An elementary kinetic model of energy coupling in biological membranes

The purpose of this work is to contribute to the understanding of the fundamental kinetic properties of the processes of energy coupling in biological membranes. For this, we consider a model of a microorganism that, in its plasma membrane, expresses two electrogenic enzymes (E(1) and E(2)) transporting the same monovalent cation C and electrodiffusive paths for C and for a monovalent anion A. E(1) (E(2)) couples transport C to the reaction S(1)<-->P(1) (S(2)<-->P(2)). We developed a mathematical model that describes the rate of change of the electrical potential difference across the membrane, of the internal concentrations of C and A, and of the concentrations of S(2) and P(2). The enzymes are incorporated via two-state kinetic models; the passive ionic fluxes are represented by classical formulations of electrodiffusion. The microorganism volume is maintained constant by accessory regulatory devices. The model is utilized for stationary and dynamic studies for the case of bacteria employing the electrochemical gradient of Na(+) as energetic intermediate. Among other conclusions, the results show that the membrane potential represents the relevant kinetic intermediate for the overall coupling between the energy donor reaction S(1)<-->P(1) and the synthesis of S(2).     

A model of a digital biological ecosystem

In this paper, we propose a model of a digital biological ecosystem of fish. Collections of fish data by scientists in Malaysia have been converted and developed into a digital biological ecosystem using computational technology and methods. We used a combination of Geographical Information System, databases and ontologies for storing, retrieving and visualizing fish species distribution and their abundance as well as their relationship with the environment. We used ArcGIS to build the fish and environmental geodatabase, which is linked to Google Earth for real-time visualization, and Surfer 8 to create contour maps which are superimposed as layers on the ArcGIS interface. Individual fish species on the map are hyperlinked to the FishBase Portal (http://www.fishbase.org/) while the published map is displayed using ArcReader. The three databases that we created contain information about fish species, environment and contours. These are also integrated using a fish ontology which will link all the available information for various fish species. The proposed system can be adopted by marine scientists to better convince economists, fishery managers, coastal developers and government bodies who make important decisions on conservation policies and laws.     

生物废水处理系统的细胞自动机模型

建立了活性污泥处理生物废水的细胞自动机模型,对活性污泥生物量与有机物浓度动态进行了研究,提出了计算活性污泥回流循环比的方法.结果表明,在Moore邻居模型下废水达标排放所需时间较Von. Neumann邻居模型少,不同生长阶段的微生物浓度波动具有时滞性.稳定期有机物浓度和生物量不受活性污泥初始浓度的影响.活性污泥处理生物废水的细胞自动机模型有助于为污水处理提供理论依据.     

Structure-activity relationships of hydrazono derivatives of biological interest

The following hydrazono derivatives (I-XXIII) of type (A), (formula; see text) where: X = NO2 (II, IV, VI, VIII, X, XIV-XXIII), X = H (I, III, V, VII, IX, XI, XII, XIII), and Y = H (I, II); 3-Cl (III, IV); 4-Cl (V, VI); 3,4-Cl2 (VII, VIII); 2,6-Cl2 (IX, X); 2-NO2 (XI); 3-NO2 (XII); 4-NO2 (XIII, XIV); 2-F (XV); 3-F (XVI); 4-F (XVII); 2-OH (XVIII); 4-OH (XIX); 2,4-(OH)2(XX); 2,4,6-(OH)3(XXI); 2,3-(OH,NO2) (XXII); 2,4-(NO2)2 (XXIII), were prepared and tested for antibacterial and antifungal activity. All of these compounds were prepared in satisfactory yield by reaction of aromatic aldehydes with 2-furoyl and 5-nitro-2-furoyl hydrazide. The hydrazono derivatives I-XXIII prepared in this investigation were screened for antimicrobial activity by a disk-diffusion assay (Kirby-Bauer modified). The organisms used were laboratory cultures of S. aureus, S. -haemoliticus, B. subtilis, M. paratuberculosis, E. coli, S. typhi, Ps. aeruginosa, K1. pneumoniae, A. niger, S. cerevisiae, C. albicans. The results of this study showed that a number of the prepared hydrazono derivatives exhibited varying degrees of activity against Gram-positive and Gram-negative bacteria. Compounds IV and XV possessed broad spectrum "in vitro" against Gram-positive and Gram-negative bacteria. Compounds XII greater than IV greater than XV showed inhibitory activity especially toward S. aureus. Compounds IV greater than XV greater than XVI were especially active against E. coli. Compounds XV greater than IV were especially inhibitory toward S. typhi and most of the prepared compounds inhibited considerably Ps. aeruginosa and K1. pneumoniae.     

A mathematical model of biological evolution

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN _n (t)/dt=(m _n (t-)N _n (t)+N _n-1(t) (n=0,1,2,3...), where N _n (t) and m _n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by is rigorously obtained for the case (i) m _n (t)=m _n is independent of t (constant fitness model), where m _n is essentially periodic with respect to n, and for the case (ii) (periodic fitness model), together with the long time average m of the average Malthusian parameter . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.An early version of this study was read at the International Symposium on Mathematical Topics in Biological held in kyoto, Japan, on September 11–12, 1978, and was published in its Procedings.     

A generalized mathematical model of biological oscillators

Biological rhythms such as circadian rhythms, biochemical rhythms and neural oscillators are based on the mathematical model of the theory of harmonic oscillators. These are solutions of certain second-order differential equations. They can also be viewed as spherical harmonics on the circle in the two-dimensional Euclidean space. The spherical harmonics on (n-1)-spheres and, more generally, the Stiefel harmonics can represent oscillatory phenomena, and we expect that they can serve as models for more complex biological rhythms.     

Diffusion with memory in two cases of biological interest

The complexity of a biological structure, such as membrane where the transport process may carry solid particles which may obstruct some of the pores, diminishing their size and making the permeability dependent on the local structure of the medium, suggests the introduction of a space-dependent diffusion constant. In this note, the profile concentration of diffusing solutes inside a cell membrane has been calculated on the basis of the Fick diffusion equation modified by introducing a memory formalism (diffusion with memory). This approach has been employed to describe the concentration profile inside the membrane when a sudden change of the concentration in the medium bathing one of its face is applied for a limited interval of time. A further application of the method concerns the so-called concentration boundary layer that occurs at the membrane-aqueous medium interface, where the solute concentration depends, even at considerable depth, on the local structure of the interface. These profiles are compared to some recent experiments concerning the diffusion of ethanol in a layer close to a nephrophane membrane. This approach generalizes the diffusion models based on the Fick equation to more complex systems, where a space-independent diffusion coefficient could be inappropriate to take into account the large variety of diffusion processes in biological systems.     

A biological model of the excitation of a second order sensory neurone

Summary Computer simulation of a relatively simple model can reproduce the main characteristics of the firing patters of some nerve cells. The abdominal stretch receptor of the crayfish has provided an analogous biological model. Synaptic input impulses were simulated by randomly distributed, short lasting transmembrane current pulses. Under these experimental conditions the stretch receptor neurone largely behaved as predicted by the computer simulations.