"When you change the way you look at things, the things you look at change."   —Max Planck


Analysis Of Miley Data
Consequences Of Partitioning The Photon Into Its Electrical And Magnetic Vectors Upon Absorption By An Electron
Nickel Transmutation and Excess Heat Model Using Reversible Thermodynamics - The Least Action Nuclear Process (LANP) Model
Re-thinking Cold Fusion Physics: An Essay
Cold Fusion and the First Law of Thermodynamics: An Essay
Can We Explain Excess Heat Uncertainty With a Law of Physics: An Essay
The Atom's Temperature
Cold Fusion and the Three Laws of Thermodynamics
Review Of Temperature Issue And My Calculations 12/8/15
Theory of Heat I - Non-equilibrium, Non-quantum, Blackbody Radiation Equation Reveals a Second Temperature Scale
Theory of Heat II - A Model of Cell Structure and Function
Theory of Heat III - Nickel Transmutation and Excess Heat Model Using Reversible Thermodynamics

Theory of Heat II
A Model of Cell Structure and Function

Daniel S Szumski, Independent Scholar
Davis, California, USA
May 9, 2003

A. Introduction

The physical principles underlying entropy relationships in matter's living state continue to baffle scientific inquiry. Despite our advances in understanding the complexity of cellular biochemistry and genetics, the physical laws that give rise to life seem to be beyond what the known laws of physics allow. This of course is not true; and in spite of arguments favoring principles outside our understanding to account for matters living state[1], there is nothing that contradicts the view that life results from extensions of existing physical laws that have not yet been coalesced into the proper theoretical framework.

Schrödinger was instrumental in explaining how the principles of physics might be applied to living systems. His insightful work[2] broke down the complexity of what was known about the cell in 1941, into concepts that could be isolated and generalized. He was among the first to describe the living state's negentropic character, its apparent ability to locally decrease entropy.

Szent-Györgyi[3] was coming to the understanding that ensembles of proteins might possess common energy bands similar to those being studied in semiconductors. He based his supposition on studies showing that large numbers of similar enzyme molecules appeared to be acting in concert to effect biochemical transformations. His belief was supported by studies on chlorophyll, urease, and fumarase among others. But it went farther, even suggesting that this type of behavior might go beyond electron tunneling among similar molecules, to perhaps, discrete energy levels within the entire cell structure. He speculated that electrons might be directed over large distances, allowing them to fall to lower energies only where they would perform useful work.

With characteristic eloquence, Monod[4] summarized the state of enzyme form and function in 1971. He wrote of the remarkable structural fidelity, precise globular forms, and unerring specificity of the enzymes that were the subject of his life's work. In the end, he concluded that something beyond genetically determined peptide sequence imparted the information content found in their condensed form. What exactly, he could not say.

That unfortunate circumstance is unchanged even today. The only thing that we can say with any certainty is that somehow within the context of the cellular environment, the enzyme's polypeptide sequence acquires large amounts of information (negentropy) which ultimately specifies both its form and a very specific function.

The biochemical data that has been amassed during the last 60 years characterizes with extraordinary precision the mass quantities within the cell. DNA, RNA, proteins, and countless other molecules have been described in both their structure and function. Their mutual interactions and their interactions with other molecular forms will soon be exhaustively catalogued. Yet it doesn't seem that we are that much closer to understanding the principle(s) that cause a linear polypeptide sequence to acquire its extraordinary negentropic character, much less, nature's closely guarded secrets of the living state.

It is this author's belief that this state of affairs reflects our continuing emphasis of life's molecular forms. This is only natural. We can see them. But, still they are only about half of the picture. The unseen half, consisting of energy fields that accompany the molecular forms and hold their covalent bond structure in a far-from-equilibrium state, are surely as important. I am not referring here to the individual energy relations in any specific molecule, but rather the overall context of the cell's covalently bonded, electro-magnetic field structure.

We should expect this electro-magnetic signature to be very precise. After all, the 'glue' that holds the atoms and molecules together should reflect the far-from-equilibrium state in those quantities. But, more to the point, it should have its own negentropic character, which once revealed, may tell us even more about life. Since the answer that eluded Schrödinger, Elsasser, Monod, Luria[5] and countless other extraordinary intellects has not yet been evident in the mass quantities, perhaps it is the radiation field that possesses Monod's ultima ratio [4].

This paper is one small step in that direction. It begins with some thoughts on non-equilibrium heat theory, and speculates on the spectral distribution of heat energy within living systems, and the nature of its far-from-equilibrium condition.

B. The Dual Nature of Heat Energy

The amount of heat energy stored in any physical system is the sum of two quantities: the energy stored in its heat radiation field, and that contained in thermal motion. The first quantity can be thought of as existing entirely in the electro-magnetic domain (radiation domain), while the second exists only in the domain of material particles (mass domain). Energy exchange between these two domains occurs continually, always driving the system toward a maximum entropy condition that an observer sees as thermal equilibrium. It was Helmholz's great contribution to physics to recognize that heat energy ultimately reduces to motion. And as long as the process is reversible, and the driving force is in the other direction, the reverse can also be true.

The distinction between these two types of heat energy is well known. We find that when two material bodies are rubbed together, the resulting molecular motion causes both to become heated. It is also possible to impart an identical amount of heat to these same two objects by exposing them to a source of electro-magnetic energy (eg. the sun). And in fact, when the heat energy distribution in both cases has reached an equilibrium, it is not possible to distinguish by which mode the equilibrium was affected. The equilibrium heat radiation spectra was first described by Planck[6]. Our understanding of thermal motion in a gas at equilibrium is associated with the revered names of Boltzman[7] and Maxwell[8].

A heat system rarely achieves true equilibrium. It generally perturbates around a quasi-equilibrium state, where microscopic changes predominant, or it evolves inexorably toward a new equilibrium state. A third non-equilibrium condition might also be possible, one in which the heat distribution of the radiation and/or the mass domain is held in a stable far-from-equilibrium state.

C. Non-Equilibrium and Far-From-Equilibrium Heat Energy Storage

I recently proposed a alternative form for Planck's blackbody radiation equation that suggests an avenue to non-equilibrium, and possibly even far-from-equilibrium solutions to the heat radiation problem[9]. The candidate, non-equilibrium blackbody spectral distribution was found to have the form:


(2)    (the Wein frequency)

(3)    (entropy operator)

  exists where its magnitude equals or exceeds , a single quanta,
 Tm is the thermodynamic temperature,
 TR is a new quantity described as the radiation temperature.

This last equation, , expresses the interconnectedness between the range of blackbody frequencies, , and the Wein frequency, . Several features of the theory behind this equation are relevant to what follows.

The first is the hypothesis that radiation absorption might take place as a two step process wherein light's one dimensional form is initially absorbed by an electron in discrete quantum amounts, and then, in the second step, it is partitioned into three dimensional electrical charge and one dimensional magnetic spin. The first step is shown to be an adiabatic reversible process; the second: entropic.

Figure 1 - Illustration showing how the equilibrium blackbody spectra at 293°K can be distorted to two far-from-equilibrium conditions. Case A increases the thermodynamic temperature, Tm, alone. Case B shows an adiabatic increase in the radiation temperature, TR, alone. The shaded area is an idealized representation showing the region where the covalent bond structure of the cell is localized.

Secondly, the theory suggests that the radiation and mass domains might be represented by independent temperature scales. Figure 1 illustrates the principle characteristics of the non-equilibrium blackbody radiation spectra. The Base Case illustrates an equilibrium solution for 293°K. It is close to, but not exactly Planck's solution. Case A is a condition where the mass domain temperature alone is increased (friction input of heat), while Case B represents a similar increase in the radiation domain temperature resulting from radiation absorption. These two cases are far-from-equilibrium states which would normally decay to an equilibrium spectra similar to, but with higher total energy than, the Base Case. At equilibrium the radiation and mass temperatures become identical.

In living systems, it seems possible that these two temperatures could remain separated in a stable far-from-equilibrium configuration by masking a portion of the blackbody spectra within the mass system's covalent bond structure. In this way, the radiation energy is isolated in a stable manner that uncouples it from the normal mechanisms of energy redistribution, and prevents its return to equilibrium. By masking a portion of the energy in this way, large quantities of heat energy can be stored without increasing the system's apparent temperature.

A third feature of the far-from-equilibrium spectral distribution is its enormous, but always finite, energy storage capacity. The far-from-equilibrium region shown for Case B represents trillions of individual quanta, each of which could, in theory, be coded with one bit of information. We will propose for the moment (because this simplicity will aid in explainig some difficult concepts), that each of these represents the energy storage in a single covalent bond. The total energy at any frequency increment can be shown to be:

where is the frequency interval 1+,
and the number of quanta at each frequency is found by dividing (4) by 1.

According to this theory, these covalent bonds exist as shared electro-magnetic quantities. The electro-magnetic waves are alternately absorbed and emitted, but always in accordance with the first step of the two-step absorption process. The light energy is completely absorbed in its one-dimensional form, but never decouples or transforms its electrical quantity to three-dimensional. Thus, it never undergoes the entropic transformation in the absorption process' second step. Instead, it is immediately re-emitted, and absorbed by its covalent electron, and so on. The electro-magnetic quantity never experiences dielectric loss. The covalent bond is said to be adiabatic invariant, and therefore, a completely reversible physical process.

If at this point, we inquire as to the amount of covalent energy storage that might occur within a cell, rough estimates are possible. Using a cell of 10-5m diameter and 30% solids by volume, having an average covalent bond density of one per atom, I calculate 1012.6 covalent bonds. I have not yet calculated the number of quantum sites represented by the frequency intersects in Equation (3)'s far-from-equilibrium emittance spectra(Figure 1) because Tm is undefined, but it is a correspondingly large number that is entirely dependent on the separation between the thermodynamic and radiation temperatures.

From this theory's perspective, the number of available covalent bond sites at 293°K could be the primary determinant of cell size. Furthermore, the relative invariance of cell size in the animal kingdom suggests that the separation between the mass and radiation temperatures is relatively constant across the spectra of living organisms. Warm blooded species would appear to have the advantage of higher total energy storage for any given separation between the thermodynamic and radiation temperatures.

D. The Principle of Thermal Quiescence

The aqueous phase outside the cell membrane consists of a complex chemistry with one common characteristic, uniformity of thermal content. As we have already seen, this heat energy is partitioned into its two components: the radiation domain's blackbody spectra, and the mass domain's thermal motion. However, if we look closely at the way that the heat energy is partitioned between the two conditions, both sides of the membrane are very different.

If we first examine the aqueous milieu outside the cell membrane of an aerobic animal cell, we find small molecules that constitute the basic building blocks of cell metabolism (simple sugars and amino acids), as well as smaller ions and simple inorganic structures involved in gas (CO2, O2) and ion (H+, NH +,Ca++, Cl, HCO3,etc.) exchange. Each of these exhibits a degree of thermal motion that is consistent with their size and temperature. This is even better illustrated at the exterior side of a plant's cell wall where the basic pre-transport structures are all very simple, and therefore, have significant thermal motion.

Within the animal cell's membrane or the plant's cell wall, the thermal condition is quite different. We find that these small sub-units, having been transported across the cell membrane, are metabolically transformed into progressively large molecules that have correspondingly little thermal motion. (In the case of the ions, many are simply transported outward again.) In effect the thermal motion of the precursor sub-units of cell synthesis, and the energy of motion that they initially contained, is no longer evident. It has been quieted. The First Law requires that this energy be conserved. The Second Law tells us how this might occur, and also, something about its significance.

The operative thermodynamic system within the cell consists of cellular enzymes and their very specific substrates. The later might be the sub-units that were transported across the cell boundary, or enzyme mediated intermediates that in turn become substrates for higher order enzyme reactions. In this system, an enzyme protein cleaves its substrate(s) at its active site. This reduces the thermal motion of the substrate to essentially zero. It is important to note that the process of attachment at the active site is electrostatic, and completely reversible. (This condition can exist only if the surrounding medium is a near perfect dielectric, i.e. pure water.) If the electrostatic force is removed, the system reverts to its previous state, and vise versa. For the moment we will assume that there is no free energy loss associated with it.

This is not a statistical process where large numbers of molecules react in a reversible or irreversible manner. Indeed, some of the enzymes and intermediates exist at such low concentrations that only a few copies exist within a cell. In addition, the enzyme/substrate cleavage makes this chemistry fundamentally different than other classes of chemical processes. It takes place only at the microscopic scale where all events are reversible and the law of entropy increase has no meaning. This is the domain of Helmholz, reversibility, and the Principle of Least Action.

According to the method of Helmholz, the free energy, H, includes both the system's heat energy (including the operative chemical potentials) and its thermal motion. The relationship between the Helmholz free energy and the systems total energy is known from thermodynamics:

Prigogine[10] refers to this equation as reflecting a competition between the system's energy, E, and its entropy, S.

In our system, there is no free energy loss, only a free energy partition, and that partition has only two parts: 1) the quieting of therman motion by the enzyme, , and 2) the substrate's decrease in chemical potential, , as they cleave. Accordingly, the Principle of Least Action may be written:

and as long as the thermodynamic temperature of the system is unchanged, the entropy decreases by an amount equivalent to the sum of and , divided by the thermodynamic temperature:

The net entropy decrease:

is the additional quantity that give enzymes their ability to surmount energy barriers. In effect, the captured thermal motion's allows the enzyme to exploit an instability in the normal thermodynamics, causing a branch to what would otherwise be an inaccessible thermodynamic state. Nicolis and Prigogine[13] have called the ordered state that emerges in this manner a dissipative structure.

Following this reasoning further, using a polypeptide chain as an example, we find that as the protein molecule increases in length, its thermal motion continually decreases; the terminal decrease occurring as the protein folds in on itself, forming its active condensed structure. Similar reductions in thermal motion occur throughout the cell interior. In all cases the biochemistry is reversible, and the thermal energy change shows up as an entropy decrease. I call this principle, Thermal Quiescence.

Accordingly, the biochemical thermodynamics of Klotz[12] and Lehninger[13] might more appropriately substitute the Helmholz free energy for that of Gibbs. In most instances, the difference tends to be small. However, substances such as molecular oxygen, a highly paramagnetic quantity, brings a higher negative free energy to the thermodynamic calculations, that favors reduction even more so than the Gibbs' thermodynamics indicate. Certain paramagnetic sulfur and iron molecules have similar characteristics, and also mediate respiratory metabolism.

By way of summary, it appears that living systems, and in particular their enzyme activity, might exploit random thermal motion to effect covalent bond formation, and localized decreases in entropy. The process by which this occurs is an adiabatic reversible one, wherein the operative free energy measure is that described by Helmholz. The cell is viewed as a localized region of reversible thermodynamic state, wherein the random motion of heat energy is harvested and transformed to chemical potential.

Electro-magnetic energy stored in the cells covalent bond structure causes small incremental increases in the systems radiation temperature alone, leaving the thermodynamic temperature of the cell unchanged. Thus, large amounts of energy accumulate in the cell without affecting its apparent temperature, and a stable far-from-equilibrium state occurs. The degree of separation in these two temperatures is a quantitative measure of that state.

E. The Cell's Covalent Bond Structure

The two temperatures, Tm and TR, describe the total amount of energy that can be stored in the theoretical far-from-equilibrium spectral fabric. Separately, they represent the environment's thermal state (Tm), and what might be thought of as the intra-cellular potential (TR). The later is a descriptor of the maximum number of covalent bond sites possible within a particular cell, at a particular time. It is this upper limit that is important in what follows.

The difficulty in using TR is that it cannot be measured. A suitable analog might be found in redox potential, pe, and more specifically the electron activity, within the cell. pe is defined as -log10 in a way that is similar to pH(-log). The cell is then described as a region of space having a high negative pe, and the electron rich cellular milieu is maintained by a continual influx of electrons across the cell membrane. These electrons are covalently bonded in enzyme mediated redox reactions, and contribute to small incremental increases in , and TR. It is this influx of electrons that is the forcing function for cell cycle changes in TR.

For the moment we will not be concerned with the form of the forcing function that continually brings electrons across the cell membrane. This will be taken as a given, and we will instead focus on the effects of electron influx.

The cell can be viewed as an enormous network built upon the energy structure of the far-from-equilibrium blackbody spectra. The last position filled was the lowest-energy spectral quantity that had been unfilled. Accordingly, there is in this spectral distribution one, and only one, position that is the next covalent bond. It awaits the addition of one more electron and has the distinction of being the covalent bond selected for by the Principle of Least Action. Regardless of where that electron is input to the system, the most likely location to which it will 'tunnel', is predetermined.

What then determines the molecular change that will occur within the cell? It is the change that occurred the last time that this cell's predecessors were in precisely the same redox state. Everything that has allowed this state to develop has followed an exact sequence. The predecessor molecules are in place. They may even be in exactly the same relative positions that the evolution of this state has predetermined. And although there may be an extraordinarily large number of things happening within the cell related to disease, environmental state, nutrition, etc., there is only one next step in the protein synthesis progression which is inexorably carrying the cell toward mitosis.

All of the processes that have been observed in the last 200 years of biological research continue to exist within this model. All that we know about the genetic predisposition in DNA, RNA, mRNA, etc, and protein synthesis, are still operative. But now there is a single process building the cell's biochemistry on the scaffold, which is the far-from-equilibrium blackbody spectrum. It is a linear progression from one redox state to the next that is unerring in its fidelity to what has come before.

If for some reason, this progression is altered in the slightest way, modifications to the cell's protein structure occur, and at some subsequent step in that cell cycle there is a variant in how the next lowest energy level is filled. Although it is not clear how this occurs, differentiation of form, and perhaps function, occurs. This could be a mutation, or a branch to a different tissue type.

F. Cell Cycle Changes in the Covalent Structure

We will treat the cells DNA as a boundary condition. More precisely, the DNA's covalent bond structure might be thought of as filled with high energy sites that emit at the far right hand side of Curve B. These describe the maximum TR in the cell's far-from-equilibrium state and a corresponding redox potential. The intervening frequency domain of a G1, S and G2 phase cell contains a region that cell synthesis fills with precisely determined numbers of covalent bonds as the redox potential increases in response to electron uptake. The ordering of this process is, for practical purposes, unerring in its precision.

Figure 2 illustrates this. It shows a generalized construct of the cell's electro-magnetic signature at several stages in the cell cycle. Curve M represents the way that the far-from-equilibrium spectral distribution is filled at, or very near to, cell division. Curve G1 is the condition following cell division. Half of the molecular and heat radiation content in the dividing cell has gone to daughter cells, leaving a large unfilled region in the spectrum's energy structure, and also leaving the cell at a lower redox state. Memory of the filled condition exists, for example, in the cell's DNA. Curve S represents what the spectral distribution might look like during the cell cycle's S stage. The region between the G1 or S curves, and the M curve can be thought of as the cell's 'synthesis potential'. It is the covalent structure that must be synthesized before the cell can divide again.

Figure 2 - Schematic representation of the covalent bond distribution at different phases of the cell cycle: G1, S1, M. The expanded scale shows how the odd numbered covalent bond frequencies are missing one quanta each. This lowers TR slightly and, according to this theory, is the principle contributor to cell aging.

The bottom section of the spectral curve in Figure 3 shows how the covalent bonds are filled at the DNA boundary late in the cell cycle's S phase. The lowest diagonal line represents the spectral emittance of a single covalently localized quanta, . This is the highest energy state possible at the operative TR during this mitotic cycle. However, this site is never replicated, and is lost at each cell division. In fact, the last filled site at each of the odd frequencies in the spectra, is lost following cell division because fractional quantum states cannot exist. This effectively reduces TR by 'quantum' amounts during each cell cycle, and thereby reduces the synthesis potential in the daughter cells.

Subsequent generations have slightly shorter DNA strands because the highest energy sites are the first to become vacant as TR and drop. Eventually TR drops to a level where the synthesis potential is too small to support replication. Furthermore, assuming that the cell's more basic functions, those associated with respiration and metabolism, are located in the lower energy portion of the spectra, their fractional reduction is smaller, and their function is only slightly effected, but never the less, diminished. This is the aging process.

G. Alterations to the Upper Boundary Condition

Now, let's assume that we change the upper boundary condition in plausible ways. Are the consequences equally plausible when compared to known cell behavior? For example, introduce into the cell a substance having a covalent bond structure that is higher energy than that in the cell's DNA (existing farther to the right). We will have to introduce this substance at sufficient concentration (or over a sufficiently long time) to significantly increase the radiation temperature within the cell, and thus, increase the upper boundary condition beyond that defined by the DNA itself. This adjustment is opposed to the aging process, which moves TR to the left. Instead, it increases TR, introduces useless information into the upper boundary condition, and causes excessive synthesis including extraneous DNA.

The introduced substance is a carcinogen. If its concentration is not large enough to change the DNA pool in a significant ways, its effect remains in the boundary condition, and further environmental exposure compounds the effect. This suggests why cancer is a disease of old age.

In a similar way, high energy radiation exposure can alter the upper boundary condition by increasing TR directly. This energy has to be captured within the cell as a covalent bond structure, and again, to the right of the DNA boundary condition. Once TR is increased in a stable manner, regardless of its cause, or the final molecular states, synthesis potential increases.

Virus can have the same effect as long as its upper covalent bond energies are higher than those in the host cell's DNA. If the virus' covalent signature is within the synthesis region, the virus is simply multiplied.

In all of these cases, so long as the cell is still viable, the altered biochemistry and DNA will continue to replicate indefinitely, or at least until TR, the synthesis potential, diminishes to the levels where replication ceases. In this way, aging and cell proliferation both appear in this theory as changes in the cell's DNA(electro-magnetic) boundary condition, or more to the point the redox state defined by that boundry condition. Aging is the condition where high-energy covalent bonds are systematically eliminated and the maximum attainable redox potential is reduced below the minimum required for mitosis. Cancer is a condition where the redox state is increased to levels exceeding that required for mitosis, and the cell machinery continues duplicating extraneous, high energy, covalent bonds until mitosis occurs...again and again and again.

H. Discussion

This theory is speculative. But then, what theory of the living state is not. Its speculative nature should not diminish the underlying concepts that brought us to this point. The first of these is our continuing emphasis on the molecular quantities, when it is entirely possible, and even probable, that the electro-magnetic signature within the cell will be at least as relevant, and provide new insight into what we now regard as life's secrets. The radiation domain is also simpler. Only three or four degrees of freedom appear to be operative: frequency, temperature(s), and covalent electron interactions.

Secondly, the cell's negentropic character implies reversible thermodynamic behavior according to the methods of Helmholtz. This removes the mystery from enzyme reactions, and permits us to see life for what it is: a process that harvests the random heat of motion, and transforms it into electro-magnetic, covalent bond energy, and localized decrease in entropy. Here, the second law operates at its lower limit: a zero net change in its free energy state.

Third, the far-from-equilibrium blackbody spectrum seems ideally suited for understanding far-from-equilibrium systems such as the living cell. It is implicitly a time dependent operator with time vectors in opposing directions, . One is the entropic direction that we live in, while the other is a negative time vector that modifies time's passage by slowing it down. In the limit, the local time stops, and physical processes enter the realm of reversibility, and the Principle of Least Action prevails. The function (where ) can be thought of as a true entropy operator.

Studies of the cell's joint energy-entropy structure, particularly those focused on its universal character, delineate areas that are ripe for study.

The literature is rich with research documenting: redox correlation with the cell cycle[14-17], cell cycle regulation[18,], redox regulated biochemistry[19-28], redox states in different cell organelles[29], Redox control in plant metabilism[30,31], and redox branching points in development[32-34], aging[35,36], death[37-40], and cancer[41-43]. This paper's proposal is a modeling framework upon which these observations can be organized in their relationship to one another. But, it goes further. In understanding the hierarchy for redox state progression over a cell cycle, we stand poised to mathematically model normal and aberrant cell function. The one essential feature of a coherent cell modeling framework that is not included in the preceding, is a mechanistic and energetic description of the forcing function(s) responsible for the continuous influx of electrons to the cell. This does not diminish this work's form and function arguments. It does, however, leave an unsatisfying gap that will have to be dealt with separately.

One final thought: I have elected to place the energy quanta associated with the far-from-equilibrium blackbody form into the cell's covalent bond structure. This is not only reasonable, but also convenient because it is simple and understandable. However, this is not the only possibility, and indeed, there is a growing body of evidence that the energy storage could also be localized in excited nuclear states. In particular, researchers beginning in the 1950s have assembled scientific data suggesting that nuclear transmutations are occurring in biological systems. If that turns out to be the case, it would be difficult to achieve TRs approaching solar core temperatures with covalent bond energy alone. The only way that I am aware of for storing such extremely high energy, in a thermodynamically reversible manner, is in excited nuclear states which are in Mausbauer resonance. This places high energy quanta resonating between identical nuclei in a completely reversible state similar to that in the covalent bond, but at energies in the realm of gamma quanta.

I. Conclusions

The far-from-equilibrium blackbody equation that lies at the core of this study's cell model describes a reasonable framework for understanding cell form and function. The blackbody form has long been known to represent the spectral distribution of energy in inanimate matter. The choice of a non-equilibrium form of the equation as a framework for energy storage in matter's living state is logical, and appears to be capable of providing useful insights.

It is also appropriate that the theory presented here distinguishes between the thermodynamic temperature and the radiation temperature. The thermodynamics presented in Section D show how the cell harvests heat of thermal motion from its environment and accumulates it within the cell's covalent bond structure. In essence, the harvested heat 'raises the temperature' at the interior of the cell, but this increase is not apparent because the electro-magnetic radiation is all masked within the cell's covalent bond structure. TR is a measure of the cell's negentropy content. Burning the cell liberates the heat equivalent of this negentropy.

This paper's findings, although speculative, appear to provide some meaningful insights into cell processes. It is particularly noteworthy that an internally consistent interpretation, provides insights to diverse cell features, including: cell size, aging and cell proliferation.

The theory also suggests that protein synthesis pathways are very exact progressions that retrace those of the cell's antecedents...progeny recapitulate endogamy. However, this does not allow for the kind of specificity that occurs in differing tissue types within a single organism. It would appear that there is a set of synthesis pathways that can be altered by the cell's local environment within the organism, or perhaps, there are more specific synthesis sequences that includes the very exacting branches that tissue differentiation requires. The former seems more plausible to this researcher.

Finally, we should note that Maxwell's demon[44,45] is present in this cell model in a very real way. Here it assumes an enzyme identity, and as in Maxwell's example, selectively harvests heat from its environment, and converts that environment to a more ordered state. This circumstance does not allow us to draw on the information processing ability of intellect to dismiss the demon's magic as Szilard[46] did. However, it is clear that a vast amount of negentropy is concentrated in the enzyme structure, information that can be drawn on to quiet substrate molecules, and order them accordingly.

The ideas presented here are an evolving process directed at understanding the nature of the living state. This is but another approach that is brought to the table for debate and criticism. As such it is not an answer in itself.

J. References

Elsasser, W.M., (1987) Reflections on a Theory of Organism, Johns Hopkins University Press, Baltimore.

Schrödinger, E., (1946) What is Life?, The Physical Aspects of the Living Cell, MacMillan Co, NY.

Szent-Györgyi, A., (1941) The Study of Energy-levels in Biochemistry, Nature148: 157-159.

Monod, J., (1971) Chance and Necessity, Alfred A. Knopf, NY.

Luria, S.E., (1973) Life - The Unfinished Experiment, Charles Scribner's Sons, NY.

M. Planck, (1900) Verhandlunger der Deutschen Physikalischen Gesellschaft, 2, 237, or in English translation: in H. Kangro (ed.), Planck's Original Papers in Quantum Physics, Volume 1 of Classic Papers in Quantum Physics, Wiley, New York, 1972.

Boltzman, L., (1964)Lectures on Gas Theory, Translated by Stephen G Brush, University of California Press, Berkeley.

Maxwell, J.C., (1892) A Treatise on Electricity and Magnetism, Clarendon Press, Oxford.

Szumski, D, Non-equilibrium Blackbody Radiation Equation Provides Insight into the Nature of Heat Processes: Possible Applications to Biological Energy Storage , Manuscript submitted to PLoS Computational Biology.

Prigogine, I., (1980) From Being to Beginning, W.H. Freeman and Company, San Francisco.

Nicolis G., Prigogine I., (1977) Self-Organization in Nonequilibrium Systems, John Wiley and Sons, NY.

Klotz, I., (1967) Energy Changes in Biochemical Reactions, Academic Press, NY.

Lehninger, A., (1965) Bioenergetics, W A Benjamin, Inc, NY.

Yukihashi, Y, Yashumitsu, O, Kazuo S, (2004) Synchronized generation of reactive oxygen species with the cell cycle, Life Science, 75: 301-311.

Conour, J, Graham, W, Gaskins, H, (2004) A combined in vitro/bioinformatics investigation of redox regulatory mechanisms governing cell cycle progression, Physiol. Genomics, 18: 196-205.

Boonstra, J, Post, J A, (2003) Molecular events associated with reactive oxygen species and cell cycle progression in mammalian cells. Gene 337: 1-13.

17. Menon, S G, Goswami, P C, (2007) A redox cycle within the cell cycle: Ring in the old with the new, Oncogene, 26: 1101-1109.

18. Schackelford, R, Kaufmann, W, Paules, R, (2000) Oxidative stress and cell cycle checkpoint function, Free Radical Biology and Medicine, 28: 1387-1404.

Nakamura, H, Nakamura, K, Yodoi, J, (1997) Redox Regulation of Cellular Activation, Annu. Rev. Immunol.,15:351-69

20. Ramos, K, (1999) Redox regulation of c-Ha-ras and osteopontin signalimg in vascular smooth muscle cells: implications in chemical atherogenesis, Annu. Rev. Pharmacol. Toxicol., 39:243-265.

Irani, K, (2000) Oxidant signaling in vascular cell growth, death, and survival: A review of the roles of reactive oxygen species in smooth muscle and endothelial cell mitogenic and apoptotic signaling, Circ. Res., 87: 179-183.

22. Fernandes, A P, Holmgren, A, (2004) Glutaredoxins: glutathione-dependent redox enzymes with functions far beyond a simple thioredoxin backup system, Antioxidants & Redox Signaling, 6: 63-74.

Sun, Y, Oberley, L W, (1996) Redox regulation of transcriptional activators, Free Radical Biology & Medicine, 21: 335-348.

24. Sen, C K, Packer, L. (1996) Antioxidant and redox regulation of gene transcription, The FASEB Journal, 10: 709-720.

25. Rhee, S G, Chang, T, Bae, Y S, Lee, S, Kang, S W, (2003) Cell regulation by hydrogen peroxide, J Am. Soc. Nephrol., 14: S211-S215.

26. Rhee, S G, (1999) Redox signaling: Hydrogen peroxide as intracellular messenger, Experimental and Molecular Medicine, 31: 53-59.

27. Powis, g, Briehl, M, Oblong, J, (1995) Redox signaling and the control of cell growth and death, Pharmac. Ther., 68: 149-173

28. Herrlich, P, Bohmer, F D, (1999) Redox regulation of signal transduction in mammalian cells, Biochemical Pharmocology, 59: 35-41.

29. Schafer, F Q, Buettner, G R, (2001) Redox environment of the cell as viewed through the redox state of the gluathione disulfide/glutathione couple, Free Radical Biology & Medicine, 30:1191-1212.

30. Buchanan, B, Balmer, Y, (2005) Redox regulation: A broadening horizon, Annu. Rev. Plant Biol., 56: 187-220

31. den Boer, B, Murphy, J, (2000) Triggering the cell cycle in plants, Trends in Cell Biology, 10: 245-250.

32. Dennery, P, (2004) Role of redox in fetal development and neonatal diseases, Antioxidants & Redox Signalling, 6: 147-153.

33. Smith, J, Ladi, E, Mayer-Proschel, M, Noble, M, (2000) Redox state is a central modulator of the balance between self-renewal and differentiation in a dividing glial precursor cell, Proc. Natl. Acad. Sci, 97: 10032-10037.

Harvey, A, Kind, K, Thompson, J, (2002) Redox regulation of early embryo development, Reproduction, 123: 479-486.

35. Hagen, T, (2003) Oxidative stress, redox imbalance, and the aging process, Antioxidants & Redox Signaling, 5: 503-506.

36. Lavrovsky, Y, Chatterjee, B, Clark, R A, Roy, A K, (2000) Role of redox regulated transcription factors in inflammation, aging, and age related disease, Experimental Gerontology, 35: 521-532.

37. Ueda, S, Masutani, H, Nakamura, H, Tanaka, T, Ueno, M, Yodoi, J, (2002) Redox control of cell death, Antioxidants & Redox Signaling, 4: 405-414.

38. Kwon, Y, Masutani, H, Nakamura, H, Ishil, Y, Yodoi, J, (2003) Redox Regulation of cell growth and death, Biol. Chem., 384:991-996.

Hall, A G, (1999) The role of glutathione in the regulation of aoptosis, European Journal of Clinical Investigations, 29: 238-245.

40. Nakashima, I, Suzuki, H, Kato, M, Akhand, A, (2002) Redox control of t-cell death, Antioxidants & Redox Signaling, 4: 353- 356.

41. Loo, G, (2003) Redox sensitive mechanisms of photochemical-mediated inhibition of cancer cell proliferation, Journal of Nutritional Biochemistry, 14: 64-73.

42, Hoffman, A, Spetner, L M, Burke, M, (2001) Cessation of cell proliferation by adjustment of cell redox potential, J. Theor. Biol., 211: 403-407.

43. Aw, T Y, (2003) Cellular redox: A modulator of intestinal epithelial cell proliferation, News Physiol. Sci., 18: 201-204.

Maxwell, J,C. (1871) Theory of Heat.

Brillouin, L., (1951) Maxwell's Demon Cannot Operate: Information and Entropy, J. of Applied Physics, 22, 334-337, 1951.

Szilard, L., On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings, translated by Anatol Rapoport and Cechilde Knoller, in B.T. Feld and G.W. Szilard(ed), The Collected Works of Leo Szilard- Scientific Papers, , MIT Press, 1972.

    Author's Statement

The unspoken goal of quantitative biology is a precise mathematical model of cellular structure and function. Most will argue that models of this type are unattainable. This paper opposes that view. Instead, I would argue that there are three obstacles in our quest for such a model:

  1. the overwhelming numbers of molecular forms in any cell,
  2. the absence of a suitable scaffold, or framework, for building such a model, and
  3. the limited attention that big-picture biology receives.

Furthermore, I believe that the answers to all of the pressing issues in biology will become much more accessible only when we understand their context, or more specifically, precisely how the cell functions.

This paper is my attempt to explore a suitable modeling framework for both cell structure and function. I have discarded frameworks built on the molecular quantities, preferring to work instead with the radiation structure within the cell's covalent bonds. This has the advantage of reducing the degrees of freedom in the model from tens of thousands to three: two temperature scales and electro-magnetic frequency. Thought experiments on cell size uniformity, aging, death, and the cancer phenotype find merit in further research along these lines. It is my hope that it inspires other related work.

The importance of the paper lies in its exploration of a modeling framework that is quantitative, and which finds its roots one tier below the biological and chemical sciences, and in the laws of physics. I believe that this is where the secrets that elude us lie.