When biology meets mathematics: modelling calcium oscillations

Calcium ions (Ca2+) are important signal molecules to relay information around cells, for example during muscle contraction in animals. In plants calcium signalling is involved in a number of processes including growth and defence against disease-causing microbes.

Calcium signals are generated during the establishment of the symbiosis between legume plants and nitrogen-fixing bacteria (rhizobia). Rhizobia present in the soil produce compounds called Nod factors (NFs) and these are then detected by receptors on the plasma membrane of plant cells on the surface of the root (Figure 1). A signal relay from the plasma membrane to the nucleus is activated. When the signal reaches the nucleus it activates oscillations in the concentration of calcium ions (known as calcium spiking). This signalling pathway results in a number of changes in gene expression in root cells that are required to set up the symbiosis.

Nod factors produced by rhizobia are detected by receptors on the plasma membrane. A signal relay to the nucleus is activated resulting in the generation of calcium oscillations in the nucleus (calcium spiking). Downstream of calcium spiking changes in gene expression required for the development of nodules and the rhizobial infection into the plant.

Figure 1: Nod factors produced by rhizobia are detected by receptors on the plasma membrane. A signal relay to the nucleus is activated resulting in the generation of nuclear calcium oscillations (calcium spiking). This then leads to changes in gene expression required for the development of nodules and rhizobial infection into the plant.

How are calcium oscillations generated in cells? There are two things to consider here. Firstly, calcium ions are positively charged and unable to diffuse through the lipid bilayers that make up cellular membranes. They can only cross membranes with the help of proteins found in the membrane (calcium channels or pumps). This provides the cell with the means to regulate the concentration of calcium ions in cell compartments by regulating the channel or pump proteins. Secondly, calcium ions are toxic to cells. Cells use energy to pump it out across the plasma membrane or into membrane-bound storage organelles such as  vesicles, the vacuole (in plants only), or the space between the inner and outer nuclear membranes (nuclear membrane lumen). In these organelles calcium-binding proteins sequester the calcium ions to keep them from causing harm.

As a result of this activity calcium concentrations are much higher outside the cell (and in organelles) than in the cytoplasm. If the plasma membrane were to become permeable to calcium then there would be a net movement of calcium ions into the cell from the outside until the concentrations of calcium in the two compartments were the same. To generate a calcium signal the membrane only has to be permeable to calcium for a short time so the actual movement of calcium ions is small, but big enough to be detected by proteins further along the signal relay.

The same principles apply to NF-induced nuclear calcium (spiking) in legumes with the calcium store being the nuclear membrane lumen. When the signal from the NF receptor proteins on the plasma membrane reaches the nucleus calcium is released from the nuclear membrane lumen into the nucleus by the opening of a calcium channel (as yet unidentified). Then the calcium is returned to the nuclear lumen by a calcium pump (a Ca2+-ATPase called MCA8) (1), which uses energy to drive calcium ions back across the membrane against the calcium concentration gradient. This creates a single spike in calcium concentration in the nucleus. This cycle is repeated to generate calcium spiking.

A potassium ion (K+) channel called DMI1 is required for calcium spiking (2). Why would potassium ion flow across the nuclear membrane be needed for generating calcium spiking? There are a couple of possibilities: potassium ions may flow into the nuclear membrane lumen to balance the flow of charge as calcium ions flow in the opposite direction, or alternatively a flow of potassium ions across the nuclear membrane may be required to activate the calcium channel.

Can the calcium channel, calcium pump (MCA8) and the cation channel (DMI1) alone generate the NF-induced calcium spiking we see in legumes? Collaboration between biologists and mathematicians has produced a mathematical model to simulate calcium oscillations using these three components (3). (I won’t go into the mathematics, if you are interested see the research paper.) The model can produce oscillations similar to those observed in legumes. Further more these oscillations are self-sustaining so do not require extra inputs once activated. However, the oscillations in the model continue indefinitely suggesting that a component is missing.

Figure 2: Model of nuclear calcium spiking. The signal realy activated by NF activates the DMI1 potassium ion channel (1.), leading to the flow of potassium ions into the nuclear membrane lumen. This activates the calcium channel resulting in the flow of calcium ions from the nuclear membrane lumen into the nculeoplasm to generate the upward part of the calcim spike. (2.) DMI1 and the calcium channel close and the calcium pump MCA8 returns calcium to the nuclear membrane lumen (the downwards part of the spike). The system is reset and the cycle repeats to generate mutliple spikes.

Figure 2: Model of nuclear calcium spiking. The signal relay activated by NF activates the DMI1 potassium ion channel (1.), leading to the flow of potassium ions into the nuclear membrane lumen (space between the inner and outer nuclear membranes. This activates the calcium channel and calcium ions flow from the nuclear membrane lumen into the nucleoplasm to generate the upward part of the calcim spike. (2.) DMI1 and the calcium channel close and the calcium pump MCA8 returns calcium to the nuclear membrane lumen (the downwards part of the spike). The system is reset and the cycle repeats to generate multiple spikes.

The group discovered that if they added nuclear calcium-binding proteins into the model, which by binding calcium effectively lower the free calcium ion concentration, they could  stop the oscillations by increasing the calcium-binding protein concentration. It is feasible that once NF-induced calcium spiking is started in the plant there is a mechanism in place that increases the concentration of calcium-binding proteins in the nucleus to stop the calcium spiking at the appropriate time. The model indicates that the DMI1 channel is acting to activate the calcium channel but also to balance the flow of charge during the generation of a calcium spike (4).

To me the most impressive thing about the model is that it proposes a mechanism for how a system made up of only four components could generate nuclear calcium oscillations in plant cells. Like all models it has limitations as it has made some assumptions and is a simplified view of what is going on in the plant cell, but it provides a working model whose predictions can then be tested experimentally. It an example of how scientists with different specialisms can work together on a research question and provide insight that might not be achieved when working separately.

References:

1) Capoen et al. (2011) Nuclear membranes control symbiotic calcium signaling of legumes. PNAS

2) Peiter et al. (2007) The Medicago truncatula DMI1 protein modulates cytosolic calcium signaling. Plant Physiology

3) Granqvist et al. (2012) Buffering Capacity Explains Signal Variation in Symbiotic Calcium Oscillations. Plant Physiology.

4) Charpentier et al. (2013) The role of DMI1 in establishing Ca2+ oscillations in legume symbioses. Plant Signal Behav

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2 thoughts on “When biology meets mathematics: modelling calcium oscillations

  1. Pingback: Imaging calcium ions using a Yellow Cameleon | Plant Scientist

  2. Pingback: CCaMK: a protein switch in plant-microbe symbioses | Plant Scientist

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