Tunneling of autowaves through unexcitable parts of active media

The mechanisms of propagation of autowaves through local heterogeneities in active media were studied by computer simulation. The model proposed by Zel'dovich and Frank-Kamenetsky and that of FitzHugh-Nagumo were used for studying autowave tunneling. It was shown that the underbarrier passage of an autowave through a nonexcitable area is limited by threshold values. It was shown that, for every fixed parameter value corresponding to the degree of nonexcitability of a local area, there exists a critical value for nonexcitable zone latitude. An autowave overcomes the barrier and continues to propagate when the value of zone latitude is less than the critical. Critical conditions for the origination of sources of secondary periodical sequences of impulses in excitable medium were found. It was shown that the properties of sources of secondary autowaves can be modified by regulating the size of the nonexcitable zone and the zone of increased excitability. In particular, the conditions were explored under which spatial irregularity behaves as a source of a unidirectional and/or an asynchronous sequence of impulses.     

Waves on the cell surface

A new theoretical model is presented which describes dynamics of interaction between the plasmic membrane, cell cortex and cytoplasmic liquid. Analysis of the equation system describing this interaction has shown that besides the uniform solution (corresponding to a flat cell surface) there exists the stable autowave solution (corresponding to standing or running harmonic waves along the cell surface). The latter solution can be related to the experimentally observed waves moving along the cell surface.     

An active-medium model of organic substance transformation in soil and its dynamic properties

An analysis of the behaviour of the soil system considered as an active medium with distributed energy sources was undertaken. This approach enabled the authors to build a heuristic model of soil which accounts for processes of organic substance production, migration and utilisation. The soil body is presented as a spatially distributed trophic chain with non-linear interactions of adjacent links. The level of this non-linearity appears to be the key parameter determining the dynamic behaviour of the model system in one-, two- and three-dimensional cases. The conditions for the existence of pulse-generating and autowave modes in this system were determined by computer simulations. Of particular interest is the behaviour of damaged soil, especially its self-regeneration potential. Inoculation autowave was proven to restore the initial state of the soil if two adjacent or separated trophic links fall out. Possible ways of the further development of the proposed model are also discussed.     

Autowave distribution of nitric oxide and its endogenous derivatives in biosystems strongly enhances their biological effects: A working hypothesis

It is hypothesized that in cells producing nitric oxide (NO), NO and its endogenous derivatives (low-molecular S-nitrosothiols and dinitrosyl iron complexes (DNIC) with thiol-containing ligands) can move in the intracellular space not only by diffusion but also in an autowave mode. This hypothesis is based on the previously obtained data on autowave distribution of DNIC with glutathione following application of a drop of a solution of Fe²⁺ + glutathione onto the surface of a thin layer of a S-nitrosoglutathione solution. The appearance of autowaves is conditioned by a self-regulating self-sustained system arising in the process. This system consists of self-convertible DNIC and S-nitrosothiols as well as free ferrous iron ions, thiols and NO and can function in the autowave regime for several seconds with subsequent passage to a steady state maintained by chemical equilibrium between DNIC and their constituent components (free Fe²⁺ ions, thiols, S-nitrosothiols and NO). Possible advantages of autowave distribution of NO and its endogenous derivatives in the intracellular space over free diffusion, which might entail higher efficiency of their biological action, are discussed.     

Biophysics at the turn of the century: autowaves

By the example of the formation of dissipative patterns in Belousov-Zhabotinsky reactions and in population waves of mobile microorganisms, an attempt was made to analyze the development of the "autowave conception" in the last ten years. New results obtained at the Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, were demonstrated. The place of the "autowave conception" among other methods of studying nonlinear cooperative bioprocesses that form the basis of synergism is shown. The review was prepared on the occasion of the 275th anniversary of the Russian Academy of Sciences and the 2nd Biophysical Meeting of Russia.     

Resonant Drift of Spiral Waves in the Complex Ginzburg-Landau Equation

Weak periodic external perturbations of an autowave medium can cause large-distance directed motion of the spiral wave. This happens when the period of the perturbation coincides with, or is close to the rotation period of a spiral wave, or its multiple. Such motion is called resonant or parametric drift. It may be used for low-voltage defibrillation of heart tissue. Theory of the resonant drift exists, but so far was used only qualitatively. In this paper, we show good quantitative agreement of the theory with direct numerical simulations. This is done for Complex Ginzburg-Landau Equation, one of the simplest autowave models.     

Application of porous teflon tubing method to automatic fed-batch culture of microorganisms. I. Mass transfer through porous teflon tubing

For the purpose of a rational design for an automatic feedback control system incorporating a porous Teflon tubing sensor in semibatch culture, steady-state mass-transfer characteristics of tubing sensors have been investigated theoretically and experimentally, and also dynamic responses have been studied experimentally. A distributed mathematical model for steady-state diffusion has been solved numerically and its solution has been shown as useful for the sensor design. The overall mass-transfer resistance of radial diffusion has been shown to be the sum of external liquid-film mass-transfer resistance and membrane diffusion resistance. The steady-state experiments using ethanol dissolved in water revealed that its transfer into the tubing was controlled by the molecular diffusion within the tubing-wall membrane. Oxygen transfer from external water into the tubing was shown experimentally to be controlled by the liquid-film resistance outside the tubing. In general, the radial mass transfer of a substance having a small Henry's constant is controlled by the liquid-film resistance. The response of the tubing sensor-detector-recorder system for the stepwise addition of ethanol into the external water could not be represented by a simple combined system of the first-order delay with lag time. The responses depend on the characteristics of the tubing as well as flow rate of the carrier gas, etc., but they were quite excellent in all cases (e.g., 90% in 20 s).     

Propagation of Curved Activation Fronts in Anisotropic Excitable Media

We study theoretical and numerical propagation of autowave fronts in excitable two-variable (activator-inhibitor) systems with anisotropic diffusion. A general curvature-velocity relation is derived for the case that the inhibitor diffusion is neglected. This relation predicts the break of an activation front when the front curvature exceeds a critical value, which is corroborated by computer simulations of a particular reaction-diffusion model. Some qualitative effects associated with the inhibitor diffusion are studied numerically. It is found that the critical value of curvature decreases with an increase in the inhibitor diffusion coefficient. The core of a spiral wave increases in size and turns through an angle which depends on the inhibitor diffusion coefficient. PACS Numbers: 05.50. +q, 05.70. Ln., 82.40. -g, 87.10. +e     

Membrane Impression and Gene Expression

The central question in the molecular biology of differentiation is: why are new parts of the genome transcribed? Different hypotheses have been suggested for the control of the cytodifferentiation process. Many of these postulate a "time programme"; others postulate a "programme of events", leading to the conversion of cells to new phenotypes. In the model discussed here the fatter postulate is favoured, suggesting that the differentiation process is guided by the continuous and sequential changes of the microenvironment of the cell. The knowledge of the regularity of these changes is integrated as "evolutive experience", as a more or less fixed programme into the genome. Specific structures in the cell membrane (receptors, receptor areas) are able to perceive and transduce the signal of the environment. The signal can be transformed and regulated in the cell on different levels. For this process—the information flux from the cell membrane to the genome—the term " membrane impression " is proposed in contrast to the information flux from the genome to the cell membrane " gene expression ". It is mentioned that the differentiation process corresponds to the alternative interaction between the cell membrane and the genome. This typical Ping Pong interaction results in cell lineage. It is postulated that membrane receptors for the next anticipated signals are coexpressed with a specific phenotype of the cell. The possibility of the existence of different receptors is discussed.     

Mass-transfer limitations for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor

A mathematical model has been developed for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor in which the enzyme-catalyzed reaction (the irreversible uni-uni competitive Michaelis-Menten kinetics is chosen as an example) was coupled with intraparticle diffusion, external mass transfer, and axial dispersion. The effects of mass-transfer limitations, competitive inhibition of substrates, deactivation on the enzyme effective enantioselectivity, and the optical purity and yield of the desired product are examined quantitatively over a wide range of parameters using the orthogonal collocation method. For a first-order reaction, an analytical solution is derived from the mathematical model for slab-, cylindrical-, and spherical-enzyme supports. Based on the analytical solution for the steady-state resolution process, a new concise formulation is presented to predict quantitatively the mass-transfer limitations on enzyme effective enantioselectivity and optical purity and yield of the desired product for a continuous steady-state kinetic resolution process in a fixed-bed reactor.     

A Computer-aided noninterfering on-line technique for monitoring oxygen-transfer characteristics during fermentation processes

The role of computers in the monitoring and control of fermentation processes has increased steadfastly. The ultimate utility of the machines will not depend on the availability of online sensors but also on the availability of techniques that combine direct measurements, leading towards estimates of variable closely related to the microbial process or its control. In this article, a methodology for on-line and noninterfering evaluation of the volumetric mass-transfer coefficient K(l)a is developed. A detailed presentation of the procedure, called "the static method," is given. Its feasibility is proved through implementation of the method on an antibiotic fermentation process. These experiments indicate that operator actions meant to modify the oxygen-transfer conditions can be checked on-line. The quantitative value of the static method is ascertained by comparing the experimental results with K(l)a estimates obtained with the "gassing-out" method. A sensitivity analysis was carried out, revealing the need for temperature and pressure corrections and showing that the precision of the oxygen analyzer determines the precision of the static method.     

An autowave model of the bifurcation behavior of transformed cells in response to polysaccharide

Isolated Helianthus tuberosus L. polysaccharide (HTLP) with a molecular weight of 1–2 MDa has a wide range of biological activities, including the ability to switch transformed cells to an apoptotic pathway. A qualitative explanation for this effect has previously been proposed on the basis of the interactions among components of intracellular signaling pathways associated with the Dectin-1, TLR-6, and TNFR1 receptors and intracellular factors involved in regulating apoptosis. In this work, an autowave model is proposed to explain the switch between alternative modes of cell behavior in response to polysaccharide. The model is based on the modified FitzHugh–Nagumo system of equations. The parameters of the model were estimated numerically.     

Influence of enzymatic reactions on blood coagulation autowave

A model of blood coagulation has been investigated. The model includes 25 “reaction-diffusion” equations describing the space-time dynamics of distribution of blood coagulation factor concentrations. The one-dimensional statement of the problem is considered. The autowave velocity has been estimated based on the spatial distribution of blood coagulation factors obtained by numerical calculation of the problem. The dependence of the autowave velocity on diffusion coefficients of prothrombin, AT-III, thrombin, and thrombin bound to α²-macroglobulin is estimated.     

Whole-cell hollow-fiber reactor: Effectiveness factors

Analytical expressions, which allow the generation of effectiveness factor graphs for a reactor system employing immobilized whole cells a biocatalyst, are presented. In particular hollow-fiber devices (such as dialysis or ultrafiltration units) are considered. Such devices are analogs to a shell-and-tube heat exchanger. Whole cells are entrapped on the shell side: a nutrient solution is circulated through the tubes, substrate diffuses from the tube side, across the fiber, and into the cell mass on the shell side, where it irreversibly reacts to form product. The product back-diffuses into the circulating nutrient solution. The overall substrate mass-transfer process is hypothesized to be either diffusion limited in the hollow-fiber tube wall and/or the shell-side cell suspension and/or reaction limited at the enzyme sites within the whole cells. The first- and zero-order limits of the Michaelis-Menten rate law are used in generating effectiveness factor expressions. The effectiveness factor is a function of reaction order, Thiele modulus, diffusion coefficient ratio (defined as the effective substrate diffusivity in the hollow-fiber membrane wall divided by the effective substrate diffusivity in the cell suspension), partition coefficient, volume of the cell suspension, and hollow-fiber width. Equations for the effectiveness factor are also detailed when the hollow-fiber mass-transfer resistance is far greater than the cell suspension mass-transfer resistance. An effectiveness factor chart is presented specifically for the commercially available C-DAK 4 dialyzer (Cordis Dow Co., Miami, Florida). In general terms the effectiveness factor expressions are applicable for characterizing diffusion and reaction within a catalytically active cylindrical annulus, Whose inner surface offers a diffusional resistance and whose outer surface is impermeable to reactants. Some generalization of the Thiele modulus is undertaken which serves to draw the asymptotes on the effectiveness factor charts together. Comment is made on the variation of the slope of the effectiveness factor graph and its relation to the change in the observed reaction activation energy. Possible application of the model to the catalytic tube wall reactor is discussed.     

Lipid droplet formation is dispensable for endoplasmic reticulum-associated degradation

Proteins that fail to fold or assemble in the endoplasmic reticulum (ER) are destroyed by cytoplasmic proteasomes through a process known as ER-associated degradation. Substrates of this pathway are initially sequestered within the ER lumen and must therefore be dislocated across the ER membrane to be degraded. It has been proposed that generation of bicellar structures during lipid droplet formation may provide an "escape hatch" through which misfolded proteins, toxins, and viruses can exit the ER. We have directly tested this hypothesis by exploiting yeast strains defective in lipid droplet formation. Our data demonstrate that lipid droplet formation is dispensable for the dislocation of a plant toxin and the degradation of both soluble and integral membrane glycoproteins.     

The autowave electromechanical activity of the <Emphasis Type="Italic">Physarum polycephalum</Emphasis> plasmodium

The aim of this work is to clarify the role of the electrical activity of the Physarum polycephalum plasmodium in the control of the contractile activity and self-organization of the directed locomotion. This single-celled organism with a non-excitable membrane is a classic object that is used in studies of amoeboid motility. Its patterns of motor behavior and signal systems are common for many tissue cells. The presence of 50 mM KCl in an agar substrate under half of a separate plasmodial strand strongly inhibits the formation of the frontal zone and leads to sharp morphological polarization of the strand, which suggests the involvement of electrical processes in the autowave self-organization of the plasmodial structure. The gigantic sizes of the plasmodium make it possible to record its electrical activity simultaneously at different parts of the cell. It has been established that potentials and currents at parts of the plasmodium that are distant from each other oscillate synchronously and differ only in the shape of the signals, probably due to differences in the phases or the number of excited harmonics. We recorded currents (~50 pA) of single ion channels of the plasmodial membrane using the classical local voltage-clamp method. It has been found that the oscillation spectrum of the current that is generated by the plasmodium has high-frequency fluctuations, which are probably connected with periodic detachments of the membrane from the cytoskeleton during the formation and growth of the pseudopodia. It has been also shown that neomycin, a substrate inhibitor of phospholipase C, prevents oscillations of both the mechanical and electrical activity of the plasmodium. This is consistent with its well-established ability to inhibit mechanosensitive Ca²⁺ channels, which are apparently present in the plasmodial membrane. These data indicate the presence of a general signal system that is linked with the dynamics of the membrane- cytoskeleton association, which could be involved in the galvano- and chemotaxis of amoeboid cells.     

Development of a three-zone simulated moving bed process based on partial-discard strategy for continuous separation of valine from isoleucine with high purity,high yield,and high product concentration

The issue of separating valine from isoleucine has been a major concern in the biotechnological process for production of valine. To address this issue, an optimal three-zone simulated moving bed (SMB) process for continuous separation of valine was developed in this study. It was first found that an Amberchrom-CG161C resin was highly suitable for the adsorbent of such SMB process. The adsorption isotherm and mass-transfer parameters of valine and isoleucine on the Amberchrom-CG161C adsorbent were then determined through multiple frontal experiments. The determined parameters were used in the next stage of optimizing the SMB for valine separation, which was performed on the basis of genetic algorithm. For the optimized SMB process, a partial-discard strategy was applied to the raffinate port in order to make a further improvement in the valine product concentration. Finally, the optimized SMB based on the partial-discard strategy was tested experimentally using the self-assembled SMB equipment. The experimental results showed that the developed process in this study was highly effective in continuous separation of valine from isoleucine while ensuring the attainment of high product concentration. The experimental data for the SMB effluent histories and the SMB column profiles were also in close agreement with the model predictions.     

Emergence of Asynchronous Local Clocks in Excitable Media

Excitable media such as the myocardium or the brain consist of arrays of coupled excitable elements, in which the local excitation of a single element can propagate to its neighbors in the form of a non-linear autowave. Since each element has to pass through a refractory period immediately after excitation, the frequency of autowaves is self-limiting. In this work, we consider the case where each element is spontaneously excited at a fixed average rate and thereby initiates a new autowave. Although these spontaneous self-excitation events are modelled as independent Poisson point processes with exponentially distributed waiting times, the travelling autowaves lead collectively to a non-exponential, unimodal waiting time distribution for the individual elements. With increasing system size, a global ‘clock’ period T emerges as the most probable waiting time for each element, which fluctuates around T with an increasingly small but non-zero variance. This apparent synchronization between asynchronous, temporally uncorrelated point processes differs from synchronization effects between perfect oscillators interacting in a phase-aligning manner. Finally, we demonstrate that asynchronous local clocks also emerge in non-homogeneous systems in which the rates of self-excitation are different for all individuals, suggesting that this novel mechanism can occur in a wide range of excitable media.     

Virus removal from bioproducts using ultrafiltration membranes modified with latex particle pretreatment

Ultrafiltration is an attractive process for virusremoval from bioproducts owing to its high throughputas well as the fact that the operation is carried outunder ambient conditions (damage to proteins is highlylimited). The principal concern regarding the adoptionof conventional ultrafiltration membranes for virusremoval is the possibility of the virus passingthrough abnormally large pores or surfaceimperfections on the membrane surface. The chiefprinciple behind the present work is to pretreat themembrane by blocking the abnormally large pores usinglatex particles. Experimental work was conducted tovalidate this pretreatment using the bacteriophagex174 as a model virus.The results attained were highly encouraging.Different sizes of latex particles were tested bytreating a 100 KD molecular weight cut-off membrane,and the transmission of phage (suspended in buffer)through this membrane assessed. In the absence of anyparticle pretreatment, a virus clearance of 4.78 logreduction value was observed for this membrane. Thetransmission of phage through the membrane could bereduced by an order of magnitude using 0.11 mlatex particles, or two orders of magnitude using acombination of 0.11 and 0.50 m particles.The application of latex particles did nothinder the transport of protein through the 100 KDmembrane. Protein sieving coefficients obtained usingthis membrane were 91%, 16% and 2%, for lysozyme,HSA and IgG, respectively.     

The reactive extraction of phenylalanine with Aliquat 336: buffer co-extraction equilibrium and mass transfer kinetics

The occurrence of significant co-extraction of buffer anions by the ion exchanger Aliquat 336 is unavoidable when high levels of system buffering is required. The co-extraction will result in inaccurate equilibrium and mass-transfer characterization of such a system unless its occurrence is taken into account, making process design and control difficult. A study of the equilibrium of phenylalanine extraction using Aliquat 336, a system where high levels of hydroxyl co-extraction occurs, was used as a model case to develop a method of accounting for co-extraction in mass-transfer modeling. Analysis of the equilibrium between bulk-aqueous-phase chloride and phenylalanine concentrations during mass transfer in a stirred-transfer cell showed there to be linear equilibrium relationships between the two parameters for a given extraction system of the form C(Cl,t) = alpha(C(A,t) - C(A,0)) for forward extraction and C(Cl,t) = epsilon C(A,t) + C(Cl,0) for backward extraction. The constants of proportionality of these relationships, or the "co-extraction constants," alpha and epsilon, were shown to be related to the selectivity of Aliquat 336 for the phenylalanine anion by the relationships alpha = -(1/S + 1) and epsilon; = -(1/S(-1) + 1). The linear equilibrium relationships were used to develop two-film theory mass-transfer models for both forward and backward extraction that account for co-extraction. These showed much higher accuracy in modeling stirred-transfer-cell data than the equivalent models which ignored co-extraction.