Application of Lineweaver Burk data transformation to explain animal and plant performance as a function of nutrient supply

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1 Livestock Production Science 98 (25) Technical note Application of Lineweaver Burk data transformation to explain animal and plant performance as a function of nutrient supply R.P. Lana*, R.H.T.B. Goes, L.M. Moreira, A.B. Mâncio, D.M. Fonseca, L.O. Tedeschi 1 Departamento de Zootecnia, Universidade Federal de Viçosa, Av. Peter Henry Rolfs, s/n, , Viçosa, Minas Gerais, Brazil Received 19 July 24; received in revised form 24 February 25; accepted 22 March 25 Abstract This study evaluates the effect of dry-season concentrate supplementation on growing cattle performance grazing tropical pasture and the impact of nitrogen fertilization on the growth rate of tropical pasture (tons of dry herbage mass/ha/11 days) and on the subsequent stocking rate and cattle performance during the rainy season (kg body weight gain/ha/11 days). The animal and plant responses were curvilinear to the increasing amount of nutrient supply and followed the typical saturation kinetics of enzyme systems, a Michaelis Menten relationship. The Lineweaver Burk data transformation explained efficiently the animal and plant responses to the nutrient supply. This methodology consists in evaluating the linear regressions of the reciprocal of animal and plant responses as a function of the reciprocal of nutrient supply. The half maximum growth rates for plant and animal to nutrient supply were verified with the proportions from.48 to.56 of the amount needed to cause.95 of theoretical maximum responses. From the curvilinear response, it can be verified that the marginal increase in animal and plant growth rate reduces as the amount of nutrient supply increases. D 25 Elsevier B.V. All rights reserved. Keywords: Cattle; Fertilization; Growth rate; Michaelis Menten; Pasture; Ration Abbreviations: ADG, average daily gain; AU, animal unit; BWG, body weight gain; DHM, dry herbage mass; ha, hectare (1, m 2 ); N, nitrogen; NUTR 5 RESPmax, the amount of nutrient (supplement or nitrogen) needed to reach half theoretical maximum growth response; RESPmax, theoretical maximum cattle weight gain and dry herbage mass availability, stocking rate, and cattle growth during 11 days; SR, stocking rate. * Corresponding author. Tel.: ; fax: address: rlana@ufv.br (R.P. Lana). 1 Department of Animal Science, Cornell University, Ithaca, NY 14853, USA. 1. Introduction Brazil has the largest commercial cattle population of the world, about 185 million animals in 22, which are commonly raised on pasture and supplemented with minerals. To increase animal performance, concentrate supplementation has been increasingly recommended for growing and finishing cattle on pasture, but the efficiency of its use on animal production has not been completely evaluated /$ - see front matter D 25 Elsevier B.V. All rights reserved. doi:1.116/j.livprodsci

2 22 R.P. Lana et al. / Livestock Production Science 98 (25) In a recent study (Lana, 24), low animal responses were verified using intermediate to high levels of concentrate. Growing cattle grazing tropical pastures during the dry season gained.1.14 kg/kg concentrate and feedlot cattle gained.1 kg/kg, giving a ratio of concentrate to gain of 7 to 1:1 for pasture and 1:1 for feedlot animals. Similarly, lactating Holstein and crossbred cows grazing pastures produced.6 F.4 kg milk/kg concentrate. Supplement conversion by growing cattle on pasture lower than 3 kg/kg accretion in daily gain (3:1) indicates nitrogen deficiency, and supplement conversion that is equal to or greater than 8:1 is typical of energy supplementation and represents inefficiency of nutrient utilization due to negative associative effects (Bodine and Purvis, 23). In a review of production and digestion data of milking cows supplemented on pasture, Bargo et al. (23) reported that the marginal response to increasing amounts of concentrates has been described as curvilinear (i.e., the marginal increase in milk per kilogram of concentrate decreases as the amount of concentrate increases). Similar findings were observed with growing animals (Goes, 24) and fertilized pastures (Moreira et al., 24a,b). The objective of this study was to demonstrate the application of Lineweaver Burk data transformation to explain animal and plant responses as a function of nutrient supply. 2. Materials and methods The effect of different levels of concentrate supplementation in the performance of steers reared on tropical pasture during the dry season (5% TDN and 4% CP) was evaluated. Fifty-five 1-month-old steers averaging 226 kg of body weight (BW) were used in this study following a completely randomized design. The dietary treatments consisted of five levels of supplement (%,.12%,.25%,.5%, and 1% of BW/animal/day). The supplements contained 24% crude protein, based on corn and soybean meal. Minerals were given separately ad libitum. In a subsequent study, tropical pastures (Brachiaria decumbens) were fertilized with four rates of nitrogen (75, 15, 225, and 3 kg N/ha/year) in three applications during the rainy season. A randomized block design with two replicates and eight experimental units (paddocks of.3 ha) was used. Dry herbage mass availability, stocking rate, and body weight gain of the animals during 11 days were evaluated. Dry herbage mass availability was evaluated three times during the 11-day period. Pasture height (2 cm) was estimated using a graduated ruler every week in 5 random points in each paddock. A continuous grazing management with 23 kg of steers and variable stocking rate (put and take technique) was used to control pasture height. The untreated control data of dry herbage mass availability, stocking rate, and body weight gain of the animals during 11 days were calculated from several studies developed previously. Linear regressions of the reciprocal of the animal (average daily gain) and plant (dry herbage mass availability, stocking rate, and cattle growth during 11 days) responses as a function of the reciprocal of nutrient supply were developed. This technique is called the Lineweaver Burk equation (Champe and Harvey, 1994), and the model is as follows: 1=Y ¼ a þ bxð1=x Þ where: Y =animal and plant responses (animal average daily gain; dry herbage mass availability, stocking rate, or cattle growth during 11 days), a = intercept, b = coefficient of the linear regression, and X = amount of nutrient (kg supplement/animal/day, or kg nitrogen/ ha/year). The theoretical maximum average daily gain (ADG) and dry herbage mass availability, stocking rate, and cattle growth during 11 days were obtained by the reciprocal of the intercept (RESPmax = 1/a). The amount of nutrient (X ) needed to reach.5 (NUTR 5 RESPmax ),.6,.7,.8,.9, and.95 of the theoretical maximum response was obtained from the model presented above by replacing Y by 1/a proportion response. The amount of nutrient needed to reach half theoretical maximum response (NUTR 5 RESPmax ) can also be obtained, dividing the coefficient of the linear regression by the intercept (b/a). 3. Results The response in weight gain of growing cattle grazing tropical pasture during the dry season as a

3 R.P. Lana et al. / Livestock Production Science 98 (25) function of concentrate supply was curvilinear; the concentrate conversion (kg supplement/kg weight gain) ranged between 1.5 and 4:1, comparing the treatment with the previous one (Fig. 1A). Linear regression of the reciprocal of ADG as a function of the reciprocal of concentrate supply is shown in Fig. 1B. The regression equation had a good fit and good estimates of ADG were obtained (Fig. 1C). Fig. 1D shows decreased response in the ADG by increasing concentrate supply. Based on the supplement used in this study, the theoretical maximum ADG (ADGmax) was.75 kg/ animal/day (or 1/a = 1/1.33) and the amount of supplement needed to reach half maximum response (SUPPL 5 ADGmax) was.2 kg/animal/day, obtained by dividing the coefficient of the linear regression by the intercept (b/a =.26/1.33) or by solving the following equation for SUPPL: 1/((1/1.33).5)=(.261/SUPPL) Responses of.6,.7,.8,.9, and.95 of the theoretical maximum weight gain occurred in levels of.29,.45,.77, 1.72, and 3.54 kg supplement/ animal/day, showing a reduction in response with increase in supplementation. The half maximum response in weight gain occurred in value next to 17.9 times lower supplement or.56 of supplementation needed to reach.95 of maximum weight gain. Linear regressions of the reciprocal of dry herbage mass availability, stocking rate, and weight gain of growing cattle during 11 days of the rainy season in tropical pasture (B. decumbens) as a function of the reciprocal of nitrogen fertilization showed similar high determination coefficients (Fig. 2B, D, and F), and allowed good parameter estimates, generally close to the observed values (Fig. 2A, C, and E). In all cases, there was a reduction in the response by increasing nitrogen fertilization. The theoretical maximum dry herbage mass availability (DHMmax) was 9 ton/ha (DHMmax =1/a =1/.111), and the amount of nitrogen needed to reach half maximum response (NITR 5 DHMmax ) was 28.1 kg N/ha/year (b/a =.312/.111) (Fig. 2A and B). Responses of.6,.7,.8,.9, and.95 of the DHMmax occurred in levels of 47, 72, 124, 279, and 589 kg of N. The half maximum response occurred in value next to 2.8 times lower nitrogen, or.48 of nitrogen fertilization needed to reach.95 of maximum response. The theoretical maximum stocking rate (SRmax) was 6.49 animal unit (AU)/ha (SRmax = 1/.154) and ADG (kg/animal/day) (1.5:1) (7.:1) (4:1) A Supplement intake (kg/animal/day) 1/ADG (kg/day) y = x r 2 = /Supplement intake (kg/animal/day) B ADG (kg/animal/day) ADGobs ADGest C Supplement intake (kg/animal/day) % ADGmax Supplement intake (kg/animal/day) D Fig. 1. Average daily weight gain (ADG) as a function of supplement intake (A), in which the values between parentheses represent concentrate conversion in kilograms per kilogram of gain, in relation to the previous treatment; reciprocal of ADG as a function of reciprocal of supplement intake (B); observed (ADGobs) and estimated (ADGest) ADG as a function of supplement intake (C); and response on ADG as a function of supplement intake (D).

4 222 R.P. Lana et al. / Livestock Production Science 98 (25) DHM (kg/ha) BWG (kg/ha/11 d) SR (AU/ha) DHMobs DHMest N (kg/ha) SRobs SRest A C N (kg/ha) N (kg/ha) BWGobs BWGest E 1/DHM (kg/ha) 1/BWG (kg/ha/11 d) B y = x r 2 = /N (kg/ha) 1/SR (AU/ha) y = x r 2 =.98 D /N (kg/ha) y = x r 2 = /N (kg/ha) Fig. 2. Dry herbage mass availability (DHM) of Brachiaria decumbens pasture as a function of nitrogen fertilization, N (A); reciprocal of DHM as a function of reciprocal of N (B); stocking rate (SR) as a function of N (C); reciprocal of SR as a function of reciprocal of N (D); body weight gain (BWG) as a function of N (E); and reciprocal of BWG as a function of reciprocal of N (F). F the amount of nitrogen needed to reach half maximum response (NITR 5 SRmax ) was 7.8 kg N/ha/year (1.9/.154) (Fig. 2C and D). Similarly, responses of.6,.7,.8,.9, and.95 of the SRmax occurred in levels of 16, 165, 283, 636, and 1341 kg of N. The half maximum response occurred in.53 of nitrogen fertilization needed to reach.95 of maximum response. The theoretical maximum weight gain by growing cattle during the rainy season (GAINmax) was 1 kg/ha/11 days (GAINmax = 1/.1) and the amount of nitrogen needed to reach half maximum response (NITR 5 GAINmax ) was 123 kg N/ha/year (.123/.1) (Fig. 2E and F). Responses of.6,.7,.8,.9, and.95 of the GAINmax occurred in levels of 185, 287, 492, 117, and 2337 kg of N. The half maximum response occurred in.53 of nitrogen fertilization needed to reach.95 of maximum response. 4. Discussion Monod (1949) verified that microbial growth rate was dependent of substrate concentration and both were related to the saturation kinetics typical of enzymatic systems. Russell (1984) confirmed that bacteria behave like enzymes because they present a curvilinear response to growth rate as a function of substrate supply, according to the model of Michaelis Menten, presented as following: k =(k max S)/(k s +S), where k is specific growth rate, k max is the maximum growth rate, S is substrate concentration, and k s is the

5 R.P. Lana et al. / Livestock Production Science 98 (25) concentration of substrate that allows the half maximum growth rate. The statistical technique, Lineweaver Burk data transformation, allows finding the constants k max and k s of the Michaelis Menten equation (Russell, 1984), by linear regression analyses of the reciprocal of microbial growth rate as a function of the reciprocal of substrate concentration. The value k max is obtained by the reciprocal of the intercept of the linear regression equation (1/a); and k s by dividing the slope by the intercept (b/a). In the same fashion, the curvilinear response on ADG (kg/animal/day) (Fig. 1) is similar to that described by Michaelis Menten for enzymatic systems and by Russell (1984) for microbial growth rate. This response can be observed in other situations, too, such as the response of pastures to fertilization (Fig. 2), and it can have large practical and economic importance for agriculture production in the tropics. The low availability of nutrients in the soil and the low nutritive value of the feeds, especially tropical forages, cause undernourished plant and animals to respond efficiently at low levels of nutrient supply (i.e., the k s constant (amount of substrate that allows half maximum growth rate response) is extremely low). The theoretical half maximum response of the ADG of growing cattle supplemented while grazing tropical pastures during the dry season, and the dry herbage mass availability, stocking rate, and cattle weight gain (kg/ha/11 days) in tropical pasture fertilized with nitrogen during the rainy season occurred in values from 17.9 to 2.8 times lower concentrate supplement or nitrogen fertilization, or.48 to.56 of the amount needed to have a.95 of maximum responses (Figs. 1 and 2). The amount of nitrogen fertilization needed to reach.95 maximum response in dry herbage mass availability, stocking rate, and cattle weight gain during the rainy season was 589, 1341, and 2337 kg, respectively. These values were overestimated by extrapolation of the regression equations, since the highest treatment level was 3 kg N/ha. Therefore,.8 maximum responses can be verified with 124, 283, and 492 kg of nitrogen, respectively, which are reasonable levels. More research is needed, including treatments with higher levels of nitrogen, in order to reach a plateau in plant growth response, and to avoid overestimation of fertilization needed to reach high plant response. A decreased response in milk production by increasing concentrate supply and progressive decrease in the net income for levels of supplementation above 2.5 kg concentrate/cow/day have been reported (Gomide, 1998; Bargo et al., 23). Studies conducted in North Australia also showed a decreased response in milk production with an increase of nitrogen fertilization in pasture of Chloris gayana. The response was from 8 to 4.5 kg milk/kg nitrogen, by increasing nitrogen levels from to 15 and from 15 to 6 kg/ha/year, respectively (Cowan et al., 1995 cited by Assis, 1997). Nonetheless, the profitability of animal supplementation and pasture fertilization depends on the favorable ratio of meat and/or milk price to supplement and/or fertilizer cost and the efficiency of their use, expressed in accretion of weight gain or milk production, per kilogram of feed supplement or fertilizer. 5. Conclusions The curvilinear response of animal and plant growth rate as a function of nutrient supply is similar to the described by Michaelis Menten for enzymatic systems and microbial growth, being explained efficiently by the Lineweaver Burk data transformation. The half maximum plant and animal growth rate responses to the nutrient supply were found to be of the amount needed to cause.95 of theoretical maximum responses. References Assis, A.G., Production of milk under grazing in Brazil. In: Gomide, J.A., Garcia, R., Pereira, O.G., Obeid, J.A., Fonseca, D.M., Rodrigues, L.F. (Eds.), Simpósio Internacional sobre Produção Animal em Pastejo. Suprema Gráfica, Viçosa, MG, Brazil, pp Bargo, F., Muller, L.D., Kolver, E.S., Delahoy, J.E., 23. Invited review: production and digestion of supplemented dairy cows on pasture. J. Dairy Sci. 86, Bodine, T.N., Purvis, H.T., 23. Effects of supplemental energy and/or degradable intake protein on performance, grazing behavior, intake, digestibility, and fecal and blood indices by beef steers grazed on dormant native tallgrass prairie. J. Anim. Sci. 81,

6 224 R.P. Lana et al. / Livestock Production Science 98 (25) Champe, P.C., Harvey, R.A., Biochemistry, 2nd ed. J.B. Lippincott Company, Philadelphia. Goes, R.H.T.B., 24. Performance of steers reared at pasture, receiving different levels and frequency of supplementation, during the autumn, in Brazilian Amazonian region. DS thesis, Universidade Federal de Viçosa, MG, Brazil. Gomide, J.A., Fatores da produção de leite a pasto. In: Pereira, A.L., Farias, D.E., Macedo, F.V.F., Cardoso, G.N., Wernersbach Filho, H.L., Martin, R.M. (Eds.), Anais do Congresso Nacional dos Estudantes de Zootecnia. Suprema Gráfica, Viçosa, MG, Brazil, pp Lana, R.P., 24. Efficiency of use of concentrate ration on weight gain and milk production by cattle under tropical pasture and intensive conditions in Brazil. J. Anim. Sci. 82 (Suppl. 1), 222. Monod, J., The growth of bacterial cultures. Annu. Rev. Microbiol. 3, Moreira, L.M., Fonseca, D.M., Mistura, C., Martuscelo, J.A., Assis, A.J., Oliveira, A.S., 24. Forage availability and structural characteristics of Brachiaria decumbens fertilized with nitrogen, under continuous grazing. Reunião Anual da Sociedade Brasileira de Zootecnia, Campo Grande, MS, Brazil. Moreira, L.M., Fonseca, D.M., Morais, R.V., Martuscelo, J.A., Assis, A.J., Fagundes, J.L., 24. Performance of steers raised in pasture of Brachiaria decumbens fertilized with nitrogen, under continuous grazing. Reunião Anual da Sociedade Brasileira de Zootecnia, Campo Grande, MS, Brazil. Russell, J.B., Factors influencing competition and composition of the ruminal bacterial flora. In: Gilchrist, F.M.C., Mackie, R.I. (Eds.), The Herbivore Nutrition in the Subtropics and Tropics. Science Press, Craighall, South Africa, pp