Power laws of complex systems from extreme physical information

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.

Signal transmission through elements of the cytoskeleton form an optimized information network in eukaryotic cells

Multiple prior empirical and theoretical studies have demonstrated wire-like flow of electrons and ions along elements of the cytoskeleton but this has never been linked to a biological function. Here we propose that eukaryotes use this mode of signal transmission to convey spatial and temporal environmental information from the cell membrane to the nucleus. The cell membrane, as the interface between intra- and extra-cellular environments, is the site at which much external information is received. Prior studies have demonstrated that transmembrane ion gradients permit information acquisition when an environmental signal interacts with specialized protein gates in membrane ion channels and producing specific ions to flow into or out of the cell along concentration gradients. The resulting localized change in cytoplasmic ion concentrations and charge density can alter location and enzymatic function of peripheral membrane proteins. This allows the cell to process the information and rapidly deploy a local response. Here we investigate transmission of information received and processed in and around the cell membrane by elements of the cytoskeleton to the nucleus to alter gene expression. We demonstrate signal transmission by ion flow along the cytoskeleton is highly optimized. In particular, microtubules, with diameters of about 30 nm, carry coarse-grained Shannon information to the centrosome adjacent to the nucleus with minimum loss of input source information. And, microfilaments, with diameters of about 4 nm, transmit maximum Fisher (fine-grained) information to protein complexes in the nuclear membrane. These previously unrecognized information dynamics allow continuous integration of spatial and temporal environmental signals with inherited information in the genome.

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.

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.