A note on the dispersionless growth law for single cells

A population of initially synchronized cells is considered wherein each cell grows according to a dispersionless growth law and the probability of cell division is determined by cell age. The first and second moments of the distribution of birth volumes are considered as functions of time and it is shown that it is impossible for both moments to approach finite, nonzero limits ast→∞. This implies that the volume distribution of the population will not approach a limiting distribution on any finite, nonzero volume interval and that the population will not attain balanced exponential growth. An illustrative example is worked out in detail. The distribution of birth volumes is also analyzed as a function of generation number and it is found that the logarithm of the birth volume in thejth generation is normally distributed asj→∞, with an unbounded variance. Generalizations and implications of these results are briefly discussed. Work supported by the U.S. Atomic Energy Commission.     

Growth factors and growth control of heterogeneous cell populations

In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth.Bull. math. Biol. 53, 639–656). The target population, a generic tumor, was modeled as a single, homogeneous population using the standard Verhulst equation of logistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represented by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumor growth, and (3) tumor growth in a radiation damaged environment, a phenomenon termed the Tumor Bed Effect (TBE). In this paper, we extend those results to include a “triad” of growth factor controls (autocrine, paracrine and endocrine) and heterogeneity of the target population. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiating tissues and tumors. Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication between differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the differentiated compartment; and (3) the development of hypoxia in a spherical tumor. The signal processing within the triad is discussed for each model and biologically reasonable constraints are defined for limits on growth control.     

Mathematical models for cellular systems. The von foerster equation. Part II

This is the continuation of Part I, which was published in the September, 1965, issue of theBulletin. The birth rate, α(t), is now assumed to be a linear functional of the age density,n. This gives a simple model of self-replenishing stem cell compartments, and leads to a necessary condition for the existence of a steady state. Some examples are presented to illustrate the formalism. They include: (a) An equivivant population with life spanD and no losses from death or migration. The total number of cells is multiplied by 2 in each time intervalD. As a special case, frequently realized in practice, the population may be increasing exponentially with time (“log-phase” of growth). (b) A compartment with “random” emigration of cells and gamma distribution of life spans. (c) An oversimplified version of L. G. Lajtha’s model describing stem cell kinetics. In section IV a simple case in which the loss function depends explicitly onn is discussed very briefly. This work was performed under the auspices of the U.S. Atomic Energy Commission.     

Antimutagenic effects of caffeine during nitrosoguanidine-induced mutagenesis ofSalmonella typhimurium cells and phages

The effect of caffeine on nitrosoguanidine-induced mutagenesis ofSalmonella typhimurium & nd its P22 and L phages was studied. The detected mutations included phage “clear” mutations, reversions of phage “amber” mutation, and prototrophic reversions of thehis ⁻ auxotroph ofSalmonella typhimurium. Neither therecA mutation of the host nor theerf mutation of the phage genome were found to affect the nitrosoguanidine-induced mutagenesis of the phage during vegetative growth. Beginning with a concentration of 0.2 mg/ml, caffeine decreased the frequency of mutants by 30–60%, attaining a maximum effect at 1.5 mg/ml and retaining this effect even at higher concentrations. A similar antimutagenic effeot was observed with the mutagenesis of the host cells. The nitrosoguanidine-induced mutagenesis does not seem to be related to the function of therecA cell gene or theerf phage gene. The mechanism of mutagenesis by nitrosoguanidine probably has two components, one of them caffeine sensitive, the other caffeine-resistant.     

The general membrane equilibrium equation: Its simple derivation and some of its biological implications

On the basis of thermodynamic considerations, expressions for the relation between thei-th andj-th ions and solvent separated into subsystems by a semi-permeable membrane are derived. From this basic equation expressions for the transfer of solvent attending solute changes are developed. The application of these expressions to biological systems involving solvent transfer, as in cellular growth, chloride shift in the red blood cell, imbibition of water into cells is discussed.     

Heptanol-induced decrease in cardiac gap junctional conductance is mediated by a decrease in the fluidity of membranous cholesterol-rich domains

To assess whether alterations in membrane fluidity of neonatal rat heart cells modulate gap junctional conductance (g _j ), we compared the effects of 2mm 1-heptanol and 20 μm 2-(methoxyethoxy)ethyl 8-(cis-2-n-octylcyclopropyl)-octanoate (A₂C) in a combined fluorescence anisotropy and electrophysiological study. Both substances decreased fluorescence steady-state anisotropy (r_ss), as assessed with the fluorescent probe 1-(4-trimethylammoniumphenyl)-6-phenyl-1,3,5-hexatriene (TMA-DPH) by 9.6±1.1% (mean ±sem,n=5) and 9.8±0.6% (n=5), respectively, i.e., both substances increased bulk membrane fluidity. Double whole-cell voltage-clamp experiments showed that 2mm heptanol uncoupled cell pairs completely (n=6), whereas 20 μm A₂C, which increased bulk membrane fluidity to the same extent, did not affect coupling at all (n=5). Since gap junction channels are embedded in relatively cholesterol-rich domains of the membrane, we specifically assessed the fluidity of the cholesterol-rich domains with dehydroergosterol (DHE). Using DHE, heptanol increased r_ss by 14.9±3.0% (n=5), i.e., decreased cholesterol domain fluidity, whereas A₂C had no effect on r_ss (−0.4±6.7%,n=5). Following an increase of cellular “cholesterol” content (by loading the cells with DHE), 2mm heptanol did not uncouple cell pairs completely:g _j decreased by 80±20% (range 41–95%,n=5). The decrease ing _j was most probably due to a decrease in the open probability of the gap junction channels, because the unitary conductances of the channels were not changed nor was the number of channels comprising the gap junction. The sensitivity of non-junctional membrane channels to heptanol was unaltered in cholesterol-enriched myocytes. These results indicate that the fluidity of cholesterol-rich domains is of importance to gap junctional coupling, and that heptanol decreasesg _j by decreasing the fluidity of cholesterol-rich domains, rather than by increasing the bulk membrane fluidity.     

Growth and reproduction in higher plants I. Theoretical analysis by mathematical models

To analyse the whole life of higher plants, an attempt was made to describe their growth and reproduction by mathematical models based on the elements determining matter production and economy of the matter. A plant body was regarded as a compound system of two parts; “productive part” and “reproductive part”. A parameter (reproductive index) was introduced to connect these two parts, and a set of the mathematical models describing the quantitative growth of these two parts were established. Two basic patterns of reproduction in higher plants were distinguished into “D-reproduction” and “I-reproduction”. The state of matter production of the mother plant determined an initial size of the daughter plant in theD-reproduction, while, in theI-reproduction, it did not determine the initial size of the daughter, but determined the number of propagules. The model of each reproduction pattern was also constructed. A formula determining the initial size of a plant in a given generation was constructed as the model of theD-reproduction. The model for theI-reproduction described the number of propagules produced in a given generation. Some aspects of the plant life, e.g. the optimum reproductive index, the switch-over time from the vegetative to the reproductive growth phase, the seed number, types of expansive reproduction, were theoretically analysed and discussed under these mathematical models.     

Contents of <Emphasis Type="Italic">Trans</Emphasis>-resveratrol in Korean Grape Cultivars,including “Kyoho”

Concentrations of trans-resveratrol were analyzed in 36 Korean-grown grape cultivars, including cv. Kyoho. This cultivar has large irregular berries and a deep-black skin and accounts for >15% of all grapevines grown in Korea. The content of trans-resveratrol is an important quality parameter, and its pattern of variability increased gradually until the time of harvest. Its distribution also fluctuated significantly among leaves, seeds, and exocarps, with the highest amount (1,477 μg g⁻¹ dry weight) occurring in the leaves. Among all cultivars evaluated here, trans-resveratrol contents were significantly higher in “Cheongsoo” and “High Bailey,” their levels being 50% above the overall mean (i.e., 2.0-mg g⁻¹ dry weight), whereas 14 cultivars had contents that were 10% less than that mean value     

Wound healing and regeneration in the imaginal wing disc ofDrosophila

Summary When complementary fragments of an imaginal disc ofDrosophila are cultured for several days prior to metamorphosis, usually one fragment will regenerate while the other will duplicate. It has been proposed that wound healing plays an important part in disc regulation (French et al. 1976; Reinhardt et al. 1977) by initiating cell proliferation and determining the mode of regulation. We tried to delay the wound healing process by leaving a region of dead cells between the wound edges. In 06 fragments (Bryant 1975a) wound healing has occurred after 1–2 days of culture and the regeneration of missing structures after 2–4 days of culture. We observed that leaving a region of dead cells between the wound edges delays both wound healing and the regeneration of missing structures by 2 days.When disc fragments are cultured in female abdomens and then exposed to³H-thymidine to label replicating cells, then the label is found to be localised around the wound. We observed that delaying wound healing does not delay this localisation of labelled nuclei indicating that wound healing may not be required to initiate DNA replication.     

Permeability properties of cell-to-cell channels: Kinetics of fluorescent tracer diffusion through a cell junction

Summary We have analyzed the intracellular and cell-to-cell diffusion kinetics of fluorescent tracers in theChironomus salivary gland. We use this analysis to investigate whether membrane potential-induced changes in junctional permeability are accompanied by changes in cell-to-cell channel selectivity. Tracers of different size and fluorescence wavelength were coinjected into a cell, and the fluorescence was monitored in this cell and an adjacent one. Rate constants,k _j , for cell-to-cell diffusion were derived by compartment model analysis, taking into account (i) cell-to-cell diffusion of the tracers; (ii) their loss from the cells; (iii) their binding (sequestration) to cytoplasmic components; and (iv) their relative mobility to cytoplasm, as determined separately on isolated cells. In cell pairs, we compared a tracer'sk _j with the electrical cell-to-cell conductance,g _j .At cell membrane resting potential, thek _j 's ranged 3.8–9.2×10^–3 sec^–1 for the small carboxyfluorescein (mol wt 376) to about 0.4×10^–3 sec^–1 for a large fluorescein-labeled sugar (mol wt 2327). Cell membrane depolarization reversibly reducedg _j andk _j for a large and a small tracer, all in the same proportion. This suggests that membrane potential controls the number of open channels, rather than their effective pore diameter or selectivity. From the inverse relation between tracer mean diameter and relativek _j we calculate an effective, permeation-limiting diameter of approximately 29 Å for the insect cell-to-cell channel. Intracellular diffusion was faster than cell-to-cell diffusion, and it was not solely dependent on tracer size. Rate constants for intracellular sequestration and loss through nonjunctional membrane were large enough to become rate-limiting for cell-to-cell tracer diffusion at low junctional permeabilities.     

In vitro and in vivo wound healing-promoting activities of beta-lapachone

Impaired wound healing is a serious problem for diabetic patients. Wound healing is a complex process that requires the cooperation of many cell types, including keratinocytes, fibroblasts, endothelial cells, and macrophages. β-Lapachone, a natural compound extracted from the bark of the lapacho tree (Tabebuia avellanedae), is well known for its antitumor, antiinflammatory, and antineoplastic effects at different concentrations and conditions, but its effects on wound healing have not been studied. The purpose of the present study was to investigate the effects of β-lapachone on wound healing and its underlying mechanism. In the present study, we demonstrated that a low dose of β-lapachone enhanced the proliferation in several cells, facilitated the migration of mouse 3T3 fibroblasts and human endothelial EAhy926 cells through different MAPK signaling pathways, and accelerated scrape-wound healing in vitro. Application of ointment with or without β-lapachone to a punched wound in normal and diabetic (db/db) mice showed that the healing process was faster in β-lapachone-treated animals than in those treated with vehicle only. In addition, β-lapachone induced macrophages to release VEGF and EGF, which are beneficial for growth of many cells. Our results showed that β-lapachone can increase cell proliferation, including keratinocytes, fibroblasts, and endothelial cells, and migration of fibroblasts and endothelial cells and thus accelerate wound healing. Therefore, we suggest that β-lapachone may have potential for therapeutic use for wound healing. cell proliferation; mitogen-activated protein kinase signaling pathways     

Organismic sets: Outline of a general theory of biological and social organisms

The discussion as to whether societies are organisms andvice versa has been going on for a long time. The question is meaningless unless a clear definition of the term “organism” is made. Once such a definition is made, the question may be answered by studying whether there exists any relational isomorphism between what the biologist calls an organism and what the sociologist calls society. Such a study should also include animal societies studied by ecologists. Both human and animal societies are sets of individuals together with certain other objects which are the products of their activities. A multicellular organism is a set of cells together with some products of their activities. A cell itself may be regarded as a set of genes together with the products of their activities because every component of the cell is either directly or indirectly the result of the activities of the genes. Thus it is natural to define both biological and social organisms as special kinds of sets. A number of definitions are given in this paper which define what we call here organismic sets. Postulates are introduced which characterize such sets, and a number of conclusions are drawn. It is shown that an organismic set, as defined here, does represent some basic relational aspects of both biological organisms and societies. In particular a clarification and a sharpening of the Postulate of Relational Forces given previously (Bull. Math. Biophysics,28, 283–308, 1966) is presented. It is shown that from the basic definitions and postulates of the theory of organismic sets, it folows that only such elements of those sets will aggregate spontaneously, which are not completely “specialized” in the performance of only one activity. It is further shown that such “non-specialized” elements undergo a process of specialization, and as a result of it their spontaneous aggregation into organismic sets becomes impossible. This throws light on the problem of the origin of life on Earth and the present absence of the appearance of life by spontaneous generation. Some applications to problems of ontogenesis and philogenesis are made. Finally the relation between physics, biology, and sociology is discussed in the light of the theory of organismic sets.     

Cell proliferation on hydrogels

Summary The adhesion and proliferation of mammalian fibroblasts (Flow 7000) on the surface of hydrophilic (copolymer ofN-vinyl-2-pyrrolidone and methyl methacrylate) and hydrophobic [polymethylmethacrylate (PMMA) stereocomplex] hydrogels with a wide range in water content were studied morphologically and quantitatively. It was demonstrated that cell proliferation on hydrogels by a static culture method decreased as the water content of the gels increased. However, it is remarkable that the cell proliferation on PMMA hydrogels with a high water content is equivalent to that on glass Petri dishes. The results obtained in the proliferation of cells on the surface of these hydrogels closely correspond to the state of cell adhesion. When fresh medium or air was perfused from the popposite side of the PMMA hydrogel membrane on which the cells were proliferating (perfusion method), the cells continued to grow into a higher density than with the conventional static culture method. In the case of fresh medium perfusion, the amount of proliferated cell was dependent on both the permeability of the membrane and the density of the membrane “scaffolding”. Virus multiplication in the cultured cells increased in proportion to the cell density, whereas the cell function was similar in both culture methods.     

Detection of gene flow from GM to non-GM watermelon in a field trial

Gene flow from genetically modified (GM) crops to conventional non-GM crops is a serious concern for protection of conventional and organic farming. Gene flow from GM watermelon developed for rootstock use, containing cucumber green mottle mosaic virus (CGMMV)-coat protein (CP) gene, to a non-GM isogenic control variety “Clhalteok” and grafted watermelon “Keumcheon” was investigated in a small scale field trial as a pilot study. Hybrids between GM and non-GM watermelons were screened from 1304 “Chalteok” seeds and 856 “Keumcheon” seeds using the duplex PCR method targeting theCGMMV- CP gene as a marker. Hybrids were found in all pollen recipient plots. The gene flow frequencies were greater for “Chaiteok” than for “KeumcheonD; with 75% outcrossing in the “Chaiteok” plot at the closest distance (0.8 m) to the GM plot. A much larger scale field trial is necessary to identify the isolation distance between GM and non-GM watermelon, as the behaviors of insect pollinators needs to be clarified in Korea.     

Bayesian image processing of data from constrained source distributions—I. non-valued,uncorrelated and correlated constraints

A series of Bayesian image processing algorithms which incorporate various classes ofa priori source information in treating data which obeys Poisson and Gaussian statistics is derived using maximum entropy considerations. The standard maximum likelihood equations are shown to be a special case of Bayesian image processing when thea priori information about a source distribution φ _j is solely that a non-vanishing probability for each element value φ _j exists only in some finite interval,a _j ≤φ _j ≤φ _j . Bayesian image processing equations for thea priori source information that all φ _j are finite -∞<φ _j <∞ and each φ _j distribution has a defined mean φ _j and a defined variance σ _j are derived. The Bayesian image processing equations are also derived when thea priori source information is that all φ _j ≥0 and that each φ _j distribution has a defined mean φ _j and a defined variance σ _j . The a priori source distribution constraint that a correlation exists among nearby elements is also considered. The results indicate improvement over standard methods.     

Myosin II activity is required for functional leading-edge cells and closure of epidermal sheets in fish skin ex vivo

Re-epithelialization in skin wound healing is a process in which epidermal sheets grow and close the wound. Although the actin–myosin system is thought to have a pivotal role in re-epithelialization, its role is not clear. In fish skin, re-epithelialization occurs around 500 μm/h and is 50 times faster than in mammalian skin. We had previously reported that leading-edge cells of the epidermal outgrowth have both polarized large lamellipodia and “purse string”-like actin filament cables in the scale-skin culture system of medaka fish, Oryzias latipes (Cell Tissue Res, 2007). The actin purse-string (APS) is a supracellular contractile machinery in which adherens junctions (AJs) link intracellular myosin II-including actin cables between neighboring cells. In this study, we developed a modified “face-to-face” scale-skin culture system as an ex vivo model to study epidermal wound healing, and examined the role of the actin–myosin system in the rapid re-epithelialization using a myosin II ATPase inhibitor, blebbistatin. A low level of blebbistatin suppressed the formation of APS and induced the dissociation of keratocytes from the leading edge without attenuating the growth of the epidermal sheet or the migration rate of solitary keratocytes. AJs in the superficial layer showed no obvious changes elicited by blebbistatin. However, two epidermal sheets without APSs did not make a closure with each other, which was confirmed by inhibiting the connecting AJs between the superficial layers. These results suggest that myosin II activity is required for functional leading-edge cells and for epidermal closure.     

Stimulation of the multiplication of Micrococcus luteus by an autocrine growth factor

Viable cells of Micrococcus luteus secrete a proteineous growth factor (Rpf) which promotes the resuscitation of dormant, nongrowing cells to yield normal, colony-forming bacteria. When washed M. luteus cells were used as an inoculum, there was a pronounced influence of Rpf on the true lag phase and cell growth on lactate minimal medium. In the absence of Rpf, there was no increase in colony-forming units for up to 10 days. When the inoculum contained less than 10⁵ cells ml^–1, macroscopically observable M. luteus growth was not obtained in succinate minimal medium unless Rpf was added. Incubation of M. luteus in the stationary phase for 100 h resulted in a failure of the cells to grow in lactate minimal medium from inocula of small size although the viability of these cells was close to 100% as estimated using agar plates made from lactate minimal medium or rich medium. The underestimation of viable cells by the most-probable-number (MPN) method in comparsion with colony-forming units was equivalent to the requirement that at least 10⁵ cells grown on succinate medium, 10³ cells from old stationary phase, or approximately 10–500 washed cells are required per millilitre of inoculum for growth to lead to visible turbidity. The addition of Rpf in the MPN dilutions led to an increase of the viable cell numbers estimated to approximately the same levels as those determined by colony-forming units. Thus, a basic principle of microbiology –“one cell-one culture”– may not be applicable in some circumstances in which the metabolic activity of “starter” cells is not sufficient to produce enough autocrine growth factor to support cell multiplication. Received: 7 December 1998 / Accepted: 7 April 1999     

Heliorestis daurensis, gen. nov. sp. nov., an alkaliphilic rod-to-coiled-shaped phototrophic heliobacterium from a Siberian soda lake

A novel alkaliphilic heliobacterium was isolated from microbial mats of a low-salt alkaline Siberian soda lake. Cells of the new organism were tightly coiled when grown in coculture with a rod-shaped bacterium, but grew as short filaments when finally obtained in pure culture. The new phototroph, designated strain BT-H1, produced bacteriochlorophyll g and a neurosporene-like pigment, and lacked internal photosynthetic membranes. Similar to other heliobacteria, strain BT-H1 grew photoheterotrophically on a limited range of organic compounds including acetate and pyruvate. Sulfide was oxidized to elemental sulfur and polysulfides under photoheterotrophic conditions; however, photoautotrophic growth was not observed. Cultures of strain BT-H1 were alkaliphilic, growing optimally at pH 9, and unlike other heliobacteria, they grew optimally at a temperature of 25 °C rather than at 40 °C or above. Analysis of the 16S rRNA gene sequence of the new organism showed that it groups within the heliobacterial clade. However, its branching order was phylogenetically basal to all previously investigated species of heliobacteria. The G+C content of the DNA of strain BT-H1 (44.9 mol%) was also quite distinct from that of other heliobacteria. This unique assemblage of properties implicates strain BT-H1 as a new genus and species of the heliobacteria, Heliorestis daurensis, named for its unusual morphology (“restis” is Latin for “rope”) and for the Daur Steppe in Russia in which these soda lakes are located. Received: 15 March 1999 / Accepted: 25 June 1999