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.     

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.     

Phase change-related variations of dome shape in Eucalyptus urophylla × Eucalyptus grandis shoot apical meristems

Shoot apical meristem (SAM) domes derived from five different outdoor and in vitro sources of juvenile and mature Eucalyptus urophylla × Eucalyptus grandis akin genotypes were compared. Overall measurements of SAM dome height H and diameter D ranged from 2 to 35 μm and 20 to 80 μm, with significant differences according to the various physiological origins of plant material investigated. SAM domes from the mature trees “Mat” were taller than those from the rejuvenated ministock plants “Rej”; from the in vitro microcuttings “IVM” of the same clone and also from the in vitro juvenile seedlings “IVJ”, whereas outdoor seedlings “Juv” exhibited intermediate SAM dome height. SAM domes from the rejuvenated material “Rej”, from the in vitro mature “IVM” and juvenile “IVJ” origins were also narrower than those from the outdoor seedlings “Juv” and to lesser extent than those from the mature trees “Mat”. Overall, the mature source “Mat” displayed bigger and somehow sharper hemispherical domes than those from “Rej” and “Juv”, physiologically more juvenile, or those from the in vitro origins “IVM” and “IVJ” which looked flatter and smaller. SAM dome height, diameter D and H/D values varied also significantly according to the plastochron. More specifically, H, D, and H/D SAM differences between the five origins were not significant during the early plastochron phase corresponding to leaf initiation, to become more salient as leaf structures started to elongate and to differentiate. This was particularly obvious for mature tree “Mat” SAM dome shapes which showed at this stage much higher H/D values than the other SAM sources. A shape index S used for characterizing more accurately dome shape confirmed these trends. These observations provide additional arguments to the view that juvenility in trees becomes more and more time- and shoot-tip restricted as ageing increases in the course of time during the ontogenetical process and could be ultimately confined to the most organogenic phase of SAM, from which shoot characteristics derive.     

Macroevolution via secondary endosymbiosis: a Neo-Goldschmidtian view of unicellular hopeful monsters and Darwin’s primordial intermediate form

Seventy-five years ago, the geneticist Richard Goldschmidt hypothesized that single mutations affecting development could result in major phenotypic changes in a single generation to produce unique organisms within animal populations that he called “hopeful monsters”. Three decades ago, Sarah P. Gibbs proposed that photosynthetic unicellular micro-organisms like euglenoids and dinoflagellates are the products of a process now called “secondary endosymbiosis” (i.e., the evolution of a chloroplast surrounded by three or four membranes resulting from the incorporation of a eukaryotic alga by a eukaryotic heterotrophic host cell). In this article, we explore the evidence for Goldschmidt’s “hopeful monster” concept and expand the scope of this theory to include the macroevolutionary emergence of organisms like Euglena and Chlorarachnion from secondary endosymbiotic events. We argue that a Neo-Goldschmidtian perspective leads to the conclusion that cell chimeras such as euglenids and dinoflagellates, which are important groups of phytoplankton in freshwater and marine ecosystems, should be interpreted as “successful monsters”. In addition, we argue that Charles Darwin had euglenoids (infusoria) in mind when he speculated on the “primordial intermediate form”, although his Proto-Euglena-hypothesis for the origin of the last common ancestor of all forms of life is no longer acceptable.     

Stem anatomy and relative growth rate in seedlings of a wide range of woody plant species and types

Stem traits were analysed in laboratory-grown seedlings of 80 European woody and semiwoody species of known potential relative growth rate (RGR) and of similar ontogenetic phase. The objectives were, firstly, to assess the relation between stem structure and plant growth potential and, secondly, to explore how stem structure varies among species differing in life form and leaf habit. Hydraulic conductance was represented by the mean diameter of the widest xylem conduits (Dmax), and structural strength by the percentage of xylem tissue occupied by cell wall material (CWx) or stem tissue density (SD). Across all species RGR showed a weak positive correlation with Dmax and weak negative ones with CWx and SD, with slow-growers showing great dispersion of stem trait values. In the RGR-Dmax relationship this dispersion disappeared when trees were removed from the analysis. None of the relationships were significant among tree species alone. It was suggested that fast-growers require a xylem with wide conduits (high Dmax) to achieve high hydraulic conductivity, and “cheaply” constructed stems (low CWx and SD) to maximise allocation to leaves. However, the possession of such traits does not guarantee fast growth, as other factors may constrain RGR elsewhere in the plant. Deciduous seedlings showed higher Dmax and lower CWx than evergreens. Higher Dmax could reflect an innate higher tolerance of conductivity loss by freeze-induced embolism in deciduous plants, which are not burdened by the maintenance of foliage in winter. In contrast, life forms were differentiated most clearly by SD. For instance, shrub seedlings had less dense stem tissues than tree seedlings, possibly because they need less investment in long-term strength and stature. Received: 3 January 1998 / Accepted: 9 April 1998     

Malaria: Origin of the Term “Hypnozoite”

The term “hypnozoite” is derived from the Greek words hypnos (sleep) and zoon (animal). Hypnozoites are dormant forms in the life cycles of certain parasitic protozoa that belong to the Phylum Apicomplexa (Sporozoa) and are best known for their probable association with latency and relapse in human malarial infections caused by Plasmodium ovale and P. vivax. Consequently, the hypnozoite is of great biological and medical significance. This, in turn, makes the origin of the name “hypnozoite” a subject of interest. Some “missing” history that is now placed on record (including a letter written by P. C. C. Garnham, FRS) shows that Miles B. Markus coined the term “hypnozoite”. While a PhD student at Imperial College London, he carried out research that led to the identification of an apparently dormant form of Cystoisospora (synonym: Isospora). In 1976, he speculated: “If sporozoites of Isospora can behave in this fashion, then those of related Sporozoa, like malaria parasites, may have the ability to survive in the tissues in a similar way.” He adopted the term “hypnozoite” for malaria in 1978 when he wrote in a little-known journal that this name would “… describe any dormant sporozoites or dormant, sporozoite-like stages in the life cycles of Plasmodium or other Haemosporina.” At that time, the existence of a hypnozoite form in the life cycle of Plasmodium was still a hypothetical notion. In 1980, however, Wojciech A. Krotoski published (together with several co-workers) details concerning his actual discovery of malarial hypnozoites, an event of considerable importance.     

An efficient ligation method in the making of an in vitro virus for in vitro protein evolution

The “in vitro virus” is a molecular construct to perform evolutionary protein engineering. The “virion(=viral particle)”(mRNA-peptide fusion), is made by bonding a nascent protein with its coding mRNA via puromycin in a test tube for in vitro translation. In this work, the puromycin-linker was attached to mRNA using the Y-ligation, which was a method of two single-strands ligation at the end of a double-stranded stem to make a stem-loop structure. This reaction gave a yield of about 95%. We compared the Y-ligation with two other ligation reactions and showed that the Y-ligation gave the best productivity. An efficient amplification of the in vitro virus with this “viral genome” was demonstrated. Published: October 28, 2002     

Indian rice “Kasalath” contains genes that improve traits of Japanese premium rice “Koshihikari”

Rice (Oryza sativa L.) chromosome segment substitution lines (CSSLs), in which chromosomal segments of the Indian landrace “Kasalath” replace the corresponding endogenous segments in the genome of the Japanese premium rice “Koshihikari”, are available and together cover the entire genome. Chromosome regions affecting a trait (CRATs) can be identified by comparison of phenotypes with genotypes of CSSLs. We detected 99 CRATs for 15 agronomic or morphological traits. “Kasalath” had positively acting alleles in 53 CRATs. Its CRATs increased panicle number per plant by up to 23.3%, grain number per panicle by up to 30.8%, and total grain number by up to 15.1%, relative to “Koshihikari”. CRATs were identified for grain size (grain thickness and width), with positive effects of about 5.0%. A CRAT on chromosome 8 almost doubled the weight of roots in uppermost soil layers compared to “Koshihikari”. Additionally, “Kasalath” possessed CRATs for higher lodging resistance (reduction in plant height and increase in stem diameter). In some cases, multiple CRATs were detected in the same chromosome regions. Therefore, CSSLs with these chromosome segments might be useful breeding materials for the simultaneous improvement of multiple traits. Five CRATs, one for plant height on chromosome 1, one for stem diameter on chromosome 8, and three for heading date on chromosomes 6, 7, and 8 overlapped with the corresponding QTLs that already had been mapped with back-crossed inbred lines of “Nipponbare” and “Kasalath”. In both “Koshihikari” CRATs and “Nipponbare” QTLs, “Kasalath” had similar effects. Both Y. Madoka and T. Kashiwagi have contributed equally to this article.     

New species of Pogonophryne (Pisces, Artedidraconidae) from the Bellingshausen Sea, Antarctica

A new species of notothenioid fish, Pogonophryne bellingshausenensis n. sp., is described from the Bellingshausen Sea, Antarctica. The new species belongs to the dorsally-spotted “mentella” group of the genus and is characterized by having a short (about 13% SL) mental barbel with a short (about 16% of barbel length), narrow (barely wider than the stalk), and relatively inconspicuous terminal expansion composed of short, irregular, fingerlike processes. Compared to most other dorsally-spotted species of Pogonophryne (“barsukovi”, “marmorata”, and “mentella” groups), P. bellingshausenensis has a relatively wide (about 7% SL) interorbital region. An unspotted patch on the median dorsal surface of the head, posterior to the posttemporal ridges and anterior to the first dorsal fin, has not been observed previously in any dorsally-spotted species. The holotype was collected at 1,947 m, one of the deepest records for any species of Pogonophryne. A revised key to the ten species of the “mentella” group of Pogonophryne is also provided.     

Iota-carrageenan from a newly farmed, rare variety of eucheumoid seaweed—“endong”

A seaweed with the local name “endong” is a rare eucheumoid variety that has recently been farmed in Tawi-Tawi, southern Philippines. Local farmers describe it as “eel-like” because of its long, slender and smooth thalli. Being somewhat similar in appearance to the dominantly farmed seaweed “tambalang” (Kappaphycus alvarezii var. tambalangii), farmers mix their harvests of “endong” with those of “tambalang”. We analyzed the hydrocolloid extract from “endong” using spectroscopic and chemical techniques. The extract’s infrared and nuclear magnetic resonance (¹H and ¹³C) spectra, and sulfate and 3,6-anhydrogalactose contents revealed carrageenan of the iota-type, similar to extracts from another farmed species, Eucheuma denticulatum. This result implies that “endong” carrageenan exhibits physico-chemical properties different from those of kappa-carrageenan of “tambalang”. The findings of this study are of significance to the seaweed industry, as carrageenan quality problems could potentially arise from a mixed harvest. Seaweed farmers are advised to separate their harvests of “endong” and “tambalang”. Presented at the 19th International Seaweed Symposium, Kobe, Japan     

Spread of information through a population with socio-structural bias: I. Assumption of transitivity

A previously derived iteration formula for a random net was applied to some data on the spread of information through a population. It was found that if the axon density (the only free parameter in the formula) is determined by the first pair of experimental values, the predicted spread is much more rapid than the observed one. If the successive values of the “apparent axon density” are calculated from the successive experimental values, it is noticed that this quantity at first suffers a sharp drop from an initial high value to its lowest value and then gradually “recovers”. An attempt is made to account for this behavior of the apparent axon density in terms of the “assumption of transitivity”, based on a certain socio-structural bias, namely, that the likely contacts of two individuals who themselves have been in contact are expected to be strongly overlapping. The assumption of transitivity leads to a drop in the apparent axon density from an arbitrary initial value to the vicinity of unity (if the actual axon density is not too small). However, the “recovery” is not accounted for, and thus the predicted spread turns out to beslower than the observed.     

In vitro separation of a rose chimera

“Fairmount 1 thorny” (“FM1 thorny”) (a Rosa multiflora Thunb ex. J. Murr.) and a thornless sport of “FM1 thorny” (“Fairmount 1” (“FM1”)) were established in vitro to investigate chimeral segregation under various levels of BA and to obtain a pure thornless rose. While the chimeral thornless sport was expected to segregate in vitro and yield both thorny and thornless plantlets, “FM1 thorny” was to yield only thorny plants. “FM1” segregated in vitro into its constituent genotypes and yielded thorny and thornless plantlets, suggesting that “FM1” is chimeral. “FM1 thorny” produced only thorny plants in vitro. These results indicate that the “FM1 thorny” clone was not chimeral (pure thorny) and that the thornless regenerates of “FM1” did not develop via somaclonal variation. There was a significant linear relationship between increasing BA concentration and the percentage of thorny plants. Among a population of 690 tissue culture derived plants from all the BA experiments, 6 plants were classified as pure thornless plants 1 year later.     

Contribution to the mathematical theory of contagion and spread of information: I. Spread through a thoroughly mixed population

An equation is derived from the spread of a “state” by contact through a thoroughly mixed population, in which the probability of transmission depends both on the over-all duration of the process and on the time an individual has been in the “state.” Cases in which this probability is a function of only one or the other of the two “times” are worked out. It is shown that in the case of dependence on “private time” alone the asymptotic value of the fraction of the population effected is the same as that derived by the random net approach.     

Stereotyped sequence of mating behavior in the Far Eastern catfish, Silurus asotus, from Lake Biwa

 Mating behavior of the Far Eastern catfish, Silurus asotus (Siluriformes: Siluridae), was observed in a ricefield system facing the shore of Lake Biwa in mid-May to early June in 1990–1997. A set behavioral sequence similar to those of two other silurid fishes, S. biwaensis and S. lithophilus, both endemic to the Lake Biwa system, was observed: “chasing,”“clinging,”“enfolding” while “squeezing” by the male, and “circling” by the spawning pair. This form of mating behavior is quite different from that of S. asotus reported from the Ooi River system in Kyoto Prefecture, which mainly spawns in running water in ditches. Received: April 10, 2001 / Revised: November 5, 2001 / Accetped: November 20, 2001     

HLA-C “blank” alleles express class I gene products. Biochemical analysis of four different HLA-C “blank” polypeptides

Monoclonal antibodies (mAbs) W6/32, HC10, and 4E were used to precipitate class I antigens from 21 selected individuals with at least oneHLA-C “blank” allele. In 19 of these individuals, characteristicHLA-C banding patterns which could be precipitated by all three HLA class I mAbs were observed on one-dimensional isoelectric focusing gels-obviously the gene products ofHLA-C “blank”. At least four allelic HLA-C “blank” gene products with different isoelectric points could be discerned. All of them segregated withHLA-C “blank” haplotypes in informative families; two of them were associated withHLA-B51, one withHLA-B38, and one withHLA-B18. Reactivity of the HLA-C “blank” heavy chains with mAb W6/32 indicates that they are able to associated with beta-2 microglobulin, and hence are most probably expressed at the cell surface.     

Etat actuel des recherches en cours sur la «lutte intégrée» dans le cas des coccides en France

Summary An attempt to associate chemical and biological control has been realised in an orchard of apple trees contamined by San Jose Scale. Prospaltella perniciosi has been liberated two years ago in the hope of controling population densities of its host, after some years. In 1961, after one hivernal spray, unapplied in the narrow plot whereP. perniciosi was liberated, a spray program has been planned against plant-diseases: applescab and applemildew and many pests:Carpocapsa pomonella, several species of aphids and mites, Tortricids. Aphelinus mali was liberated to check an outbreak ofEriosoma lanigerum, late in the spring (june). The first experiment resulted in a sufficient control by means of fungicides and a good enough protection against insects, exceptCarpocapsa in the case of the apple variety “Reinette of Canada” (the most readily attacked by this pest). The evolution of population density ofP. perniocisi was not influenced by the control measures, but efficacity of parasitism was not yet sufficient to bring scale population beneath “tolerance-limits”.      

On the equilibrium distribution of population in space

Spatial equilibrium distributions of population are derived from the spatial distribution of net rates of reproduction, and from a relationship between migratory flow and gradients of population density and of locational “attractiveness.” Conditions are discussed for which population approaches a uniform spatial density. Under certain conditions a particularly simple statement of the equilibrium conditions is possible in terms of the “potential of population,” a concept introduced by demographers (J. Q. Stewart,Geographical Review,37, 46–85, 1947) to measure the proximity of a point to people. This paper was first written at the Center for Advanced Study in the Behavioral Sciences.