Long-term prediction of fish growth under varying ambient temperature using a multiscale dynamic model

Abstract

Background: Feed composition has a large impact on the growth of animals, particularly marine fish. We have developed a quantitative dynamic model that can predict the growth and body composition of marine fish for a given feed composition over a timespan of several months. The model takes into consideration the effects of environmental factors, particularly temperature, on growth, and it incorporates detailed kinetics describing the main metabolic processes (protein, lipid, and central metabolism) known to play major roles in growth and body composition.

Results: For validation, we compared our model's predictions with the results of several experimental studies. We showed that the model gives reliable predictions of growth, nutrient utilization (including amino acid retention), and body composition over a timespan of several months, longer than most of the previously developed predictive models.

Conclusion: We demonstrate that, despite the difficulties involved, multiscale models in biology can yield reasonable and useful results. The model predictions are reliable over several timescales and in the presence of strong temperature fluctuations, which are crucial factors for modeling marine organism growth. The model provides important improvements over existing models.

Figure 1

Comparison to experiments. Prediction of growth under conditions of varying temperature: (a) Simulation of growth in the new model (red solid), old model (red dashed circles), and experimental data (circle dashed) with the FPH15 diet given every 24 hours over the course of 68 days [23]. The black dashed curve indicates the temperature fluctuations encountered during the experiments.

Figure 2

Body composition. Body composition (% total wet body mass) with the FPH15 diet given every 24 hours over the course of 68 days. Simulated crude protein (□) and lipid (■) in the new model compared to lipid (●) in the old model. Experimental data on protein and lipid [23] are indicated by (△) and (▲), respectively.

Figure 3

Long-term predictions. Long-term prediction: Body mass (left) and body fat and protein (right) over a timespan of 121 days with strong temperature variations (left, gray dotted); two different feeding strategies are shown for the new model (black curves), the model from [19] (blue curves), and experimental results (circles).

Figure 4

Short timescale regulation. Short timescale regulation: ATP levels (left) and AcCoA levels (right) simulated using the same conditions as in Figure 3, presented here for days 80-83 (given also by hours) for the new model (black dashed curve), the old model [19] (blue curve), and experimental results (circles [24], squares [25], diamonds [26]). Due to improved regulation in the TCA cycle, energy homeostasis (constant ATP levels) is predicted more accurately in the new model (black dashed curve) compared to the old one (blue curve).

Figure 5

Short timescale dynamics. Short timescale dynamics: Comparison of simulated concentrations of several essential AAs with measurements from experiments on salmonids (rainbow trout) [27] (circles), experiments consisting of feeding with casein and AA diets [29] (full and empty squares, respectively), and casein-only diets [28] (triangles).

Figure 6

Effect of temperature. The effect of temperature after 68 days using the FM diet [23]: (a) Prediction of body mass as a function of temperature for the new model (blue dots) and the old model [19] (red squares). (b) Protein turnover rates K_g taken from: New model simulations (blue solid dots), previous model (red squares), [15] (dashed), [59] (triangle at 12°C), and [31] (diamond at 10°C), as a function of temperature.

Figure 7

Amino acid retention. Deviation of the AA retention (%) in the presented model (squares), and earlier model (circles) [23]. The dashed line indicates perfect prediction.

Figure 8

The model. A schematic representation of the model. The main processes in the model are lipid, protein, and TCA metabolism, which are interconnected by mass flow.

Figure 9

Protein metabolism sub-model. Overview of the protein metabolism model with arrows describing material flow. AAs are used for protein synthesis in a specific composition satisfying the profile of the tissue protein. Remaining AAs are broken down into TCA metabolites and enter the intermediate metabolism. Protein synthesis and degradation are energy and temperature dependent. The fraction f_p of AAs emerging from protein degradation is reused for protein synthesis, and the fraction f_t = 1 - f_p is broken down.

Figure 10

Modeled temperature. Modeled temperature-dependent prefactors of protein synthesis (dashed line, equation 4) and degradation (solid line, equation 7).

Figure 11

Lipid metabolism sub-model. Schematic drawing of lipid metabolism. Cytosolic AcCoA entering the lipid metabolism compartment from the intermediate metabolism is used for FA synthesis. FAs are either broken down, leading to AcCoA in the mitochondria, which fuels the TCA cycle, or are used for TAG synthesis, thereby increasing the body weight. ATP inhibits TAG degradation and FA breakdown. TAG deposit levels inhibit (⊗) TAG synthesis, and citrate levels in the mitochondria promote () FA synthesis.

Figure 12

Central metabolism sub-model. Regulation in the tricarboxylic acid (TCA) cycle model. Intermediates from AA catabolism enter the cycle, leading to NADH production. U_i represent regulatory functions. U_pdh and U_keto are inhibited (⊗) by ATP, whereas U_oxal and U_mal are promoted () by AcCoA and oxaloacetate, respectively.