Work rate (PF)
Figure 3.3 The energetics of maintaining the internal environment. a: A potential energy difference (PEi-PEe) drives a thermodynamically favored flux, Jtff, across the integument. The environment does work on the organism, at a rate Wtff, the product of the flux and the potential energy difference driving it. b: To maintain the internal environment, the organism must do work on the environment, which drives a physiological flux, Jpf, of matter across its outer boundary, at a rate WpF.
environment will therefore require work to drive an equal flux of matter or energy opposite to the TFF (Fig. 3.3), which we shall call the physiological flux (PF). Maintenance of body temperature in the cold requires a physiological flux of heat into the body, which is released by the metabolism of glucose or fats, for example.
Conventionally, physiological fluxes, like the performance of any physiological work, are powered by the metabolic energy stream (Fig 3.2). In Chapter 2's example of the fish in fresh water, the potential energy gradient driving the TFFs of water and solutes arose from the different concentrations of solutes and from the resulting differences in osmotic concentration inside and outside the animal. The fish then had to use metabolic energy to drive PFs of water out and solutes in. In this case, the metabolic energy powers two kinds of work, and the metabolic energy stream divides into two roughly parallel substreams (Fig. 3.2). Reproductive work makes progeny. Physiological work powers the fluxes of matter and energy that are necessary to maintain the internal environment.
Adaptation involving conventional physiology can be fitted comfortably into mainstream Darwinian thinking. As far as we know, the only type of energy that can power reproductive work is the chemical potential energy in food. That is, reproductive work must come from the metabolic energy stream. Presumably, this is because the only means by which organisms transmit information about themselves is chemical (through DNA), and the maintenance, synthesis, and replication of DNA are chemical processes that require chemical energy to drive them. If reproductive work requires maintenance of a particular internal environment, then infrastructure that provides this environment efficiently will be favored by natural selection, because proportionally more energy will be available for reproductive work if less energy is needed for "overhead." To the extent the infrastructure is coded for genetically, conventional Darwinism is adequate for explaining physiological adaptation.
Keep in mind, however, that much of the physiological work is fairly prosaic—maintaining gradients of temperature, pressure, solute concentration. Thermo-dynamically, there seems to be no fundamental reason why the metabolic energy stream must do all this work. Indeed, if some other source of energy could be used to power physiological work, even more of the metabolic energy stream might be diverted to reproductive work. Even if this diversion is small, its evolutionary consequences could be large.
Making energy do work means capturing and channeling it so that it flows in a controlled way down a potential energy gradient. Usually a structure of some sort—whether it be an imperfection in a silicon crystal, an enzyme molecule, or a crankshaft—directs the flow of energy. If physiological work is to be powered by the physical energy stream, there must be a structure of some sort that can capture and channel the energy.
Most engineering done by humans is devoted to figuring out clever ways of manipulating energy. Surprisingly, there turn out to be just four: energy flows can be resisted, they can be rectified, they can be switched and they can be stored for use later. These common patterns will help us organize our thoughts about how animals can build structures to do physiological work.
One of the great achievements of nineteenth-century physics was to show that energy can exist in many interchangeable forms. In itself, this is a remarkable feature of the universe: we just have to let that claim stand for the time being. I offer it for practical reasons, for it provides a very powerful tool for thinking about how energy moves and works. The tool is this: if all forms of energy are potentially interchangeable, it follows that a description of how one form of energy does work will also describe how other forms of energy do work. Understand one and (on at least one level) you understand them all.
Let us illustrate by relating two superficially unrelated processes: the flow of electrical current across a resistor and the flow of water in a pipe. The flow of current can be described by Ohm's law, which relates how current (energy) flows under a voltage (potential energy) difference between two points:
where I is electrical current in amperes, AV is the voltage difference driving the current, and Re is an electrical resistance, in ohms, that impedes the current. The flow of water down a pipe, on the other hand, is described by Poiseuille's law:
where V is the volume of water flowing through the pipe per second, L and r are the pipe's length and radius, respectively, n is the water's viscosity, and AP is the difference in pressure between the two ends of the pipe.
Poiseuille's law is a complicated equation that seems to bear little relation to Ohm's law. However, we can simplify Poiseuille's law by lumping several of the terms together into one: a hydraulic resistance, Rh, that describes those things that impede the flow of water through the pipe. These include the dimensions of the pipe (it is harder to get water to flow through a long or narrow pipe than it is through a short or wide pipe) and the fluid flowing through it (it is harder to get a viscous fluid like syrup to flow through a pipe than it is to get water to flow). If we do a little algebra on equation 3.2, we can easily formulate the hydraulic resistance so:
We can now rewrite Poiseuille's law as follows:
With the equation in this form, Ohm's law and Poiseuille's law look very similar. Indeed, we could write both using common terms:
flux of matter or energy
= potential energy difference / resistance to flux [3.5a]
Some prefer to express a resistance as its inverse, or conductance, in which case we can rewrite as follows:
I shall do the same here, using concepts, terminology, and symbols familiar in electrical engineering to discuss how structures built by animals could alter or manipulate flows of physical energy and make them do physiological work. This is, in fact, a very widely used method known as the electrical analogy, and it is one I use often through this book. Furthermore, just as the number of possible electrical circuits is vast, so too will be the analogues that animals could build for powering their external physiology. Let me close the chapter now by illustrating, in a very general way, how externally built structures might be employed by animals to make external physiology work.
Assume first that there is a potential energy (PE) difference between the environment and the Earth—it could be sunlight, wind, gradients in temperature or water vapor. Formalize this difference in words:
PE difference = environmentalPE — Earth's PE or as an equation:
If it drove a flux of matter or energy in just the right way, this potential energy difference could be made to do work. The rate at which the work is done, or the power, will be the product of the flux rate and the potential energy difference driving it. In words:
flux of matter or energy
= conductance X potential energy difference [3.5b]
The generality implied by these equations makes possible a kind of intellectual piggybacking: if we know a lot about one kind of energy flow, then we know a lot about all kinds of energy flow. If, for example, electrical engineers have been more clever than hydraulic engineers at figuring out how to make electrical energy do work, hydraulic engineers can take these clever ideas and adapt them to their own problem of making water do work.
power = work rate = flux rate X PE difference
As indicated in equation 3.5a, the flux rate (J) is determined by the PE difference and a resistance to the flux:
Thus, any structure that imposes a resistance to the flow of energy between the environment and Earth is potentially capable of powering work.
In the absence of our hypothetical structure, the flow of energy down the PE difference between the environment and Earth could be represented as an analogue electrical circuit, or equivalent circuit (Fig. 3.4). The equivalent circuit is simplicity itself: two points, each of which has a particular potential energy, bridged by a resistor that limits the rate that energy can flow.
Suppose now that an animal builds a structure that is interposed between PEenv and PEEarth (Fig. 3.4). There are several ways we could represent the effect of this structure on the flow of energy. One thing the structure might do is simply to impede the flow of energy between PEenv and PEEarth. In an equivalent circuit, this can be represented by a new resistor, which we shall call Rstr, that is connected in series with Re (Fig. 3.4). The point of connection between Rstr and Re represents a new potential energy, PEstr, which, of course, introduces a new potential energy difference that can drive a flux between the structure and environment or between the structure and the Earth. When PEenv is greater than PEEarth, the energy in the environment will do work on the structure. Conversely, when PEenv is less than PEEarth, the energy in the Earth will do work on the structure.
A resistor is a passive component because it is, by definition, insensitive to control: a resistor will as easily (or as poorly) impede the flow of energy in one direction as it will in another. In many circumstances, this feature of resistance is irrelevant, but often it undermines the possibilities for adaptive control. Suppose, for example, that our hypothetical structure is useful to the animal that built it only when the environment does work on it, not when the Earth does work on it. In other words, the structure is useful only when energy flows in one direction (environment ^ structure ^ Earth), not in the other (Earth ^ structure ^ environment).
This is a common problem in making electrical circuits work properly, and one of the many solutions electrical engineers employ is to interpose a device that allows current to flow only in one direction and not the other. These devices are known as rectifiers, and the process whereby a current is limited to a cer-
Figure 3.4 a: Energy flows down a potential energy difference between the environment (PEenv) and the Earth (PEEarth). The direction of energy flow will be determined by which potential energy is greater, and it will be restrained by some resistance, Re. b: A hypothetical structure can be made to do work by imposing an additional resistance, Rstr, between the potential energies of the Earth and environment.
tain direction is known as rectification. The most common type of rectifier is a simple device known as a diode (Fig. 3.5a). Just as a resistor in an equivalent circuit symbolizes the limitation of energy flow down a gradient, a diode symbolizes the rectification of energy flow. For the kind of rectification proposed in the last paragraph, the structure would be equivalent to the resistor, Rstr and a diode, Dstr, in series (Fig. 3.5). At its simplest, the flow of energy through the structure would be represented by the conditional equation:
J = (PEstr - PEEarth)/Rstr [IF (PEstr - PEEarth) > 0] [3.8]
A diode is a simple logic device that "decides," on the basis of its direction, whether to let a current flow across it. There may be circumstances, however, in which the decision is best based upon other criteria. In our hypothetical structure, capturing environmental energy may be useful only under some conditions and not others. This would imply there is an alternative pathway for the energy to flow when the organism does not want it to flow through the structure. Again, this is a common problem in electrical circuits, and the device used to solve it is the switch. Switches come in a variety of forms—for our purposes, we will use a common type, the transistor. In a transistor, a small current fed into a terminal called the base (or gate) switches a
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