[First posted: 1.29.17/most recent edits & additions: 2.28.17]

Preamble: this conjecture explores the common driving force in the circadian rhythm shared by all animals and insects on earth. It relates foremost to III. Gravitational Cycles & Induced Torque Into the Cell, but is also relevant to Topics I: Isotopes in the Cell, VII: Isotopes, Nuclear Spin & Chirality, and IV: Asymmetry in the Cell Nucleus as a Means for Driving Torque.

Hypothesis: All plants, insects and animals have a shared 24-hr (circadian) periodicity. During the last two decades it has been shown that this period is expressed within each cell. The hypothesis offered here is that the regulating mechanism is more fundamental than that which can be provided by chemical processes alone, and that they are at least partially driven by the shared circadian periodicity in the gravitational acceleration experienced by every body on earth. When we treat molecules in the cell as comprised, fundamentally, of coupled, oscillating spinning elements, then it can be observed that the period in which these elements precess is governed by their geometry and by the strength of the acceleration field they reside in.

With respect to the need for a precise geometry, life has had three billion years of trial and error folding amino acids into proteins, and if certain shapes were able to deliver the benefits provided by a circadian precession then there is a good chance those shapes would have survived. With respect to the acceleration field, there is no more accurate clock than the gravitational rhythm induced by the rotation of the earth in relation to the sun and the moon, for the period is stable from day to day to within .5-billionths of a second.

[Reference I: Circadian (24-hr) rhythms were originally thought to be regulated by the suprachiasmatic nucleus (SCN) and influenced by patterns associated with day/night rhythms - in particular, the patterns associated with food consumption and the exposure to sunlight. However, two decades ago, biologists identified the CLOCK gene and showed that the circadian rhythm is expressed at the cellular level. The SCN is now believed to be the master regulator of a more complex system that is ultimately driven by contributions from smaller scale processes within the cell. Those process have not yet been fully identified.]

When first exposed to cell biology, it is not uncommon for a person to be left with two 'first-impressions': first, how can each of us share so many common rhythms at such a fundamental level when we each live out our lives detached from each other? That is, what is the common driving force that we share? And, second, what could possibly steer all these crazy objects around in such a precise manner to sustain the order? What is the motivation? After all, even the chaos found on the floor of the stock exchange has some order to it - doesn’t it? How order appears at the stock exchange, and how order appears in the cell may be traced to their respective shared motivations. This becomes the focus for this section...we begin with an engineering task.

If we were assigned the task of building a clock mechanism that could fit inside a ten-micron sized container that could be used to measure time intervals of 24-hrs reliably over the course of a billion years...how might we begin? Such a conjectural exercise is useful to help understand the options available to the cell as it regulates its circadian cycle.

To impose further constraints that will make this engineering task more relevant, we'll need the clock to be designed to operate in environments that vary in pressure, temperature, and acidity; the clock will need to operate when moving and endure a full spectrum of vibrations; and lastly, the clock must be adaptable to operate in either bright light or in near total darkness. This final constraint is important for the CLOCK gene operates within cells that often have no exposure to natural light.

Of course, we'll need to work with components that are sub-micron sized; at least 10^-6 meters small to give us a little wiggle room. But if the clock is to have any significant complexity to it, we'll more likely need to work with components much smaller, perhaps 10^-8 or 10^-9 meters in diameter. Proteins become an obvious good material candidate because, with an average size of ~ 20 Angstroms, they not only will fit inside the container, but proteins can be folded into almost an infinite number of shapes, each with very a precise and distinct geometry. The image of the watch above is a reminder of the type of precision we'll need.

There are two characteristics common to all mechanical oscillating devices: an inertial body that possesses a controllable asymmetry in configuration states - one that is identifiable by an external observer - and a sufficiently reliable force that can act on the inertial body to drive the changes in these states. Since no real mechanism can operate in a perfectly frictionless environment, we need a source of power to compensate for the energy loss. That power might come from an internal battery-type device, such as is found in a nuclear submarine, but that is a tough task for it must fit within our ten-micron sized container and last for a billion years. Thus, while we may need a battery for short intervals, it is more likely that the energy must be collected/harvested from an outside source - one that will not be interrupted for any substantial length of time or depleted over 10^9 years.

Are chemical processes, by themselves, a viable option to use to regulate time intervals? Can we obtain the precision we seek under each of the constraints stated above? Can enzymes be relied upon to maintain chemical balance with sufficient accuracy?

Further, perhaps of greater consequence to inquire about: can we expect the fidelity of chemical processes to be sufficiently true such that after many hundreds of millions of years of evolution in separated and varied environments, the period of their rhythms would be the same?

These are rhetorical questions. As is the consideration of using long-lived isotopes for time-keeping when we ask whether their half-lives can be used to provide cues for both short and long intervals?

Rather than attempt to answer these questions, we'd like to offer conjecture about a method that does have the potential to provide such fidelity and evolutionary [universality/consistency], and thus - perhaps - might have been selected by the cell for its time keeping purposes: the precession rate of spinning elements when subjected to the gravitational rhythms experienced by all bodies on earth.

Simply put, there is no better choice for modeling the force that drives cellular rhythm than one which utilizes the gravitational rhythm introduced by the rotation of the earth. The period of the earth's rotation is stable to within .5-billionths of a second per day, and it has been so for over 4 billion years.* That is an accuracy not obtainable or sustainable in chemical reactions. Further, this period is experienced by every body on earth independent of their location, their orientation, the temperature or pressure of their environment, and whether they are on the land or in deep in the sea.** Equally critical it that this same period is experienced by objects independent of size, configuration or exposure to the environment.

If we're looking for a language that is common to every body and every cell on earth, then the language of gravitation is the place to start. It is not presumptuous or new to conjecture that our cell biology may have evolved in a manner that took advantage of this built in language - our question is to consider methods by which the cell might have tapped into it.

[* Losing roughly 1/1000th of a second per century].
[** More precisely, there is a slight relativistic change in vibration frequency of any oscillator within the cell due to their respective differences in altitude and latitude; this typically amounts to variations of about 10^-7 seconds].

Note that to observe the rhythm requires that there exist an angular asymmetry in the environment otherwise there would be no variation with our orientation. The gravitational field of the sun and the moon provide this asymmetry. We accelerate downwards towards the earth at the rate of 9.8 m/s^2, but we also accelerate towards the sun at the very non-trivial rate of ~ 0.006 m/s^2 and towards the moon at a still significant 0.00003 m/s^2. (In our working hypothesis, we discussed the importance of tracking activity described by numbers far to the right of the decimal point; these numbers are only 'a little ways to the right' and relatively large.) As will be derived below and as will be conjectured about in other arguments on this site, the magnitude of the acceleration towards the sun and the moon varies significantly with the time of day, the position of the moon, and the position of the earth in its orbit. These are not exactly new or original ideas. Nor is associating our 24-hr circadian rhythm with the rotation of the earth, or the female menstrual cycle with the 28-day period of the moon. But with the discovery of the CLOCK gene and the realization that the internal rhythm of the cell is expressed at deeper, more fundamental scales, perhaps out models need to re-consider ideas that are tied to forces that are more fundamental too. And, thus - since there is no force more fundamental than Newtonian gravitation - this now becomes the focus for our modeling.

To properly convey the arguments, we need to revisit some of the basic principles associated with gravitational and rotational dynamics. We will simplify much of the sun-earth-moon orbital geometries; while this will mask other smaller rhythms, it makes the subject more approachable - especially to the authors. Much more sophisticated derivations can be found in any good physics or astronomy library.

The simple diagram below illustrates the relative strength of the gravitational force produced by the sun, the moon, and the earth, acting on a (body) mass standing at the earth's equator. Worth noting is that the gravitational force from the earth is only about 1700 times as strong as that from the sun. This means that a person who weighs 150 pounds (~ 70 kg) will see their weight oscillate by an ounce or two (~ 40 g) depending on the position of the sun (time of day). And while this may seem like a trivial variation, it should be remembered that the tidal force from the moon that produces the rhythm in our oceans is the result a variation in gravitational strength of only one part in 10^7th. As the calculation below also shows, the sun's gravity is 175 times as strong as the moon's.*
*[Note: although the sun's gravitational strength is stronger than the moon's, tidal forces result from gradients in the force, which are about twice as strong from the moon as they are from the sun.]

These next diagrams illustrate the relationship between the angular momentum that a body has when spinning about its geometrical axis and the precession rate the body has when placed in a gravitational field.

When a spinning mass is placed into a gravitational field, it is subjected to a torque which causes it to precess at a rate that is directly proportional to the sum of accelerations. These relationships are given by:

If we re-write the weight as the product of the mass times the acceleration (W=mg) then the precession formula becomes:

Mass, m; distance from center of mass to the supporting tip, r; moment of inertia, I; angular velocity of the spining mass, w. Each of these variables in the parentheses is a function of the spinning mass; notice that the precession rate is not a function of the orientation of the mass. Whatever angle we orient the top at - whether oriented almost veritically, or lying almost flat down, the precession rate will be the same. Thus, as long as we don't change our spin geometry (shape and spin rate), and our gravitational acceleration remains constant, then the orientation of the top can be changed without altering the precession rate. Further, if we were to build any number of such tops with similar geometry and spin, then scatter them around the environment, they will all precess at the same rate.

The associated precession energy is given by:

[This is important because the cell cycle is all about managing internal torque and energy. (And critical to the growth associated with cancer is that the cancerous cell must find a method for stealing that energy.) Note that if we alter the acceleration (gravitational or centrifugal), or we alter the shape of the object, then the precession rate will also be directly altered. Note too, that if we switch out a more common isotopic version of an element for a less common - [example] - then we also alter the normal/expected precession rhythm.]

Accordingly, we can make an extended series of arguments that the geometry of biological molecules (DNA, proteins, enzymes, etc…) has evolved to best manage the torque and energy cycles associated with precession which result from the combined gravitational and centrifugal acceleration environment our cells reside in. The statistical edge in this debate is strengthened when we recognize that life has had three billion years of biological trial and error to test for configurations that produce the most compatible rhythms.

This is really not so radical a thought. Scientists are very comfortable stating that every time we raise our arms or legs and every time our hearts beat, the action requires that we expend energy either fighting the gravitational pull of the earth or the pressure gradient that results from it. Yet, there is commonly skepticism when an argument is presented that includes the possible energy expended by a body to combat the gravitation pull from the sun (which causes a small but significant acceleration of roughly 6 x 10^-3 g’s) or the moon (a small but significant 3 x 10^-5 g’s). These values are small, but they are only a few decimal points to the right of 1g and the cell must manage these energy expenditures too.

This argument will be extended in the next few weeks to include:
1: Gravitational Rhythms & "Effective weight"

2.The precise folding of proteins to match precession.

3. The altered precession rate of isotopes.

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