Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach

Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, “Average Relative Growth Rate” is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.     

Importance of scaling exponents and other parameters in growth mechanism: an analytical approach

The growth process of a living organism is studied with the help of a mathematical model where a part of the surplus power is assumed to be used for growth. In the present study, the basic mathematical framework of the growth process is based on a pioneering theory proposed by von Bertalanffy and his work is the main intellectual driving force behind the present analysis. Considering the existence of an optimum size for which the surplus power becomes maximum, it has been found that the scaling exponent for the intake rate must be smaller than the exponent for the metabolic cost. A relationship among the empirical constants in allometric scaling has also been established on the basis of the fact that an organism never ceases to generate surplus energy. The growth process is found to continue forever, although with a decreasing rate. Beyond the optimum point the percentage of shortfall in energy has been calculated and its dependence on scaling exponents has been determined. The dependence of optimum mass on the empirical constants has been shown graphically. The functional dependence of mass variation on time has been obtained by solving a differential equation based on the concept of surplus energy. The dependence of the growth process on scaling exponent and empirical constants has been shown graphically.     

Plant growth analysis: towards a synthesis of the classical and the functional approach

A method of calculating relative growth rates (RGR) and net assimilation rates is presented. The method is based on the fitting of a polynomial through the relative growth rate values calculated by the 'classical' approach rather than through the In-transformed plant weights as in the 'functional' method. Additional ways of reducing the harvest-to-harvest variation characteristic of the classical approach are discussed. The main advantages of the present approach over the functional one are: (1) The degree of the polynomial can be increased (within certain limits) without inducing spurious fluctuations in RGR. Thus, quite complex trends in RGR can be described. (2) There is little interference between RGR values in different parts of the experiment. The main advantages over the classical approach are: (1) The erratic fluctuations in RGR are dampened. (2) As frequent small harvests are allowed, the workload at each harvest can be diminished and a more reliable impression of ontogenetic drift in RGR can be obtained. (3) RGR is described by a continuous function, thus facilitating further calculations and compilations.     

Phytoplankton growth rate as a function of cell size: an experimental test in Lake Biwa

It is well known that algal growth rates decrease with increasing cell size. Most of these findings were, however, obtained under laboratory conditions. It is not clear if these allometric relationships are also applicable to in situ conditions. In the present study, the relationship between growth rates and cell size of algal species was examined seasonally in Lake Biwa by in situ dilution bioassays. The bioassays revealed that the highest growth rate of each species throughout the experiments was negatively correlated with cell size consistent with known allometric relationships. At each incubation experiment, however, growth rates were not necessarily correlated with cell size. This was true even when both macro- and micronutrients were added, although a substantial number of species responded to nutrient enrichment. These results showed that nutrient supplies affected algal species differently regardless of cell size and that factors other than nutrient supplies limited the growth rate of some algal species. Due to such species-specific differences in limiting factors, at any given time in situ growth rates of algae are not determined exclusively by cell size. Received: August 24, 2000 / Accepted: March 2, 2001     

Countergradient variation in growth rate: compensation for length of the growing season among Atlantic silversides from different latitudes

Summary How do organisms adapt to the differences in temperature and length of the growing season that occur with latitude? Among Atlantic silversides (Menidia menidia) along the east coast of North America, the length of the first growing season declines by a factor of about 2.5 with increasing latitude. Yet body size at the end of the first growing season does not decline. High-latitude fish must, therefore, grow faster within the growing season than do low-latitude fish. This geographical pattern has a genetic basis. Laboratory experiments on fish from six different locations revealed a latitudinal gradient in the capacity for growth (i.e., maximum growth potential). In two subsequent experiments using fish from Nova Scotia (NS), New York (NY) and South Carolina (SC) that had been separately reared in a common environment for several generations, differences in growth rate among populations were highly significant. The rank order was NS>NY>SC, but the difference among populations depended on temperature. High-latitude fish outperformed those from low latitudes primarily at the high temperatures that low-latitude fish would be expected to experience most often in nature. These results suggest that instead of being adapted for growth at low temperatures, fish from high latitudes are adapted for rapid elevation of growth rate during the brief interval of the year when high temperatures occur. Selection on growth rate results from sizedependent winter mortality: the importance to winter survival of being large increases with latitude but the length of the growing season simultaneously decreases. The end result is countergradient variation in growth rate, a phenomenon that may be much more widespread than currently recognized.     

The response of fast- and slow-growing Acacia species to elevated atmospheric CO2: an analysis of the underlying components of relative growth rate

In this study we assessed the impact of elevated CO₂ with unlimited water and complete nutrient on the growth and nitrogen economy of ten woody Acacia species that differ in relative growth rate (RGR). Specifically, we asked whether fast- and slow-growing species systematically differ in their response to elevated CO₂. Four slow-growing species from semi-arid environments (Acacia aneura, A. colei, A. coriacea and A. tetragonophylla) and six fast-growing species from mesic environments (Acacia dealbata, A. implexa, A. mearnsii, A. melanoxylon, A. irrorata and A. saligna) were grown in glasshouses with either ambient (˜350 ppm) or elevated (˜700 ppm) atmospheric CO₂. All species reached greater final plant mass with the exception of A. aneura, and RGR, averaged across all species, increased by 10% over a 12-week period when plants were exposed to elevated CO₂. The stimulation of RGR was evident throughout the 12-week growth period. Elevated CO₂ resulted in less foliage area per unit foliage dry mass, which was mainly the result of an increase in foliage thickness with a smaller contribution from greater dry matter content per unit fresh mass. The net assimilation rate (NAR, increase in plant mass per unit foliage area and time) of the plants grown at elevated CO₂ was higher in all species (on average 30% higher than plants in ambient CO₂) and was responsible for the increase in RGR. The higher NAR was associated with a substantial increase in foliar nitrogen productivity in all ten Acacia species. Plant nitrogen concentration was unaltered by growth at elevated CO₂ for the slow-growing Acacia species, but declined by 10% for faster-growing species. The rate of nitrogen uptake per unit root mass was higher in seven of the species when grown under elevated CO₂, and leaf area per unit root mass was reduced by elevated CO₂ in seven of the species. The absolute increase in RGR due to growth under elevated CO₂ was greater for fast- than for slow-growing Acacia species. Received: 21 December 1998 / Accepted: 31 May 1999     

Stoichiometry in an ecological context: testing for links between <Emphasis Type="Italic">Daphnia</Emphasis> P-content,growth rate and habitat preference

We used laboratory experiments with ten Daphnia taxa to test for links between Daphnia P-content, growth rate and habitat preference. The taxa represent a wide range of body sizes and most show distinct preferences for one of three habitats: shallow lakes, deep, stratified lakes or fishless ponds. Previous studies show that taxa from shallow lakes and fishless ponds experience high predation risk and rich food resources, whereas taxa from deep lakes experience low predation risk, strong food limitation and potentially P-deficient resources. Thus, we predicted higher P-content and higher maximal growth rates in taxa from ponds and shallow lakes and lower P-content, lower maximal growth but reduced sensitivity to P-limitation in taxa preferring stratified lakes. In each of 25 experiments, a clonal Daphnia cohort was cultured for 4 days on a P-sufficient (molar C:P ratio 70) or a P-deficient (C:P 1,000) diet of a green alga at a high concentration (1 mg C l^–1). The P-content of adult Daphnia fed the P-sufficient diet ranged from 1.52 to 1.22% mass. Small-bodied taxa from shallow lakes had higher P-content than larger-bodied taxa from deep lakes or fishless ponds. However, we found a nonsignificant negative correlation between P-content and growth on the P-sufficient diet, rather than the positive relationship predicted by the growth rate hypothesis. The P-deficient diet resulted in declines in both growth rate and P-content compared with the P-sufficient controls and the extent of the declines differed between taxa. Taxa from ponds showed a marginally greater decline in growth with the P-deficient diet compared with taxa from shallow or deep lakes. However, contrary to stoichiometric theory, no relationship was found between a species P-content and growth depression on the P-deficient diet. Although we found evidence for habitat adaptations, our results show that factors other than Daphnia P-content are important in determining differences between Daphnia species in both maximal growth rate and sensitivity to P-limited growth.     

Age and growth studies of chondrichthyan fishes: the need for consistency in terminology, verification, validation, and growth function fitting

Validated age and growth estimates are important for constructing age-structured population dynamic models of chondrichthyan fishes, especially those which are exploited. We review age and growth studies of chondrichthyan fishes, using 28 recent studies to identify areas where improvements can be made in describing the characteristics of ageing structures (both traditional and novel) utilized to estimate ages of sharks, rays, and chimaeras. The topics identified that need consistency include the: (1) terminology used to describe growth features; (2) methods used to both verify and validate age estimates from chondrichthyan calcified structures, especially edge and marginal increment analyses; and (3) the functions used to produce and describe growth parameters, stressing the incorporation of size at birth (L ₀) and multiple functions to characterize growth characteristics, age at maturity and longevity.     

Nanoparticle-biomolecular corona: A new approach for the early detection of non-small-cell lung cancer

Lung cancer (LC) is the most common type of cancer and the second cause of death worldwide in men and women after cardiovascular diseases. Non-small-cell lung cancer (NSCLC) is the most frequent type of LC occurring in 85% of cases. Developing new methods for early detection of NSCLC could substantially increase the chances of survival and, therefore, is an urgent task for current research. Nowadays, explosion in nanotechnology offers unprecedented opportunities for therapeutics and diagnosis applications. In this context, exploiting the bio-nano-interactions between nanoparticles (NPs) and biological fluids is an emerging field of research. Upon contact with biofluids, NPs are covered by a biomolecular coating referred to as “biomolecular corona” (BC). In this study, we exploited BC for discriminating between NSCLC patients and healthy volunteers. Blood samples from 10 NSCLC patients and 5 subjects without malignancy were allowed to interact with negatively charged lipid NPs, leading to the formation of a BC at the NP surface. After isolation, BCs were characterized by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE). We found that the BCs of NSCLC patients was significantly different from that of healthy individuals. Statistical analysis of SDS-PAGE results allowed discriminating between NSCLC cancer patients and healthy subjects with 80% specificity, 80% sensitivity and a total discriminate correctness rate of 80%. While the results of the present investigation cannot be conclusive due to the small size of the data set, we have shown that exploitation of the BC is a promising approach for the early diagnosis of NSCLC.     

Application of the principles of enzyme kinetics to clonal growth rate assays: an approach for delineating interactions among growth promoting agents.

The interaction of mitogenic factors on a single cell type and the comparative activity of a given factor in diverse cell types have been studied by applying the principles of Michaelis-Menten kinetics to clonal growth data. Such comparisons are facilitated by derivation of two parameters; Km mitogen, the mitogen concentration that gives half-maximal clonal growth and a theoretical maximal growth rate, RMAX T. Both parameters are analogous to the Km and VMAX as applied to enzymatic reactions. Use of these parameters permits meaningful comparisons between cells with different growth rates. Using kinetic analysis of dose-response data, we found that normal human epithelial cells require 200 times more fetal bovine serum protein (FBSP) than a malignant line to multiply at their respective half-maximal rates. Further, the Km FBSP of normal cells was reduced to that of the malignant line by the inclusion of growth factors (EGF or FGF, and hydrocortisone) in the medium. On the other hand, even though greater levels of serum were required when growth factors and hydrocortisone were not present, their inclusion did not alter RMAX T. Interactions between mitogenic factors were shown to be unidirectional. Although EGF reduced the Km FBSP, FBSP did not change the Km EGF. The same type of analysis revealed that hydrocortisone, which potentiated the mitogenic activity of EGF did not change the Km EGF. Kinetic analysis of cell growth should prove useful in studies on the relation between growth and tumor promotion as well as in the evaluation of growth-inhibiting chemotherapeutic agents.     

Role of XIAP in inhibiting cisplatin-induced caspase activation in non-small cell lung cancer cells: a small molecule Smac mimic sensitizes for chemotherapy-induced apoptosis by enhancing caspase-3 activation

X-linked IAP (XIAP) suppresses apoptosis by binding to initiator caspase-9 and effector caspases-3 and -7. Smac/DIABLO that is released from mitochondria during apoptosis can relieve its inhibitory activity. Here we investigated the role of XIAP in the previously found obstruction of chemotherapy-induced caspase-9 activation in non-small cell lung cancer (NSCLC) cells. Endogenously expressed XIAP bound active forms of both caspase-9 and caspase-3. However, downregulation of XIAP using shRNA or disruption of XIAP/caspase-9 interaction using a small molecule Smac mimic were unable to significantly induce caspase-9 activity, indicating that despite a strong binding potential of XIAP to caspase-9 it is not a major determinant in blocking caspase-9 in NSCLC cells. Although unable to revert caspase-9 blockage, the Smac mimic was able to enhance cisplatin-induced apoptosis, which was accompanied by increased caspase-3 activity. Additionally, a more detailed analysis of caspase activation in response to cisplatin indicated a reverse order of activation, whereby caspase-3 cleaved caspase-9 yielding an inactive form. Our findings indicate that the use of small molecule Smac mimic, when combined with an apoptotic trigger, may have therapeutic potential for the treatment of NSCLC.     

Evaluation of the target dose coverage of stereotactic body radiotherapy for lung cancer using helical tomotherapy: A dynamic phantom study

AimTo evaluate the target dose coverage for lung stereotactic body radiotherapy (SBRT) using helical tomotherapy (HT) with the internal tumor volume (ITV) margin settings adjusted according to the degree of tumor motion.BackgroundLung SBRT with HT may cause a dosimetric error when the target motion is large.Materials and methodsTwo lung SBRT plans were created using a tomotherapy planning station. Using these original plans, five plans with different ITV margins (4.0–20.0 mm for superior-inferior [SI] dimension) were generated. To evaluate the effects of respiratory motion on HT, an original dynamic motion phantom was developed. The respiratory wave of a healthy volunteer was used for dynamic motion as the typical tumor respiratory motion. Five patterns of motion amplitude that corresponded to five ITV margin sizes and three breathing cycles of 7, 14, and 28 breaths per minute were used. We evaluated the target dose change between a static delivery and a dynamic delivery with each motion pattern.ResultsThe target dose difference increased as the tumor size decreased and as the tumor motion increased. Although a target dose difference of <5 % was observed at ≤10 mm of tumor motion for each condition, a maximum difference of -9.94 % ± 7.10 % was observed in cases of small tumors with 20 mm of tumor motion under slow respiration.ConclusionsMinimizing respiratory movement is recommended as much as possible for lung SBRT with HT, especially for cases involving small tumors.     

Predictive biochemical-markers for the development of brain metastases from lung cancer: Clinical evidence and future directions

BackgroundBrain metastases are a common complication of patients with lung cancer and lung cancer is one of the most common causes of brain metastases. The occurrence of brain metastases is associated with poor prognosis and high morbidity, even after intensive multimodal therapy. Therefore, identifying lung cancer patients with who are at high risk of developing brain metastases and applying effect intervention is important to reduce or delay the incidence of brain metastases. Biochemical-markers may meet an unmet need for following patients’ mechanisms of brain metastases.MethodsData for this review were identified by searches of Pubmed and Cochrane databases, and references from relevant articles using the search terms “lung cancer” and “brain metastasis”. Meeting abstracts, unpublished reports and review articles were not considered.ResultsClinical results for pathological and circulating markers including cancer molecular subtypes, miRNA, single nucleotide polymorphisms, and other markers are presented. However, these biochemical-markers are not yet established surrogate assessments for prediction of brain metastases.ConclusionsBiochemical-markers reported allowed physicians to identify which patients with lung cancer are at high risk for brain metastases. Prospective randomized clinical studies are needed to further assess the utility of these biochemical-markers.     

Growth of captive leatherback turtles, Dermochelys coriacea, with inferences on growth in the wild: Implications for population decline and recovery

Leatherback turtles (Dermochelys coriacea) are endangered, and declining population trends suggest that they are vulnerable to becoming extinct in the Pacific Ocean. Population recovery depends on strong conservation measures (e.g., nest protection, reduction of bycatch, and foraging habitat preservation) and on how fast leatherbacks grow and reach maturity, making the latter of grave concern. The research reported here marks the first time that several leatherback turtles have been maintained in captivity for nearly 2 years, from hatchlings (6.31 ± 0.13 cm straight carapace length (SCL) and 46.0 ± 1 g) to juveniles (largest, 72.0 cm SCL and 42.65 kg). Leatherbacks maintained an average growth rate of 31.9 ± 2.8 cm year^− 1 in SCL throughout the study period. A length-mass relationship of the form, mass (kg) = 0.000214 ? SCL (cm) 2.86, fitted our data and data from four other captive studies, 11 wild juveniles, and five studies of adult leatherbacks. Von Bertalanffy, Gompertz and logistic growth functions predicted age-at-maturity for leatherbacks of 16.1, 8.7 and 6.8 years, respectively. The accuracy of these age-at-maturity estimates is discussed in the light of skeletochronological studies as well as estimates obtained from conservation and genetic studies. Our data, in combination with data from sightings, suggest that leatherbacks spend their early years (0 to 5 years of age) growing in the warmer waters of the tropical and subtropical seas before entering cooler temperate waters. Information obtained from turtles incidentally captured in fisheries, supplemented with growth curve data, indicates that leatherbacks are vulnerable to entanglement or hooking in various pelagic gear types, such as drift gill nets and longline within 3 years from nest emergence. Consequently, leatherbacks are exposed to threats from marine fisheries for > 80% of their early life before carapace length characteristic of reproductive maturity is attained.     

Let-7a elevates p21 levels by targeting of NIRF and suppresses the growth of A549 lung cancer cells

Down-regulation of let-7 microRNA (miRNA) is a key event in lung cancer. Despite recent advances in survival signaling, the roles of let-7 in the context of lung cancer are not fully clear. In this study, we showed that let-7a, a member of let-7 family, negatively regulated the expression of NIRF through NIRF 3′ UTR. We also showed that NIRF was required for the let-7a-mediated elevation of p21^WAF1. These findings suggest that growth-inhibitory effect of let-7a on the A549 cells in vitro and in vivo may be explained in part by le-7a-induced suppression of NIRF and elevation of p21^WAF1. This work reveals a novel regulatory mechanism for let-7a in the control of cellular proliferation and lung carcinogenesis.     

Growth temperature influences the underlying components of relative growth rate: an investigation using inherently fast- and slow-growing plant species

We examined the effect of growth temperature on the underlying components of growth in a range of inherently fast‐ and slow‐growing plant species. Plants were grown hydroponically at constant 18, 23 and 28 °C. Growth analysis was conducted on 16 contrasting plant species, with whole plant gas exchange being performed on six of the 16 species. Inter‐specific variations in specific leaf area (SLA) were important in determining variations in relative growth rate (RGR) amongst the species at 23 and 28 °C but were not related to variations in RGR at 18 °C. When grown at 18 °C, net assimilation rate (NAR) became more important than SLA for explaining variations in RGR. Variations in whole shoot photosynthesis and carbon concentration could not explain the importance of NAR in determining RGR at the lower temperatures. Rather, variations in the degree to which whole plant respiration per unit leaf area acclimated to the different growth temperatures were responsible. Plants grown at 28 °C used a greater proportion of their daily fixed carbon in respiration than did the 18 and 23 °C‐grown plants. It is concluded that the relative importance of the underlying components of growth are influenced by growth temperature, and the degree of acclimation of respiration is of central importance to the greater role played by NAR in determining variations in RGR at declining growth temperatures.     

Invasion of an occupied niche by the crayfish Orconectes rusticus: potential importance of growth and mortality

We are exploring mechanisms of an invasion that contradicts the oft-cited generalization that species invade vacant niches. In northern Wisconsin lakes, the introduced crayfish Orconectes rusticus is replacing two ecologically similar resident congeners, O. virilis and O. propinquus. In laboratory experiments, we compared growth and mortality of individually maintained crayfish offered one of five ad libitum diets: invertebrates, macrophytes, dentritus, periphyton or all items combined. Mortality was highest for O. virilis and lowest for O. rusticus. Macrophyte diets yielded the highest mortality. All three species grew best on invertebrate and combination diets but grew little or not at all on diets of periphyton, detritus or macrophytes. O. rusticus and O. virilis grew more than O. propinquus. O. rusticus grew more quickly and/or was better able to survive overall than its congeners. Therefore, O. rusticus would probably have advantages over O. virilis and O. propinquus in competitive interactions, reproductive success and avoiding size-selective fish predation. Subtle interspecific differences may interact strongly with other ecological factors and contribute to the displacement of resident species from a well-occupied niche.     

Replacement perfusion of cultured eucaryotic cells: A method for the accurate measurement of the rates of growth,protein synthesis,and protein turnover

The fractional rates of protein synthesis (k_s) and degradation (k_p) were studied in the myeloma cell line SP2/0-AG14 grown at different rates (k_g). Cells in spinner flask suspension cultures were maintained at constant cellular density for prolonged periods by replacement perfusion of labeling medium at a rate equivalent to the rate of growth. Total protein synthesis was calculated from the specific-radioactivity of labeled L-leucine in the precursor (medium) and cellular protein. Fractional synthesis rates determined by approach to equilibrium labeling were the same as those determined by equilibrium-pulse labeling kinetics and pulse-chase kinetics. The rate of protein degradation was determined from the established relationship k_g = k_s – k_p. Protein synthesis rates remained constant over a threefold range in the rate of cell growth. At relatively slow growth rates (k_g = 0.017/hr) turnover represented a major fraction of total synthesis (k_p = 0.032/hr = 0.65ks). At rapid growth rates (k_g = 0.058/hr) the value of k_p was less than 0.005/hr. No major difference was observed between the k_s determined for individual cellular proteins (separated by SDS-polyacrylamide (7.5%) gel electro-phoresis) from rapid- and slow-growing cultures. Thus, with an invariable k_s, any change in growth rate is due to an inverse change in the rate of turnover. Since turnover is the balance between synthesis and degradation and since synthesis is unchanging then changes in the growth rate of SP2/0-AG14 should be due to changes in the rate of protein degradation. Experiments were therefore performed to determine the origin of the degradative machinery, ie, cytosolic or lysosomal; autolysis of prelabeled cellular protein (in vitro) was observed only at acidic pH (4.2) and WUS totally inhibited by addition of lcupcptin (10 μM) and pepstatin (2 μM), the specific inhibitors of lysosomal cathepsins B (L) and D, respectively. Since growth rate appears to be regulated by the alterations in the rate of protein degradation and degradation (in vitro) in SP2/0-AG14 appearsto be lysosomal, then one should be able to alter the rate of cellular growth by interfering with rate of lysosomal proteolysis. Indeed, when the lysosomotropic amine NH ₄Cl (10 mM) is added to cells growing with a k_g of 0.018/hr ± 0.001 (k_s = 0.050/hr ± 0.002) the growth rate increased to 0.051/hr ± 0.002 without change in the rate of protein synthesis (k_s = 0.049/hr ± 0.003). It is suggested from our data that the cellular growth rate of SP2/0-AG14 is regulated by the lysosomal apparatus; whether this regulation is itself regulated by either a specific compartmentalization of the lysosomal proteinases and/or their substrates or by endogenous protease inhibitors, should prove to be an exciting area for future investigation.     

Ethanol evolution rate: a new parameter to determine the feeding rate for the production of avermectins by Streptomyces avermitilis

A new parameter ethanol evolution rate (EER) was developed to aid in the determination of glucose feeding rate in avermectin production. The EER characterized the level of primary metabolism and its value was affected mainly by the supply of O2 and glucose. In an abnormal batch, over-feeding of glucose led to 2.5-fold increase of the maximum EER value compared to the normal one, and the production was thus decreased by nearly 80%. Together with other criteria, the EER helped to control utilization of substrate, so it has been successfully used to control glucose feeding in an industrial process.