Bimolecular systems: II. Nonlinear systems of complexes

This paper deals with bimolecular systems in which also complex-complex interactions occur. Because of the complexity of the problem, an approximation in a form of coupled linear systems of complexes (Bull. Math. Biophysics,29, 1–16, 1967) is considered. Two types of couplings, serial and parallel, are studied. In the serial coupling the nonlinear system of complexes has the same behavior as its subsystems. An entity, initial sensitivity, has interesting properties: in serial coupling it is at most equal to the product and in parallel coupling, at most equal to the sum of partial initial sensitivities.     

Chance vs. necessity in living systems: a false antinomy

The concepts of order and randomness are crucial to understand 'living systems' structural and dynamical rules. In the history of biology, they lay behind the everlasting debate on the relative roles of chance and determinism in evolution. Jacques Monod [1970] built a theory where chance (randomness) and determinism (order) were considered as two complementary aspects of life. In the present paper, we will give an up to date version of the problem going beyond the dichotomy between chance and determinism. To this end, we will first see how the view on living systems has evolved from the mechanistic one of the 19th century to the one stemming from the most recent literature, where they emerge as complex systems continuously evolving through multiple interactions among their components and with the surrounding environment. We will then report on the ever increasing evidence of "friendly" co-existence in living beings between a number of "variability generators", fixed by evolution, and the "spontaneous order" derived from interactions between components. We will propose that the "disorder" generated is "benevolent" because it allows living systems to rapidly adapt to changes in the environment by continuously changing, while keeping their internal harmony.     

Tungsten vs. Molybdenum in models for biological systems.

Biological systems show a marked preference for molybdenum over tungsten. Studies with methyliminodiacetic acid and L-cysteine have shown that the formation constants of the complexes with Mo(Vi) and W(VI) are very similar. These results imply that these elements would be bound with roughly equal strengths to an apoenzyme or a carrier whether or not these proteins contain a ligating sulfhydryl group. Similarly, transport across a membrane would not be expected to distinguish compounds of these metals providing they are carried in the same oxidation states. However, molybdenum could be distinguished from tungsten through the greater ease of reduction of the compounds of molybdenum.     

Nonlinear annihilation of excitations in photosynthetic systems.

The theory of the singlet-singlet annihilation in quasi-homogeneous photosynthetic antenna systems is developed further. In the new model, the following important contributions are taken into account: 1) the finite excitation pulse duration, 2) the occupation of higher excited states during the annihilation, 3) excitation correlation effects, and 4) the effect of local heating. The main emphasis is concentrated on the analysis of pump-probe kinetic measurements demonstrating the first two above possible contributions. The difference with the results obtained from low-intensity fluorescence kinetic measurements is highlighted. The experimental data with picosecond time resolution obtained for the photosynthetic bacterium Rhodospirillum rubrum at room temperature are discussed on the basis of this theory.     

Nonlinear systems in medicine

Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.     

Odor identification by males and females: predictions vs performance

More than 200 males and females estimated the identifiabilityof 80 common odorous objects (e.g., chocolate, beer, mustard,rubber). The two genders agreed rather closely in their estimates.The groups also agreed closely in their relative judgementsof whether males or females could identify the objects better.Both groups anticipated that males would be superior for onlya small number of substances, mainly substances that seem stereotypically‘male’ (e.g., cigar butts, beer, machine oil). Thegroups anticipated female superiority for not only stereotypically‘female’ substances (e.g., Ivory soap, Johnson'sbaby powder, nail polish remover), but also for virtually allfoods, including foods presumably consumed equally by both sexes(e.g., potato chips, Juicy Fruit gum, grape drink). The resultssuggested the existence of a second stereotype, namely thatfemales will be superior at identifying all substances not clearlyin the male domain. An experiment that explored the performanceof 46 males and females over five sessions revealed generalfemale superiority. The superiority extended to odors considered‘male’. Males seemed educable and could apparentlyovercome their disadvantage eventually with merely some helpin the retrieval of odor names. Blockage of retrieval seemsa strong limiting factor in odor identification for femalesas well as for males. Irrespective of gender, when persons havethe veridical name of a well-known odor made available by oneor another means, they exhibit considerable talent at identifyingobjects by smell. ¹Supported by NIH Grant ES 00592     

Metabarcoding vs. morphological identification to assess diatom diversity in environmental studies

Diatoms are frequently used for water quality assessments; however, identification to species level is difficult, time‐consuming and needs in‐depth knowledge of the organisms under investigation, as nonhomoplastic species‐specific morphological characters are scarce. We here investigate how identification methods based on DNA (metabarcoding using NGS platforms) perform in comparison to morphological diatom identification and propose a workflow to optimize diatom fresh water quality assessments. Diatom diversity at seven different sites along the course of the river system Odra and Lusatian Neisse from the source to the mouth is analysed with DNA and morphological methods, which are compared. The NGS technology almost always leads to a higher number of identified taxa (270 via NGS vs. 103 by light microscopy LM), whose presence could subsequently be verified by LM. The sequence‐based approach allows for a much more graduated insight into the taxonomic diversity of the environmental samples. Taxa retrieval varies considerably throughout the river system, depending on species occurrences and the taxonomic depth of the reference databases. Mostly rare taxa from oligotrophic parts of the river systems are less well represented in the reference database used. A workflow for DNA‐based NGS diatom identification is presented. 28 000 diatom sequences were evaluated. Our findings provide evidence that metabarcoding of diatoms via NGS sequencing of the V4 region (18S) has a great potential for water quality assessments and could complement and maybe even improve the identification via light microscopy.     

Single-channel autocorrelation functions: the effects of time interval omission.

We present a general mathematical framework for analyzing the dynamic aspects of single channel kinetics incorporating time interval omission. An algorithm for computing model autocorrelation functions, incorporating time interval omission, is described. We show, under quite general conditions, that the form of these autocorrelations is identical to that which would be obtained if time interval omission was absent. We also show, again under quite general conditions, that zero correlations are necessarily a consequence of the underlying gating mechanism and not an artefact of time interval omission. The theory is illustrated by a numerical study of an allosteric model for the gating mechanism of the locust muscle glutamate receptor-channel.     

Spatial autocorrelation in biology 1. Methodology

Spatial autocorrelation analysis tests whether the observed value of a nominal, ordinal, or interval variable at one locality is independent of values of the variable at neighbouring localities. The computation of autocorrelation coefficients for nominal, ordinal, and for interval data is illustrated, together with appropriate significance tests. The method is extended to include the computation of correlograms for spatial autocorrelation. These show the autocorrelation coefficient as a function of distance between pairs of localities being considered, and summarize the patterns of geographic variation exhibited by the response surface of any given variable.
Autocorrelation analysis is applied to microgeographic variation of allozyme frequencies in the snail Helix aspersa. Differences in variational patterns in two city blocks are interpreted.
The inferences that can be drawn from correlograms are discussed and illustrated with the aid of some artificially generated patterns. Computational formulae, expected values and standard errors are furnished in two appendices.     

Nonlinear diffusion in biological systems

Diffusion problem with variabale diffusion coefficient in a spherical biological system is investigated. Also included in this study is the biological reaction of the Michaelis-Menten type. The problem formulated consists of a highly nonlinear differential equation which, however, can be efficiently solved by the orthogonal collocation method on a digital computer. The effects of the dimensionless governing parameters on the transient and steady state concentration responses are parametrically examined for the diffusion system with and without biological reaction.     

Nonlinear diffusion in metabolic systems

Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system. A portion of this work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies, assigned to the Mathematics Panel, Oak Ridge National Laboratory.     

Unbiased vs. biased approaches to the identification of cancer signatures: the case of lung cancer

Expression profiling analysis of human cancers is a promising approach to obtain precise molecular classification of cancers, to develop stratification tools for therapeutic regimens, and to predict the biological behavior of neoplasia. Direct profiling of human cancers (herein defined as “the unbiased approach”) presents, however, intrinsic problems connected with the high genetic noise embedded in the system. This, in turn, leads to fitting of the noise in the data (the so-called “overtraining”) with consequent instability of the identified signatures, when applied on different cohorts of patients. To circumvent these problems, “biased approaches” - which exploit the molecular knowledge of cancer obtained in model systems - are being developed. Biased approaches, however, are not problem-free, in that they provide information limited to single oncogenic events, thereby failing, at least in principle, to capture the complex repertoire of alterations of human cancers. In this review, we compare the two approaches and provide a test case, from our studies, of how “integrated” strategies, which combine biased and unbiased approaches, might lead to the identification of stable and reliable predictive signatures in cancer.     

The control of cell metabolism for homogeneous vs. heterogeneous enzyme systems

Metabolic control theories, based on such parameters as "elasticity coefficients" and "flux-control coefficients", have emerged in recent years. These offer a potentially unifying, holistic paradigm for understanding the regulation of cell metabolism. Much of the foundation relies on the supposition that the system is a homogeneous bulk-phase solution of individual enzymes. We examine some of the tenets of such theories, in the light of increasing knowledge of enzyme organization in vivo. We cast the control parameters into a more general form applicable to the linear kinetic regime, using a newly defined unit--the kinetic power, which allows complete specification in terms of any and all factors which bear upon the conversion of free substrate to free product in situ. Extending the control theory to heterogeneous states of enzyme organization, we make a formal distinction between "solution connectivity" and "structural connectivity" in a multienzyme system. The use of "structural" rate expressions leads to the definition of a flux-control coefficient which specifies the interdependence of the individual rate processes in an organized system. The problems and limitations in applying the control theory to experimental analysis of real systems in situ are discussed. "We have arrived at last at a point which comes rather close to what might be defined as 'molecular control of cellular activity', only to discover that the 'controlling' molecules have themselves acquired their specific configurations, which are the key to their power of control, by virtue of their membership in the population of an organized cell, hence under 'cellular control'." (Weiss, 1963).     

On-line identification of sensory systems using pseudorandom binary noise perturbations.

A technique of on-line identification of linear system characteristics from sensory systems with spike train or analog voltage outputs was developed and applied to the semicircular canal. A pseudorandom binary white noise input was cross-correlated with the system's output to produce estimates of linear system unit impulse responses (UIRs), which were then corrected for response errors of the input transducers. The effects of variability in the system response characteristics and sensitivity were studied by employing the technique with known linear analog circuits. First-order unit afferent responses from the guitarfish horizontal semicircular canal were cross-correlated with white noise rotational acceleration inputs to produce non-parametric UIR models. In addition, the UIRs were fitted by nonlinear regression to truncated exponential series to produce parametric models in the form of low-order linear system equations. The experimental responses to the white noise input were then compared with those predicted from the UIR models linear convolution, and the differences were expressed as a percent mean-square-error (%MSE). The average difference found from a population of 62 semicircular canal afferents was relatively low mean and standard deviation of 10.2 +/- 5.9 SD%MSE, respectively. This suggests that relatively accurate inferences can be made concerning the physiology of the semicircular canal from the linear characteristics of afferent responses.     

The identification of nonlinear biological systems: LNL cascade models

Systems that can be represented by a cascade of a dynamic linear (L), a static nonlinear (N) and a dynamic linear (L) subsystem are considered. Various identification schemes that have been proposed for these LNL systems are critically reviewed with reference to the special problems that arise in the identification of nonlinear biological systems. A simulated LNL system is identified from limited duration input-output data using an iterative identification scheme.