7.2‑2)

• Sieve‑tube elements
  • Elongated, living cells that become enucleate and lose their vacuole at maturity.
  • End walls are modified into porous sieve plates that permit rapid passage of sap.
  • Plasmodesmata connect adjacent elements, forming a continuous tube.
• Companion cells
  • Small, metabolically active cells closely associated with each sieve‑tube element via numerous plasmodesmata.
  • Supply ATP and the enzymatic machinery for the sucrose‑H⁺ symporter that actively loads sucrose at the source (and, where required, actively unloads at the sink).

Integration with Photosynthetic Assimilate Production

Photosynthesis in the source leaf generates the sucrose that is loaded into the phloem. Thus phloem transport is the link between the “production” part of Topic 7 (photosynthetic assimilates) and the “distribution” part of the same topic.

The Münch Pressure‑Flow Hypothesis (Syllabus 7.2‑3)

The accepted model for phloem transport is the Münch pressure‑flow hypothesis. It can be summarised in four stages:

1. Active loading of sucrose (and other solutes) into sieve‑tube elements at the source, driven by a sucrose‑H⁺ symporter that uses ATP supplied by the companion cell.
2. Loading raises solute concentration, lowering the water potential (Ψ_w) inside the tube. Water therefore enters osmotically from the adjacent xylem (the water originates from the xylem, linking the two transport systems), raising the hydrostatic (turgor) pressure P in the source region.
3. The resulting pressure difference between source (P_source) and sink (P_sink) drives **passive bulk flow** of the sap along the sieve tube.
4. Active or passive unloading of sucrose at the sink (active when a sucrose‑H⁺ symporter is required). Unloading reduces solute concentration, raises Ψ_w, and allows water to leave the tube, lowering P_sink.

Only the loading and unloading steps require metabolic energy; the movement of sap between source and sink is driven solely by the hydrostatic pressure gradient.

Quantitative Description (Syllabus 7.2‑4)

Phloem flow can be approximated by an analogue of Hagen–Poiseuille’s law for laminar flow in a cylindrical tube:

• Q = volumetric flow rate (m³ s⁻¹)
• r = radius of a sieve‑tube element (m)
• η = dynamic viscosity of the phloem sap (Pa·s)
• L = length of the tube segment considered (m)
• ΔP = P_source – P_sink = hydrostatic pressure difference (Pa)

The pressure difference is generated osmotically:

• R = universal gas constant (8.314 J mol⁻¹ K⁻¹)
• T = absolute temperature (K)
• ΔC = difference in solute concentration between source and sink (mol m⁻³)

Example calculation

Given: r = 10 µm = 1.0 × 10⁻⁵ m, η = 1 cP = 1 × 10⁻³ Pa·s, L = 5 cm = 0.05 m, ΔP = 0.2 MPa = 2 × 10⁵ Pa.

Plugging into Hagen–Poiseuille:

This tiny flow rate per individual tube illustrates why many parallel sieve tubes are required to meet the plant’s carbohydrate demand.

Step‑by‑Step Process (Syllabus 7.2‑3)

Factors Influencing Mass Flow (Syllabus 7.2‑5)

Implications for the syllabus: For each factor, students should be able to explain *why* it changes the flow rate (e.g., “Increasing r reduces hydraulic resistance because resistance is inversely proportional to r⁴”). This links the qualitative table to the quantitative equations above.

Bidirectional Flow

When a plant has several sources and sinks (e.g., mature leaves, young leaves, developing fruits), phloem can conduct sap in opposite directions in different sieve‑tube strands. The pressure‑flow model still applies locally: each source‑sink pair establishes its own pressure gradient, allowing simultaneous, opposite flows within the same vascular bundle.

Physiological Significance

• Provides a rapid, long‑distance conduit for carbohydrates, hormones, amino acids and signalling molecules.
• Supports growth of sink organs, storage of reserves, and rapid plant responses to environmental stresses.
• Integrates with the xylem: water that enters the phloem at the source is ultimately returned to the xylem, maintaining whole‑plant water balance.

Suggested Diagram

A longitudinal cross‑section of a plant showing a mature leaf (source), a network of phloem sieve tubes, and a sink organ (root tip or fruit). Use arrows to indicate the direction of bulk flow and label the hydrostatic pressure gradient (higher at source, lower at sink). Include a small inset showing the companion cell‑sieve‑tube interface with a sucrose‑H⁺ symporter.

Common Misconceptions

• “Phloem transport is active throughout the pathway.” – Only loading and unloading require ATP; the movement between source and sink is passive, driven by the pressure gradient.
• “Phloem flow is unidirectional like xylem.” – Phloem can conduct sap in opposite directions simultaneously, depending on the distribution of multiple sources and sinks.

Summary

Mass flow in phloem sieve tubes is a pressure‑driven bulk movement of soluble assimilates and water from regions of high hydrostatic (turgor) pressure at the source to regions of lower pressure at the sink. The process hinges on:

• Active loading (and often active unloading) of sucrose by companion‑cell‑powered sucrose‑H⁺ symporters.
• Osmotic water influx from the xylem, creating the pressure gradient.
• The physical properties of the sieve‑tube network, described quantitatively by the Hagen–Poiseuille and osmotic pressure equations.
• Modulation by radius, viscosity, pathway length, temperature and solute concentration differences.

Understanding these principles enables students to interpret experimental data, perform simple calculations, and explain how plants efficiently distribute the products of photosynthesis throughout their bodies.