Fractional-Order Models for Biochemical Processes

Biochemical processes present complex mechanisms and can be described by various computational models. Complex systems present a variety of problems, especially the loss of intuitive understanding. The present work uses fractional-order calculus to obtain mathematical models for erythritol and mannitol synthesis. The obtained models are useful for both prediction and process optimization. The models present the complex behavior of the process due to the fractional order, without losing the physical meaning of gain and time constants. To validate each obtained model, the simulation results were compared with experimental data. In order to highlight the advantages of fractional-order models, comparisons with the corresponding integer-order models are presented.

Erythritol and mannitol clearances with taurocholate and secretin-induced cholereses.

The biliary clearances of [14C]erythritol (Cery) and [3H]mannitol (Cmann) were measured simultaneously in dogs during cholereses induced by sodium taurocholate and by secretin. Cery increased equally with the increase in bile flow induced by taurocholate, whereas mannitol entry into bile was partially restricted; deltaCery/deltabile flow averaged 0.96; deltaCmann/deltaCery averaged 0.81. Values for erythritol clearance exceeded bile flow by a constant volume over a wide range of bile flows, a result that suggests distal reabsorption of a fixed amount of fluid, independent of canalicular bile production. During secretin-induced choleresis both Cery and Cmann accompanied 30-40% of the increase in bile flow, and the ratio of Cmann/Cery was 1.02. Thus the secretin-responsive region is permeable to both erythritol and mannitol. This affects the extent to which measured erythritol clearance accurately reflects canalicular bile formation; Cery may underestimate or overestimate canalicular bile flow. The electrolyte composition of bile remained relatively constant over a broad range of bile flows although the characteristics of taurocholate- and secretin-induced biles differed from each other. Taurocholate-stimulated bile was virtually isotonic. Secretin-induced bile had a high total concentration of electrolyte (mean concentration 367 meq/liter) rich in chloride and bicarbonate and was hypertonic.

On the Mechanism of Isoosmotic Transport of Fluid Across the Small Intestine. The Effect of the Staverman Reflection Coefficient of the Solute Used to Increase the Osmolality of the Mucosal Solution on the Composition of the Absorbate

The objective of the present study was to investigate the mechanism by which the fluid transported across the small intestine becomes isoosmotic with the mucosal solution. The osmolality of the mucosal solution of a unilateral preparation (the serosal side was not bathed) was increased with water soluble, nonelectrolyte solutes of different Staverman reflection coefficients (σ), and the composition of the undiluted absorbate was studied. The solutes ('hyperosmotic agents') used were formamide, urea, erythritol, and mannitol. In a series of separate experiments, utilizing a method based on potential difference depression, we found that the σ's of these solutes in the hamster small intestine were 0.26, 0.85, 0.93, and 1.00, respectively. Our data on transport across the unilateral preparation showed that when the intestine was incubated in an isotonic mucosal solution (Krebs–Ringer bicarbonate solution containing 10 mM glucose, 292 mosmol/kg), the absorbate was essentially isotonic, although its composition was significantly different from that of the mucosal solution. When the osmolality of the mucosal solution was increased to 342, 392, or to 442 mosmol/kg with any of the hyperosmotic agents, the absorbate was always isoosmotic with the mucosal solution. With formamide (low σ) as the hyperosmotic agent, the concentration of electrolytes and glucose in the absorbate was the same as that in the absorbate of the control preparation (incubated in the isotonic mucosal solution), and the transported fluid became isoosmotic with the mucosal solution exclusively due to the presence of formamide in the absorbate. When the osmolality of the mucosal solution was increased with urea, erythritol, or mannitol, the concentration of these hyperosmotic agents in the absorbate decreased linearly with the increase in their σ, and the absorbate became isoosmotic with the mucosal solution due to a linear increase in the concentration of electrolytes and glucose. In addition, we found that the transport of fluid, solutes, and fluid/solute (ml/mmol per gram dry intestine) decreased linearly with the increase in σ of the hyperosmotic agents. Further calculation of the data showed that the increase in the concentration of electrolytes and glucose with the increase in σ of the hyperosmotic agents was almost exclusively due to a linear decrease in fluid/solute transport.