Identification of neurotransmitter receptor genes under significantly relaxed selective constraint by orthologous gene comparisons between humans and rodents

Neurotransmitter receptors (neuroreceptors) are classified into two types, G protein-coupled receptors (GPCRs) and ligand-gated ion channels. The former occupies a small part of the large GPCR superfamily, whereas the latter consists of three superfamilies. In these superfamilies, humans and rodents share almost the same set of neuroreceptor genes. This neuroreceptor gene set is good material to examine the degree of selective constraint exerted on each member gene of a given superfamily. If there are any neuroreceptor genes under the degree of selective constraint that is very different from that of the other member genes, they may have influenced the functional features characteristic of human neural activities. With the aim of identifying such neuroreceptor genes, we collected sequence data of orthologous neuroreceptor genes for humans, mice, and rats by database searches. This data set included ortholog pairs for 141 kinds of neuroreceptor genes, which covered almost the whole set of neuroreceptor genes known to be expressed in the human brain. The degree of selective constraint was estimated by computing the ratio (d(N)/d(S)) of the number of nonsynonymous substitutions to that of synonymous substitutions. We found that the d(N)/d(S) ratio ranged widely and its distribution fitted a gamma distribution. In particular, we found that four neuroreceptor genes are under the significantly relaxed selective constraint. They are an ionotropic glutamate receptor subunit NMDA-2C, two GABA(A) receptor subunits, i.e., GABA(A)-epsilon and GABA(A)-theta, and a dopamine receptor D4. Interestingly, these neuroreceptors have been reported to be associated with cognitive abilities such as memory and learning, and responsiveness to novel stimuli. These cognitive abilities can influence the behavioral features of an individual. Thus, it suggests that the relaxed-constraint neuroreceptor genes have evolved, assuring that the nervous system responds to a variety of stimuli with proper flexibility.     

Dynamic attractor for the Berendsen thermostat an the slow dynamics of biomacromolecules

It was shown that the nonlinear relaxation of a model system confined to the Berendsen's thermostat is determined by an attractor regime. The latter does not correspond generally to the true thermodynamic state of the system. Therefore, the use of the Berendsen's thermostat for molecular dynamics simulations, even in the case of large protein molecules at trajectory lengths of more than 10 ns, can lead to wrong conclusions. Our results agree with the concept of slow dynamics for macroscopic systems considered within the framework of the topological approach to stochastic dynamics.     

Fractional Poisson–Nernst–Planck Model for Ion Channels I: Basic Formulations and Algorithms

In this work, we propose a fractional Poisson–Nernst–Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker–Planck equation. Then, it is generalized to the macroscopic fractional Poisson–Nernst–Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.     

Cyclic AMP-lowering mediator of insulin

What appears to be a mediator of insulin action has been successfully produced in rat adipocytes plasma membrane upon its treatment with insulin at concentrations of 50-200 microunits/ml. This apparent mediator, when isolated and presented to adipocyte cells, mimics insulin action in the lowering of hormonally stimulated cAMP levels as well as in stimulating lipogenesis and antilipolysis. The cAMP-lowering activity of such a mediator can be quantitated as insulin-activity equivalents. Insulin at 200 microunits/ml causes, in terms of insulin-activity equivalents, a generation of as much as 50 times more of insulin mediator. The magnitude of amplification is even greater when the amount of insulin bound to its receptor is taken into account in this calculation. The action of insulin in the generation of cAMP-lowering mediator is abolished by the insulin antibody. Inactive insulin analogs do not effectively generate such a mediator activity. On the other hand, while the cAMP-lowering action of insulin shown in the bioassay system is completely inhibited by the insulin antibody, the action of such a mediator is only slightly inhibited by the same antibody. The mediator has a low molecular weight and attributes that resemble a peptide. It can be separated from insulin in a Sephadex G-25 column and has a molecular size smaller than the insulin A-chain but larger than ATP. The molecular weight of this mediator is similar to the insulin mediators isolated by other investigators. In view of the fact that it is small in size and mimics several actions of insulin when used in extracellular situations, its theoretical, as well as practical, implications are substantial.     

Modeling of the two wave response of ATP receptors to jumps of the agonist concentration in pheochromocytoma cells

A model for the kinetics of conformational transitions of ionotropic ATP receptors in pheochromocytoma cells was elaborated. The contribution of the states of ionotropic receptors (upon the blockage of the "open" channel state) to the kinetics of postsynaptic currents was estimated at mediator concentrations studied. The model enables one to determine the contribution of various conformational states of the receptor, in particular in the "closed" state, to the dynamics of ionic current that is registered upon stimulation of ATP receptors. It is shown that after the cessation of the agonist application, a secondary current wave can arise. The rate constants for conformational transitions of ATP receptors were determined.     

Mean-field Boolean network model of a signal transduction network

In this paper we provide a mean-field Boolean network model for a signal transduction network of a generic fibroblast cell. The network consists of several main signaling pathways, including the receptor tyrosine kinase, the G-protein coupled receptor, and the Integrin signaling pathway. The network consists of 130 nodes, each representing a signaling molecule (mainly proteins). Nodes are governed by Boolean dynamics including canalizing functions as well as totalistic Boolean functions that depend only on the overall fraction of active nodes. We categorize the Boolean functions into several different classes. Using a mean-field approach we generate a mathematical formula for the probability of a node becoming active at any time step. The model is shown to be a good match for the actual network. This is done by iterating both the actual network and the model and comparing the results numerically. Using the Boolean model it is shown that the system is stable under a variety of parameter combinations. It is also shown that this model is suitable for assessing the dynamics of the network under protein mutations. Analytical results support the numerical observations that in the long-run at most half of the nodes of the network are active.     

Correlation between experimentally indicated and atomistically simulated roles of EGFR N-glycosylation*

Epidermal Growth Factor Receptor (EGFR) is a glycosylated tyrosine kinase receptor associated with several cancers. EGFR plays an important role in cancer therapy and inspired several experimental and computational (molecular dynamics simulation) studies to investigate its function and dynamics. N-glycosylation is a critical aspect of EGFR functioning that was mainly unexplained until recently due to the challenges in obtaining and analysis of the structural data involving the glycan moieties. Latest simulations of glycosylated EGFR suggest atomistic mechanisms underlying the experimentally proposed functions of N-glycans in: EGFR increased ligand binding, reduced flexibility and arrangement within the cell membrane. It was shown that the increase in the ligand binding of glycosylated EGFR is mediated by the interaction between the two glycans attached to the growth factor binding subdomains resulting in stabilization of the growth factor binding site. Persistent hydrogen bonds’ formation between the glycans and EGFR contributes to proper folding and reduced flexibly of the glycosylated receptor. Assembly of the cell-integrated EGFR and its relative distance from the membrane are acquired by the lift-up action of the attached glycans. These findings can be used as a framework for implementation of computational techniques to obtain atomistic details of protein glycosylation as one of the most important areas of structural biology.     

Co-operative dynamics in organelles

Some organelles produce elementary life phenomena which are characterized by the spontaneous formation and/or maintenance of ordered macroscopic dynamics like e.g. the shortening of sarcomeres in striated muscle and the transmission of electrical impulses in an axon. It has been widely accepted that such organelles are organized molecular systems where molecular elements work independently under constraint of a more or less rigid and regular structure of the system. On the other hand, such organelles should be regarded as self-organizing systems if the ordered macroscopic dynamics are self-organized. As the macroscopic dynamics gradually emerge, the microscopic dynamics of its elements become linked to each other through a feedback loop. It is crucial for the feedback loop to operate that the macroscopic dynamics are "free" in their behavior. In the present paper, it is pointed out that the traditional view of independent molecular elements has been obtained from experiments in which, by means of external constraint, the macroscopic dynamics is "clamped". Under such conditions, the self-organizing system may behave as an organized one. Based on synergetics we propose criterions for proving self-organizing systems, and, by applying the criterions, we conclude that skeletal muscle actomysin is a co-operative element in the sense of self-organization.     

Long and short distance movements of β(2)-adrenoceptor in cell membrane assessed by photoconvertible fluorescent protein dendra2-β(2)-adrenoceptor fusion

Local movements of receptors in the plasma membrane have been extensively studied, as it is generally believed that the dynamics of membrane distribution of receptors regulate their functions. However, the properties of large-scale (>5μm) receptor movements in the membrane are relatively obscure. In the present study, we addressed the question as to whether the large-scale movement of receptor in the plasma membrane at the whole cell level can be explained quantitatively by its local diffusive properties. We used HEK 293 cells transfected with human β2-adrenoceptor fused to photoconvertible fluorescent protein dendra2 as a model system; and found that 1) functional integrity of the dendra2-tagged receptor remains apparently intact; 2) in a mesoscopic scale (~4μm), ~90% of the receptors are mobile on average, and receptor influx to, and out-flux from a membrane area can be symmetrically explained by a diffusion-like process with an effective diffusion coefficient of ~0.1μm(2)/s; 3) these mobility parameters are not affected by the activity state of the receptor (assessed by using constitutively active receptor mutants); 4) in the macroscopic scale (4-40μm), although a slowly diffusing fraction of receptors (with D<0.01μm(2)/s) is identifiable in some cases, the movement of the predominant fraction is perfectly explained by the same effective diffusion process observed in the mesoscopic scale, suggesting that the large scale structure of the cell membrane as felt by the receptor is apparently homogeneous in terms of its mesoscopic properties. We also showed that intracellular compartments and plasma membrane are kinetically connected even at steady-state.     

A competitive coexistence principle?

Competitive exclusion – n species cannot coexist on fewer than n limiting resources in a constant and isolated environment – has been a central ecological principle for the past century. Since empirical studies cannot universally demonstrate exclusion, this principle has mainly relied on mathematical proofs. Here we investigate the predictions of a new approach to derive functional responses in consumer/resource systems. Models usually describe the temporal dynamics of consumer/resource systems at a macroscopic level – i.e. at the population level. Each model may be pictured as one time-dependent macroscopic trajectory. Each macroscopic trajectory is, however, the product of many individual fates and from combinatorial considerations can be realized in many different ways at the microscopic – or individual – level. Recently it has been shown that, in systems with large enough numbers of consumer individuals and resource items, one macroscopic trajectory can be realized in many more ways than any other at the individual – or microscopic – level. Therefore, if the temporal dynamics of an ecosystem are assumed to be the outcome of only statistical mechanics – that is, chance – a single trajectory is near-certain and can be described by deterministic equations. We argue that these equations can serve as a null to model consumer-resource dynamics, and show that any number of species can coexist on a single resource in a constant, isolated environment. Competition may result in relative rarity, which may entail exclusion in finite samples of discrete individuals, but exclusion is not systematic. Beyond the coexistence/exclusion outcome, our model also predicts that the relative abundance of any two species depends simply on the ratio of their competitive abilities as computed from – and only from – their intrinsic kinetic and stoichiometric parameters.     

Model-driven approaches for in vitro combination therapy using ONYX-015 replicating oncolytic adenovirus

Replicating genetically modified adenoviruses have shown promise as a new treatment approach against cancer. Recombinant adenoviruses replicate only in cancer cells which contain certain mutations, such as the loss of functional p53, as is the case in the virus ONYX-015. The successful entry of the viral particle into target cells is strongly dependent on the presence of the main receptor for adenovirus, the coxsackie- and adenovirus receptor (CAR). This receptor is frequently down-regulated in highly malignant cells, rendering this population less vulnerable to viral attack. It has been shown that the use of MEK inhibitors can up-regulate CAR expression, resulting in enhanced adenovirus entry into the cells. However, inhibition of MEK results in G1 cell cycle arrest, rendering infected cells temporarily unable to produce virus. This forces a tradeoff. While drug mediated up-regulation of CAR enhances virus entry into cancer cells, the consequent cell cycle arrest inhibits production of new virus particles and the replication of the virus. Optimal control-based schedules of MEK inhibitor application should increase the efficacy of this treatment, maximizing the overall tumor toxicity by exploiting the dynamics of CAR expression and viral production. We introduce a mathematical model of these dynamics and show simple optimal control based strategies which motivate this approach.     

A Mathematical Model for Basepair Opening in a DNA Double Helix

In this paper, we consider a mathematical model that draws an analogy between a DNA molecule and a mechanical system consisting of two chains of interconnected pendulums. This model is designed to explore the dynamics of the system determined by rotational movements of nucleobases around a double-stranded pentose phosphate backbone. The workability of this model is assessed with respect to various factors: inhomogeneity of the chain of nucleobases, the properties of bonds in complementary pairs, and the formation of open states. It has been shown that simplified models for averaging the characteristics of the chain of nucleobases or simplification of the type of hydrogen bond in their complementary pairs influence the type of solution significantly, impairing the validity of the results. Therefore, the approach to the solution of rotational DNA molecule dynamics developed here is more consistent with its actual biomechanics. It is shown that the emergence of open states within nucleobase pairs and restoration of the closed structure may occur in the tested mathematical model.     

Theoretical effects of radioligand diffusional gradients and microscopic neuroreceptor distribution inin vivo kinetic studies

A simplified one-dimensional model system was used to test the possibility that physically realistic parameters would lead to the prediction of microscopic heterogeneity of radioligand distribution in the brain and that microscopic heterogeneity of radioligand and neuroreceptor distribution could influence the macroscopically observedin vivo kinetics. The model was represented mathematically by a partial differential equation which is similar to the heat diffusion equation, but with special boundary conditions. The equation was solved analytically under the condition of negligible receptor occupancy by inversion of the Laplace transform and in the more general case of arbitrary receptor occupancy by cubic spline approximation. In simulations with physically reasonable values for rate constants and parameters, we find that significant radioligand gradients can occur. Thus, the level of radioligand in the immediate vicinity of the receptor may be substantially different from the average level in a macroscopically measured region of interest. In order to analyze the simulated data, we derived a rigorous steady-state solution, including both a statement of necessary and sufficient conditions for the validity of the steady-state approximation as well as a demonstration of the proper technique for assessing the consistency of the derived parameter with the requirements of the approximation. The radioligand heterogeneity leads to significant errors in the parameters estimated in the steady-state kinetic analysis. In particular, the pseudo first-order rate constant for radioligand-neuroreceptor association, which is often used as a measure of the total amount of neuroreceptor, is underestimated. The first-order rate constant for radioligand-neuroreceptor dissociation is also underestimated. These effects can partially account for the experimentally-observed discrepancy betweenin vivo andin vitro estimates of these kinetic parameters.     

A method of statistical neurodynamics

A method of statistical neurodynamics is presented for treating ensembles of nets of randomly connected neuron-like elements. The concept of a macrostate plays a fundamental role in statistical neurodynamics and a criterion is given for ascertaining that given macroscopic quantities together constitute a macrostate. The activity of a nerve net is shown to be a macrostate and the equation of the dynamics of the activity is elucidated for various ensembles of random nerve nets. It is shown that the distance between two microstates can also be treated as a macrostate in a generalized sense. The equation of its dynamics represents how the distance between two states changes in the course of state transitions. The dynamics of distance reveals interesting microscopic properties of random nerve nets, such as the stability of state-transition, the transient lengths, etc.     

Current fluctuations in discrete transport systems far from equilibrium. Breakdown of the fluctuation dissipation theorem

A recently developed theoretical approach to transport fluctuations around stable steady states in discrete biological transport systems is used in order to investigate general fluctuation properties at nonequilibrium. An expression for the complex frequency dependent admittance at nonequilibrium is derived by calculation of the linear current response of the transport systems to small disturbances in the applied external voltage. It is shown that the Nyquist or fluctuation dissipation theorem, by which at equilibrium the macroscopic admittance or linear response can be expressed in terms of fluctuation properties of the system, breaks down at nonequilibrium. The spectral density of current fluctuations is decomposed into one term containing the macroscopic admittance and a second term which is bilinear in current. This second term is generated by microscopic disturbances, which cannot be excited by external macroscopic perturbations. At special examples it is demonstrated that this second term is decisive for the occurrence of excess noise e.g. the 1/f(2)-Iorentzian noise generated by the opening and closing of nerve channels in biological membranes.     

Can Quick Release Experiments Reveal the Muscle Structure? A Bionic Approach

The goal of this study was to understand the macroscopic mechanical structure and function of biological muscle with respect to its dynamic role in the contraction.A recently published muscle model,deriving the hyperbolic force-velocity relation from first-order mechanical principles,predicts different force-velocity operating points for different load situations.With anew approach,this model could be simplified and thus,transferred into a numerical simulation and a hardware experiment.Two types of quick release experiments were performed in simulation and with the hardware setup,which represent two extreme cases of the contraction dynamics:against a constant force (isotonic) and against an inertial mass.Both experiments revealed hyperbolic or hyperbolic-like force-velocity relations.Interestingly,the analytical model not only predicts these extreme cases,but also additionally all contraction states in between.It was possible to validate these predictions with the numerical model and the hardware experiment.These results prove that the origin of the hyperbolic force-velocity relation can be mechanically explained on a macroscopic level by the dynamical interaction of three mechanical elements.The implications for the interpretation of biological muscle experiments and the realization of muscle-like bionic actuators are discussed.