A new hypothesis on mitotic control mechanism in eukaryotic cells: cell-specific mitosis-inhibiting protein excretion hypothesis.

Recent experimental studies on the regulatory mechanism of cell division in the regenerating rat liver have suggested that α₁acid glycoprotein is a primary mitotic inhibitor, whose intracellular concentration over a critical level inhibits cell division, while α₁-antitrypsin is one of secondary mitotic inhibitors, whose extracellular concentration below a critical level facilitates the excretion of the primary mitotic inhibitor from the hepatocyte, allowing cell division. Based on these findings, the essential part of the mitotic control mechanism in the regenerating rat liver is concretely discussed.To expand the basic concept to more general biological phenomena, the cell-specific mitosis-inhibiting protein excretion hypothesis is proposed. The hypothesis depends on two basic presuppositions: (1) Every cell has a cell-specific mitosis-inhibiting protein synthesized by the cell itself. (2) Every cell will be released from the suppression of cell division when the cell-specific mitosis-inhibiting protein has been excreted and the intracellular concentration of the protein has fallen below a critical level.On the basis of this hypothesis, the mitotic control mechanism in normal eukaryotic cells is briefly discussed on the level of the interrelation between cell division and cell differentiation, and the core of the puzzle of carcinogenesis, the problem of the so-called indefinite or autonomous proliferation of the cancer cell in the host, is also discussed.     

A theoretical consideration of perception at lower levels

In discussing possible mechanisms of the apprehension of either brightness gradients or contours in the retina, the late Kenneth J. W. Craik (in press) proposed a process of differentiation of the output of the bacillary layer in the several subjacent strata of the bipolar layer, such that each cell would compute the difference of the output between two adjacent pairs of rods or cones as shown in Figure 1, and the neurons of subjacent layers the output of neurons above them.     

A theoretical consideration of perception at lower levels

In discussing possible mechanisms of the apprehension of either brightness gradients or contours in the retina, the late Kenneth J. W. Craik (in press) proposed a process of differentiation of the output of the bacillary layer in the several subjacent strata of the bipolar layer, such that each cell would compute the difference of the output between two adjacent pairs of rods or cones as shown in Figure 1, and the neurons of subjacent layers the output of neurons above them.     

A theoretical description of biological rates

The rates of complex multi-enzyme systems, which may contain diffusion processes, can be written in a standard polynomial form. Approximation of this formula leads to the derivation of equations which provide a theoretical basis for the use of log-log plots (for rate-size and rate-substrate relationships), and Arrhenius plots (for rate-temperature relationships) in biology. Sharp discontinuities or “breaks” on such plots can be explained by summations of simple functions and the powers to which these must be raised prior to summation. It has been found unnecessary to have large enthalpies (or activation energies) to produce sharp breaks on Arrhenius plots of the rates of complicated biological systems.     

A new theoretical approach to biological self-assembly

Upon biological self-assembly, the number of accessible translational configurations of water in the system increases considerably, leading to a large gain in water entropy. It is important to calculate the solvation entropy of a biomolecule with a prescribed structure by accounting for the change in water–water correlations caused by solute insertion. Modeling water as a dielectric continuum is not capable of capturing the physical essence of the water entropy effect. As a reliable tool, we propose a hybrid of the angle-dependent integral equation theory combined with a multipolar water model and a morphometric approach. Using our methods wherein the water entropy effect is treated as the key factor, we can elucidate a variety of processes such as protein folding, cold, pressure, and heat denaturating of a protein, molecular recognition, ordered association of proteins such as amyloid fibril formation, and functioning of ATP-driven proteins.     

A systems theoretical approach to biological membranes

Zusammenfassung In der vorliegenden Arbeit wird die Eindeutigkeit der Beschreibung erregbarer Membranen mit Hilfe von Ersatzschaltungen untersucht. Bei Voraussetzung der Existenz verschiedener Membrankanäle für den Ionentransport läßt sich unter Berücksichtigung nichtlinearer Eigenschaften eine weitgehend eindeutige Ersatzschaltung für einen Kanal angeben. Als wesentliches Kriterium erweist sich dabei das Vorhandensein eines konstanten Gleichgewichts-potentials für jeden Kanal. Der lonentransport durch die Membran wird durch ein einfaches Elektrodiffusionsmodell beschrieben. Hierin ist der Potentialverlauf in der Membran durch physiko-chemische Eigenschaften der Membran und nicht durch die transportierten Ionen bestimmt. Die Leitfähigkeit eines bestimmten Kanals verändert eine Steuervariable, deren Wert sich mit Hilfe einer algebraischen Beziehung aus den Zustandsvariablen eines linearen Differentialgleichungssystems ergibt (dessen Koeffizienten vom Potential über der Zellmembran abhängen). Die Zusammenfassung mehrerer Kanäle (passives Transportsystem) und die Einführung von Stromgeneratoren für den aktiven Transport (deren Effektivität von der chemischen Zusammensetzung der an die Membran angrenzenden Lösungen abhängt) führt zu einer allgemeinen Ersatzschaltung für die erregbare Membran. Die so gewonnene Beschreibung ist hinreichend allgemeingültig, um als Grundlage für die Analyse von Problemen der Informationsverarbeitung im Nervensystem bzw. für die weitere Aufklärung der in der erregbaren Membran ablaufenden physikalisch-chemischen Prozesse zu dienen.

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Presented in part at the IV. Intern. Biophysics Congress, Moscow, August 1972.     

A method for the analysis of biological transduction phenomena

Biological transduction can be defined as the triggering of a cellular response by the binding of molecules of effector substances to specific cellular sites. An example of biological transduction, analyzed in this report, is the triggering of T-cell proliferation by the binding of T-cell growth factor (TCGF) to specific TCGF-binding sites on responsive T-cells. Sigmoidal or S-shaped curves often result when measurements of biological response are plotted as a function of concentration of effector substance. Such curves suggest that effector molecules must bind a critical number of cellular sites, and this critical number of bound complexes must undergo secondary events (cross-linking, association, internalization, second messenger release, etc.) in order to initiate the biological response. The method described here estimates the critical number of cellular sites (R) and the probability of these secondary events (PS/B) as follows: (1) The total number of cellular sites (N) is estimated from binding data, and the probabilities (PB) of effector molecules binding to a site are estimated from response data. (2) The response data are assumed to follow the summed binomial distribution function, which is equated to the incomplete beta function. (3) R and PS/B are estimated by applying nonlinear regression to the incomplete beta function. The T-cell data to which the method was applied gave N = 15,000, R = 5, and PS/B = 7.22 x 10(-4). These results show that the binding of very few TCGF molecules is required for activation of T-cells and that the probability of the secondary events leading to cell proliferation is much smaller than the probability of TCGF binding to T-cells. The method described can be used to analyze any biological transduction experiments where both binding and biological response data are available.     

A model for switch-like phenomena in biological systems.

We present a model for the activity of protein clusters based on a simultaneous desorption of an activator (agonist, substrate molecule, etc.) and an inactivator (antagonist, inhibitor, etc.) caused by the collision or interaction between two effector molecules (e.g. receptors, enzymes). This model gives rise to switch-like dose-response curves, which are difficult to explain by ordinary co-operativity. It fits with recent experimental results obtained on single cells. Some other interesting aspects of the model are also pointed out. The model is similar to the model used to explain steep 'dose-response curves' in heterogeneous catalysis, caused by the reaction between two different molecules or atoms on the surface of the catalyst.     

A new hypothesis for the evolution of biological electron transport

A new hypothesis for the evolution of biological electron transport is presented. According to this hypothesis biological electron transport originated close to the potential of the hydrogen electrode and evolved in various advantageous directions including, when molecular oxygen became available on the Earth, that of the oxygen electrode. This implies stepwise evolution along and across the potential scale. The hypothesis is based mainly on existing information obtained from studies of primary and tertiary structural relationships of proteins. It is hoped to provide a framework for closer understanding of both evolution and mechanisms of cellular oxidation-reduction as well as energy coupling reactions.     

A theoretical approach to cluster formation in biological membranes

A theoretical analysis of cluster formation within the lipid matrix of biological membranes is presented. Various models are analysed: (a) one-dimensional monolayer, (b) two-dimensional monolayer and (c) one dimensional bilayer. Furthermore, lipid-protein interactions are considered. The model is based on differential equations for the probabilities a_i and b₁ which characterize the occupation of the lattice site i by the lipids A and B, respectively. These differential equations are an approximation of the Master-equation. Steady states as well as time-dependent variations are analysed. Depending on the interaction energies of the two lipids, different stationary lipid distributions are obtained, including clusters of lipids A or B and alternating structures. The distributions may be dynamically stable or unstable. It is shown that phase transitions within the lipid matrix may be induced by alteration of the composition of the membrane, by changing the interaction energies of the lipids, by variation of the temperature or by lipid-protein interactions. The transitions between different stationary distributions are studied by use of bifurcation diagrams. The analysis of time-dependent states reveals that unstable structures of the membrane may be important for certain time periods. Consideration of the lipid bilayer leads to a great number of possible distributions, which may be symmetric or asymmetric with respect to the outer and inner leaflets of the membrane.     

Amyloidogenesis in its biological environment: challenging a fundamental issue in protein misfolding diseases

The inability of a protein to adopt its native and soluble conformation (protein misfolding) is the origin of an increasing number of human diseases. The misfolding of a protein is often associated with its assembly into extracellular fibrillar aggregates, commonly termed amyloid fibrils. Despite the many efforts expended to characterise amyloid formation in vitro, it is increasingly evident that the biological environment in which aggregation occurs naturally influences the mechanism and rate of the process, as well as the structure and stability of the resulting fibrils. This problem is not trivial because of the inherent complexity of biology and difficulty to design proper experiments able to address the molecular level of the phenomenon in vivo. We will show successful approaches that have been used recently and will illustrate some of the results that have contributed to elucidate important structural aspects of amyloid formation in vivo.     

Spontaneous epistaxis; theoretical consideration of etiologic factors and treatment

In a study of data on 136 hemorrhages in 14 patients with posterior epistaxis it was noted that the incidence of bleeding was higher at some hours of the day than at others. The times of highest incidence were more or less inverse to hours of peak systolic blood pressure in normal subjects, suggesting that bleeding occurs as a result of dislodgement of an embolus at times of vasodilation. If that is true, then it should be possible to control bleeding by giving vasoconstrictive drugs. There are not as yet enough data on trial of that method to warrant conclusions.     

Oxalate patinas on ancient monuments: the biological hypothesis

Summary Whewellite and weddellite, calcium oxalate monohydrate and dihydrate respectively, have been found in the form of thin surface layers on limestone and marble monuments and artifacts of various historical periods at different sites. Experimental results indicate that the formation of both minerals must be attributed essentially to the action of oxalic acid secreted by microorganisms (lichens) which live and proliferate on the stone. Oxalic acid attacks the calcium carbonate of the stone surface giving rise to the precipitation of calcium oxalate.     

Diffusion of molecules on biological membranes of nonplanar form. A theoretical study.

Lateral mobility of molecules on cell membranes has been recently studied by fluorescence photobleaching recovery (FPR) techniques. The interpretation of these results in terms of diffusion along the membranes is based on the assumption that the surface is planar, although biological membranes may have blebs and microvilli. To study the effect of nonplanarity on the diffusion rate, the diffusion equation along curved surfaces was derived and was solved numerically for a "wavy" surface of the form A cos kx cos ky. Calculations show that for k = 10 pi micrometer-1 and a bleached spot of 1 micrometer in diameter, the time dependence of the intensity of fluorescence in the bleached spot depends on A at A less than 0.5 micrometer, while at higher values of A (a and 2 micrometer) the dependence is weak. If one calculates diffusion coefficients from FPR measurements and assumes that the membrane is planar, the resulting diffusion coefficient is not less than about half of the real one. Because of the tortuous shape of the spot boundary, increasing the microvilli length from 0.5 micrometer to 1 or 2 micrometer does not change the diffusion rates. These considerations are valid for times when the diffusion is dominated by molecules that were initially located close to the spot boundary.     

A generic theoretical model for biological control of foliar plant diseases

We have developed a generic modelling framework to understand the dynamics of foliar pathogen and biocontrol agent (BCA) populations in order to predict the likelihood of successful biocontrol in relation to the mechanisms involved. The model considers biocontrol systems for foliar pathogens only and, although it is most applicable to fungal BCA systems, does not address a specific biocontrol system. Four biocontrol mechanisms (competition, antibiosis, mycoparasitism and induced resistance) were included within the model rubric. Because of the wide range of mechanisms involved we use Trichoderma/Botrytis as an exemplar system. Qualitative analysis of the model showed that the rates of a BCA colonising diseased and/or healthy plant tissues and the time that the BCA remains active are two of the more important factors in determining the final outcome of a biocontrol system. Further evaluation of the model indicated that the dynamic path to the steady-state population levels also depends critically on other parameters such as the host-pathogen infection rate. In principle, the model can be extended to include other potential mechanisms, including spatio-temporal heterogeneity, fungicide effects, non-fungal BCA and strategies for BCA application, although with a cost in model tractability and ease of interpretation.     

A mathematical consideration of the word-composition vector method in comparison of biological sequences

To measure the similarity or dissimilarity between two given biological sequences, several papers proposed metrics based on the "word-composition vector". The essence of these metrics is as follows. First, we count the appearance frequencies of all the K-tuple words throughout each of two given sequences. Then, the two given sequences are transformed into their respective word-composition vectors. Next, the distance metrics, for example the angle between the two vectors, are calculated. A significant issue is to determine the optimal word size K. With a mathematical model of mutational events (including substitutions, insertions, deletions and duplications) that occur in sequences, we analyzed how the angle between the composition vectors depends on the mutational events. We also considered the optimal word size (=resolution) from our original approach. Our results were verified by computational experiments using artificially generated sequences, amino acid sequences of hemoglobin and nucleotide sequences of 16S ribosomal RNA.