Models in biology: form and function

The relationships between physical and biological sciences are important in science education. This is shown in the links between the structure of biological science and the use of models. Although the physical sciences contain many principles of wide application, much of biology consists of very distinct examples. When these examples are used as models of organisms or processes, misunderstanding can occur if the characteristics of the model are used to make inaccurate generalizations. In biological education, stress on the importance of unique features must continually accompany the demonstration of similarities.

Theoretical models are constructed and reconstructed by students learning science, particularly in relation to broadly applicable principles. In biology a student may build a theoretical model of a subject which is itself a model used as an example. Distinct features of biological science may influence a variety of learning situations including problem solving.     

Entropic criteria for protein folding derived from recurrences: six residues patch as the basic protein word

Some research has suggested that patches of six constitute an important amino acid window length in proteins for conveying information. We present database evidence that supports this conjecture, as well as additional recurrence-based data that characterization and quantification of these words affect the folding/aggregation features of proteins. Other indirect evidence is presented and discussed.     

On the application of statistical physics to evolutionary biology

There is a close analogy between statistical thermodynamics and the evolution of allele frequencies under mutation, selection and random drift. Wright's formula for the stationary distribution of allele frequencies is analogous to the Boltzmann distribution in statistical physics. Population size, 2N, plays the role of the inverse temperature, 1/kT, and determines the magnitude of random fluctuations. Log mean fitness, , tends to increase under selection, and is analogous to a (negative) energy; a potential function, U, increases under mutation in a similar way. An entropy, S_H, can be defined which measures the deviation from the distribution of allele frequencies expected under random drift alone; the sum gives a free fitness that increases as the population evolves towards its stationary distribution. Usually, we observe the distribution of a few quantitative traits that depend on the frequencies of very many alleles. The mean and variance of such traits are analogous to observable quantities in statistical thermodynamics. Thus, we can define an entropy, S_Ω, which measures the volume of allele frequency space that is consistent with the observed trait distribution. The stationary distribution of the traits is ; this applies with arbitrary epistasis and dominance. The entropies S_Ω, S_H are distinct, but converge when there are so many alleles that traits fluctuate close to their expectations. Populations tend to evolve towards states that can be realised in many ways (i.e., large S_Ω), which may lead to a substantial drop below the adaptive peak; we illustrate this point with a simple model of genetic redundancy. This analogy with statistical thermodynamics brings together previous ideas in a general framework, and justifies a maximum entropy approximation to the dynamics of quantitative traits.     

Gaia again

The ideas of the Gaia hypothesis from the 1960s are today largely included in global ecology and Earth system sciences. The interdependence between biosphere, oceans, atmosphere and geosphere is well-established by data from global monitoring. Nevertheless the theory underlying the holistic view of the homeostatic Earth has remained obscure. Here the foundations of Gaia theory are examined from the recent formulation of the 2nd law of thermodynamics as an equation of motion. According to the principle of increasing entropy, all natural processes, inanimate just as animate, consume free energy, the thermodynamic driving force. All species, abiotic just as biotic are viewed as mechanisms of energy transduction for the global system to evolve toward a stationary state in its surroundings. The maximum entropy state displays homeostasis by being stable against internal fluctuations. When surrounding conditions change or when new mechanisms emerge, the global system readjusts its flows of energy to level newly appeared gradients. Thus, the propositions of Gaia theory and holistic understanding of the global system are recognized as consequences of thermodynamic imperatives.     

Analyzing variable behavioral contingencies: Are certain complex skills homologous with locomotion?

This paper considers behavioral contingencies that change as a function of time, of the individual's own behavior (as in locomotion and reading), of the behavior of other parties or of interactions with them. A detailed analysis of locomotion and of reading out loud shows that the behavioral contingencies for these are virtually the same. The terrain being traversed and the locomotion behavior involved are shown to be analogous to a segment of text being read and the articulation of the words. In both cases, successive upcoming segments are perceived and processed, and during the processing phases, motor behavior is formulated. In both, the smooth concatenation of the motor phases for successive segments requires buffering. Both involve corrective or digressive actions in response to obstacles or unanticipated stimuli encountered. Both involve looking ahead at the upcoming segment and processing it while the motor phase of the prior segment is still in progress. For both, the size, entropy, familiarity, and other attributes of the upcoming segment are parameters of the performance. It is suggested that locomotion has similar parallels with certain other complex skills, such as listening, copying, receiving Morse code, simultaneous interpreting, and certain types of performance, and may therefore be their phylogenetic prototype and biological homologue.     

The Critical Aggregation Concentration of β-Lactoglobulin-Based Fibril Formation

The critical aggregation concentration (CAC) for fibril formation of β-lactoglobulin (β-lg) at pH 2 was determined at 343, 353, 358, 363, and 383 K using a Thioflavin T assay and was approximately 0.16 wt%. The accuracy of the CAC was increased by measuring the conversion into fibrils at different stirring speeds. The corresponding binding energy per mol, as determined from the CAC, was 13 RT (∼40 kJ mol⁻¹) for the measured temperature range. The fact that the CAC was independent of temperature within the experimental error indicates that the fibril formation of β-lg at pH 2 and the measured temperature range is an entropy-driven process.     

The dynamics of EEG entropy

The scaling properties of human EEG have so far been analyzed predominantly in the framework of detrended fluctuation analysis (DFA). In particular, these studies suggested the existence of power-law correlations in EEG. In DFA, EEG time series are tacitly assumed to be made up of fluctuations, whose scaling behavior reflects neurophysiologically important information and polynomial trends. Even though these trends are physiologically irrelevant, they must be eliminated (detrended) to reliably estimate such measures as Hurst exponent or fractal dimension. Here, we employ the diffusion entropy method to study the scaling behavior of EEG. Unlike DFA, this method does not rely on the assumption of trends superposed on EEG fluctuations. We find that the growth of diffusion entropy of EEG increments of awake subjects with closed eyes is arrested only after approximately 0.5 s. We demonstrate that the salient features of diffusion entropy dynamics of EEG, such as the existence of short-term scaling, asymptotic saturation, and alpha wave modulation, may be faithfully reproduced using a dissipative, first-order, stochastic differential equation—an extension of the Langevin equation. The structure of such a model is utterly different from the “noise+trend” paradigm of DFA. Consequently, we argue that the existence of scaling properties for EEG dynamics is an open question that necessitates further studies.     

Cardioviral RNA structure logo analysis: entropy, correlations, and prediction

In recent years, there has been an increased number of sequenced RNAs leading to the development of new RNA databases. Thus, predicting RNA structure from multiple alignments is an important issue to understand its function. Since RNA secondary structures are often conserved in evolution, developing methods to identify covariate sites in an alignment can be essential for discovering structural elements. Structure Logo is a technique established on the basis of entropy and mutual information measured to analyze RNA sequences from an alignment. We proposed an efficient Structure Logo approach to analyze conservations and correlations in a set of Cardioviral RNA sequences. The entropy and mutual information content were measured to examine the conservations and correlations, respectively. The conserved secondary structure motifs were predicted on the basis of the conservation and correlation analyses. Our predictive motifs were similar to the ones observed in the viral RNA structure database, and the correlations between bases also corresponded to the secondary structure in the database.     

Introduction to the special issue: Thermodynamic aspects of cryobiology

This brief paper introduces the subject of thermodynamics and the papers of the special issue on thermodynamic aspects of cryobiology. Thermodynamic terminology is defined for the non-specialist.     

Disruption of the H-bond network in the main access channel of catalase-peroxidase modulates enthalpy and entropy of Fe(III) reduction

Catalase-peroxidases are the only heme peroxidases with substantial hydrogen peroxide dismutation activity. In order to understand the role of the redox chemistry in their bifunctional activity, catalatically-active and inactive mutant proteins have been probed in spectroelectrochemical experiments. In detail, wild-type KatG from Synechocystis has been compared with variants with (i) disrupted KatG-typical adduct (Trp122-Tyr249-Met275), (ii) mutation of the catalytic distal His123-Arg119 pair, and (iii) altered accessibility to the heme cavity (Asp152, Ser335) and modified charge at the substrate channel entrance (Glu253). A valuable insight into the mechanism of reduction potential (E°′) modulation in KatG has been obtained from the parameterization of the corresponding enthalpic and entropic components, determined from the analysis of the temperature dependence of E°′. Moreover, model structures of ferric and ferrous Synechocystis KatG have been computed and used as reference to analyze and discuss the experimental data. The results, discussed by reference to published resonance Raman data on the strength of the proximal iron-imidazole bond and catalytic properties, demonstrate that E°′ of the Fe(III)/Fe(II) couple is not strongly correlated with the bifunctional activity. Besides the importance of an intact Trp-Tyr-Met adduct, it is the architecture of the long and constricted main channel that distinguishes KatGs from monofunctional peroxidases. An ordered matrix of oriented water dipoles is important for H₂O₂ oxidation. Its disruption results in modification of enthalpic and entropic contributions to E°′ that reflect reduction-induced changes in polarity, electrostatics, continuity and accessibility of solvent to the metal center as well as alterations in solvent reorganization.