Biochemistry of Plants harnessing heat-energy when blue-shifted light is scarce

Question

What biochemical reactions might be employed by plants to harvest heat energy when light energy is scarce or even missing? What is the temperature range over which this biochemical reaction can work?

Background: A red-dwarf M-star, emitting most of its energy in the red and infrared side of the spectrum. The planet is tidally locked to its star. Some red-shifted light irradiates on one side of the planet while the other side is in perpetual darkness...

Constraints: According to the laws of thermodynamics, you cannot convert heat into useful energy, you can convert HEAT DIFFERENCE into useful energy. Alas, tidally-locked planets don't seem to allow much temperature fluctuations which create enough HEAT DIFFERENCE in one area. I will soon suggest possible solutions to circumvent the problem without violating the laws of thermodynamics.

CREATING HEAT DIFFERENCE IN THE FIRST PLACE

1- Capturing radiative heat: A leaf exposed to the heat of the star absorbs more heat. If the leaf is black, it heats-up above the AMBIENT AIR TEMPERATURE. The other side of the leaf loses heat and there is a heat difference between the two sides of the leaf. Leaf thickness is a significant factor, here. This strategy works well for land plants and plants floating on the high seas.

2- Doing the "Yo-Yo": This is a good strategy for aquatic plants on the dark side (receiving no radiative heat from the star): If the plants had a controllable buoyancy bladder, they can do the yo-yo in cycles: By adjusting the bladder's buoyancy, the plant moves up and down to juggle between currents of hot and cold water.

BIOCHEMICAL PRINCIPLE OF HEAT ENERGY

This is what I'm looking for -- What chemical reactions could harness heat energy in that manner? The thermo-chemical energy harvesting is a reversible process which works as follows: Assuming there are two substances, named A and B. The two molecules recombine to form a molecule AB.

Upon exposure to heat, the molecule AB decomposes into two constituents A and B:

AB + Heat --> A + B

The molecules cannot recombine as long as heat exposure continues. Upon exposure to colder temperatures, the opposite happens:

A + B --> AB + energy.

This recombination can be used as an electron donor, just as oxygen and hydrogen combine to make water in a fuel cell. The electron donor drives photosynthesis.

HARNESSING HEAT DIFFERENCE AS SOURCE OF ENERGY

There are two modes of making use of heat difference:

• Passive transfer: The example of aquatic plants being able to move up and down between hot and cold regions. The constituents A and B are "locked" via specialized enzymes so that the plant allows their recombination in a controlled manner. Single-celled organisms do the same as they are carried away between hot and cold currents.

• Active transfer: Plants under the red sun may have the equivalent of blood vessels moving a fluid between the side facing the sun (absorbing radiative heat) and the other side (radiating heat back to the environment). This means that any "plant" will be more complex and comparable to animals.

Answer 1

M-type dwarves emit a lot of electromagnetic energy

The surface of an M-type star is generally pretty hot. An M0V star has effecive surface temperature of 3800 K at 7.2% of the sun's luminosity; an M9V has temp 2300 K and luminosity 0.015%.

Let us assume that we are dealing with a M4V star at 3000 K as given in the chart above. Peak irradiance is at about 800-1000 nm at about 6% of what we see from the sun. Lower at around 700 nm, we might get 4% of what we see from the sun.

The solar spectrum seen at sea level is affected by the absorption of the atmosphere.

You can see that there is an unfortunate water absorption band right in the middle of our desired range, but wavelengths at about 850nm and 1000nm will be good. The area around 700nm would also be useful.

If we integrate a 25nm wide bandwidth around 700nm, 850nm and 1000nm, given the ratios of absorption seen in the Earth's atmosphere, and multiplying by 4%, 6% and 6%, we get incident radiation of 1.2W/m$^2$, 1.4W/m$^2$, and 1.0W/m$^2$.

These numbers are incident energies in potential photosynthetic bands. Compare them to about 100 W/m$^2$ average sunny day irradiance in the tropics in the photosyntheically active range.

Plants could use energy in these wavelengths

In particular, there do exist pigments to capture light in the near-infrared regions, at 700 nm. Chloropyll-d and Chloropyll-f will both absorb in this region. It is entirely possible for plants evolved on this world to develop accessory pigments specialization in the near infra-red band, just as deep water plants on Earth have pigments specializing in the green and yellow bands.

In particular, it is important to note plant's chlorophyll and animal's eyes are both using the most abundantly energetic light band. On Earth that is the 'visible' light range, though there is nothing special about that range. On an M-type dwarf, it would be reasonable for the 'visible' range that all creatures use to be 700-1000 nm.

If plants use the three bands mentioned above, then they will have something like 5% if the energy available to them, as compared to the energy available on Earth.

This compares well with a heat engine

Your alternative suggested is using some sort of heat engine to generate energy. The maximum theoretical energy generation of a reversible (which your chemical reaction appears to be) reaction is limited by Carnot efficiency to $$\eta = 1-\frac{T_C}{T_H}.$$ Assuming, somewhat liberally, that your planet has near Earth-like conditions and can somehow utilize a temperate gradient of $T_C=280K$ to $T_H=330K$, then maximum efficiency is $$\eta=1-\frac{280}{330}=15\%.$$

Let us assume that the plant can utilize all the energy differential between water at 300K and 280K. The specific heat of water is 4.184 kJ/kg; so 1kg of water has 84 kJ of energy, or 13 kJ/kg at 15% efficiency.

Comparison

A plant on a red-dwarf world has about 0.7 W of energy generated as glucose available to it per minute per square meter of surface area. This energy has a well established on Earth path for utilization; the photosyntheic pathways exist, the pigments for at least some of the frequency bands exist, and it is reasonable to assume that life would evolve optimized pigments.

Lets make some practical efficiency assumptions for the plant using a heat engine method.

• The plant must store a 'hot' reservoir 20 K above the 'cold' reservoir environment. Let us assume the plant must 'pump' the working fluid at 20% efficiency against 1 meter of head to keep there reservoirs separated. This works out to about 50 J per kg that need to be transferred.

• The plant loses 50% of the heat energy that it has stored to heat transfer dissipation.

• Instead of 15% Carnot efficiency, the plant can get 0.5% of the available heat energy absorbed by ATP. A thermo-electric generator has efficiency of 5%; but keep in mind solar powers are 10x more efficient than photosynthesis, so 0.5% seems like a reasonable estimate.

• This plant has the same ~30$ ATP to glucose efficiency that plants on Earth have.

The energy output works out to 63 J per kilogram; minus the pumping requirements, we have 13 J per kg.

We are sort of comparing apples to oranges here. There are some obvious ways that this plant could be getting more energy from heat than it could from solar EM radiation. If the heat gradient was strong and constant, like a volcanic hot springs, then this plant could get a lot of energy. However, for your proposal that a buoyant plant captures maybe 100 kg of warm shallow water, then processes it in the deeps, you would get maybe 1.3kJ energy per cycle. Meanwhile, a photosyntheic plant would get the same energy in half an hour.

Finally, let me stress again that a plant's photosynthetic efficiency is well documented, but the thermal processes I am proposing and totally conjectural and possibly optimistic.

Conclusion

The energy math wasn't as clear as I was hoping that it would be, but I have convinced myself at least that the energy that can be possibly extracted between a hot and cold reservoir is not very much compared to what you would get from the sun.

For the conjectural numbers I used, you would have to move 3 kg per minute between hot and cold reservoirs 20 K apart to get the equivalent of 1 m$^2$ of leaf area. Leaves are relatively cheap to make for a plant; they seems energetically very favorable compared to a heat pump.

I conclude that your plants best bet on a M-type dwarf star is to use the available near-IR radiation and do the best they can with photosynthesis; heat pump reactions are probably not worth it energetically.

Answer 2

The heat eater uses a conformation change to turn ATP synthase and generate ATP. The conformation change is produced by a bladder partly filled with liquid which expands when heated and later contracts on cooling.

1. ATP synthase. Consider a motor. It converts electrical energy to mechanical rotation. But if you spin the motor with a crank, the motor becomes a generator and will put out electricity.

ATP is the energy currency of the cell. ATP synthase is much like a motor / generator. ATP synthase converts mechanical energy (rotation) into chemical energy by phosphorylating ATP. It can also run backwards, hydrolyzing ATP to ADP and rotating in reverse.

The rotary machine in the cell, ATP synthase. Noji H, Yoshida M. J Biol Chem. 2001 Jan 19;276(3):1665-8.

ATP synthase, a major ATP supplier in the cell, is a rotary machine found next to the bacterial flagella motor in the biological world. This enzyme is composed of two motors, F0 and F1, connected by a common rotor shaft to exchange the energy of proton translocation and ATP synthesis/hydrolysis through mechanical rotation. Rotation of the isolated F1 motor driven by ATP hydrolysis was directly observed with an optical microscope, and its marvelous performance has been revealed. The motor rotates with discrete 120° steps, each driven by hydrolysis of one ATP molecule with nearly perfect energy efficiency. Apparently a cooperative domain bending motion of the catalytic β subunits initiated by ATP binding generates the torque. In the F0motor, which we know less about, it has been proposed that torque may be generated by the large twist of one helix of F0 c subunits or by the change in electrostatic forces between rigid subunits.

Generally in cells of any sort the rotation is provided by protons moving across a gradient. In the heat eater, mechanical energy produced by a phase change (liquid to vapor) is translated to an elastic conformational change which turns ATP synthase.

A good way to capture heat energy as mechanical energy is via a phase change. The change of solid or liquid to gas involves large changes of pressure which can be captured as mechanical energy. A steam engine is a fine example: heat turns water to steam and mechanical energy can be captured from this to turn an engine.

The heat eater will use an elastic, distendable bladder containing liquid. As it is heated, the vapor pressure increases and the bladder will distend and stretch. Water could be the liquid. Acetone is compatible with biological systems (our own bodies make it!) and the vapor pressure at 40 C is 400mmHg, as opposed to 40 mmHg for water.

The bladder is made of some elastic protein like elastin that can elongate and then come back to normal. In the heat eater, as the elastin stretches it turns ATP synthase and generates ATP.

Later when the sun goes down and the bladder cools and contracts, its contents condensing back to liquid, the recovering elastin is unhooked so it does not turn ATP synthase backwards to hydrolyze ATP.

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The heat eaters would look like a field of big bladders in the sun. Why, if so easy, are there not loads of organisms which make use of this mechanism? I suspect it is not so easy to evolve alternate methods of turning ATP synthase.