Ion-Based Cellular Signal Transmission, Principles of Minimum Information Loss, and Evolution by Natural Selection.

: The Extreme Physical Information EPI principle states that maximum information transmission or, equivalently, a minimum information loss is a fundamental property of nature. Prior work has demonstrated the universal EPI principle allows derivation of nearly all physical laws. Here, we investigate whether EPI can similarly give rise to the fundamental law of life: Evolution. Living systems require information to survive and proliferate. Heritable information in the genome encodes the structure and function of cellular macromolecules but this information remains fixed over time. In contrast, a cell must rapidly and continuously access, analyze, and respond to a wide range of continuously changing spatial and temporal information in the environment. We propose these two information dynamics are linked because the genes encode the structure of the macromolecules that form information conduits necessary for the dynamical interactions with the external environment. However, because the genome does not have the capacity to precisely locate the time and location of external signals, we propose the cell membrane is the site at which most external information is received and processed. In our model, an external signal is detected by gates on transmembrane ion channel and transmitted into the cytoplasm through ions that flow along pre-existing concentration gradients when the gate opens. The resulting cytoplasmic ion "puff" is localized in both time and space, thus producing spatial and temporal information. Small, localized signals in the cytoplasm are "processed" through alterations in the function and location of peripheral membrane proteins. Larger perturbations produce prolonged or spatially extensive changes in cytoplasmic ion concentrations that can be transmitted to other organelles via ion flows along elements of the cytoskeleton. An evolutionary constraint to the ever-increasing acquisition of environmental information is the cost of doing so. One solution to this trade-off is the evolution of information conduits that minimize signal loss during transmission. Since the structures of these conduits are encoded in the genome, evolution of macromolecular conduits that minimize signal loss is linked to and, in fact, governed by a universal principle, termed extreme physical information (EPI). Mathematical analysis of information dynamics based on the flow of ions through membrane channels and along wire-like cytoskeleton macromolecules fulfills the EPI principle. Thus, the empirically derived model of evolution by natural selection, although uniquely applicable to living systems, is theoretically grounded in a universal principle that can also be used to derive the laws of physics. Finally, if minimization of signal loss is a mechanism to overcome energy constraints, the model predicts increasing information and associated complexity are closely linked to increased efficiency of energy production or improved substrate acquisition.

Cellular information dynamics through transmembrane flow of ions.

We propose cells generate large transmembrane ion gradients to form information circuits that detect, process, and respond to environmental perturbations or signals. In this model, the specialized gates of transmembrane ion channels function as information detectors that communicate to the cell through rapid and (usually) local pulses of ions. Information in the ion "puffs" is received and processed by the cell through resulting changes in charge density and/or mobile cation (and/or anion) concentrations alter the localization and function of peripheral membrane proteins. The subsequent changes in protein binding to the membrane or activation of K+, Ca2+ or Mg2+-dependent enzymes then constitute a cellular response to the perturbation. To test this hypothesis we analyzed ion-based signal transmission as a communication channel operating with coded inputs and decoded outputs. By minimizing the Kullback-Leibler cross entropy [Formula: see text] between concentrations of the ion species inside [Formula: see text] and outside [Formula: see text] the cell membrane, we find signal transmission through transmembrane ion flow forms an optimal Shannon information channel that minimizes information loss and maximizes transmission speed. We demonstrate the ion dynamics in neuronal action potentials described by Hodgkin and Huxley (including the equations themselves) represent a special case of these general information principles.

Investigating Information Dynamics in Living Systems through the Structure and Function of Enzymes.

Enzymes are proteins that accelerate intracellular chemical reactions often by factors of 105-1012s-1. We propose the structure and function of enzymes represent the thermodynamic expression of heritable information encoded in DNA with post-translational modifications that reflect intra- and extra-cellular environmental inputs. The 3 dimensional shape of the protein, determined by the genetically-specified amino acid sequence and post translational modifications, permits geometric interactions with substrate molecules traditionally described by the key-lock best fit model. Here we apply Kullback-Leibler (K-L) divergence as metric of this geometric "fit" and the information content of the interactions. When the K-L 'distance' between interspersed substrate pn and enzyme rn positions is minimized, the information state, reaction probability, and reaction rate are maximized. The latter obeys the Arrhenius equation, which we show can be derived from the geometrical principle of minimum K-L distance. The derivation is first limited to optimum substrate positions for fixed sets of enzyme positions. However, maximally improving the key/lock fit, called 'induced fit,' requires both sets of positions to be varied optimally. We demonstrate this permits and is maximally efficient if the key and lock particles pn, rn are quantum entangled because the level of entanglement obeys the same minimized value of the Kullback-Leibler distance that occurs when all pn ≈ rn. This implies interchanges pn ⇄ brn randomly taking place during a reaction successively improves key/lock fits, reducing the activation energy Ea and increasing the reaction rate k. Our results demonstrate the summation of heritable and environmental information that determines the enzyme spatial configuration, by decreasing the K-L divergence, is converted to thermodynamic work by reducing Ea and increasing k of intracellular reactions. Macroscopically, enzyme information increases the order in living systems, similar to the Maxwell demon gedanken, by selectively accelerating specific reaction thus generating both spatial and temporal concentration gradients.

Cancer suppression by compression.

Recent experiments indicate that uniformly compressing a cancer mass at its surface tends to transform many of its cells from proliferative to functional forms. Cancer cells suffer from the Warburg effect, resulting from depleted levels of cell membrane potentials. We show that the compression results in added free energy and that some of the added energy contributes distortional pressure to the cells. This excites the piezoelectric effect on the cell membranes, in particular raising the potentials on the membranes of cancer cells from their depleted levels to near-normal levels. In a sample calculation, a gain of 150 mV in is so attained. This allows the Warburg effect to be reversed. The result is at least partially regained function and accompanying increased molecular order. The transformation remains even when the pressure is turned off, suggesting a change of phase; these possibilities are briefly discussed. It is found that if the pressure is, in particular, applied adiabatically the process obeys the second law of thermodynamics, further validating the theoretical model.

Principle of maximum Fisher information from Hardy's axioms applied to statistical systems.

Consider a finite-sized, multidimensional system in parameter state a. The system is either at statistical equilibrium or general nonequilibrium, and may obey either classical or quantum physics. L. Hardy's mathematical axioms provide a basis for the physics obeyed by any such system. One axiom is that the number N of distinguishable states a in the system obeys N=max. This assumes that N is known as deterministic prior knowledge. However, most observed systems suffer statistical fluctuations, for which N is therefore only known approximately. Then what happens if the scope of the axiom N=max is extended to include such observed systems? It is found that the state a of the system must obey a principle of maximum Fisher information, I=I(max). This is important because many physical laws have been derived, assuming as a working hypothesis that I=I(max). These derivations include uses of the principle of extreme physical information (EPI). Examples of such derivations were of the De Broglie wave hypothesis, quantum wave equations, Maxwell's equations, new laws of biology (e.g., of Coulomb force-directed cell development and of in situ cancer growth), and new laws of economic fluctuation and investment. That the principle I=I(max) itself derives from suitably extended Hardy axioms thereby eliminates its need to be assumed in these derivations. Thus, uses of I=I(max) and EPI express physics at its most fundamental level, its axiomatic basis in math.

Cell development obeys maximum Fisher information.

Eukaryotic cell development has been optimized by natural selection to obey maximal intracellular flux of messenger proteins. This, in turn, implies maximum Fisher information on angular position about a target nuclear pore complex (NPR). The cell is simply modeled as spherical, with cell membrane (CM) diameter 10 micrometer and concentric nuclear membrane (NM) diameter 6 micrometer. The NM contains approximately 3000 nuclear pore complexes (NPCs). Development requires messenger ligands to travel from the CM-NPC-DNA target binding sites. Ligands acquire negative charge by phosphorylation, passing through the cytoplasm over Newtonian trajectories toward positively charged NPCs (utilizing positive nuclear localization sequences). The CM-NPC channel obeys maximized mean protein flux F and Fisher information I at the NPC. Therefore the first-order change in I = 0. But also, the 2nd-order change in I is likewise close to zero, indicating significant stability to environmental perturbations. Many predictions are confirmed, including the dominance of protein pathways of from 1-4 proteins, a 4 nm size for the EGFR protein and the flux value F approximately 10(16) proteins/m2-s. After entering the nucleus, each protein ultimately delivers its ligand information to a DNA target site with maximum probability, i.e. maximum Kullback-Liebler entropy H(KL). In a smoothness limit H(KL) --> I(DNA)/2, so that the total CM-NPC-DNA channel obeys maximum Fisher I. It is also shown that such maximum information --> a cell state far from thermodynamic equilibrium, one condition for life.

The critical roles of information and nonequilibrium thermodynamics in evolution of living systems.

Living cells are spatially bounded, low entropy systems that, although far from thermodynamic equilibrium, have persisted for billions of years. Schrödinger, Prigogine, and others explored the physical principles of living systems primarily in terms of the thermodynamics of order, energy, and entropy. This provided valuable insights, but not a comprehensive model. We propose the first principles of living systems must include: (1) Information dynamics, which permits conversion of energy to order through synthesis of specific and reproducible, structurally-ordered components; and (2) Nonequilibrium thermodynamics, which generate Darwinian forces that optimize the system.Living systems are fundamentally unstable because they exist far from thermodynamic equilibrium, but this apparently precarious state allows critical response that includes: (1) Feedback so that loss of order due to environmental perturbations generate information that initiates a corresponding response to restore baseline state. (2) Death due to a return to thermodynamic equilibrium to rapidly eliminate systems that cannot maintain order in local conditions. (3) Mitosis that rewards very successful systems, even when they attain order that is too high to be sustainable by environmental energy, by dividing so that each daughter cell has a much smaller energy requirement. Thus, nonequilibrium thermodynamics are ultimately responsible for Darwinian forces that optimize system dynamics, conferring robustness sufficient to allow continuous existence of living systems over billions of years.

Motion-dependent levels of order in a relativistic universe.

Consider a generally closed system of continuous three-space coordinates x with a differentiable amplitude function ψ(x). What is its level of order R? Define R by the property that it decreases (or stays constant) after the system is coarse grained. Then R turns out to obey R=8(-1)L(2)I,where quantity I=4∫dx[nabla]ψ(*)·[nabla]ψ is the classical Fisher information in the system and L is the longest chord that can connect two points on the system surface. In general, order R is (i) unitless, and (ii) invariant to uniform stretch or compression of the system. On this basis, the order R in the Universe was previously found to be invariant in time despite its Hubble expansion, and with value R=26.0×10(60) for flat space. By comparison, here we model the Universe as a string-based "holostar," with amplitude function ψ(x)[proportionality]1/r over radial interval r=(r(0),r(H)). Here r(0) is of order the Planck length and r(H) is the radial extension of the holostar, estimated as the known value of the Hubble radius. Curvature of space and relative motion of the observer must now be taken into account. It results that a stationary observer observes a level of order R=(8/9)(r(H)/r(0))(3/2)=0.42×10(90); while for a free-falling observer R=2(-1)(r(H)/r(0))(2)=0.85×10(120). Both order values greatly exceed the above flat-space value. Interestingly, they are purely geometric measures, depending solely upon ratio r(H)/r(0). Remarkably, the free-fall value ~10(120) of R approximates the negentropy of a universe modeled as discrete. This might mean that the Universe contains about equal amounts of continuous and discrete structure.

Intracellular electric field and pH optimize protein localization and movement.

Mammalian cell function requires timely and accurate transmission of information from the cell membrane (CM) to the nucleus (N). These pathways have been intensively investigated and many critical components and interactions have been identified. However, the physical forces that control movement of these proteins have received scant attention. Thus, transduction pathways are typically presented schematically with little regard to spatial constraints that might affect the underlying dynamics necessary for protein-protein interactions and molecular movement from the CM to the N. We propose messenger protein localization and movements are highly regulated and governed by Coulomb interactions between: 1. A recently discovered, radially directed E-field from the NM into the CM and 2. Net protein charge determined by its isoelectric point, phosphorylation state, and the cytosolic pH. These interactions, which are widely applied in elecrophoresis, provide a previously unknown mechanism for localization of messenger proteins within the cytoplasm as well as rapid shuttling between the CM and N. Here we show these dynamics optimize the speed, accuracy and efficiency of transduction pathways even allowing measurement of the location and timing of ligand binding at the CM--previously unknown components of intracellular information flow that are, nevertheless, likely necessary for detecting spatial gradients and temporal fluctuations in ligand concentrations within the environment. The model has been applied to the RAF-MEK-ERK pathway and scaffolding protein KSR1 using computer simulations and in-vitro experiments. The computer simulations predicted distinct distributions of phosphorylated and unphosphorylated components of this transduction pathway which were experimentally confirmed in normal breast epithelial cells (HMEC).

Order in a multidimensional system.

We show that any convex K-dimensional system has a level of order R that is proportional to its level of Fisher information I. The proportionality constant is 1/8 the square of the longest chord connecting two surface points of the system. This result follows solely from the requirement that R decrease under small perturbations caused by a coarse graining of the system. The form for R is generally unitless, allowing the order for different phenomena, or different representations (e.g., using time vs frequency) of a given phenomenom, to be compared objectively. Order R is also invariant to uniform magnification of the system. The monotonic contraction properties of R and I define an arrow of time and imply that they are entropies, in addition to their usual status as informations. This also removes the need for data, and therefore an observer, in derivations of nonparticipatory phenomena that utilize I. Simple graphical examples of the new order measure show that it measures as well the level of "complexity" in the system. Finally, an application to cell growth during enforced distortion shows that a single hydrocarbon chain can be distorted into a membrane having equal order or complexity. Such membranes are prime constituents of living cells.

Information dynamics in living systems: prokaryotes, eukaryotes, and cancer.

BACKGROUND: Living systems use information and energy to maintain stable entropy while far from thermodynamic equilibrium. The underlying first principles have not been established. FINDINGS: We propose that stable entropy in living systems, in the absence of thermodynamic equilibrium, requires an information extremum (maximum or minimum), which is invariant to first order perturbations. Proliferation and death represent key feedback mechanisms that promote stability even in a non-equilibrium state. A system moves to low or high information depending on its energy status, as the benefit of information in maintaining and increasing order is balanced against its energy cost. Prokaryotes, which lack specialized energy-producing organelles (mitochondria), are energy-limited and constrained to an information minimum. Acquisition of mitochondria is viewed as a critical evolutionary step that, by allowing eukaryotes to achieve a sufficiently high energy state, permitted a phase transition to an information maximum. This state, in contrast to the prokaryote minima, allowed evolution of complex, multicellular organisms. A special case is a malignant cell, which is modeled as a phase transition from a maximum to minimum information state. The minimum leads to a predicted power-law governing the in situ growth that is confirmed by studies measuring growth of small breast cancers. CONCLUSIONS: We find living systems achieve a stable entropic state by maintaining an extreme level of information. The evolutionary divergence of prokaryotes and eukaryotes resulted from acquisition of specialized energy organelles that allowed transition from information minima to maxima, respectively. Carcinogenesis represents a reverse transition: of an information maximum to minimum. The progressive information loss is evident in accumulating mutations, disordered morphology, and functional decline characteristics of human cancers. The findings suggest energy restriction is a critical first step that triggers the genetic mutations that drive somatic evolution of the malignant phenotype.

Coulomb interactions between cytoplasmic electric fields and phosphorylated messenger proteins optimize information flow in cells.

BACKGROUND: Normal cell function requires timely and accurate transmission of information from receptors on the cell membrane (CM) to the nucleus. Movement of messenger proteins in the cytoplasm is thought to be dependent on random walk. However, Brownian motion will disperse messenger proteins throughout the cytosol resulting in slow and highly variable transit times. We propose that a critical component of information transfer is an intracellular electric field generated by distribution of charge on the nuclear membrane (NM). While the latter has been demonstrated experimentally for decades, the role of the consequent electric field has been assumed to be minimal due to a Debye length of about 1 nanometer that results from screening by intracellular Cl- and K+. We propose inclusion of these inorganic ions in the Debye-Huckel equation is incorrect because nuclear pores allow transit through the membrane at a rate far faster than the time to thermodynamic equilibrium. In our model, only the charged, mobile messenger proteins contribute to the Debye length. FINDINGS: Using this revised model and published data, we estimate the NM possesses a Debye-Huckel length of a few microns and find this is consistent with recent measurement using intracellular nano-voltmeters. We demonstrate the field will accelerate isolated messenger proteins toward the nucleus through Coulomb interactions with negative charges added by phosphorylation. We calculate transit times as short as 0.01 sec. When large numbers of phosphorylated messenger proteins are generated by increasing concentrations of extracellular ligands, we demonstrate they generate a self-screening environment that regionally attenuates the cytoplasmic field, slowing movement but permitting greater cross talk among pathways. Preliminary experimental results with phosphorylated RAF are consistent with model predictions. CONCLUSION: This work demonstrates that previously unrecognized Coulomb interactions between phosphorylated messenger proteins and intracellular electric fields will optimize information transfer from the CM to the NM in cells.

Quantifying system order for full and partial coarse graining.

We show that Fisher information I and its weighted versions effectively measure the order R of a large class of shift-invariant physical systems. This result follows from the assumption that R decreases under small perturbations caused by a coarse graining of the system. The form found for R is generally unitless, which allows the order for different phenomena to be compared objectively. The monotonic contraction properties of R and I in time imply that they are entropies, in addition to their usual status as information. This removes the need for data, and therefore an observer, in physical derivations based upon their use. Thus, this recognizes complementary scenarios to the participatory observer of Wheeler, where (now) physical phenomena can occur in the absence of an observer. Simple applications of the new order measure R are discussed.

Adaptive therapy.

A number of successful systemic therapies are available for treatment of disseminated cancers. However, tumor response is often transient, and therapy frequently fails due to emergence of resistant populations. The latter reflects the temporal and spatial heterogeneity of the tumor microenvironment as well as the evolutionary capacity of cancer phenotypes to adapt to therapeutic perturbations. Although cancers are highly dynamic systems, cancer therapy is typically administered according to a fixed, linear protocol. Here we examine an adaptive therapeutic approach that evolves in response to the temporal and spatial variability of tumor microenvironment and cellular phenotype as well as therapy-induced perturbations. Initial mathematical models find that when resistant phenotypes arise in the untreated tumor, they are typically present in small numbers because they are less fit than the sensitive population. This reflects the "cost" of phenotypic resistance such as additional substrate and energy used to up-regulate xenobiotic metabolism, and therefore not available for proliferation, or the growth inhibitory nature of environments (i.e., ischemia or hypoxia) that confer resistance on phenotypically sensitive cells. Thus, in the Darwinian environment of a cancer, the fitter chemosensitive cells will ordinarily proliferate at the expense of the less fit chemoresistant cells. The models show that, if resistant populations are present before administration of therapy, treatments designed to kill maximum numbers of cancer cells remove this inhibitory effect and actually promote more rapid growth of the resistant populations. We present an alternative approach in which treatment is continuously modulated to achieve a fixed tumor population. The goal of adaptive therapy is to enforce a stable tumor burden by permitting a significant population of chemosensitive cells to survive so that they, in turn, suppress proliferation of the less fit but chemoresistant subpopulations. Computer simulations show that this strategy can result in prolonged survival that is substantially greater than that of high dose density or metronomic therapies. The feasibility of adaptive therapy is supported by in vivo experiments. [Cancer Res 2009;69(11):4894-903] Major FindingsWe present mathematical analysis of the evolutionary dynamics of tumor populations with and without therapy. Analytic solutions and numerical simulations show that, with pretreatment, therapy-resistant cancer subpopulations are present due to phenotypic or microenvironmental factors; maximum dose density chemotherapy hastens rapid expansion of resistant populations. The models predict that host survival can be maximized if "treatment-for-cure strategy" is replaced by "treatment-for-stability." Specifically, the models predict that an optimal treatment strategy will modulate therapy to maintain a stable population of chemosensitive cells that can, in turn, suppress the growth of resistant populations under normal tumor conditions (i.e., when therapy-induced toxicity is absent). In vivo experiments using OVCAR xenografts treated with carboplatin show that adaptive therapy is feasible and, in this system, can produce long-term survival.

Conditions for correspondence between Hartree scattering and biological growth.

The population dynamics of a weakly scattering system can often be characterized by Hartree equations, and those of a living system by Lotka-Volterra (LV) equations. In principle, can the population statistics of the quantum scattering system follow those of the living system? The answer is yes, provided the interactive potentials of the Hartree equations are made equal, on a one-to-one basis, to corresponding fitness functions of the LV equations. Of course this correspondence can be achieved only if the requirements of the Hartree approximation are satisfied, including that the scatter occurs within the coherence time of the quantum system. Examples are given of Hartree systems that obey the population dynamics of required predator-prey systems.

Inducing catastrophe in malignant growth.

Mathematical catastrophe theory is used to describe cancer growth during any time-dependent program a(t) of therapeutic activity. The program may be actively imposed, e.g. as chemotherapy, or occur passively as an immune response. With constant therapy a(t), the theory predicts that cancer mass p(t) grows in time t as a cosine-modulated power law, with power = 1.618..., the Fibonacci constant. The cosine modulation predicts the familiar relapses and remissions of cancer growth. These fairly well agree with clinical data on breast cancer recurrences following mastectomy. Two such studies of 3183 Italian women consistently show an immune system's average activity level of about a = 2.8596 for the women. Fortunately, an optimum time-varying therapy program a(t) is found that effects a gradual approach to full remission over time, i.e. to a chronic disease. Both activity a(t) and cancer mass p(t) monotonically decrease with time, the activity a(t) as 1/(ln t) and mass remission as t--94{-0.382}. These predicted growth effects have a biological basis in the known presence of multiple alleles during cancer growth.

Information theory in living systems, methods, applications, and challenges.

Living systems are distinguished in nature by their ability to maintain stable, ordered states far from equilibrium. This is despite constant buffeting by thermodynamic forces that, if unopposed, will inevitably increase disorder. Cells maintain a steep transmembrane entropy gradient by continuous application of information that permits cellular components to carry out highly specific tasks that import energy and export entropy. Thus, the study of information storage, flow and utilization is critical for understanding first principles that govern the dynamics of life. Initial biological applications of information theory (IT) used Shannon's methods to measure the information content in strings of monomers such as genes, RNA, and proteins. Recent work has used bioinformatic and dynamical systems to provide remarkable insights into the topology and dynamics of intracellular information networks. Novel applications of Fisher-, Shannon-, and Kullback-Leibler informations are promoting increased understanding of the mechanisms by which genetic information is converted to work and order. Insights into evolution may be gained by analysis of the the fitness contributions from specific segments of genetic information as well as the optimization process in which the fitness are constrained by the substrate cost for its storage and utilization. Recent IT applications have recognized the possible role of nontraditional information storage structures including lipids and ion gradients as well as information transmission by molecular flux across cell membranes. Many fascinating challenges remain, including defining the intercellular information dynamics of multicellular organisms and the role of disordered information storage and flow in disease.

Power laws of complex systems from extreme physical information.

Many complex systems obey allometric, or power, laws y=Y x(a) . Here y > or = 0 is the measured value of some system attribute a , Y> or =0 is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values n/4 , n=0, +/-1, +/-2.... Here x is the mass of a randomly selected creature in the population. These quarter-power laws hold for many attributes, such as pulse rate (n=-1) . Allometry has, in the past, been theoretically justified on a case-by-case basis. An ultimate goal is to find a common cause for allometry of all types and for both living and nonliving systems. The principle I-J=extremum of extreme physical information is found to provide such a cause. It describes the flow of Fisher information J-->I from an attribute value a on the cell level to its exterior observation y . Data y are formed via a system channel function y identical to f (x,a) , with f (x,a) to be found. Extremizing the difference I-J through variation of f (x,a) results in a general allometric law f (x,a) identical to y=Y x(a) . Darwinian evolution is presumed to cause a second extremization of I-J , now with respect to the choice of a . The solution is a=n/4 , n=0,+/-1,+/-2..., defining the particular powers of biological allometry. Under special circumstances, the model predicts that such biological systems are controlled by only two distinct intracellular information sources. These sources are conjectured to be cellular DNA and cellular transmembrane ion gradients.

The role of non-genomic information in maintaining thermodynamic stability in living systems.

Living systems represent a local exception, albeit transient, to the second law of thermodynamics, which requires entropy or disorder to increase with time. Cells maintain a stable ordered state by generating a steep transmembrane entropy gradient in an open thermodynamic system far from equilibrium through a variety of entropy exchange mechanisms. Information storage in DNA and translation of that information into proteins is central to maintenance thermodynamic stability, through increased order that results from synthesis of specific macromolecules from monomeric precursors while heat and other reaction products are exported into the environment. While the genome is the most obvious and well-defined source of cellular information, it is not necessarily clear that it is the only cellular information system. In fact, information theory demonstrates that any cellular structure described by a nonrandom density distribution function may store and transmit information. Thus, lipids and polysaccharides, which are both highly structured and non-randomly distributed increase cellular order and potentially contain abundant information as well as polynucleotides and polypeptides Interestingly, there is no known mechanism that allows information stored in the genome to determine the highly regulated structure and distribution of lipids and polysaccha- riedesin the cellular membrane suggesting these macromolecules may store and transmit information not contained in the genome. Furthermore, transmembrane gradients of H(+), Na(+), K(+), Ca(+), and Cl(-) concentrations and the consequent transmembrane electrical potential represent significant displacements from randomness and, therefore, rich potential sources of information.Thus, information theory suggests the genome-protein system may be only one component of a larger ensemble of cellular structures encoding and transmitting the necessary information to maintain living structures in an isoentropic steady state.

Information dynamics in carcinogenesis and tumor growth.

The storage and transmission of information is vital to the function of normal and transformed cells. We use methods from information theory and Monte Carlo theory to analyze the role of information in carcinogenesis. Our analysis demonstrates that, during somatic evolution of the malignant phenotype, the accumulation of genomic mutations degrades intracellular information. However, the degradation is constrained by the Darwinian somatic ecology in which mutant clones proliferate only when the mutation confers a selective growth advantage. In that environment, genes that normally decrease cellular proliferation, such as tumor suppressor or differentiation genes, suffer maximum information degradation. Conversely, those that increase proliferation, such as oncogenes, are conserved or exhibit only gain of function mutations. These constraints shield most cellular populations from catastrophic mutator-induced loss of the transmembrane entropy gradient and, therefore, cell death. The dynamics of constrained information degradation during carcinogenesis cause the tumor genome to asymptotically approach a minimum information state that is manifested clinically as dedifferentiation and unconstrained proliferation. Extreme physical information (EPI) theory demonstrates that altered information flow from cancer cells to their environment will manifest in-vivo as power law tumor growth with an exponent of size 1.62. This prediction is based only on the assumption that tumor cells are at an absolute information minimum and are capable of "free field" growth that is, they are unconstrained by external biological parameters. The prediction agrees remarkably well with several studies demonstrating power law growth in small human breast cancers with an exponent of 1.72+/-0.24. This successful derivation of an analytic expression for cancer growth from EPI alone supports the conceptual model that carcinogenesis is a process of constrained information degradation and that malignant cells are minimum information systems. EPI theory also predicts that the estimated age of a clinically observed tumor is subject to a root-mean square error of about 30%. This is due to information loss and tissue disorganization and probably manifests as a randomly variable lag phase in the growth pattern that has been observed experimentally. This difference between tumor size and age may impose a fundamental limit on the efficacy of screening based on early detection of small tumors. Independent of the EPI analysis, Monte Carlo methods are applied to predict statistical tumor growth due to perturbed information flow from the environment into transformed cells. A "simplest" Monte Carlo model is suggested by the findings in the EPI approach that tumor growth arises out of a minimally complex mechanism. The outputs of large numbers of simulations show that (a) about 40% of the populations do not survive the first two-generations due to mutations in critical gene segments; but (b) those that do survive will experience power law growth identical to the predicted rate obtained from the independent EPI approach. The agreement between these two very different approaches to the problem strongly supports the idea that tumor cells regress to a state of minimum information during carcinogenesis, and that information dynamics are integrally related to tumor development and growth.