Lattices and lattice-valued relations in biology

Rashevsky's treatment of general binary relations between sets of biological elements is extended using the novel mathematical concept of lattice-valued relation (l.v.r.). This yields a quantitative measure of the strength of the relations between components of a biological organism, and some illustrative examples are given. Specific l.v.r.'s are used to define (more precisely than in Rashevsky's preliminary theory of binary relations) the biologically important relationships amongst hormones, metabolism and energy exchange involved in metabolic reactions. The ‘strongest link’ between the set of hormones and the set of metabolic reactions is quantified using a special l.v.r., and other specific biological realisations of lattice-valued relations in abstract-relational biology are presented. L.v.r.'s may also be regarded as a form ofG-relation in relational biology, or as a particular case of generating diagrams. Further possible developments of this approach, using more complex tools of the newly developed mathematical theory of lattice-valued relations, such as function space l.v.r., group l.v.r., l.v.r. morphisms, l.v.r. homology andn-ary l.v.r.'s are suggested.     

Topological biology: A note on Rashevsky's transformation T.

In the bio-topological transformation between graphs denoted by (T ⁽¹⁾ X) N. Rashevsky (Bull. Math. Biophysics,18, 173–88, 1956) considers the number of fundamental sets which (a) have only one specialized point as source (and no other sources), (b) have no points in common (are “disjoined”); he proves that this number is an invariant of the transformation. In this note we show that Rashevsky's Theorem can be extended as follows:The number of fundamental sets of the first category is an invariant of the transformation. We must, however, count the subsidiary points of the transformed graph as specialized points. We recall that fundamental sets of the first category are those whose sources consist of specialized points only (Trucco,Bull. Math. Biophysics,18, 65–85, 1956). But in this modified version of the Theorem the fundamental sets may have more than one source and need not be disjoined.     

Some theorems in topology and a possible biological implication

In a previous paper (Bull. Math. Biophysics,16, 317–48, 1954) a transformationT of one graph into another was suggested, which may describe the relations between organisms of different complexity. In this paper some topological properties of the transformationT are studied. It is shown that the fundamental group of the transformed graph is homomorph to the fundamental group of the original graph. An expression is derived for the number of points in a point base of the transformed graph in terms of the number of points of the point base of the original when the point base of the latter consists only of residual points, and it is shown that the ratio of the number of points of the point base to the total number of points of the graph is in that case greater in the transformed graph than in the original. A combinatorial problem arising in connection with the transformationT is solved by deriving the number of possible ways in whichn-n _i indistinguishable elements may be arranged inn _i classes, permitting some of then _i classes to be empty. The possible biological meaning of the increased ratio of the number of points of the point base to the total number of points of the graph is discussed. It is suggested that it may be interpreted as a decrease of regenerating ability with increase of differentiation of the organism. Those considerations suggest the possibility of deriving some general biological laws from the consideration of the properties of the transformation only, regardless of the choice of the primordial graph.     

Number of floral organs in Circaeaster agrestis (Circaeasteraceae) and possible homeosis among floral organs

98.9% of 5092 flowers from 1041 individuals of Circaeaster agrestis have five floral organs, the formula is P₃A₁G₁ (73.13%), P₂A₂G₁ (25.59%), and P₂A₁G₂ (0.22%). Only 0.4% of the flowers have six floral organs and the formula is P₃A₁G₂ (20 flowers) or P₃A₂G₁ (one flower). All these flowers have one vascular bundle in the pedicel and were considered to be normal ones. There are 33 flowers (0.65%) with six or more floral organs and two vascular bundles in the pedicel and we found traces of fusion of different degree of two flowers into one. These flowers were considered as abnormal. Therefore the normal number of floral organs of C. agrestis is five and occasionally six, and the floral formulas are P₃A₁G₁ or P₂A₂G₁, sometimes P₂A₁G₂, and occasionally P₃A₁G₂ or P₃A₂G₁. A tepal in P₃A₁G₁ may be replaced by a stamen in P₂A₂G₁ or by a carpel in P₂A₁G₂ or in reverse. A carpel in P₃A₁G₂ may be replaced by a stamen in P₃A₂G₁ or in reverse. We hypothesize that there are two possibilities for the number of the floral organs to be five (six), the result of reduction from P₃A₂G₂, or there exists homeosis among floral organs.     

Notes on Estimation of the General Odds Ratio and the General Risk Difference for Paired‐Sample Data

Under the matched‐pair design, this paper discusses estimation of the general odds ratio OR_G for ordinal exposure in case‐control studies and the general risk difference RD_G for ordinal outcomes in cross‐sectional or cohort studies. To illustrate the practical usefulness of interval estimators of OR_G and RD_G developed here, this paper uses the data from a case‐control study investigating the effect of the number of beverages drunk at “burning hot” temperature on the risk of possessing esophageal cancer, and the data from a cross‐sectional study comparing the grade distributions of unaided distance vision between two eyes. Finally, this paper notes that using the commonly‐used statistics related to odds ratio for dichotomous data by collapsing the ordinal exposure into two categories: the exposure versus the non‐exposure, tends to be less efficient than using the statistics related to OR_G proposed herein.     

Natural hybridization of Yezo and Sakhalin spruce in central Hokkaido,revealed by DNA markers with contrasting modes of inheritance

Yezo spruce (Picea jezoensis var. jezoensis) and Sakhalin spruce (Picea glehnii) occur across Hokkaido and co‐occur in some forest habitats. This leads to the potential for natural hybridization between these two species, which has been shown to occur at low frequencies. The purpose of this study was to identify these hybrids and their possible mating patterns, using various Pinaceae DNA markers with different modes of inheritance. The markers used were maternally inherited mitochondrial DNA (mtDNA), paternally inherited chloroplast DNA (cpDNA) and biparentally inherited nuclear microsatellites (nSSRs). Seven putative natural hybrids, four artificially‐crossed F₁ hybrids, four parent plants from each species, and two artificially‐backcrossed hybrids of putative natural hybrids and their parents were analyzed using the diagnostic DNA markers developed in this study. We found Yezo spruce and Sakhalin spruce to be distinct (J and G types, respectively), and the modes of inheritance held true for the two species, as was previously reported to be the case in Pinaceae. Four of the seven putative natural hybrids harbored J‐type cpDNA, G‐type mtDNA and J/G‐type nSSRs, indicating that natural F₁ hybrids are likely to arise from a G (female) × J (male) crossing. One natural hybrid harbored G‐type cpDNA, J‐type mtDNA and J/G‐type nSSRs, which implies that hybrids produced by J (female) × G (male) crossings occur at low frequencies. The two remaining hybrids harbored J‐type cpDNA and mtDNA with either J/G or J/J‐type nSSRs, suggesting that they may be F₂ hybrids resulting from backcrossing between an F₁ hybrid and a Yezo spruce.     

Estimating photosynthetic electron transport via chlorophyll fluorometry without Photosystem II light saturation

Estimates of thylakoid electron transport rates (J_e) from chlorophyll fluorometry are often used in combination with leaf gas exchange measurements to provide detailed information about photosynthetic activity of leaves in situ. Estimating J_e requires accurate determination of the quantum efficiency of Photosystem II (Φ_P), which in turn requires momentary light saturation of the Photosystem II light harvesting complex to induce the maximum fluorescence signal (F_M′). In practice, full saturation is often difficult to achieve, especially when incident photosynthetic photon flux density (Q) is high and energy is effectively dissipated by non-photochemical quenching. In the present work, a method for estimating the true F_M′ under high Q was developed, using multiple light pulses of varying intensity (Q′). The form of the expected relationship between the apparent F_M′ and Q′ was derived from theoretical considerations. This allowed the true F_M′ at infinite Q′ to be estimated from linear regression. Using a commercially available leaf gas exchange/ chlorophyll fluorescence measurement system, J_e was compared to gross photosynthetic CO₂ assimilation (A_G) under conditions where the relationship between J_e and A_G was expected to be linear. Both in C₄ leaves (Zea mays) in ambient air and also in C₃ leaves (Gossypium hirsutum) under non-photorespiratory conditions the apparent ratio between J_e and A_G declined at high Q when Φ_P was calculated from F_M′ measured simply using the highest available saturating pulse intensity. When F_M′ was determined using the multiple pulse / linear regression technique, the expected relationship between J_e and A_G at high Q was restored, indicating that the Φ_P estimate was improved. This method of determining F_M′ should prove useful for verifying when saturating pulse intensities are sufficient, and for accurately determining Φ_P when they are not. This revised version was published online in June 2006 with corrections to the Cover Date.     

High energy phosphate concentrations and AMPK phosphorylation in skeletal muscle from mice with inherited differences in hypoxic exercise tolerance

The effect of chronic hypobaric hypoxia (1/2 atmospheric pressure) on high energy phosphate (HEP) compounds was investigated in slow (soleus; SOL) and fast twitch (extensor digitorum longus; EDL) muscle from 3 strains of mice with large differences in hypoxic exercise tolerance (HET). Phosphocreatine concentration ([PCr]) decreased 16–29% following hypoxia in EDL and SOL in all strains, while [ADP] and [AMP] increased. In the EDL, HET was negatively correlated with the PCr/ATP ratio and positively correlated with the ATP/P_i ratio. The free energy of ATP hydrolysis (ΔG_obs) remained constant despite the substantial changes that occurred in HEP profiles. The alteration of HEP set points and preservation of ΔG_obs are consistent with the notion that (1) maximal rates of steady-state ATP turnover are reduced under hypoxia, and (2) HEP perturbations during rest to work transitions are reduced in skeletal muscle from hypoxia acclimated animals. We therefore expected a lower phosphorylation ratio of AMP-activated protein kinase (AMPK-P/AMPK) during stimulation in hypoxic acclimated animals. However, neither the resting nor stimulated AMPK-P/AMPK was influenced by hypoxia, although there were significant differences among strains.     

Differential effects of nitrogen mustard in vivo on the cancer and host cells in MCa-11 tumours

We analysed the effects of nitrogen mustard (HN₂) on the growth, cell cycle distributions, and ratios of tumour cells to host cells for MCa-11 tumours grown in vivo. Treatment of tumour-bearing BALB/c mice with 3 mg/kg of HN₂ produced a significant slowing of MCa-11 tumour growth. Seventy-two hours after treatment in vivo with either 3 or 4 mg/kg of HN₂, the host cells in the treated tumours showed a significantly decreased G₀/G₁ peak and an increased G₂/M peak (P < 0.01), whereas the cancer cells in the treated tumours showed significant increases in the G₀/G₁ peak coupled with relatively decreased proportions of S and G₂/M tumour cells (P < 0.001). The ratio of the total number of cancer cells to the total number of host cells in the tumours was significantly increased 72 h after HN₂ administration (P<0.01). Thirty-two days after treatment with HN₂, the cell cycle distributions of the host and tumour cells in the treatment and control tumours had returned to being identical, but the ratio of the total number of cancer cells to the total number of host cells remained increased in the treated tumours (P<0.01). These results show that the administration in vivo of HN₂ can lead to entirely different cell cycle effects for the host and cancer cells in the same tumour, and that the partial growth arrest of MCa-11 tumours from HN₂ treatment may be due in part to the preferential destruction of host cells rather than solely to a direct cytotoxic effect on the cancer cells.     

Predictors for self‐directed aggression in Italian prisoners include externalizing behaviors,childhood trauma and the serotonin transporter gene polymorphism 5‐HTTLPR

Suicidal behavior and self‐mutilation can be regarded as the expression of self‐directed aggression and both are common in prison populations. We investigated the influence of externalizing behaviors, depressive symptoms, childhood trauma, 5‐HTTLPR variants on self‐directed aggression (N = 145) in a group of 702 male Italian prisoners. Participants were comprehensively evaluated, including for psychiatric disorders, impulsive traits, lifetime aggressive behavior [Brown‐Goodwin Lifetime History of Aggression (BGHA)], hostility, violent behavior during incarceration, depressive symptomatology [Hamilton Depression Rating Scale (HDRS)], childhood trauma [Childhood Trauma Questionnaire (CTQ)]. Logistic regression analysis showed false discovery rate corrected independent main effects of externalizing behaviors: BGHA (P = 0.001), violent behavior in jail (P = 0.007), extraversion (P = 0.015); HDRS (P = 0.0004), Axis I disorders (P = 0.015), CTQ (P = 0.004) and 5‐HTTLPR genotype (P = 0.02). Carriers of 5‐HTTLPR high (L_AL_A), intermediate (L_AL_G, SL_A) activity variants were more likely to have exhibited self‐directed aggression relative to the low activity (L_GL_G, SL_G, SS) variant: high/low: odds ratio (OR) = 2.3, 95% confidence interval (CI) 1.27–4.68, P = 0.007; intermediate/low: OR = 1.96, 95% CI 1.09–3.68, P = 0.025. The CTQ main effect was driven by physical abuse. There was no interactive effect of 5‐HTTLPR and CTQ. Secondary logistic regression analyses in (1) all suicide attempters (N = 88) and (2) all self‐mutilators (N = 104), compared with controls showed that in both groups, childhood trauma (P = 0.008–0.01), depression (P = 0.0004–0.001) were strong predictors. BGHA, violent behavior in jail predicted self‐mutilation (P = 0.002) but not suicide attempts (P = 0.1). This study was able to distinguish differing influences on self‐directed aggression between groups of closely related predictor variables within the externalizing behavioral domain. 5‐HTTLPR had an independent, variant dosage effect.     

Molecular set theory: II. An aspect of the biomathematical theory of sets

In an earlier paper (Molecular Set Theory: I.Bull. Math. Biophysics,22, 285–307, 1960) the author proposed a “Molecular Set Theory” as a formal mathematical meta-theoretic system for representing complex reactions not only of biological interest, but also of general chemical interest. The present paper is a refinement and extension of the earlier work along more formal algebraic lines. For example the beginnings of an algebra of molecular transformations is presented. It also emphasizes that this development, together with the genetical set theory of Woodger's and Rashevsky's set-theoretic contributions to Relational Biology, points to the existence of a biomathematical theory of sets which is not deducible from the general mathematical, abstract theory of sets.     

Photosynthesis in leaves,fruits, stem and petioles of greenhouse-grown tomato plants

Gross photosynthetic capacity (P _G ) of greenhouse-grown tomato plants (Lycopersicon esculentum Mill.) decreased as the leaf aged. The P _G of the 10th, 15th and 18th leaves from the top was only 76, 37, and 18 % of P _G of the 5th leaf, respectively. Quantum yield (Y _Q ) and dark respiration rate (R _D ) were also lower in older leaves than in the younger ones. Net photosynthetic rate (P _G ) was apparent in young fruits (about 10 g FM) or young petioles but no P _N was found in large fruits (40 g or more FM) and stems because of high R _D . Both P _G and R _D were lower in older fruits and petioles or in lower parts of the stem compared to the younger ones or upper parts of stem. A sharp decrease in chlorophyll (Chl) content was only measured in the senescing 18th leaf. The Chl content in petioles, stems and fruits was proportional to P _G . Decreases in P _G of older leaves were attributed to decreases in content rather than activity of ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBPCO) since soluble protein content was lower in older leaves than in the younger ones but the specific activity (activity per unit of protein) of RuBPCO was not so. The estimated values of P _N of the 10th, 15th and 18th leaves inside the canopy were only 50, 21, and 7 % of that in the 5th leaf. Therefore, leaves below the 18th can be removed in order to ensure a good air circulation and prevent diseases. The significance of photosynthesis in fruit, stem and petioles is not negligible because photosynthesis re-fixes the respired CO₂. This revised version was published online in September 2006 with corrections to the Cover Date.     

A Kinetic Theory of First Order Cyclical Processes—Phytochrome Controlled Red Light Induced Cereal Leaf Unfolding Compared with Theory

The phytochrome controlled unfolding of cereal leaves was studied as a function of irradiation time and light intensity (narrowband red light) over a wide energy range (5 decades). With different intensities, a family of similarly shaped response curves appear with distinct time-dependent maxima and minima. A theoretical kinetic model based upon a cyclical phytochrome photoconversion scheme has been calculated by us. The theoretical calculations and the experimental findings are in excellent agreement. The same model explains the early photoresponses (first maxima) as an effect of one active phytochrome form, P₂, and the delayed photoresponses as an effect of a second active form P_n. The active transitory form, P₂ (although it may not be the primary product), is formed upon light absorption from P₁. The P₂ decays by a first order dark reaction through several inactive intermediates to P_n (active). The effect of the intermediates is mainly to delay the production of the second active product. It is possible to identify the two active products, P₂ and P_n, as P_fr and P*_fr, respectively. The presented cyclical phytochrome reaction scheme is a special case of a general first order kinetic cycle which includes all possible feed back loops. The latter scheme also has been calculated and programmed since it has a more general application.     

Cell cycle regulation during growth-dormancy cycles in pea axillary buds

Accumulation patterns of mRNAs corresponding to histones H2A and H4, ribosomal protein genes rpL27 and rpL34, MAP kinase, cdc2 kinase and cyclin B were analyzed during growth-dormancy cycles in pea (Pisum sativum cv. Alaska) axillary buds. The level of each of these mRNAs was low in dormant buds on intact plants, increased when buds were stimulated to grow by decapitating the terminal bud, decreased when buds ceased growing and became dormant, and then increased when buds began to grow again. Flow cytometry was used to determine nuclear DNA content during these developmental transitions. Dormant buds contain G₁ and G₂ nuclei (about 3:1 ratio), but only low levels of S phase nuclei. It is hypothesized that cells in dormant buds are arrested at three points in the cell cycle, in mid-G₁, at the G₁/S boundary and near the S/G₂ boundary. Based on the accumulation of histone H2A and H4 mRNAs, which are markers for S phase, cells arrested at the G₁/S boundary enter S within one hour of decaptitation. The presence of a cell population arrested in mid-G₁ is indicated by a second peak of histone mRNA accumulation 6 h after the first peak. Based on the accumulation of cyclin B mRNA, a marker for late G₂ and mitosis, cells arrested at G₁/S begin to divide between 12 and 18 h after decapitation. A small increase in the level of cyclin B mRNA at 6 h after decapitation may represent mitosis of the cells that had been arrested near the S/G₂ boundary. Accumulation of MAP kinase, cdc2 kinase, rpL27 and rpL34 mRNAs are correlated with cell proliferation but not with a particular phase of the cell cycle.     

Approximating the Non-Null Distribution of the Likelihood Ratio Test Statistic

This paper is concerned with investigation into the behavior of the likelihood ratio test statistic G² when the alternative hypothesis M (QQ) is the true model. Exact moments of G² are computed empirically and three approximations are considered for approximating the non-null distribution of G². Our results show that the two parameter gamma distribution provides a closer approximation to the exact powers of G². A randomized procedure was employed to obtain critical values based on 1000 simulated samples.     

Mathematical biophysics of cellular forms and movements

Rashevsky's equations for describing the joint variation of cell shape and concentration of a metabolite are discussed. Conditions for the existence of non-spherical equilibria and the location of these are obtained and involve only two parametersa andA. Sufficient (but not necessary) conditions for the stability of these equilibria can also be expressed in terms of these parameters alone. Necessary conditions involve in some cases a third parameterB. Quasi-periodic fluctuations about a stable nonspherical equilibrium may occur, but only in caseB lies on a certain finite range which can be defined in terms ofa andA.     

cAMP and PMA enhance the effects of IGF-I in the proliferation of endometrial adenocarcinoma cell line HEC-1-A by acting at the G1 phase of the cell cycle

The present study was undertaken to determine whether endometrial cancer cell line HEC-1-A differ from nontransformed cells, in that the cAMP and protein kinase C pathways may enhance IGF-I effects in mitogenesis by acting at the G₁ phase of the cell cycle instead of G₀. Immunofluorescence staining of HEC-1-A cells using the proliferating cell nuclear antigen (PCNA) monoclonal antibody and flow cytometric analysis determined that HEC-1-A cells do not enter the G₀ phase of the cell cycle when incubated in a serum-free medium. Approximately 51% of the cells were in G₁, 12% were in S and 37% in G₂ phase of the cell cycle prior to treatment. Forskolin and phorbol-12-myristate 13-acetate (PMA) were used to stimulate cAMP production and protein kinase C activity, respectively. IGF-I, forskolin and PMA each increased (P <0.01) [³H]-thymidine incorporation in a dose and time dependent manner. The interaction of forskolin and PMA with IGF-I was then determined. Cells preincubated with forskolin or PMA followed by incubation with IFG-I incorporated significantly more (P <0.01) [³H]-thymidine into DNA than controls or any treatment alone. It is concluded that forskolin and, to a lesser extent, PMA exert their effect at the G₁ phase of the cycle to enhance IGF-I effects in cell proliferation.     

蚯蚓对废纸屑再利用及养分贫瘠土壤综合质量的影响

办公废纸屑作为常见有机废弃物,由于体积小且转化为再生纸成本高,因而再利用很难。但其含有大量有机碳(特别是纤维素)可能有助于退化土壤修复。蚯蚓对土壤有机质分解和其他土壤功能有重要影响,办公废纸屑和蚯蚓共同作用如何影响养分贫瘠土壤质量至今未知。研究以赤子爱胜蚓为接种蚯蚓,将办公废纸屑添加到养分贫瘠土壤中,分别设置纯土壤培养为对照组(S)、单独添加废纸屑(SP)、单独接种赤子爱胜蚓(SE)和添加废纸屑并接种赤子爱胜蚓的处理(SPE),比较培养90 d后各处理理化指标(pH、有机碳、全氮、全磷、全钾、碱解氮、速效磷、速效钾、交换性阳离子钾、钠、钙、镁等)、微生物磷脂脂肪酸(PLFAs)总含量和微生物结构的差异,在此基础上综合评价土壤质量,阐明废纸屑和赤子爱胜蚓在养分贫瘠土壤改良修复中的作用。结果显示：SPE处理较SP处理显著提高废纸屑的分解率89.48%。与对照相比,SP处理能够显著提高土壤pH值2.94个单位,SPE处理能够使其维持在中性水平;前者显著提高土壤有机碳(SOC)125.76%,交换性钠钙镁(Na_Ex、Ca_Ex、Mg_Ex     

Does GST underestimate genetic differentiation from marker data?

The widely applied genetic differentiation statistics F_ST and G_ST have recently been criticized for underestimating differentiation when applied to highly polymorphic markers such as microsatellites. New statistics claimed to be unaffected by marker polymorphisms have been proposed and advocated to replace the traditional F_ST and G_ST. This study shows that G_ST gives accurate estimates and underestimates of differentiation when demographic factors are more and less important than mutations, respectively. In the former case, all markers, regardless of diversity (H_S), have the same G_ST value in expectation and thus give replicated estimates of differentiation. In the latter case, markers of higher H_S have lower G_ST values, resulting in a negative, roughly linear correlation between G_ST and H_S across loci. I propose that the correlation coefficient between G_ST and H_S across loci, r_GH, can be used to distinguish the two cases and to detect mutational effects on G_ST. A highly negative and significant r_GH, when coupled with highly variable G_ST values among loci, would reveal that marker G_ST values are affected substantially by mutations and marker diversity, underestimate population differentiation, and are not comparable among studies, species and markers. Simulated and empirical data sets are used to check the power and statistical behaviour, and to demonstrate the usefulness of the correlation analysis.