Some plane truths about pictures: notes on Wagemans, Lamote, and van Gool (1997)

Wagemans, Lamote, and van Gool (1997) have attempted to show that observers can determine the geometric equivalence of shapes seen in perspective, or in projective transformation. Artifacts of measurement in their procedures forestall such a conclusion. Their experiment fails to control projective properties adequately, and also confounds the transformations of shear and compression. Their evidence that observers can discern the equivalence of shapes under perspective can be reconstrued as evidence for sensitivity to different, unrelated properties: to the plane compression that follows from the depiction of flat shapes in perspective, and to gross differences in shape not specific to projective geometry. An improved set of procedures is proposed for the measurement of stimuli in the study of visual shape constancy.     

How many processes are responsible for phenotypic evolution?

SUMMARY In addressing phenotypic evolution, this article reconsiders natural selection, random drift, developmental constraints, and internal selection in the new extended context of evolutionary developmental biology. The change of perspective from the "evolution of phenotypes" toward an "evolution of ontogenies" (evo-devo perspective) affects the reciprocal relationships among these different processes. Random drift and natural selection are sibling processes: two forms of post-productional sorting among alternative developmental trajectories, the former random, the latter nonrandom. Developmental constraint is a compound concept; it contains even some forms of natural ("external" and "internal") selection. A narrower definition ("reproductive constraints") is proposed. Internal selection is not a selection caused by an internal agent. It is a form of environment-independent selection depending on the level of the organism's internal developmental or functional coordination. Selection and constraints are the main deterministic processes in phenotypic evolution but they are not opposing forces. Indeed, they are continuously interacting processes of evolutionary change, but with different roles that should not be confused.     

Thermodynamic stability of ecosystems

The stability of ecosystems during periods of stasis in their macro-evolutionary trajectory is studied from a non-equilibrium thermodynamic perspective. Individuals of the species are considered as units of entropy production and entropy exchange in an open thermodynamic system. Within the framework of the classical theory of irreversible thermodynamics, and under the condition of constant external constraints, such a system will naturally evolve toward a globally stable thermodynamic stationary state. It is thus suggested that the ecological steady state, or stasis, is a particular case of the thermodynamic stationary state, and that the evolution of community stability through natural selection is a manifestation of non-equilibrium thermodynamic directives. Furthermore, it is argued that punctuation of stasis leading to ecosystem succession, may be a manifestation of non-equilibrium "phase transitions" brought on by a change of external constraints through a thermodynamic critical point.     

Thermodynamic perspectives on genetic instructions, the laws of biology and diseased states

This article examines in a broad perspective entropy and some examples of its relationship to evolution, genetic instructions and how we view diseases. Living organisms are programmed by functional genetic instructions (FGI), through cellular communication pathways, to grow and reproduce by maintaining a variety of hemistable, ordered structures (low entropy). Living organisms are far from equilibrium with their surrounding environmental systems, which tends towards increasing disorder (increasing entropy). Organisms free themselves from high entropy (high disorder) to maintain their cellular structures for a period of time sufficient to allow reproduction and the resultant offspring to reach reproductive ages. This time interval varies for different species. Bacteria, for example need no sexual parents; dividing cells are nearly identical to the previous generation of cells, and can begin a new cell cycle without delay under appropriate conditions. By contrast, human infants require years of care before they can reproduce. Living organisms maintain order in spite of their changing surrounding environment that decreases order according to the second law of thermodynamics. These events actually work together since living organisms create ordered biological structures by increasing local entropy. From a disease perspective, viruses and other disease agents interrupt the normal functioning of cells. The pressure for survival may result in mechanisms that allow organisms to resist attacks by viruses, other pathogens, destructive chemicals and physical agents such as radiation. However, when the attack is successful, the organism can be damaged until the cell, tissue, organ or entire organism is no longer functional and entropy increases.     

Thermodynamics of Terrestrial Evolution

The causal element of biological evolution and development can be understood in terms of a potential function which is generalized from the variational principles of irreversible thermodynamics. This potential function is approximated by the rate of entropy production in a configuration space which admits of macroscopic excursions by fluctuation and regression as well as microscopic ones. Analogously to Onsager's dissipation function, the potential takes the form of a saddle surface in this configuration space. The path of evolution following from an initial high dissipation state within the fixed constraint provided by the invariant energy flux from the sun tends toward the stable saddle point by a series of spontaneous regressions which lower the entropy production rate and by an alternating series of spontaneous fluctuations which introduce new internal constraints and lead to a higher entropy production rate. The potential thus rationalizes the system's observed tendency toward "chemical imperialism" (high dissipation) while simultaneously accommodating the development of "dynamic efficiency" and complication (low dissipation).     

A farewell to arms and legs: a review of limb reduction in squamates

Elongated snake-like bodies associated with limb reduction have evolved multiple times throughout vertebrate history. Limb-reduced squamates (lizards and snakes) account for the vast majority of these morphological transformations, and thus have great potential for revealing macroevolutionary transitions and modes of body-shape transformation. Here we present a comprehensive review on limb reduction, in which we examine and discuss research on these dramatic morphological transitions. Historically, there have been several approaches to the study of squamate limb reduction: (i) definitions of general anatomical principles of snake-like body shapes, expressed as varying relationships between body parts and morphometric measurements; (ii) framing of limb reduction from an evolutionary perspective using morphological comparisons; (iii) defining developmental mechanisms involved in the ontogeny of limb-reduced forms, and their genetic basis; (iv) reconstructions of the evolutionary history of limb-reduced lineages using phylogenetic comparative methods; (v) studies of functional and biomechanical aspects of limb-reduced body shapes; and (vi) studies of ecological and biogeographical correlates of limb reduction. For each of these approaches, we highlight their importance in advancing our understanding, as well as their weaknesses and limitations. Lastly, we provide suggestions to stimulate further studies, in which we underscore the necessity of widening the scope of analyses, and of bringing together different perspectives in order to understand better these morphological transitions and their evolution. In particular, we emphasise the importance of investigating and comparing the internal morphology of limb-reduced lizards in contrast to external morphology, which will be the first step in gaining a deeper insight into body-shape variation.     

Detection of Charge-Neutral Near-Equilibrium Processes at Na-Metal Electrodes by Electrochemical Microcalorimetry

Investigations on electrochemical kinetics usually rely on the measurement of current or potential as a function of time. Charge-neutral process steps or side reactions are naturally disguised in the electrical signals and have only indirect impact. However, all processes will contribute to heat evolution. In this work, heat absorption/liberation is measured as a function of time for pulsed Na deposition/dissolution on a Na-electrode in a 1 m NaPF₆/diglyme solution, in addition to the standard electrochemical signals. While potential and current transients both exhibited sharp rectangular shapes, indicating instantaneous electrochemical Na deposition or dissolution on the time scale of the pulse (10 ms), heat absorption or liberation continued up to about 0.5 s after the pulse. Since heat evolution is to large extent reversible, this corresponded to entropy changes in the absence of external electric current flow, pointing to a reversible, charge-neutral chemical process accompanying Na deposition or dissolution. From the observed entropy changes, it is suggested that upon Na deposition solvated Na⁺ ions are instantaneously transferred into the outer layers of the solid electrolyte interphase, followed by slow desolvation.     

Trypanosoma brucei: differential requirement of membrane potential for import of proteins into mitochondria in two developmental stages

Trypanosome alternative oxidase (TAO) and the cytochrome oxidase (COX) are two developmentally regulated terminal oxidases of the mitochondrial electron transport chain in Trypanosoma brucei. Here, we have compared the import of TAO and cytochrome oxidase subunit IV (COIV), two stage-specific nuclear encoded mitochondrial proteins, into the bloodstream and procyclic form mitochondria of T. brucei to understand the import processes in two different developmental stages. Under in vitro conditions TAO and COIV were imported and processed into isolated mitochondria from both the bloodstream and procyclic forms. With mitochondria isolated from the procyclic form, the import of TAO and COIV was dependent on the mitochondrial inner membrane potential (delta psi) and required protein(s) on the outer membrane. Import of these proteins also depended on the presence of both internal and external ATP. However, import of TAO and COIV into isolated mitochondria from the bloodstream form was not inhibited after the mitochondrial delta psi was dissipated by valinomycin, CCCP, or valinomycin and oligomycin in combination. In contrast, import of these proteins into bloodstream mitochondria was abolished after the hydrolysis of ATP by apyrase or removal of the ATP and ATP-generating system, suggesting that import is dependent on the presence of external ATP. Together, these data suggest that nuclear encoded proteins such as TAO and COIV are imported in the mitochondria of the bloodstream and the procyclic forms via different mechanism. Differential import conditions of nuclear encoded mitochondrial proteins of T. brucei possibly help it to adapt to different life forms.     

Thermodynamics in the present progressive mode and its role in the context of the origin of life.

The origin and evolution of biological organizations proceeding on Earth are put in a nonequilibrium thermodynamic framework within a cosmological context. The dynamic process responsible for chemical evolution leading to the origin of biological being depends upon consumer-dominating thermodynamics, in which the heat sink is taken to be active in extracting heat energy from a body at a higher temperature. Consumer-dominating thermodynamics follows from the fact that when a small hot body contacts a cold heat sink, it decreases the temperature at the possible fastest rate. The fastest temperature drop, when applied to chemical products being synthesized through the energy supplied from an external heat source, is selective in keeping only those products that can decrease the temperature at the fastest rate among the available alternatives. Synthesis of small organic molecules in the small ice grains in interstellar diffuse clouds irradiated by ultraviolet radiation is a representative case of consumer-dominating thermodynamics, in which diffuse clouds serve as cold heat sinks in the cosmological context. Another case of consumer-dominating thermodynamics predominant on Earth especially in the perspective of the origin and evolution of life is with submarine hydrothermal vents, in which the surrounding cold seawater constantly serves as the cold heat sink.     

A generic geometric transformation that unifies a wide range of natural and abstract shapes

To study forms in plants and other living organisms, several mathematical tools are available, most of which are general tools that do not take into account valuable biological information. In this report I present a new geometrical approach for modeling and understanding various abstract, natural, and man-made shapes. Starting from the concept of the circle, I show that a large variety of shapes can be described by a single and simple geometrical equation, the Superformula. Modification of the parameters permits the generation of various natural polygons. For example, applying the equation to logarithmic or trigonometric functions modifies the metrics of these functions and all associated graphs. As a unifying framework, all these shapes are proven to be circles in their internal metrics, and the Superformula provides the precise mathematical relation between Euclidean measurements and the internal non-Euclidean metrics of shapes. Looking beyond Euclidean circles and Pythagorean measures reveals a novel and powerful way to study natural forms and phenomena.     

The role of information in cell regulation

The organised state of living cells must derive from information internal to the system; however, there are strong reasons, based on sound evidence, to reject the base sequence information encoded in the genomic DNA as being directly relevant to the regulation of cellular phenotype. Rather, it is argued here that highly specific relational information, encoded on the gene products, mainly proteins, is responsible for phenotype. This regulatory information emerges as the peptide folds into a tertiary structure in much the same way as enzymic activity emerges under the same circumstances. The DNA coding sequence serves as a “data base” in which a second category of relational information is stored to enable accurate reproduction of the cellular peptides. In the context of the cell, therefore, information is physical in character and contributes, through its ability to dissipate free energy, to the maximisation of the entropy of the cell according to the 2nd law of thermodynamics.     

Mode dynamics of interacting neural populations by bi-orthogonal spectral decomposition

A system of coupled bistable Hopf oscillators with an external periodic input source was used to model the ability of interacting neural populations to synchronize and desynchronize in response to variations of the input signal. We propose that, in biological systems, the settings of internal and external coupling strengths will affect the behaviour of the system to a greater degree than the input frequency. While input frequency and coupling strength were varied, the spatio-temporal dynamics of the network was examined by the bi-orthogonal decomposition technique. Within this method, effects of variation of input frequency and coupling strength were analyzed in terms of global, spatial and temporal mode entropy and energy, using the spatio-temporal data of the system. We observed a discontinuous evolution of spatio-temporal patterns depending sensitively on both the input frequency and the internal and external coupling strengths of the network. Received: 10 June 1998 / Accepted in revised form: 9 August 1999     

Mathematical model allowing the coexistence of closely related competitors at the initial stage of evolution

The mathematical model presented here aims to elucidate the essential mechanisms of coexistence of species, especially those of closely related forms, as a result of competition in the same environment. It describes a system where the fate of the competitors or mutants is observed at the initial stage of evolution. The model encompasses both the external variables and the internal state of the competitors, which differ only in one of the metabolic rate constants. Results of simulations, even with the simplified form of the model, show that stable coexistence of closely related forms in a uniform environment is possible. In addition, the model allows the analysis of the limitations on the level of differences and similarities among the competitors for achieving a state of coexistence. The essential mechanisms for the coexistence of closely related competitors are proposed to be the involvement of the metabolic network in allowing the same growth rate of competitors which have different internal states, and the interplay between the internal states of the competitors and the external variables of their environment.     

Three-dimensional topology optimization model to simulate the external shapes of bone

Elucidation of the mechanism by which the shape of bones is formed is essential for understanding vertebrate development. Bones support the body of vertebrates by withstanding external loads, such as those imposed by gravity and muscle tension. Many studies have reported that bone formation varies in response to external loads. An increased external load induces bone synthesis, whereas a decreased external load induces bone resorption. This relationship led to the hypothesis that bone shape adapts to external load. In fact, by simulating this relationship through topology optimization, the internal trabecular structure of bones can be successfully reproduced, thereby facilitating the study of bone diseases. In contrast, there have been few attempts to simulate the external structure of bones, which determines vertebrate morphology. However, the external shape of bones may be reproduced through topology optimization because cells of the same type form both the internal and external structures of bones. Here, we constructed a three-dimensional topology optimization model to attempt the reproduction of the external shape of teleost vertebrae. In teleosts, the internal structure of the vertebral bodies is invariable, exhibiting an hourglass shape, whereas the lateral structure supporting the internal structure differs among species. Based on the anatomical observations, we applied different external loads to the hourglass-shaped part. The simulations produced a variety of three-dimensional structures, some of which exhibited several structural features similar to those of actual teleost vertebrae. In addition, by adjusting the geometric parameters, such as the width of the hourglass shape, we reproduced the variation in the teleost vertebrae shapes. These results suggest that a simulation using topology optimization can successfully reproduce the external shapes of teleost vertebrae. By applying our topology optimization model to various bones of vertebrates, we can understand how the external shape of bones adapts to external loads.     

Coupling thermodynamics applied in chemical morphogenesis; influence of environmentally organized space-time structures upon nonequilibrium entropy functions of multivariate biosystems

In this paper is proposed the so-called coupling thermodynamics which deals with coupled variables or elementary units which are influenced by input-output relations. In contrast to the usual definition of nonequilibrium entropy, external influences are considered directly in the entropy function dependent on space and time. The employment in morphology leads to a model of organized growth.     

Non-equilibrium thermodynamics and biological growth and development.

It is shown that there exists in principle no incompatibility between the observed increase in specific dissipation during early embryogenesis and the theorem of minimum entropy production based on linear irreversible thermodynamics. As a specific illustration we exhibit a linear model for which the time evolution of the three terms in the entropy balance is parallel to that of the evolution of living systems.     

Living organisms from Prigogine’s perspective: an opportunity to introduce students to biological entropy balance

All living structures, from archaea to human, are open thermodynamic systems analysed through nonequilibrium thermodynamics. Nonequilibrium thermodynamics is a field with important applications to life sciences, which is very often left out of life science courses. A three-step method is suggested to make an easy introduction of nonequilibrium thermodynamics to life science students. The first step is to introduce the Prigogine equation dS = d_eS + d_iS, and explain the meaning of the entropy exchange with the surroundings d_eS and internal entropy generation in the system d_iS. The second step is to show that the Prigogine equation is connected to the equilibrium thermodynamics already known to students. This can be done by deriving the Clausius inequality dS ≥ dq/T, from the Prigogine equation applied to reversible and irreversible processes in closed systems. Reversible and irreversible processes are discussed separately and the results are then combined into the Clausius inequality. The third step is to introduce the fact that the Prigogine equation has a variety of applications in life sciences. This would give the students an opportunity to understand the entropy balance of physiological processes in cells and organisms. The import and accumulation of entropy, entropy generation, and entropy export could be made easier for students to adopt.     

Evolution as resistance to entropy. I. Mechanisms of species homeostasis

The idea is discussed that the common output of any evolution is creation of the entities that are increasingly resistant to further evolution. The moving force of evolution is entropy, the tendency to disorder. This general aspiration for chaos is a cause of the mortality of organisms and species, however, being prerequisite for any movement, it creates (by chance) novelties, which may occur (by chance) more resistant to further decay and thus survive. The surviving of those who survive is the most general principle of evolution discovered by Darwin for particular case of biological evolution. The second law of thermodynamics states that our Universe is perishing but its ontology is such that it creates resistance to destruction. The evolution is a history of this resistance. Not only those who die do not survive but also those who evolve. The entities that change (evolve) rapidly disappear rapidly and by this reason they are not observed among both the fossils and now-living organisms. We know only about long-living species. All the existing organisms are endowed with an ability to resist other changing. The following main achievements of the species homeostasis are discussed: high fidelity of DNA replication and effective mechanisms of DNA repair; diploidy; normalizing selection; truncated selection; heterozygote superiority; ability to change phenotype adaptively without changing genotype; parental care and the K-strategy of reproduction; behavior that provides independence of the environment. The global resistance of the living systems to entropy is provided the state that all the essential in biology is determined not by physical-chemical interactions but could semantic rules. A conception of "potential zygotic information" that determines the rules of ontogenesis is proposed. A zygote does not contain this information in explicit form. It is created de novo step by step during ontogenesis and it could not be decoded beforehand. The experimental data on the adaptive mutagenesis and the relevant hypothesis are discussed. It is concluded that the special mechanisms for speeding-up of evolution as created by evolution are impossible conceptually.