Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models

Mathematical cell models are effective tools to understand cellular physiological functions precisely. For detailed analysis of model dynamics in order to investigate how much each component affects cellular behaviour, mathematical approaches are essential. This article presents a numerical analysis technique, which is applicable to any complicated cell model formulated as a system of ordinary differential equations, to quantitatively evaluate contributions of respective model components to the model dynamics in the intact situation. The present technique employs a novel mathematical index for decomposed dynamics with respect to each differential variable, along with a concept named instantaneous equilibrium point, which represents the trend of a model variable at some instant. This article also illustrates applications of the method to comprehensive myocardial cell models for analysing insights into the mechanisms of action potential generation and calcium transient. The analysis results exhibit quantitative contributions of individual channel gating mechanisms and ion exchanger activities to membrane repolarization and of calcium fluxes and buffers to raising and descending of the cytosolic calcium level. These analyses quantitatively explicate principle of the model, which leads to a better understanding of cellular dynamics.     

Comprehensive Analyses of Ventricular Myocyte Models Identify Targets Exhibiting Favorable Rate Dependence

Reverse rate dependence is a problematic property of antiarrhythmic drugs that prolong the cardiac action potential (AP). The prolongation caused by reverse rate dependent agents is greater at slow heart rates, resulting in both reduced arrhythmia suppression at fast rates and increased arrhythmia risk at slow rates. The opposite property, forward rate dependence, would theoretically overcome these parallel problems, yet forward rate dependent (FRD) antiarrhythmics remain elusive. Moreover, there is evidence that reverse rate dependence is an intrinsic property of perturbations to the AP. We have addressed the possibility of forward rate dependence by performing a comprehensive analysis of 13 ventricular myocyte models. By simulating populations of myocytes with varying properties and analyzing population results statistically, we simultaneously predicted the rate-dependent effects of changes in multiple model parameters. An average of 40 parameters were tested in each model, and effects on AP duration were assessed at slow (0.2 Hz) and fast (2 Hz) rates. The analysis identified a variety of FRD ionic current perturbations and generated specific predictions regarding their mechanisms. For instance, an increase in L-type calcium current is FRD when this is accompanied by indirect, rate-dependent changes in slow delayed rectifier potassium current. A comparison of predictions across models identified inward rectifier potassium current and the sodium-potassium pump as the two targets most likely to produce FRD AP prolongation. Finally, a statistical analysis of results from the 13 models demonstrated that models displaying minimal rate-dependent changes in AP shape have little capacity for FRD perturbations, whereas models with large shape changes have considerable FRD potential. This can explain differences between species and between ventricular cell types. Overall, this study provides new insights, both specific and general, into the determinants of AP duration rate dependence, and illustrates a strategy for the design of potentially beneficial antiarrhythmic drugs.     

Quantitative Models of In Vitro Bacteriophage–Host Dynamics and Their Application to Phage Therapy

Phage therapy is the use of bacteriophages as antimicrobial agents for the control of pathogenic and other problem bacteria. It has previously been argued that successful application of phage therapy requires a good understanding of the non-linear kinetics of phage–bacteria interactions. Here we combine experimental and modelling approaches to make a detailed examination of such kinetics for the important food-borne pathogen Campylobacter jejuni and a suitable virulent phage in an in vitro system. Phage-insensitive populations of C. jejuni arise readily, and as far as we are aware this is the first phage therapy study to test, against in vitro data, models for phage–bacteria interactions incorporating phage-insensitive or resistant bacteria. We find that even an apparently simplistic model fits the data surprisingly well, and we confirm that the so-called inundation and proliferation thresholds are likely to be of considerable practical importance to phage therapy. We fit the model to time series data in order to estimate thresholds and rate constants directly. A comparison of the fit for each culture reveals density-dependent features of phage infectivity that are worthy of further investigation. Our results illustrate how insight from empirical studies can be greatly enhanced by the use of kinetic models: such combined studies of in vitro systems are likely to be an essential precursor to building a meaningful picture of the kinetic properties of in vivo phage therapy.     

On the Characterization and Software Implementation of General Protein Lattice Models

Abstract models of proteins have been widely used as a practical means to computationally investigate general properties of the system. In lattice models any sterically feasible conformation is represented as a self-avoiding walk on a lattice, and residue types are limited in number. So far, only two- or three-dimensional lattices have been used. The inspection of the neighborhood of alpha carbons in the core of real proteins reveals that also lattices with higher coordination numbers, possibly in higher dimensional spaces, can be adopted. In this paper, a new general parametric lattice model for simplified protein conformations is proposed and investigated. It is shown how the supporting software can be consistently designed to let algorithms that operate on protein structures be implemented in a lattice-agnostic way. The necessary theoretical foundations are developed and organically presented, pinpointing the role of the concept of main directions in lattice-agnostic model handling. Subsequently, the model features across dimensions and lattice types are explored in tests performed on benchmark protein sequences, using a Python implementation. Simulations give insights on the use of square and triangular lattices in a range of dimensions. The trend of potential minimum for sequences of different lengths, varying the lattice dimension, is uncovered. Moreover, an extensive quantitative characterization of the usage of the so-called “move types” is reported for the first time. The proposed general framework for the development of lattice models is simple yet complete, and an object-oriented architecture can be proficiently employed for the supporting software, by designing ad-hoc classes. The proposed framework represents a new general viewpoint that potentially subsumes a number of solutions previously studied. The adoption of the described model pushes to look at protein structure issues from a more general and essential perspective, making computational investigations over simplified models more straightforward as well.     

A Quantitative Comparison of the Behavior of Human Ventricular Cardiac Electrophysiology Models in Tissue

Numerical integration of mathematical models of heart cell electrophysiology provides an important computational tool for studying cardiac arrhythmias, but the abundance of available models complicates selecting an appropriate model. We study the behavior of two recently published models of human ventricular action potentials, the Grandi-Pasqualini-Bers (GPB) and the O''Hara-Virág-Varró-Rudy (OVVR) models, and compare the results with four previously published models and with available experimental and clinical data. We find the shapes and durations of action potentials and calcium transients differ between the GPB and OVVR models, as do the magnitudes and rate-dependent properties of transmembrane currents and the calcium transient. Differences also occur in the steady-state and S1–S2 action potential duration and conduction velocity restitution curves, including a maximum conduction velocity for the OVVR model roughly half that of the GPB model and well below clinical values. Between single cells and tissue, both models exhibit differences in properties, including maximum upstroke velocity, action potential amplitude, and minimum diastolic interval. Compared to experimental data, action potential durations for the GPB and OVVR models agree fairly well (although OVVR epicardial action potentials are shorter), but maximum slopes of steady-state restitution curves are smaller. Although studies show alternans in normal hearts, it occurs only in the OVVR model, and only for a narrow range of cycle lengths. We find initiated spiral waves do not progress to sustained breakup for either model. The dominant spiral wave period of the GPB model falls within clinically relevant values for ventricular tachycardia (VT), but for the OVVR model, the dominant period is longer than periods associated with VT. Our results should facilitate choosing a model to match properties of interest in human cardiac tissue and to replicate arrhythmia behavior more closely. Furthermore, by indicating areas where existing models disagree, our findings suggest avenues for further experimental work.     

Electrophysiology of Heart Failure Using a Rabbit Model: From the Failing Myocyte to Ventricular Fibrillation

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart. Specifically, in accordance with the heart failure literature, we modified the cell EP by changing both membrane currents and calcium handling. At the tissue level, we modeled the increased gap junction lateralization and lower conduction velocity due to downregulation of Connexin 43. At the biventricular level, we reduced the apex-to-base and transmural gradients of action potential duration (APD). The failing cell model was first validated by reproducing the longer action potential, slower and lower calcium transient, and earlier alternans characteristic of heart failure EP. Subsequently, we compared the electrical wave propagation in one dimensional cables of healthy and failing cells. The validated cell model was then used to simulate the EP of heart failure in an anatomically accurate biventricular rabbit model. As pacing cycle length decreases, both the normal and failing heart develop T-wave alternans, but only the failing heart shows QRS alternans (although moderate) at rapid pacing. Moreover, T-wave alternans is significantly more pronounced in the failing heart. At rapid pacing, APD maps show areas of conduction block in the failing heart. Finally, accelerated pacing initiated wave reentry and breakup in the failing heart. Further, the onset of VF was not observed with an upregulation of SERCA, a potential drug therapy, using the same protocol. The changes introduced at the cell and tissue level have increased the failing heart’s susceptibility to dynamic instabilities and arrhythmias under rapid pacing. However, the observed increase in arrhythmogenic potential is not due to a steepening of the restitution curve (not present in our model), but rather to a novel blocking mechanism.     

钙激活氯通道电生理特性及调节机制

钙激活氯通道(Calcium-activated Chloride Channels,CaCC)在许多生理过程中起着重要作用,如分泌蛋白及盐的跨上皮转运、神经元兴奋、平滑肌生理特性的维持、卵母细胞受精和心脏动作电位的复极化等.CaCC电生理特性较复杂,其全细胞电流随胞内钙离子浓度和刺激电压的不同而表现出不同整流特性和时间电压依赖性,不同组织的单通道电导有很大差异,大小介于1～70pS.CaCC可被NFA、9-AC、DPC、DIDS所阻断.目前CaCC通道蛋白的分子结构还不清楚,已克隆的两种蛋白家族CLCA和Bestrophin可作为其候选分子.本文综述了CaCC的电生理特性、调节机制、分子结构和生理功能.     

Relationship of the Electrophysiological Property of Tobacco Cultured Cells to Their Regeneration Ability

The electrophysiological properties of the high-density fractionof tobacco cultured cells (cell clusters) which formed leafprimordia in high yield in Linsmaier-Skoog's medium containingkinetin were compared with those of low-density cell fractionsin which leaf primordia hardly differentiated. Cells of theformer fraction had a higher membrane potential and an electrogenicmechanism which responded to sugars and amino acids. (Received February 12, 1983; Accepted March 23, 1984)     

Immunity in Mammals to Helminths of the Circulatory and Lymphatic Systems, Emphasizing Nonhuman Primate Models and Their Comparison to Human Infections and Rodent Models

The host—parasite relationship of intravascular helminthsin mammalian hosts is complex, consisting of several interrelatedaspects. These organisms are often very long lived in thesehosts that possess highly evolved immune systems, which impliesthe existence of mechanisms in these complex parasites for evadingthe immune response. On the other hand, mammalian hosts appearto be very successful in limiting their worm burdens, mainlyby preventing reinfection. Thus, a balance between host andparasite is often achieved. This balance extends to the immunopathologicalconsequences of the infections as well. Especially in the schistosomes,where relatively more is known about immunopathology, it isbecoming increasingly apparent that immunopathological reactionsto the eggs are multifunctional and paradoxical: they causedisease, they limit disease, and they even serve the schistosomeby making possible the escape of its eggs, laid deep withinthe tissues, from the host's body to propagate the life cycle.The comparative approach, using different species of schistosomesand filarids in different mammalian hosts, has proved to bevaluable for understanding the immunological basis of thesecomplex relationships. The knowledge gained from these modelsystems is already being vigorously applied to the human diseases,two of the great scourges of the tropics, schistosomiasis andlymphatic filariasis, to the end of their eradication from theearth by mass immunization.     

新型东亚钳蝎小分子成分的生化性质及其对大鼠心室肌细胞Ito的作用

分离纯化获得了两个东亚钳蝎小分子活性多肽ＢｍＰ０２和ＢｍＰ０３。经质谱鉴定二者皆为单一峰,分子量分别为２．９５０ｋＤ和２．９３５ｋＤ。ＢｍＰ０２的氨基酸序列已被测定。用全细胞膜片箝方法记录到ＢｍＰ０２对大鼠心室肌细胞短暂外向钾电流（Ｉｔｏ）具有明显的抑制作用（ｎ＝５）,冲洗后可部分恢复,且其抑制活性具有浓度依赖性和电压非依赖性。进一步研究表明,ＢｍＰ０２可影响短暂外向钾通道的失活化和恢复过程,但却不影响其激活过程     

Usefulness of Behavioral and Electrophysiological Studies in Transgenic Models of Alzheimer's Disease

Over the past several years researchers have engineered many transgenic models of Alzheimer's disease. Since loss of memory is one of the major hallmarks of the disorder, the phenotypic characterization of these animals has included both behavioral tests which aim to evaluate learning abilities, and electrophysiological studies to analyze synaptic transmission and long-term potentiation, a widely studied cellular model of learning and memory. These studies are fundamental for the design of novel therapies for the treatment and/or prevention of Alzheimer's disease.     

Behavioral and Electrophysiological Characterization of Dyt1 Heterozygous Knockout Mice

DYT1 dystonia is an inherited movement disorder caused by mutations in DYT1 (TOR1A), which codes for torsinA. Most of the patients have a trinucleotide deletion (ΔGAG) corresponding to a glutamic acid in the C-terminal region (torsinA^ΔE). Dyt1 ΔGAG heterozygous knock-in (KI) mice, which mimic ΔGAG mutation in the endogenous gene, exhibit motor deficits and deceased frequency of spontaneous excitatory post-synaptic currents (sEPSCs) and normal theta-burst-induced long-term potentiation (LTP) in the hippocampal CA1 region. Although Dyt1 KI mice show decreased hippocampal torsinA levels, it is not clear whether the decreased torsinA level itself affects the synaptic plasticity or torsinA^ΔE does it. To analyze the effect of partial torsinA loss on motor behaviors and synaptic transmission, Dyt1 heterozygous knock-out (KO) mice were examined as a model of a frame-shift DYT1 mutation in patients. Consistent with Dyt1 KI mice, Dyt1 heterozygous KO mice showed motor deficits in the beam-walking test. Dyt1 heterozygous KO mice showed decreased hippocampal torsinA levels lower than those in Dyt1 KI mice. Reduced sEPSCs and normal miniature excitatory post-synaptic currents (mEPSCs) were also observed in the acute hippocampal brain slices from Dyt1 heterozygous KO mice, suggesting that the partial loss of torsinA function in Dyt1 KI mice causes action potential-dependent neurotransmitter release deficits. On the other hand, Dyt1 heterozygous KO mice showed enhanced hippocampal LTP, normal input-output relations and paired pulse ratios in the extracellular field recordings. The results suggest that maintaining an appropriate torsinA level is important to sustain normal motor performance, synaptic transmission and plasticity. Developing therapeutics to restore a normal torsinA level may help to prevent and treat the symptoms in DYT1 dystonia.     

Conformational Properties of Seven Toac-Labeled Angiotensin I Analogues Correlate with Their Muscle Contraction Activity and Their Ability to Act as ACE Substrates

Conformational properties of the angiotensin II precursor, angiotensin I (AngI) and analogues containing the paramagnetic amino acid TOAC (2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid) at positions 0, 1, 3, 5, 8, 9, and 10, were examined by EPR, CD, and fluorescence. The conformational data were correlated to their activity in muscle contraction experiments and to their properties as substrates of the angiotensin I-converting enzyme (ACE). Biological activity studies indicated that TOAC⁰-AngI and TOAC¹-AngI maintained partial potency in guinea pig ileum and rat uterus. Kinetic parameters revealed that only derivatives labeled closer to the N-terminus (positions 0, 1, 3, and 5) were hydrolyzed by ACE, indicating that peptides bearing the TOAC moiety far from the ACE cleavage site (Phe⁸-His⁹ peptide bond) were susceptible to hydrolysis, albeit less effectively than the parent compound. CD spectra indicated that AngI exhibited a flexible structure resulting from equilibrium between different conformers. While the conformation of N-terminally-labeled derivatives was similar to that of the native peptide, a greater propensity to acquire folded structures was observed for internally-labeled, as well as C-terminally labeled, analogues. These structures were stabilized in secondary structure-inducing agent, TFE. Different analogues gave rise to different β-turns. EPR spectra in aqueous solution also distinguished between N-terminally, internally-, and C-terminally labeled peptides, yielding narrower lines, indicative of greater mobility for the former. Interestingly, the spectra of peptides labeled at, or close, to the C-terminus, showed that the motion in this part of the peptides was intermediate between that of N-terminally and internally-labeled peptides, in agreement with the suggestion of turn formation provided by the CD spectra. Quenching of the Tyr⁴ fluorescence by the differently positioned TOAC residues corroborated the data obtained by the other spectroscopic techniques. Lastly, we demonstrated the feasibility of monitoring the progress of ACE-catalyzed hydrolysis of TOAC-labeled peptides by following time-dependent changes in their EPR spectra.     

The Effects of Temperature upon Contraction and Ionic Exchange in Rabbit Ventricular Myocardium : Relation to control of active state

The mechanical responses (active and resting tension, dP/dt, TPT) and ionic exchange characteristics (Ca⁺⁺, K⁺, Na⁺) which follow upon a variation in temperature, rate, and [K⁺]₀ were studied in the rabbit papillary muscle and arterially perfused rabbit interventricular setpum. Abrupt changes in temperature provided a means of separating the contributions of rate of development (intensity) of active state and duration of active state to total active tension development (approximated by isometric tension). Threefold changes in duration of active state with proportional changes in active tension can be induced without evidence for alteration of Ca⁺⁺, K⁺, or Na⁺ exchange. Abrupt cooling produced a moderate (~15%) increase of dP/dt which suggests an augmentation of active state intensity. Evidence is presented to suggest that this increase of dP/dt is based upon an increase in membrane Ca⁺⁺ concentration which occurs secondary to inhibition of active Na⁺ transport. The alterations in ionic exchange and active state produced by variation of temperature are discussed in terms of a five-component control system.     

Monoclonal Antibodies to Substance P: Production, Characterization of Their Fine Specificities, and Use in Immunocytochemistry

Five hybrid clones secreting antibodies to the neuropeptide substance P have been obtained by somatic cell fusion of mouse myeloma cells with splenocytes from immunized mice of the Biozzi strain. To perform rapid and sensitive screening tests as well as to study the fine specificities of each monoclonal antibody, we developed a new enzyme immunoassay of substance P using acetylcholinesterase as label. All five monoclonal antibodies were directed to the C-terminal pentapeptide of substance P, especially to the Phe7 residue. They cross-reacted with neurokinin A and to some extent with neurokinin B but not with other nontachykinin mammalian peptides. One monoclonal antibody (SP 14) was used for immunocytochemical experiments in the rat spinal cord and spinal ganglion, both at the light and electron microscopic levels. A strong specific neurokinin-like immunoreactivity was observed in cell bodies, nerve fibers, and terminals, with a very low background staining. Finally, the affinities of several analogues of substance P for SP 14 monoclonal antibody were shown to be correlated with their biological activities, as measured by their hypotensive effects in vivo. These findings suggested a strong structural resemblance between the combining site of the antibody and that of the physiological substance P receptor.     

Molecular and Electrophysiological Characterization of a Novel Cation Channel of Trypanosoma cruzi

We report the identification, functional expression, purification, reconstitution and electrophysiological characterization of a novel cation channel (TcCat) from Trypanosoma cruzi, the etiologic agent of Chagas disease. This channel is potassium permeable and shows inward rectification in the presence of magnesium. Western blot analyses with specific antibodies indicated that the protein is expressed in the three main life cycle stages of the parasite. Surprisingly, the parasites have the unprecedented ability to rapidly change the localization of the channel when they are exposed to different environmental stresses. TcCat rapidly translocates to the tip of the flagellum when trypomastigotes are submitted to acidic pH, to the plasma membrane when epimastigotes are submitted to hyperosmotic stress, and to the cell surface when amastigotes are released to the extracellular medium. Pharmacological block of TcCat activity also resulted in alterations in the trypomastigotes ability to respond to hyperosmotic stress. We also demonstrate the feasibility of purifying and reconstituting a functional ion channel from T. cruzi after recombinant expression in bacteria. The peculiar characteristics of TcCat could be important for the development of specific inhibitors with therapeutic potential against trypanosomes.