The Intransitive Logic of Directed Cycles and Flipons Enhances the Evolution of Molecular Computers by Augmenting the Kolmogorov Complexity of Genomes

Cell responses are usually viewed as transitive events with fixed inputs and outputs that are regulated by feedback loops. In contrast, directed cycles (DCs) have all nodes connected, and the flow is in a single direction. Consequently, DCs can regenerate themselves and implement intransitive logic. DCs are able to couple unrelated chemical reactions to each edge. The output depends upon which node is used as input. DCs can also undergo selection to minimize the loss of thermodynamic entropy while maximizing the gain of information entropy. The intransitive logic underlying DCs enhances their programmability and impacts their evolution. The natural selection of DCs favors the persistence, adaptability, and self-awareness of living organisms and does not depend solely on changes to coding sequences. Rather, the process can be RNA-directed. I use flipons, nucleic acid sequences that change conformation under physiological conditions, as a simple example and then describe more complex DCs. Flipons are often encoded by repeats and greatly increase the Kolmogorov complexity of genomes by adopting alternative structures. Other DCs allow cells to regenerate, recalibrate, reset, repair, and rewrite themselves, going far beyond the capabilities of current computational devices. Unlike Turing machines, cells are not designed to halt but rather to regenerate.

Thermodynamics, organisms and behaviour

The physical origin of behaviour in biological organisms is distinct from those of non-living systems in one significant way: organisms exhibit intentionality or goal-directed behaviour. How may we understand and explain this important aspect in physical terms, grounded in laws of physics and chemistry? In this article, we discuss recent experimental and theoretical progress in this area and future prospects of this line of thought. The physical basis for our investigation is thermodynamics, though other branches of physics and chemistry have an important role. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

Entropy, Ecology and Evolution: Toward a Unified Philosophy of Biology

Darwin proposed that the capacity of organisms to produce more offspring that can be supported by the environment would lead to a struggle for existence, and individuals that are most fit for survival and reproduction would be selected through natural selection. Ecology is the science that studies the interaction between organisms and their environment within the context of Darwinian evolution, and an ecosystem is defined as a community of living organisms in conjunction with the nonliving components of their environment, interacting as a system. One topic that has been very much understudied and largely ignored in evolutionary biology is the overarching context of thermodynamics in controlling all biological processes and the evolution of life. Most fundamentally, organisms are self-replicating dissipative structures. Evolution is the process whereby variation in the structure of organisms have differential fitness in terms of their effectiveness at building and maintaining their structure, efficiently consuming free energy, and effectively reproducing and passing on those heritable variations, leading to change in the frequency of genetic variation and associated change in the characteristics in the population. The central process is dissipation of free energy according to the second law of thermodynamics, and evolution therefore is better conceptualized as the emergence of self-replicating dissipative structures that through natural selection become increasingly more efficient at degrading free energy. Ecosystems are linked series of dissipative structures with heat engine dynamics driven by random dissipation of energy and increasing entropy. The structure and composition of ecosystems across scales are emergent dissipative structures driven by the flow of energy and the increase in entropy. Communities and ecosystems are emergent properties of a system that has evolved to most efficiently dissipate energy and increase entropy. By focusing on the fundamental entity (energy), and the fundamental process (dissipation and disordering of energy and increasing of entropy), we are able to have a much clearer and powerful understanding of what life is, from the level of biochemistry, to evolution, to the nature of the organism itself, and to the emergent structures of ecosystems, food webs and communities.

Formation of dissipative structures in microscopic models of mixtures with species interconversion

The separation of substances into different phases is ubiquitous in nature and important scientifically and technologically. This phenomenon may become drastically different if the species involved, whether molecules or supramolecular assemblies, interconvert. In the presence of an external force large enough to overcome energetic differences between the interconvertible species (forced interconversion), the two alternative species will be present in equal amounts, and the striking phenomenon of steady-state, restricted phase separation into mesoscales is observed. Such microphase separation is one of the simplest examples of dissipative structures in condensed matter. In this work, we investigate the formation of such mesoscale steady-state structures through Monte Carlo and molecular dynamics simulations of three physically distinct microscopic models of binary mixtures that exhibit both equilibrium (natural) interconversion and a nonequilibrium source of forced interconversion. We show that this source can be introduced through an internal imbalance of intermolecular forces or an external flux of energy that promotes molecular interconversion, possible manifestations of which could include the internal nonequilibrium environment of living cells or a flux of photons. The main trends and observations from the simulations are well captured by a nonequilibrium thermodynamic theory of phase transitions affected by interconversion. We show how a nonequilibrium bicontinuous microemulsion or a spatially modulated state may be generated depending on the interplay between diffusion, natural interconversion, and forced interconversion.

Towards the First Principles in Biology and Cancer: New Vistas in Computational Systems Biology of Cancer

These days many leading scientists argue for a new paradigm for cancer research and propose a complex systems-view of cancer supported by empirical evidence. As an example, Thea Newman (2021) has applied "the lessons learned from physical systems to a critique of reductionism in medical research, with an emphasis on cancer". It is the understanding of this author that the mesoscale constructs that combine the bottom-up as well as top-down approaches, are very close to the concept of emergence. The mesoscale constructs can be said to be those effective components through which the system allows itself to be understood. A short list of basic concepts related to life/biology fundamentals are first introduced to demonstrate a lack of emphasis on these matters in literature. It is imperative that physical and chemical approaches are introduced and incorporated in biology to make it more conceptually sound, quantitative, and based on the first principles. Non-equilibrium thermodynamics is the only tool currently available for making progress in this direction. A brief outline of systems biology, the discovery of emergent properties, and metabolic modeling are introduced in the second part. Then, different cancer initiation concepts are reviewed, followed by application of non-equilibrium thermodynamics in the metabolic and genomic analysis of initiation and development of cancer, stressing the endogenous network hypothesis (ENH). Finally, extension of the ENH is suggested to include a cancer niche (exogenous network hypothesis). It is expected that this will lead to a unifying systems-biology approach for a future combination of the analytical and synthetic arms of two major hypotheses of cancer models (SMT and TOFT).

A Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks

Dissipative accounts of structure formation show that the self-organisation of complex structures is thermodynamically favoured, whenever these structures dissipate free energy that could not be accessed otherwise. These structures therefore open transition channels for the state of the universe to move from a frustrated, metastable state to another metastable state of higher entropy. However, these accounts apply as well to relatively simple, dissipative systems, such as convection cells, hurricanes, candle flames, lightning strikes, or mechanical cracks, as they do to complex biological systems. Conversely, interesting computational properties-that characterize complex biological systems, such as efficient, predictive representations of environmental dynamics-can be linked to the thermodynamic efficiency of underlying physical processes. However, the potential mechanisms that underwrite the selection of dissipative structures with thermodynamically efficient subprocesses is not completely understood. We address these mechanisms by explaining how bifurcation-based, work-harvesting processes-required to sustain complex dissipative structures-might be driven towards thermodynamic efficiency. We first demonstrate a simple mechanism that leads to self-selection of efficient dissipative structures in a stochastic chemical reaction network, when the dissipated driving chemical potential difference is decreased. We then discuss how such a drive can emerge naturally in a hierarchy of self-similar dissipative structures, each feeding on the dissipative structures of a previous level, when moving away from the initial, driving disequilibrium.

Self-Organization and Information Processing: From Basic Enzymatic Activities to Complex Adaptive Cellular Behavior

One of the main aims of current biology is to understand the origin of the molecular organization that underlies the complex dynamic architecture of cellular life. Here, we present an overview of the main sources of biomolecular order and complexity spanning from the most elementary levels of molecular activity to the emergence of cellular systemic behaviors. First, we have addressed the dissipative self-organization, the principal source of molecular order in the cell. Intensive studies over the last four decades have demonstrated that self-organization is central to understand enzyme activity under cellular conditions, functional coordination between enzymatic reactions, the emergence of dissipative metabolic networks (DMN), and molecular rhythms. The second fundamental source of order is molecular information processing. Studies on effective connectivity based on transfer entropy (TE) have made possible the quantification in bits of biomolecular information flows in DMN. This information processing enables efficient self-regulatory control of metabolism. As a consequence of both main sources of order, systemic functional structures emerge in the cell; in fact, quantitative analyses with DMN have revealed that the basic units of life display a global enzymatic structure that seems to be an essential characteristic of the systemic functional metabolism. This global metabolic structure has been verified experimentally in both prokaryotic and eukaryotic cells. Here, we also discuss how the study of systemic DMN, using Artificial Intelligence and advanced tools of Statistic Mechanics, has shown the emergence of Hopfield-like dynamics characterized by exhibiting associative memory. We have recently confirmed this thesis by testing associative conditioning behavior in individual amoeba cells. In these Pavlovian-like experiments, several hundreds of cells could learn new systemic migratory behaviors and remember them over long periods relative to their cell cycle, forgetting them later. Such associative process seems to correspond to an epigenetic memory. The cellular capacity of learning new adaptive systemic behaviors represents a fundamental evolutionary mechanism for cell adaptation.

Functional Interdependence in Coupled Dissipative Structures: Physical Foundations of Biological Coordination

Coordination within and between organisms is one of the most complex abilities of living systems, requiring the concerted regulation of many physiological constituents, and this complexity can be particularly difficult to explain by appealing to physics. A valuable framework for understanding biological coordination is the coordinative structure, a self-organized assembly of physiological elements that collectively performs a specific function. Coordinative structures are characterized by three properties: (1) multiple coupled components, (2) soft-assembly, and (3) functional organization. Coordinative structures have been hypothesized to be specific instantiations of dissipative structures, non-equilibrium, self-organized, physical systems exhibiting complex pattern formation in structure and behaviors. We pursued this hypothesis by testing for these three properties of coordinative structures in an electrically-driven dissipative structure. Our system demonstrates dynamic reorganization in response to functional perturbation, a behavior of coordinative structures called reciprocal compensation. Reciprocal compensation is corroborated by a dynamical systems model of the underlying physics. This coordinated activity of the system appears to derive from the system’s intrinsic end-directed behavior to maximize the rate of entropy production. The paper includes three primary components: (1) empirical data on emergent coordinated phenomena in a physical system, (2) computational simulations of this physical system, and (3) theoretical evaluation of the empirical and simulated results in the context of physics and the life sciences. This study reveals similarities between an electrically-driven dissipative structure that exhibits end-directed behavior and the goal-oriented behaviors of more complex living systems.

Dissipative Structures, Organisms and Evolution

Self-organization in nonequilibrium systems has been known for over 50 years. Under nonequilibrium conditions, the state of a system can become unstable and a transition to an organized structure can occur. Such structures include oscillating chemical reactions and spatiotemporal patterns in chemical and other systems. Because entropy and free-energy dissipating irreversible processes generate and maintain these structures, these have been called dissipative structures. Our recent research revealed that some of these structures exhibit organism-like behavior, reinforcing the earlier expectation that the study of dissipative structures will provide insights into the nature of organisms and their origin. In this article, we summarize our study of organism-like behavior in electrically and chemically driven systems. The highly complex behavior of these systems shows the time evolution to states of higher entropy production. Using these systems as an example, we present some concepts that give us an understanding of biological organisms and their evolution.

Observation and modelling of vegetation spirals and arcs in isotropic environmental conditions: dissipative structures in arid landscapes

We report for the first time on the formation of spirals like vegetation patterns in isotropic and uniform environmental conditions. The vegetation spirals are not waves and they do not rotate. They belong to the class of dissipative structures found out of equilibrium. Isolated or interacting spirals and arcs observed in South America (Bolivia) and North Africa (Morocco) are interpreted as a result of curvature instability that affects the circular shape of localized patches. The biomass exhibits a dynamical behaviour with arcs that transform into spirals. Interpretation of observations and of the predictions provided by the theory is illustrated by recent measurements of peculiar plant morphology (the alfa plant, or Stipa tenacissima L.) originated from northwestern Africa and the southern part of the Iberian Peninsula.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

The Thermodynamics of Development in Bioartificial Tissue Design

The fabrication of bioartificial tissues with authentic structures that could assure their clinical efficacy remains a challenging problem. A new paradigm has emerged that designs bioartificial tissues as intermediate in development tissue forms, which can inherently progress autonomously on developmental pathways, self-organizing their cells into tissue structures as in their in vivo development. Biological processes involved in energy exchange between co-developing tissues are responsible for cell organization into the thermodynamically robust cellular patterns of tissue structures. Bioartificial tissue design rules that aim towards in vitro recapitulation of these processes can ensure the thermodynamic operation of developing tissues, leading to formation of the cellular patterns of tissue structures.

Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves

The goal of this review article is to assess how relevant is the concept of dissipative structure for understanding the dynamical bases of non-equilibrium self-organization in biological systems, and to see where it has been applied in the five decades since it was initially proposed by Ilya Prigogine. Dissipative structures can be classified into four types, which will be considered, in turn, and illustrated by biological examples: (i) multistability, in the form of bistability and tristability, which involve the coexistence of two or three stable steady states, or in the form of birhythmicity, which involves the coexistence between two stable rhythms; (ii) temporal dissipative structures in the form of sustained oscillations, illustrated by biological rhythms; (iii) spatial dissipative structures, known as Turing patterns; and (iv) spatio-temporal structures in the form of propagating waves. Rhythms occur with widely different periods at all levels of biological organization, from neural, cardiac and metabolic oscillations to circadian clocks and the cell cycle; they play key roles in physiology and in many disorders. New rhythms are being uncovered while artificial ones are produced by synthetic biology. Rhythms provide the richest source of examples of dissipative structures in biological systems. Bistability has been observed experimentally, but has primarily been investigated in theoretical models in an increasingly wide range of biological contexts, from the genetic to the cell and animal population levels, both in physiological conditions and in disease. Bistable transitions have been implicated in the progression between the different phases of the cell cycle and, more generally, in the process of cell fate specification in the developing embryo. Turing patterns are exemplified by the formation of some periodic structures in the course of development and by skin stripe patterns in animals. Spatio-temporal patterns in the form of propagating waves are observed within cells as well as in intercellular communication. This review illustrates how dissipative structures of all sorts abound in biological systems.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

The rehabilitation of irreversible processes and dissipative structures' 50th anniversary

In 2017, Ilya Prigogine would have been 100 years of age. As for any human being, this centenary is a notable event. For him, as a scientist, 2017 was also above all the 50th anniversary of dissipative structures It was indeed in 1967 that for the first time he used this denomination at the occasion of an important scientific event and in publications. The attribution of this qualification for self-organized behaviours of matter only possible far from equilibrium coincided with the outcome of a research effort of more than 25 years. Centred in thermodynamics and statistical physics on the role played by irreversible processes in the physical evolution of matter, the aim of this research is clear from the outset of his scientific career. With visionary personal intuition and iron-willed determination, it was pursued. The road to success had been long and sinuous, but finally it led to what he called the rehabilitation of irreversible processes The progresses that stand out as major landmarks of this endeavour that imposed a U-turn with respect to conceptions of classical physics deeply rooted since the nineteenth century will be described. This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (Part 1)'.

Methods for Measuring Viability and Evaluating Viability Indicators

Life and other dissipative structures involve nonlinear dynamics that are not amenable to conventional analysis. Advances are being made in theory, modeling, and simulation techniques, but we do not have general principles for designing, controlling, stabilizing, or eliminating these systems. There is thus a need for tools that can transform high-level descriptions of these systems into useful guidance for their modification and design. In this article we introduce new methods for quantifying the viability of dissipative structures. We then present an information-theoretical approach for evaluating the quality of viability indicators, measurable quantities that covary with, and thus can be used to predict or influence, a system's viability.

Cascading time evolution of dissipative structures leading to unique crystalline textures

This article reports unique pattern formation processes and mechanisms via crystallization of materials under external flow fields as one of the general problems of open nonequilibrium phenomena in statistical physics. The external fields effectively reduce step-by-step the exceedingly large free energy barriers associated with the reduction of the enormously large entropy necessary for crystallization into unique crystalline textures in the absence of the fields. The cascading reduction of the free energy barrier was discovered to be achieved as a consequence of a cascading evolution of a series of dissipative structures. Moreover, this cascading pattern evolution obeys the Ginzburg-Landau law. It first evolves a series of large-length-scale amorphous precursors driven by liquid-liquid phase separation under a relatively low bulk stress and then small-length-scale structures driven by a large local stress concentrated on the heterogeneous amorphous precursors, eventually leading to the formation of unique crystalline textures which cannot be developed free from the external fields. Here the multi-length-scale heterogeneous structures developed in the amorphous precursors play a dominant role in the triggering of the crystallization in the local regions subjected to a large stress concentration even under a relatively small applied bulk stress.

Chemical morphogenesis: recent experimental advances in reaction-diffusion system design and control

In his seminal 1952 paper, Alan Turing predicted that diffusion could spontaneously drive an initially uniform solution of reacting chemicals to develop stable spatially periodic concentration patterns. It took nearly 40 years before the first two unquestionable experimental demonstrations of such reaction-diffusion patterns could be made in isothermal single phase reaction systems. The number of these examples stagnated for nearly 20 years. We recently proposed a design method that made their number increase to six in less than 3 years. In this report, we formally justify our original semi-empirical method and support the approach with numerical simulations based on a simple but realistic kinetic model. To retain a number of basic properties of real spatial reactors but keep calculations to a minimal complexity, we introduce a new way to collapse the confined spatial direction of these reactors. Contrary to similar reduced descriptions, we take into account the effect of the geometric size in the confinement direction and the influence of the differences in the diffusion coefficient on exchange rates of species with their feed environment. We experimentally support the method by the observation of stationary patterns in red-ox reactions not based on oxihalogen chemistry. Emphasis is also brought on how one of these new systems can process different initial conditions and memorize them in the form of localized patterns of different geometries.

Hierarchical adaptive nanostructured PVD coatings for extreme tribological applications: the quest for nonequilibrium states and emergent behavior

Adaptive wear-resistant coatings produced by physical vapor deposition (PVD) are a relatively new generation of coatings which are attracting attention in the development of nanostructured materials for extreme tribological applications. An excellent example of such extreme operating conditions is high performance machining of hard-to-cut materials. The adaptive characteristics of such coatings develop fully during interaction with the severe environment. Modern adaptive coatings could be regarded as hierarchical surface-engineered nanostructural materials. They exhibit dynamic hierarchy on two major structural scales: (a) nanoscale surface layers of protective tribofilms generated during friction and (b) an underlying nano/microscaled layer. The tribofilms are responsible for some critical nanoscale effects that strongly impact the wear resistance of adaptive coatings. A new direction in nanomaterial research is discussed: compositional and microstructural optimization of the dynamically regenerating nanoscaled tribofilms on the surface of the adaptive coatings during friction. In this review we demonstrate the correlation between the microstructure, physical, chemical and micromechanical properties of hard coatings in their dynamic interaction (adaptation) with environment and the involvement of complex natural processes associated with self-organization during friction. Major physical, chemical and mechanical characteristics of the adaptive coating, which play a significant role in its operating properties, such as enhanced mass transfer, and the ability of the layer to provide dissipation and accumulation of frictional energy during operation are presented as well. Strategies for adaptive nanostructural coating design that enhance beneficial natural processes are outlined. The coatings exhibit emergent behavior during operation when their improved features work as a whole. In this way, as higher-ordered systems, they achieve multifunctionality and high wear resistance under extreme tribological conditions.

Quantitative analysis of cellular metabolic dissipative, self-organized structures

One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life.

Cyclic-AMP-controlled oscillations in suspended Dictyostelium cells: their relation to morphogenetic cell interactions

Periodic spikes of decreased optical density were recorded in cell suspensions of Dictyostelium discoideum. Spike formation as well as changes in the redox state of cytochrome b are facultatively and independently coupled to an oscillating system which is under developmental control and presumably underlies signal transmission in aggregating cells. Cyclic AMP triggers a double response, the slow component resembling the spikes formed during spontaneous oscillations. The fast component shows characteristics of the chemotactic response to cyclic AMP. The receptor system is suggested to sense changes of cyclic AMP concentration in time. Cyclic AMP pulses interact with the oscillating system, resulting in phase shift or suppression of spike formation, and in the induction of oscillations in an early stage of development before the onset of spontaneous oscillations. Continuous flow application of cyclic AMP does not change frequency up to flow rates which extinguish oscillations.

Patterns of spatiotemporal organization in an allosteric enzyme model

The behavior of a model for an allosteric enzyme oscillator activated by the reaction product is analyzed in the presence of diffusion. When the concentrations of the chemicals are fixed at the boundaries, dynamic dissipative structures are shown to arise in the form of propagating concentration waves. The model is applied to the phosphofructokinase reaction and suggests that a spatiotemporal organization may originate at a macroscopic (supracellular) level from the glycolytic system.