C lambda 2 and C lambda 4 immunoglobulin light chain genes in a wild-derived inbred mouse strain

A genomic clone containing the lambda constant (C) region genes (C lambda 2S and C lambda 4S) has been isolated from a genomic library from the mouse strain SPE. SPE is an inbred strain derived from progenitors trapped near Grenada in Spain and has been classified as mus 3 or mus spretus. The sequence of the C lambda 2S gene is virtually identical to that of BALB/c both in the coding region and in flanking sequences, suggesting that it is an expressed gene in the SPE strain. By contrast, the C lambda 4S gene on the same cluster has diverged in sequence from that of BALB/c and contains a large deletion that precludes its normal expression. Whereas BALB/c J lambda 4 region contains substitutions that probably preclude its usage, the SPE J lambda 4 gene includes all sequences required for a functional J gene. Comparison of the C lambda 2S and C lambda 4S gene sequences with those available for BALB/c C lambda 3 and C lambda 1 confirms the close relationship between the C lambda 1-C lambda 4 and C lambda 2-C lambda 3 gene pairs. The C lambda 3 gene of BALB/c is more closely related to C lambda 2S than is C lambda 1 of BALB/c to C lambda 4S. If it is assumed that C lambda 1 and C lambda 2 are respective duplicates of C lambda 4 and C lambda 3 and that these duplications occurred at the same time, then the C lambda 2 gene has been under stronger selective pressure than C lambda 4.     

Conservation of the immunoglobulin C lambda 5 gene in the Mus gene.

A gene encoding the lambda 5 light chain constant region was isolated from a genomic library from the SPE mouse strain (C lambda 5S). SPE is an inbred wild mouse strain belonging to the Mus 3 or Mus spretus group that has been genetically isolated from Mus 1 (the group to which laboratory mice belong) for a period of 1-3 million years. The sequence of the C lambda 5S gene shows strong homology to C lambda 5 of (C57BL/6J x DBA/2)F1 both in the coding region (98% identity) and in the 5'- and 3'-flanking regions (98 and 95% identity, respectively). Sequence comparison of C lambda 5 genes with C lambda 1 of BALB/c shows only few substitutions in the C lambda 5 coding regions and suggests that the three genes have a common ancestor. These data indicate that the C lambda 5 gene has evolved under strong selective pressure and probably encodes a functional gene product. The conservation of the C lambda 5 gene in various Mus species was observed by high stringency Southern blot analyses using a C lambda 5S probe on DNA sample from members of four different groups of wild mice. All the laboratory and wild mouse strains tested, including those with amplified sets of C lambda 1 and C lambda 2 hybridizing sequences, showed only single C lambda 5 hybridizing fragments. Little variation in size of restriction fragments detected with the C lambda 5 probe was seen in the different Mus species suggesting a high degree of conservation.(ABSTRACT TRUNCATED AT 250 WORDS)     

The Ig light chain restricted B6.kappa(-)lambda(SEG) mouse strain suggests that the IGL locus genomic organization is subject to constant evolution

In laboratory mice, the different Ig lambda light chain subtypes (lambda 1, lambda 2, lambda x and lambda 3) are expressed on 60, 16, 16 and 8%, respectively, of the lambda-positive peripheral B cells. Eighteen years ago, our laboratory characterized a lambda 1(-) wild mouse strain: SPE ( Mus spretus). In this report, we describe the characterization of another wild-derived Mus spretus inbred strain, SEG, that presents the same characteristic, namely the absence of lambda 1 expression. An almost congenic strain, B6.lambda(SEG), was detected in a series of recombinant congenic strains carrying 2% of SEG/Pas genome in a C57BL/6J background. This B6.lambda(SEG) strain was crossed to Igh (a) C kappa (-) mice in order to derive two different additional congenic strains: B6.kappa(-)lambda(SEG) Igh (a) and B6.kappa(-)lambda(SEG) Igh (b). In this paper, we characterize the genomic organization and the expression of the SEG IGL locus. Altogether, our data show that the SEG IGL locus is constituted by a single functional IGLJ2SEG-IGLC2SEG, two pseudo IGLJ4SEG1/2-IGLC4SEG1/2 gene clusters and two V gene segments: IGLV2SEG and IGLVXSEG. In particular, we show the absence of IGLV1 and IGLVSD26 gene segments. IGLVSD26 was reported to be present in some Mus m. musculus mice and absent in BALB/c. Here, we confirm its presence not only in other Mus m. musculus mice but also in Mus spretus mice. Consequently, we propose that IGLVSD26-related gene segments define a new family that we name V lambda 4. The study of the organization of different IGL loci, in addition to the V lambda 4(+) reported here, could elucidate questions concerning the evolution of the lambda locus.     

New antibiotic no. 792 formed by Actinomyces bottropensis

An actinomycetes strain 792 producing a new antibiotic was isolated under the programme of antitumor antibiotic screening. By its morphological and cultural properties strain 792 was classified as belonging to species Actinomyces bottropensis. Antibiotic 792 was recovered from the culture fluid of the strain by the extraction method in the form of a crystalline orange substances. lambda max 235, 305, 410 nm (E 1% 1cm 705, 105, 168), m. p. 232-255 degrees (dec), molecular weight 340, C 67 per cent, H 4.8 per cent, no nitrogen, sulphur or halogens. The antibiotic was inactivated in alkaline solutions forming a hardly soluble compound crystallizing in the form of red needles, lambda max 256, 485 nm (E 1% 1ct 800, 195), m. p. 202-204 degrees (dec), molecular weight 320, C 69.5 per cent, H 4.7 per cent. Antibiotic 792 had antitumor and antimicrobial activity.     

Influence of prophage on the efficiency of plating of Escherichia coli K12

The efficiency of plating of Escherichia coli K12 and its derivatives K12 C600 and K12 C600(lambda) is diminished during the transition period from the lag of the exponential growth phase in cultures grown in tryptone broth. The phenomenon is suppressed in cultures of the strain K12 C600(lambda ind). The reduction in the efficiency of plating is transitory and not influenced by temperature between 30 and 42 degrees C.     

P2 growth restriction on an rpoC mutant is suppressed by alleles of the Rz1 homolog lysC

Escherichia coli strain 397c carries a temperature-sensitive mutation, rpoC397, that removes the last 50 amino acids of the RNA polymerase beta' subunit and is nonpermissive for plating of bacteriophage P2. P2 gor mutants productively infect 397c and define a new gene, lysC, encoded by a reading frame that extensively overlaps the P2 lysis accessory gene, lysB. The unusual location of lysC with respect to lysB is reminiscent of the Rz/Rz1 lysis gene pair of phage lambda. Indeed, coexpression of lysB and lysC complemented the growth defect of lambda Rz/Rz1 null mutants, indicating that the LysB/C pair is similar to Rz/Rz1 in both gene arrangement and function. Cells carrying the rpoC397 mutation exhibited an early onset of P2-induced lysis, which was suppressed by the gor mutation in lysC. We propose that changes in host gene expression resulting from the rpoC397 mutation result in changes in the composition of the bacterial cell wall, making the cell more susceptible to P2-mediated lysis and preventing accumulation of progeny phage sufficient for plaque formation.     

Quantum thermodynamics approach to phosphorylation and heterotrophic growth yields

A model of cell growth is presented which is based on the double postulates of quantized loss of energy during phosphorylation and reversible biosynthesis of cell structure. An immediate consequence of the postulates is the identical value for the energy efficiency of the phosphorylation and for that of the whole growth process. Another consequence is the relationship between the energy level of the biomass and the phosphorylation potential as embodied in the equation: EO = gamma'M X EATP, where EO is the heat of transfer of a pair of electrons to oxygen, EATP, the molar heat of hydrolysis of ATP, and gamma'M, the degree of reduction of the biomass, gamma M being constant and equal to 5. The model predicts five levels of growth yields corresponding to five permissible values for the P/O ratio (r = 0, 1, 2, 3, and 4). Any growth process would be characterized by a set of two integers N and lambda; N is the maximal P/O ratio prescribed by the energy content of the substrate as compared with that of the biomass, and lambda the number of further downward quantum jumps of the P/O ratio resulting from the adversity of the growth condition (N - lambda = r). Under full aerobiosis, one has 0 less than or equal to lambda less than or equal to N less than or equal to 3. When growth is limited only by the energy content of the substrate (lambda = 0), the time-independent dispersion of N, owing to substrate-level phosphorylations and (or) dephosphorylations, leads to effective values which are higher than the nominal ones for the yield per mole of oxygen and the heat of transfer of a pair of electrons. Under adverse conditions (lambda greater than 0), the apparent variations of the yields and the P/O ratio in function of the growth rate are shown to be an effect of the random dispersion of lambda and of the existence of a maximal rate of substrate consumption. Statistical evidence for the macroscopic quantum effect in heterotrophic growth is presented.     

Plasmid-Controlled Variation in the Content of Methylated Bases in Bacteriophage Lambda Deoxyribonucleic Acid

The N(6)-methyladenine (MeAde) and 5-methylcytosine (MeC) contents in deoxyribonucleic acid (DNA) of bacteriophage lambda has been analyzed as a function of host specificity. The following facts have emerged: (i) lambda grown on strains harboring the P1 prophage contain ca. 70 more MeAde residues/DNA molecule than lambda grown either in the P1-sensitive parent, or in a P1 immune-defective lysogen which does not confer P1 modification; (ii) lambda grown on strains harboring the N-3 drug-resistance factor contain ca. 60 more MeC residues/DNA molecule than lambda grown on the parental strain lacking the factor; (iii) lambda grown in Escherichia coli B strains is devoid of MeC, whereas lambda grown in a B (N-3) host contains a high level of MeC; (iv) the MeAde content in lambda DNA is not affected by the N-3 factor. These results suggest that P1 controls an adenine-specific DNA methylase, and that the N-3 plasmid controls a cytosine-specific DNA methylase. The N-3 factor has been observed previously to direct cytosine-specific methylation of phage P22 DNA and E. coli B DNA in vivo; in vitro studies presented here demonstrate this activity.     

Modulation of bladder function by luminal adenosine turnover and A1 receptor activation

The bladder uroepithelium transmits information to the underlying nervous and musculature systems, is under constant cyclical strain, expresses all four adenosine receptors (A(1), A(2A), A(2B), and A(3)), and is a site of adenosine production. Although adenosine has a well-described protective effect in several organs, there is a lack of information about adenosine turnover in the uroepithelium or whether altering luminal adenosine concentrations impacts bladder function or overactivity. We observed that the concentration of extracellular adenosine at the mucosal surface of the uroepithelium was regulated by ecto-adenosine deaminase and by equilibrative nucleoside transporters, whereas adenosine kinase and equilibrative nucleoside transporters modulated serosal levels. We further observed that enriching endogenous adenosine by blocking its routes of metabolism or direct activation of mucosal A(1) receptors with 2-chloro-N(6)-cyclopentyladenosine (CCPA), a selective agonist, stimulated bladder activity by lowering the threshold pressure for voiding. Finally, CCPA did not quell bladder hyperactivity in animals with acute cyclophosphamide-induced cystitis but instead exacerbated their irritated bladder phenotype. In conclusion, we find that adenosine levels at both surfaces of the uroepithelium are modulated by turnover, that blocking these pathways or stimulating A(1) receptors directly at the luminal surface promotes bladder contractions, and that adenosine further stimulates voiding in animals with cyclophosphamide-induced cystitis.     

Influence of the environmental temperature on the metabolic use of dietary energy and nitrogen in the growing rat

Sixty-seven male rats of the Wistar CF strain were used in two trials to study the effect of ambient temperature on nitrogen and energy balances (experiment 1) and on the variations of certain biochemical parameters of metabolism (experiment 2). In both cases, the rats, housed individually in metal cages and fed ad libitum, were kept under three different temperatures : 21 degrees C (control), 3 degrees C (cold), 31 degrees C (hot). Compared to the controls, the rats at 3 degrees C showed a significant increase (P less than 0.01) in food intake and a significant decrease (P less than 0.01) in daily growth rate and feed efficiency ratio; body fat content was unchanged. Compared to the controls, the rats at 31 degrees C showed a decrease (P less than 0.01) in food intake and growth rate, a better feed efficiency ratio (P less than 0.01) and a significant increase in carcass lipid content. When compared to rats at 21 degrees C, those at 3 degrees C had a much lower nitrogen retention; at 31 degrees C this retention was only slightly lower. The urinary nitrogen excretion, increased by the cold temperature, reflected higher nitrogen catabolism, while its increase at a high temperature was probably due to a decrease in protein synthesis, and a subsequent degradation of excess ingested nitrogen. Energy retention increased (P less than 0.01) as the ambient temperature increased from 3 to 31 degrees C, and wide variations in the amounts of fixed energy in the form of proteins or lipids were observed. The balance results obtained have been discussed in relation to the variations of some biochemical parameters of metabolism such as free fatty acids, free glycerol, lipoprotein-lipase activity and in vitro utilization of labelled glucose.     

Increasing myocardial contraction and blood pressure in C57BL/6 mice during early postnatal development

Knowledge of the developmental changes of cardiovascular parameters in the genetic background of a mouse strain is important for understanding phenotypic changes in transgenic or knockout mouse models for heart disease. We studied arterial blood pressure and myocardial contractility in mice of the common background strain C57BL/6, aged 21 days [postnatal day 21 (P21)] to 580 days. Heart rate increased during maturation from 396 beats/min at P21 to 551 beats/min at postnatal day 50 (P50), and mean arterial blood pressure increased in parallel from 86 to 110 mmHg and remained constant afterward. Echocardiographically determined left ventricular myocardial wall dimensions (R = 0.79, P < 0.0001) and left ventricular mass calculated using the area-length algorithm correlated strongly with histomorphometrical measurements (R = 0.93, P < 0.001). Sarcomere shortening records from isolated ventricular myocytes used as a measure for myocardial contractility revealed a negative shortening-frequency relation under a pacing frequency of 2 Hz and a positive relation above 2 Hz. Shortening amplitudes recorded from P21 myocytes were smaller, and the shortening-frequency relation was less steep than in adult myocytes. A stimulation pause was followed by a negative "staircase" at pacing frequency of < or =6 Hz and a positive staircase at > or =6 Hz. P21 myocytes developed positive staircases at 8 and 10 Hz, and adult myocytes also developed them at 6 Hz. Blood pressure increase during maturation until P50 may originate from increasing single cardiomyocyte contractility.     

Nonlinear Electrical Effects in Lipid Bilayer Membranes: II. Integration of the Generalized Nernst-Planck Equations

In this paper the ion transport across a thin lipid membrane is treated using a generalized form of the Nernst-Planck equations. An additional term is introduced into the flux equations to account for the image force acting on the ion. As the membrane thickness is of the same order of magnitude as the range of the image forces, the potential energy of the ion in the membrane is strongly dependent on position. The integration of the flux equations leads to a general expression for the integral membrane conductance lambda as a function of the voltage u. The ratio lambda(u)/lambda(0) (lambda(0) = membrane conductance in the limit u --> 0) depends on the dielectric constant and the thickness of the membrane, but is independent of the ionic radius. When the numerical values of the potential energy function, as calculated by the method of electrical images, are inserted into the expression for lambda(u)/lambda(0), a strongly non-linear current-voltage characteristic is obtained. The theoretical current-voltage curve agrees satisfactorily with the experimental data at a low ionic strength and at low voltages; at higher voltages the observed membrane conductance exceeds the predicted value.     

小球藻两个品系在自养与异养条件下的生长、能荷与色素差异

Chlorella protothecoides中国品系(C品系)与美国品系(A品系)在自养培养基中生长正常。在高浓度葡萄糖、低浓度有机氮的异养生长条件下,C品系仍为绿色,细胞生长与繁殖缓慢,指数期生长速率降低,细胞内腺苷酸能荷值(AEC)下降,但细胞仍保留叶绿素;A品系细胞转变成乳黄色,细胞生长与繁殖加快,指数期生长速率是自养细胞的2倍,细胞内腺苷酸能荷值仍保持高水平,向异养条件转换后约24h,细胞内叶绿素基本消失,重新向自养条件转换后细胞内叶绿素又逐渐恢复。AEC值是判别微藻在异养条件下能量代谢与生理状态的良好指标。同一种小球藻不同品系间的上述差异可能与细胞内基因调控的差异相关联。     

Remodeling of Strain Energy Function of Common Bile Duct post Obstruction

Biliary duct obstruction is an important clinical condition that affects millions of people worldwide. We have previously shown that the common bile duct (CBD) undergoes significant growth and remodelling post obstruction. The mechanical stress-strain relation is expected to change due to growth and remodeling in response to obstruction and hence pressure-overload. The objective of the present study was to characterize the material properties of the CBD of the sham group and at 3 hours, 12 hours, 2 days, 8 days and 32 days (n=5 in each group) after obstruction. The Fung's exponential strain energy function was used to relate stress to strain of the normal and remodeled ducts. The Marquardt-Levenberg and genetic algorithm methods were used for the determination of material constants for the exponential strain energy function. The elastic constants obtained by the two methods did not differ (P>0.254). We obtained stable and convergent material constants at every time point. The material constant that dictates the nonlinear rate of change in the circumferential stress with respect to strain increased significantly after obstruction acutely in the first 12 hrs., decreased at 2 days and finally increased montonically during the remaining 30 days. The acute initial increase in stiffness was simply due to the elastic response. The chronic remodeling process results in an initial circumferential softening followed by stiffening of the CBD. This study has important clinical significance for patients with CBD obstruction and for endoscopists and surgeons who treat the condition.     

High-density functional display of proteins on bacteriophage lambda

We designed a bacteriophage lambda system to display peptides and proteins fused at the C terminus of the head protein gpD of phage lambda. DNA encoding the foreign peptide/protein was first inserted at the 3' end of a DNA segment encoding gpD under the control of the lac promoter in a plasmid vector (donor plasmid), which also carried lox P(wt) and lox P(511) recombination sequences. Cre-expressing cells were transformed with this plasmid and subsequently infected with a recipient lambda phage that carried a stuffer DNA segment flanked by lox P(wt) and lox P(511) sites. Recombination occurred in vivo at the lox sites and Amp(r) cointegrates were formed. The cointegrates produced recombinant phage that displayed foreign protein fused at the C terminus of gpD. The system was optimised by cloning DNA encoding different length fragments of HIV-1 p24 (amino acid residues 1-72, 1-156 and 1-231) and the display was compared with that obtained with M13 phage. The display on lambda phage was at least 100-fold higher than on M13 phage for all the fragments with no degradation of displayed products. The high-density display on lambda phage was superior to that on M13 phage and resulted in selective enrichment of epitope-bearing clones from gene-fragment libraries. Single-chain antibodies were displayed in functional form on phage lambda, strongly suggesting that correct disulphide bond formation takes place during display.This lambda phage display system, which avoids direct cloning into lambda DNA and in vitro packaging, achieved cloning efficiencies comparable to those obtained with any plasmid system. The high-density display of foreign proteins on bacteriophage lambda should be extremely useful in studying low-affinity protein-protein interactions more efficiently compared to the M13 phage-based system.     

Temperature dependence of the rate constants of the Escherichia coli RNA polymerase-lambda PR promoter interaction. Assignment of the kinetic steps corresponding to protein conformational change and DNA opening

The kinetics of formation and of dissociation of open complexes (RPo) between Escherichia coli RNA polymerase (R) and the lambda PR promoter (P) have been studied as a function of temperature in the physiological range using the nitrocellulose filter binding assay. The kinetic data provide further evidence for the mechanism R + P in equilibrium I1 in equilibrium I2 in equilibrium RPo, where I1 and I2 are kinetically distinguishable intermediate complexes at this promoter which do not accumulate under the reaction conditions investigated. The overall second-order association rate constant (ka) increases dramatically with increasing temperature, yielding a temperature-dependent activation energy in the range 20 kcal (near 37 degrees C) to 40 kcal (near 13 degrees C) (1 kcal = 4.184 kJ). Both isomerization steps (I1----I2 and I2----RPo) appear to be highly temperature dependent. Except at low temperatures (less than 13 degrees C) the step I1----I2, which we attribute to a conformational change in the polymerase with a large negative delta Cp degrees value, is rate-limiting at the reactant concentrations investigated and hence makes the dominant contribution to the apparent activation energy of the pseudo first-order association reaction. The subsequent step I2----RPo, which we attribute to DNA melting, has a higher activation energy (in excess of 100 kcal) but only becomes rate-limiting at low temperature (less than 13 degrees C). The initial binding step R + P in equilibrium I1 appears to be in equilibrium on the time-scale of the isomerization reactions under all conditions investigated; the equilibrium constant for this step is not a strong function of temperature and is approximately 10(7) M-1 under the standard ionic conditions of the assay (40 mM-Tris . HCl (pH 8.0), 10 mM-MgCl2, 0.12 M-KC1). The activation energy of the dissociation reaction becomes increasingly negative at low temperatures, ranging from approximately -9 kcal near 37 degrees C to -30 kcal near 13 degrees C. Thermodynamic (van't Hoff) enthalpies delta H degrees of open complex formation consequently are large and temperature-dependent, increasing from approximately 29 to 70 kcal as the temperature is reduced from 37 to 13 degrees C. The corresponding delta Cp degrees value is approximately -2.4 kcal/deg. We propose that this large negative delta Cp degrees value arises primarily from the burial of hydrophobic surface in the conformational change (I1 in equilibrium I2) in RNA polymerase in the key second step of the mechanism.(ABSTRACT TRUNCATED AT 400 WORDS)     

Analysis of the involvement of human N-acetyltransferase 1 in the genotoxic activation of bladder carcinogenic arylamines using a SOS/umu assay system

Human acetyltransferase genes NAT1 or NAT2 were expressed in a Salmonella typhimurium strain used to detect the genotoxicity of bladder carcinogens. To clarify whether the human and rodent bladder carcinogenic arylamines are activated via either NAT1 or NAT2 to cause genotoxicity, a SOS/umu genotoxicity assay was used, with the strains S. typhimurium NM6001 (NAT1-overexpressing strain), S. typhimurium NM6002 (NAT2-overexpressing strain), and S. typhimurium NM6000 (O-AT-deficient parent strain). Genotoxicity was measured by induction of SOS/umuC gene expression in the system, which contained both an umuC"lacZ fusion gene and NAT1 or NAT2 plasmids. 4-Aminobiphenyl, 2-acetylaminofluorene, beta-naphthylamine, o-tolidine, o-anisidine, and benzidine exhibited dose-dependent induction of the umuC gene in strain NM6001. Although the induction of umuC by these chemicals was observed in the NM6002 strain, the induction was considerably lower than in the NM6001 strain. In the parent strain, NM6000, none of these compounds induced umuC gene expression. We also determined activation of these chemicals by recombinant human cytochrome P450 (P450 or CYP) 1A2 enzyme in three S. typhimurium tester strains. The activation of the chemicals was stronger in the NM6001 strain than that in NM6002. The specific NAT1 inhibitor 5-iodosalicylic acid inhibited umuC gene expression induced by aromatic amines used. These results could provide evidence that the bladder carcinogenic aromatic amines are mainly activated by the NAT1 enzyme to produce DNA damage rather than NAT2. The NAT1-overexpressing strain can be used to determine the genotoxic activation of bladder carcinogenic arylamines in the umu test and could provide a tool for predicting the carcinogenic potential of arylamines.     

Suppression of induction of SOS functions in an Escherichia coli tif-1 mutant by plasmid R100.1.

The tif-1 mutation in the recA gene of Escherichia coli caused, at 40 degrees C, lethal cell filamentation, induction of the recA protein, mutagenesis, and, in lambda lysogens, prophage induction. The presence of plasmid R100.1 in tif-1 strains suppressed tif-mediated cell filamentation and killing, recA protein induction, and prophage induction in lysogens. It also reduced mutagenesis in a tif-1 sfiA11(R100.1) strain. Plasmids F'lac, P1, and pMB9, in contrast, had little or no effect on tif-mediated induction of lambda. The presence of R100.1 did not inhibit the induction of the recA protein or of lambda by ultraviolet irradiation or mitomycin C treatment of tif-1(R100.1) or tif-1(lambda)(R100.1) strains.     

Relation between left ventricular cavity pressure and volume and systolic fiber stress and strain in the wall.

Pumping power as delivered by the heart is generated by the cells in the myocardial wall. In the present model study global left-ventricular pump function as expressed in terms of cavity pressure and volume is related to local wall tissue function as expressed in terms of myocardial fiber stress and strain. On the basis of earlier studies in our laboratory, it may be concluded that in the normal left ventricle muscle fiber stress and strain are homogeneously distributed. So, fiber stress and strain may be approximated by single values, being valid for the whole wall. When assuming rotational symmetry and homogeneity of mechanical load in the wall, the dimensionless ratio of muscle fiber stress (sigma f) to left-ventricular pressure (Plv) appears to depend mainly on the dimensionless ratio of cavity volume (Vlv) to wall volume (Vw) and is quite independent of other geometric parameters. A good (+/- 10%) and simple approximation of this relation is sigma f/Plv = 1 + 3 Vlv/Vw. Natural fiber strain is defined by ef = In (lf/lf,ref), where lf,ref indicates fiber length (lf) in a reference situation. Using the principle of conservation of energy for a change in ef, it holds delta ef = (1/3)delta In (1 + 3Vlv/Vw).