Kinetic modeling in physiology

The author discusses the construction of model biochemical/physiological systems to fit experimental data which is always incomplete. He suggests that the first experiments on any system should be first-order (usually tracer) perturbations of steady-state systems. The proposed model can then be given a preliminary fit to the data; criteria for best fit, consistency, and uniqueness of fit are suggested. More data may then be obtained by perturbations at another steady-state, and finally by studying transient situations.References are included to some of the author's own publications in which these matters are discussed in detail.     

Structured modeling of the anaerobic digestion of biomass particulates

Anaerobic digestion of biological organic particulates to methane has been described by a structured mathematical model based on multiple-reaction stoichiometry, conventional material balances, and liquid phase equilibrium chemistry. A general stoichiometric treatment for any set of multiple biological reactions is derived based on a unit mass of oxggen equivalents of the reactions limiting substrate. The model agrees well with two existing experimental studies of anaerobic digestion of biomass particulates. Hypothetical computer simulations are presented to illustrate possible instabilities of the anaerobic process under various operating scenarios.     

Regulatory volume decrease and P receptor signaling in fish cells: mechanisms, physiology, and modeling approaches

For animal cell plasma membranes, the permeability of water is much higher than that of ions and other solutes, and exposure to hyposmotic conditions almost invariably causes rapid water influx and cell swelling. In this situation, cells deploy regulatory mechanisms to preserve membrane integrity and avoid lysis. The phenomenon of regulatory volume decrease, the partial or full restoration of cell volume following cell swelling, is well-studied in mammals, with uncountable investigations yielding details on the signaling network and the effector mechanisms involved in the process. In comparison, cells from other vertebrates and from invertebrates received little attention, despite of the fact that e.g. fish cells could present rewarding model systems given the diversity in ecology and lifestyle of this animal group that may be reflected by an equal diversity of physiological adaptive mechanisms, including those related to cell volume regulation. In this review, we therefore present an overview on the most relevant aspects known on hypotonic volume regulation presently known in fish, summarizing transporters and signaling pathways described so far, and then focus on an aspect we have particularly studied over the past years using fish cell models, i.e. the role of extracellular nucleotides in mediating cell volume recovery of swollen cells. We, furthermore, present diverse modeling approaches developed on the basis of data derived from studies with fish and other models and discuss their potential use for gaining insight into the theoretical framework of volume regulation.     

Teaching pulmonary gas exchange physiology using computer modeling

Students often have difficulty understanding the relationship of O(2) consumption, CO(2) production, cardiac output, and distribution of ventilation-perfusion ratios in the lung to the final arterial blood gas composition. To overcome this difficulty, I have developed an interactive computer simulation of pulmonary gas exchange that is web based and allows the student to vary multiple factors simultaneously and observe the final effect on the arterial blood gas composition (available at www.siumed.edu/medicine/pulm/vqmodeling.htm). In this article, the underlying mathematics of the computer model is presented, as is the teaching strategy. The simulation is applied to a typical clinical case drawn from the intensive care unit to demonstrate the interdependence of the above factors as well as the less-appreciated importance of the Bohr and Haldane effects in clinical pulmonary medicine. The use of a computer to vary the many interacting factors involved in the arterial blood gas composition appeals to today's students and demonstrates the importance of basic physiology to the actual practice of medicine.     

Structured population on two patches: modeling dispersal and delay

We derive from the age-structured model a system of delay differential equations to describe the interaction of spatial dispersal (over two patches) and time delay (arising from the maturation period). Our model analysis shows that varying the immature death rate can alter the behavior of the homogeneous equilibria, leading to transient oscillations around an intermediate equilibrium and complicated dynamics (in the form of the coexistence of possibly stable synchronized periodic oscillations and unstable phase-locked oscillations) near the largest equilibrium.     

Structured modeling of a microbial system: I. A theoretical study of lactic acid fermentation

Most fermentation models presented in the literature are unstructured, i.e., the biomass composition is assumed constant during all operating conditions. These models are unable to simulate experiments carried out at widely different operating conditions. It is therefore interesting to examine simple structured models where knowledge of the cell physiology is taken into account in the modeling phase. In this article, a simple structured model is presented. The model is based on experimental work with the lactic acid bacteria Streptococcus cremoris, but due to the similarities in basic metabolism for many microorganisms it is applicable also for other fermentation system. The basic assumption in the model is that the biomass can be divided into two parts (compartments)-an active part and a mainly inactive structural part. The size of the active part has a pivotal role in the model.     

Nonlinear modeling of the atrioventricular node physiology in atrial fibrillation

A nonlinear model of the atrioventricular (AV) node physiology in atrial fibrillation (AF) is proposed based on three assumptions: (1) normal distribution of atrial impulses, (2) right-skewed distribution of R-R intervals, (3) increase in the refractory period of the AV node due to rapid bombardment from the atria. Simulation resulted in the following conclusions, all of which are in agreement with previous experience: (1) the entry speed of atrial impulses into the AV node in AF is inversely proportional to the ventricular rate, (2) the autocorrelation function of R-R intervals is zero at all delays, (3) a newly introduced index, sign of first difference, has a negative autocorrelation function at the first delay and zero ones at all others. In spite of its simplicity, the model is able to explain what happens in atrial premature complexes, sinus tachycardia and sinus bradycardia. Different rhythms, some of which rarely seen clinically, can be reproduced by changing input patterns or by slightly manipulating the model parameters. In order to make possible a long irregular time series of R-R interval, aperiodic changes in atrial signals are shown to be necessary. In conclusion, we proposed a simple model for the AV node physiology capable of explaining the previously known facts about AF as well as predicting interesting properties of some other supraventricular arrhythmias.     

Structured motifs search.

In this paper, we describe an algorithm for the localization of structured models, i.e. sequences of (simple) motifs and distance constraints. It basically combines standard pattern matching procedures with a constraint satisfaction solver, and it has the ability, not present in similar tools, to search for partial matches. A significant feature of our approach, especially in terms of efficiency for the application context, is that the (potentially) exponentially many solutions to the considered problem are represented in compact form as a graph. Moreover, the time and space necessary to build the graph are linear in the number of occurrences of the component patterns.     

Gamete physiology, fertilization and egg activation in teleost fish

The fertilization and activation of fishoocytes are vital, but unfortunatelyoverlooked, processes in fisheries research.This paper sets out to review our presentunderstanding of these important events inteleost fish and, drawing comparisons withmammalian research, to highlight areas in whichresearch effort is urgently required. Presently, the commercial culture of manyimportant freshwater, but especially marine,teleosts is beset by problems associated withfertilization, hatching and early embryonicdevelopment. These problems have beenparticularly acute in certain species leadingto the application of spawning inductiontechnologies in an effort to optimizeproduction. Increased knowledge of theprocesses of egg activation and fertilizationin these groups of fish is likely to makesignificant contribution to commercialaquaculture. Studies of a wide variety ofanimal and plant species has demonstrated thatdevelopment at fertilization is triggered by anincrease in intracellular Ca²⁺concentration within the egg that occurs aseither a single transient or a series ofdistinctive oscillations depending upon thespecies under investigation. This increase inintracellular Ca²⁺ activates the egg andalso appears to play an important role in laterembryonic development. Teleost reproductivestrategies and more importantly, teleostoocytes and spermatozoa, exhibit a remarkablevariety of adaptations. Currently, studies ofegg activation in teleosts are confined tolaboratory species such as medaka Oryziaslatipes and zebrafish Brachydanio rerio.Nevertheless, even between these two species,although an increase in intracellular Ca²⁺appears to be the trigger in both cases, themechanism of Ca²⁺ release may be quitedifferent. Activation in medaka is initiatedonly through direct contact with conspecificsperm, suggesting the involvement of asperm-specific factor, while zebrafish eggsappear to require only contact with theexternal spawning medium. In view of the highlyvariable fertility rates evident in manycommercially cultured teleosts, it could bevery rewarding to investigate the mechanism ofegg activation in representative teleost groupsusing the findings and theories emerging fromother animal groups as a starting point. Inorder to successfully conduct such aninvestigation, it will be necessary to employ acombination of physiological, molecular andrecombinant approaches.     

Observations on the blood physiology of five South African freshwater fish

Various parameters of the blood physiology of five South African species of fish have been investigated. The results show that plasma and serum samples differ in electrophoretic pattern, and also in the number of fractions and the protein concentration of these fractions. Red blood cell measurements, hemoglobin concentrations and blood glucose concentrations differ from fish to fish, and appear to be species specific. The values reported here are comparable with similar results obtained by other workers.     

The physiology of hyper-salinity tolerance in teleost fish: a review

Hyper-saline habitats (waters with salinity >35 ppt) are among the harshest aquatic environments. Relatively few species of teleost fish can tolerate salinities much above 50 ppt, because of the challenges to osmoregulation, but those that do, usually estuarine, euryhaline species, show a strong ability to osmoregulate in salinities well over 100 ppt. Typically, plasma Na⁺ and Cl⁻ concentrations rise slowly or not at all up to about 65 ppt. At higher salinities ion levels do rise, but the increase is small relative to the magnitude of increase in concentrations of the surrounding water. A number of adjustments are responsible for such strong osmoregulation. Reduced branchial water permeability is indicated by the observation that with the exposure to hyper-salinities drinking rates rise more slowly than the branchial osmotic gradient. Lower water permeability limits osmotic water loss and greatly reduces the salt load incurred in replacing it. Still, increased gut Na⁺/K⁺-ATPase (NAK) activity is necessary to absorb the larger gut salt load and increased HCO₃ ⁻ secretion is required to precipitate Ca²⁺ and some Mg²⁺ in the imbibed water to facilitate water absorption. All Na⁺ and Cl⁻ taken up must be excreted and increased branchial salt excreting capacity is indicated by elevated mitochondrion-rich cell density and size, gill NAK activity and expression of chloride channels. Excretion of Na⁺ and Cl⁻ occurs against a larger gradient than in seawater and calculation of the equilibrium potential for Na⁺ across the gill epithelium indicates that the trans-epithelial potential required for excretion of Na⁺ climbs with salinity up to about 65 ppt before leveling off due to the increasing plasma Na⁺ levels. During acute transition to SW or mildly hyper-saline waters, some species have shown the ability to upregulate branchial NAK activity rapidly and this may play an important role in limiting disturbances at higher salinities. It does not appear that the opercular epithelium, which in SW acts in a way that is functionally similar to the gills, continues to do so in hyper-saline waters. Little is know about the hormones involved in acclimation to hyper-salinity, but the few studies available suggest a role for cortisol, but not growth hormone and insulin-like growth factor. Despite the increased transport capacity evident in both the gill and gut in hyper-saline waters there is no clear trend toward increased metabolic rate. These studies provide a general outline of the mechanisms of osmoregulation in these species, but significant questions still remain.     

Structured morphological modeling as a framework for rational strain design of Streptomyces species

Successful application of a computational model for rational design of industrial Streptomyces exploitation requires a better understanding of the relationship between morphology—dictated by microbial growth, branching, fragmentation and adhesion—and product formation. Here we review the state-of-the-art in modeling of growth and product formation by filamentous microorganisms and expand on existing models by combining a morphological and structural approach to realistically model and visualize a three-dimensional pellet. The objective is to provide a framework to study the effect of morphology and structure on natural product and enzyme formation and yield. Growth and development of the pellet occur via the processes of apical extension, branching and cross-wall formation. Oxygen is taken to be the limiting component, with the oxygen concentration at the tips regulating growth kinetics and the oxygen profile within the pellet affecting the probability of branching. Biological information regarding the processes of differentiation and branching in liquid cultures of the model organism Streptomyces coelicolor has been implemented. The model can be extended based on information gained in fermentation trials for different production strains, with the aim to provide a test drive for the fermentation process and to pre-assess the effect of different variables on productivity. This should aid in improving Streptomyces as a production platform in industrial biotechnology.     

Effects of dietary fatty acids on the respiratory and cardiovascular physiology of fish

In animals, the composition of fatty acids (FAs) in body pools reflects dietary intake. This paper reviews evidence that the manipulation of tissue lipids of farmed fish, by feeding them different natural oils, can have significant effects on their respiratory and cardiovascular physiology. Sturgeon and eels with tissue lipids rich in highly unsaturated FAs of the n-3 series (n-3HUFAs, accumulated from dietary menhaden oil) had significantly lower metabolic rates than fish with tissues rich in saturated FAs (SFAs, from coconut oil), although they grew equally well. In sturgeon, the difference in metabolism influenced tolerance of hypoxia. Degrees of hypoxia that depressed oxygen uptake and spontaneous activity in fish rich in SFAs had no such effects on fish rich in n-3HUFAs. In the isolated sturgeon heart working in vitro, reduced oxygen supply depressed the performance of hearts with lipids rich in SFAs but not that of hearts rich in n-3HUFAs. In salmon fed diets with graded mixtures of menhaden and canola oils, there was no relationship between tissue n-3HUFA content (from menhaden oil) and any measured aspect of swimming performance, but a linear relationship between maximum sustainable swimming speed and muscle oleic acid levels (from canola oil). Such exploratory studies indicate that an animal's responses to its environment may be profoundly affected by the oils and FAs it consumes in its diet.     

Structured modeling of recombinant protein production in batch and fed-batch culture of baculovirus-infected insect cells

The infection of insect cells with baculovirus was described in a mathematical model as a part of the structured dynamic model describing whole animal cell metabolism. The model presented here is capable of simulating cell population dynamics, the concentrations of extracellular and intracellularviral components, and the heterologous product titers. The model describes the whole processes of viral infection and theeffect of the infection on the host cell metabolism. Dynamic simulation of the model in batch and fed-batch mode gave goodagreement between model predictions and experimental data. Optimum conditions for insect cell culture and viral infectionin batch and fed-batch culture were studied using the model.     

Sympatric variability of isotopic baselines influences modeling of fish trophic patterns

Stable isotope signatures of freshwater snails and mussels have been established as a convenient baseline measurement at the primary consumer level for food-web coupling studies. We measured δ¹⁵N and δ¹³C of primary consumers, including mussels (Anodonta woodiana, Cristaria plicata, and Unio douglasiae), snails (Bellamya aeruginosa and Hippeutis sp.), and zooplankton from the same habitat within a shallow eutrophic lake. Primary consumers showed positive relationship between δ¹⁵N and δ¹³C, indicating a linkage between planktonic and benthic habitats in this system. The variation in isotope ratios was higher in short-lived primary consumers (zooplankton) compared with the long-lived primary consumers (mussels and snails), suggesting limited availability of short-lived primary consumers as isotopic baselines in aquatic food-web assessment. Significant differences in isotope ratios were also found among three species of mussels, and when using these mussels separately as pelagic baselines to calculate trophic position and contribution of planktonic and benthic sources of fishes, bias and even misestimates were observed. This finding suggests that caution is needed when multiple primary consumers coexist in the same habitat, and it is important to assess potential effects of different baselines used.