Minimal model for human ventricular action potentials in tissue

Modeling the dynamics of wave propagation in human ventricular tissue and studying wave stability require models that reproduce realistic characteristics in tissue. We present a minimal ventricular (MV) human model that is designed to reproduce important tissue-level characteristics of epicardial, endocardial and midmyocardial cells, including action potential (AP) amplitudes and morphologies, upstroke velocities, steady-state action potential duration (APD) and conduction velocity (CV) restitution curves, minimum APD, and minimum diastolic interval. The model is then compared with three previously published human ventricular cell models, the Priebe and Beuckelmann (PB), the Ten Tusscher–Noble–Noble–Panfilov (TNNP), and the Iyer–Mazhari–Winslow (IMW). For the first time, the stability of reentrant waves for all four models is analyzed, and quantitative comparisons are made among the models in single cells and in tissue. The PB, TNNP, and IMW models exhibit quantitative differences in APD and CV rate adaptation, as well as completely different reentrant wave dynamics of quasi-breakup, stability, and breakup, respectively. All the models have dominant frequencies comparable to clinical values except for the IMW model, which has a large range of frequencies extending beyond the clinical range for both ventricular tachycardia (VT) and ventricular fibrillation (VF). The TNNP and IMW models possess a large degree of short-term memory and we show for the first time the existence of memory in CV restitution. The MV model also can be fitted to reproduce the dynamics of other models and is computationally more efficient: the times required to simulate the MV, TNNP, PB and IMW models follow the ratio 1:31:50:8084.     

Study of the combined action of an antibiotic and an immunostimulator using mathematical modeling

A mathematical model of antibiotic and immunostimulator (IMS) combined effect on various elements of the immune system and general state of patients with infectious diseases is described. The model was constructed as a system including 6 usual differential equations of the 1st order. With the use of this model and a computer many diverse variants of infection development under conditions of treatment with IMS at the background of antibiotic therapy were modeled. Ii was shown that IMS-antibiotic complexes markedly improved the indices of antibiotic therapy as compared to the use of the antibiotics alone. In combined use of IMS and antibiotics it was possible to lower the antibiotic doses without lowering the antimicrobial effect. The use of IMS at the optimal period led to balanced activation of the host specific and nonspecific resistance factors at the background of antibacterial therapy. The results of the mathematical modeling corresponded to the data on protective effect of salmozan (IMS) and doxycycline (antibiotic) combination in animals (albino mice). It was concluded that the described mathematical model was adequate for validation and optimization of schemes for combined use of IMS and antibacterial agents.     

A biophysical model of Sugarcane growth

Scientists predict that global agricultural lands will expand over the next few decades due to increasing demands for food production and an exponential increase in crop‐based biofuel production. These changes in land use will greatly impact biogeochemical and biogeophysical cycles across the globe. It is therefore important to develop models that can accurately simulate the interactions between the atmosphere and important crops. In this study, we develop and validate a new process‐based sugarcane model (included as a module within the Agro‐IBIS dynamic agro‐ecosystem model) which can be applied at multiple spatial scales. At site level, the model systematically under/overestimated the daily sensible/latent heat flux (by ?10.5% and 14.8%, H and λE, respectively) when compared against the micrometeorological observations from southeast Brazil. The model underestimated ET (relative bias between ?10.1% and –12.5%) when compared against an agro‐meteorological field experiment from northeast Australia. At the regional level, the model accurately simulated average yield for the four largest mesoregions (clusters of municipalities) in the state of São Paulo, Brazil, over a period of 16 years, with a yield relative bias of ?0.68% to 1.08%. Finally, the simulated annual average sugarcane yield over 31 years for the state of Louisiana (US) had a low relative bias (?2.67%), but exhibited a lower interannual variability than the observed yields.     

A biophysical model of lysozyme self-association.

The concentration dependence of the self-association of hen egg-white lysozyme was studied spectrophotometrically at pH 6, 25 degrees C, and low ionic strength within a concentration range of 2.5-50 micrograms/ml. Of several possible mathematical models, an ideal or nearly ideal two-stage model representing an equilibrium between monomers and dimers and between dimers and trimers best describes the data. The dimerization and trimerization constants were found to be 2.5 x 10(-2) and 38 x 10(-2). Dialysis experiments confirmed that the mechanism involves three associating species. A "head-to-tail" contact between the associating sites was inferred from dialysis studies of the effect of indole and imidazole derivatives on lysozyme self-association.     

A pharmacodynamic model for the action of the antibiotic imipenem onPseudomonas aeruginosa populationsin vitro

The standard method for measuringin vitro antibiotic efficacy is based on a point observation of bacterial activity 18 hours after inoculation. The method, while simple, forgoes significant information by ignoring the dynamics of the interations between antibiotic and bacteria. This paper proposes a simple dynamic model describing these interactions. The model consists of two non-linear differential equations of the S-system type. Its parameter values are estimated, through the minimization of residual errors, from data on the effect of the carbapenem antibiotic imipenem onPseudomonas aeruginosa. The model adequately describes the dynamic behavior of the bacterial populations in the presence of the antibiotic: beginning with drug administration, then through the decline of the bacterial population and possibly ending with bacterial resurgence.     

An antibiotic factory caught in action

The synthesis of aromatic polyketides, such as actinorhodin, tetracycline and doxorubicin, begins with the formation of a polyketide chain. In type II polyketide synthases (PKSs), chains are polymerized by the heterodimeric ketosynthase-chain length factor (KS-CLF). Here we present the 2.0-A structure of the actinorhodin KS-CLF, which shows polyketides being elongated inside an amphipathic tunnel approximately 17 A in length at the heterodimer interface. The structure resolves many of the questions about the roles of KS and CLF. Although CLF regulates chain length, it does not have an active site; KS must catalyze both chain initiation and elongation. We provide evidence that the first cyclization of the polyketide occurs within the KS-CLF tunnel. The mechanistic details of this central PKS polymerase could guide biosynthetic chemists in designing new pharmaceuticals and polymers.     

A basic biophysical model for bursting neurons

Presented here is a basic biophysical cell model for bursting, an extension of our previous model (Av-Ron et al. 1991) for excitability and oscillations. By changing a limited set of model parameters, one can describe different patterns of bursting behavior in terms of the burst cycle, the durations of oscillation and quiescence, and firing frequency.     

Structural origins of gentamicin antibiotic action.

Aminoglycoside antibiotics that bind to the ribosomal A site cause misreading of the genetic code and inhibit translocation. The clinically important aminoglycoside, gentamicin C, is a mixture of three components. Binding of each gentamicin component to the ribosome and to a model RNA oligonucleotide was studied biochemically and the structure of the RNA complexed to gentamicin C1a was solved using magnetic resonance nuclear spectroscopy. Gentamicin C1a binds in the major groove of the RNA. Rings I and II of gentamicin direct specific RNA-drug interactions. Ring III of gentamicin, which distinguishes this subclass of aminoglycosides, also directs specific RNA interactions with conserved base pairs. The structure leads to a general model for specific ribosome recognition by aminoglycoside antibiotics and a possible mechanism for translational inhibition and miscoding. This study provides a structural rationale for chemical synthesis of novel aminoglycosides.     

Mechanism of the antibiotic action pyocyanine.

Exposure of Escherichia coli growing in a rich medium to pyocyanine resulted in increased intracellular levels of superoxide dismutase and of catalase. When these adaptive enzyme syntheses were prevented by nutritional paucity, the toxic action of pyocyanine was augmented. The antibiotic action of pyocyanine was dependent upon oxygen and was diminished by superoxide dismutase and by catalase, added to the suspending medium. Pyocyanine slightly augmented the respiration of E. coli suspended in a rich medium, but greatly increased the cyanide-resistant respiration. Pyocyanine was able to cause the oxidation of reduced nicotinamide adenine dinucleotide, with O2- production, in the absence of enzymatic catalysis. It is concluded that pyocyanine diverts electron flow and thus increases the production of O2- and H2O2 and that the antibiotic action of this pigment is largely a reflection of the toxicity of these products of oxygen reduction.     

A biophysical model for buzz pollination in angiosperms

The stamens of most of the world's flowering plants are longitudinally dehiscent, releasing their pollen passively, whereupon floral visitors may collect it. In nearly 400 genera in 65 plant families, the anthers dehisce by means of short apical slits or true pores. In these forms, the small light pollen can only be efficiently released by native bees capable of vibrating these stamens. This intrafloral behavior propels pollen out of the pores striking the bees on their venters. It is then collected for use in larval cell provisions. Aspects of the historical development of this novel pollination syndrome, known as “buzz” or vibratile (equals vibrational) pollination, are presented including a discussion and figures of a poricidal anther, a buzzing bee and the model system.A biophysical model for the pollen/locule wall interactions resulting in pollen expulsion upon bee or artificial vibration is developed. The model was created with the morphology of anthers of Solanum (Solanaceae) in mind, but the results obtained are generally applicable to any apically dehiscent flower which is vibrated by bees to release pollen.The anthers were modeled as a tall rectangular box with an apical pore and containing numerous small particles. As the box vibrates, particles striking the walls rebound elastically. If a pollen grain strikes a receding wall, it loses energy. If a grain strikes an advancing wall, it gains energy in the collision. In each oscillation, there is a net gain in the energy of the particles. As the anther (box) is shaken, vibrational energy is transmitted from the pterothorax of the bees to the flower, the pollen grains gaining significant energy. As the energy increases and the particles begin to move about more and more vigorously, they will begin to escape through the hole in the box (or stamina] pore). The rate at which particles leave the box and time required to empty the box are calculated as functions of the geometry of the model system and the frequency of vibration.In order to test the influence of air currents, Bernolli effects and viscous drag, the flowers were mecahnically vibrated in vacuum. The pollen cloud thus produced was virtually unchanged ans so it seems unlikely that air plays any significant role in the phenomenon of vibrational pollen release.Finally, variables such as: inelastic interactions, electrostatic forces, slightly sticky pollen due to presence of “pollenkitt”, duration and types of bee buzzes are discussed in relation to the mathematical model presented.     

A biophysical model for defibrillation of cardiac tissue.

We propose a new model for electrical activity of cardiac tissue that incorporates the effects of cellular microstructure. As such, this model provides insight into the mechanism of direct stimulation and defibrillation of cardiac tissue after injection of large currents. To illustrate the usefulness of the model, numerical stimulations are used to show the difference between successful and unsuccessful defibrillation of large pieces of tissue.     

Generation of the endocochlear potential: a biophysical model

The generation and maintenance of the endocochlear potential (EP) by the stria vascularis is essential for proper function of the cochlea. We present a mathematical model that captures the critical biophysical interactions between the distinct cellular layers that generate the EP. By describing the relationship between the K⁺ concentration in the intrastrial space and the intermediate cell transmembrane potential, we rationalize the presence of a large intermediate cell K⁺ conductance and predict that the intrastrial [K⁺] is ∼4 mM at steady state. The model also predicts that the stria vascularis is capable of buffering the EP against external perturbations in a manner modulated by changes in intrastrial [K⁺], thus facilitating hearing sensitivity across the broad dynamic range of the auditory system.     

Minimal model: perspective from 2005

The minimal model was proposed over 25 years ago. Despite (or because of) its simplicity it continues to be used today - both as a clinical tool and an approach to understanding the composite effects of insulin secretion and insulin sensitivity on glucose tolerance and risk for type 2 diabetes mellitus. The original assumptions of the model have led to an understanding of the kinetics of insulin in vivo, as well as the relative importance of beta-cell compensatory failure in the pathogenesis of diabetes. The disposition index (DI), a parameter emerging from the model, represents the ability of the pancreatic islets to compensate for insulin resistance. There is evidence that a locus on chromosome 11 codes for the DI, which has a significant heritability and can predict type 2 diabetes better than any known genetic locus. Even today, the model continues to be a subject of scientific discovery and discourse.