Structural basis and synergism of ATP and Na+ activation in bacterial K+ uptake system KtrAB.

The K+ uptake system KtrAB is essential for bacterial survival in low K+ environments. The activity of KtrAB is regulated by nucleotides and Na+. Previous studies proposed a putative gating mechanism of KtrB regulated by KtrA upon binding to ATP or ADP. However, how Na+ activates KtrAB and the Na+ binding site remain unknown. Here we present the cryo-EM structures of ATP- and ADP-bound KtrAB from Bacillus subtilis (BsKtrAB) both solved at 2.8 Å. A cryo-EM density at the intra-dimer interface of ATP-KtrA was identified as Na+, as supported by X-ray crystallography and ICP-MS. Thermostability assays and functional studies demonstrated that Na+ binding stabilizes the ATP-bound BsKtrAB complex and enhances its K+ flux activity. Comparing ATP- and ADP-BsKtrAB structures suggests that BsKtrB Arg417 and Phe91 serve as a channel gate. The synergism of ATP and Na+ in activating BsKtrAB is likely applicable to Na+-activated K+ channels in central nervous system.

H-Theorem in an Isolated Quantum Harmonic Oscillator.

We consider the H-theorem in an isolated quantum harmonic oscillator through the time-dependent Schrödinger equation. The effect of potential in producing entropy is investigated in detail, and we found that including a barrier potential into a harmonic trap would lead to the thermalization of the system, while a harmonic trap alone would not thermalize the system. During thermalization, Shannon entropy increases, which shows that a microscopic quantum system still obeys the macroscopic thermodynamics law. Meanwhile, initial coherent mechanical energy transforms to incoherent thermal energy during thermalization, which exhibiting the decoherence of an oscillating wave packet featured by a large decreasing of autocorrelation length. When reaching thermal equilibrium, the wave packet comes to a halt, with the density distributions both in position and momentum spaces well-fitted by a microcanonical ensemble of statistical mechanics.

Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation.

The classical Poisson-Boltzmann model can only work when ion concentrations are very dilute, which often does not match the experimental conditions. Researchers have been working on the modification of the model to include the steric effect of ions, which is non-negligible when the ion concentrations are not dilute. Generally the steric effect was modeled to correct the Helmholtz free energy either through its internal energy or entropy, and an overview is given here. The Bikerman model, based on adding solvent entropy to the free energy through the concept of volume exclusion, is a rather popular steric-effect model nowadays. However, ion sizes are treated as identical in the Bikerman model, making an extension of the Bikerman model to include specific ion sizes desirable. Directly replacing the ions of non-specific size by specific ones in the model seems natural and has been accepted by many researchers in this field. However, this straightforward modification does not have a free energy formula to support it. Here modifications of the Bikerman model to include specific ion sizes have been developed iteratively, and such a model is achieved with a guarantee that: (1) it can approach Boltzmann distribution at diluteness; (2) it can reach saturation limit as the reciprocal of specific ion size under extreme electrostatic conditions; (3) its entropy can be derived by mean-field lattice gas model.

Electric discharge of electrocytes: Modelling, analysis and simulation.

In this paper, we investigate the electric discharge of electrocytes by extending our previous work on the generation of electric potential. We first give a complete formulation of a single cell unit consisting of an electrocyte and a resistor, based on a Poisson-Nernst-Planck (PNP) system with various membrane currents as interfacial conditions for the electrocyte and a Maxwell's model for the resistor. Our previous work can be treated as a special case with an infinite resistor (or open circuit). Using asymptotic analysis, we simplify our PNP system and reduce it to an ordinary differential equation (ODE) based model. Unlike the case of an infinite resistor, our numerical simulations of the new model reveal several distinct features. A finite current is generated, which leads to non-constant electric potentials in the bulk of intracellular and extracellular regions. Furthermore, the current induces an additional action potential (AP) at the non-innervated membrane, contrary to the case of an open circuit where an AP is generated only at the innervated membrane. The voltage drop inside the electrocyte is caused by an internal resistance due to mobile ions. We show that our single cell model can be used as the basis for a system with stacked electrocytes and the total current during the discharge of an electric eel can be estimated by using our model.

Electric potential generation of electrocytes: Modelling, analysis, and computation.

In this paper, we developed a one-dimensional model for electric potential generation of electrocytes in electric eels. The model is based on the Poisson-Nernst-Planck system for ion transport coupled with membrane fluxes including the Hodgkin-Huxley type. Using asymptotic analysis, we derived a simplified zero-dimensional model, which we denote as the membrane model in this paper, as a leading order approximation. Our analysis provides justification for the assumption in membrane models that electric potential is constant in the intracellular space. This is essential to explain the superposition of two membrane potentials that leads to a significant transcellular potential. Numerical simulations are also carried out to support our analytical findings.

Selectivity of the KcsA potassium channel: Analysis and computation.

Ion channels regulate the flux of ions through cell membranes and play significant roles in many physiological functions. Most of the existing literature focuses on computational approaches based on molecular dynamics simulation or numerical solution of the modified Poisson-Nernst-Planck (PNP) system. In this paper, we present an analytical and computational study of a mathematical model of the KcsA potassium channel, including the effects of ion size (Bikerman model) and solvation energy (Born model). Under equilibrium conditions, we obtain an analytical solution of our modified PNP system, which is used to explain selectivity of KcsA of various ions (K^{+}, Na^{+}, Cl^{-}, Ca^{2+}, and Ba^{2+}) due to negative permanent charges inside the filter region and the effect of ion sizes. Our results show that K^{+} is always selected over Na^{+}, as smaller Na^{+} ions have larger solvation energy. As the amount of negative charges in the filter exceeds a critical value, divalent ions (Ca^{2+} and Ba^{2+}) can enter the filter region and block the KcsA channel. For the nonequilibrium cases, due to difficulties associated with a pure analytical or numerical approach, we use a hybrid analytical-numerical method to solve the modified PNP system. Our predictions of selectivity of KcsA channels and saturation phenomenon of the current-voltage (I-V) curve agree with experimental observations.

High Response CO Sensor Based on a Polyaniline/SnO2 Nanocomposite.

A polyaniline (PANI)/tin oxide (SnO2) composite for a CO sensor was fabricated using a composite film composed of SnO2 nanoparticles and PANI deposition in the present study. Tin oxide nanoparticles were synthesized by the sol-gel method. The SnO2 nanoparticles provided a high surface area to significantly enhance the response to the change in CO concentration at low operating temperature (<75 °C). The excellent sensor response was mainly attributed to the relatively good properties of PANI in the redox reaction during sensing, which produced a great resistance difference between the air and CO gas at low operating temperature. Therefore, the combination of n-type SnO2 nanoparticles with a high surface area and a thick film of conductive PANI is an effective strategy to design a high-performance CO gas sensor.

Continuum Gating Current Models Computed with Consistent Interactions.

The action potential of nerve and muscle is produced by voltage-sensitive channels that include a specialized device to sense voltage. The voltage sensor depends on the movement of charges in the changing electric field as suggested by Hodgkin and Huxley. Gating currents of the voltage sensor are now known to depend on the movements of positively charged arginines through the hydrophobic plug of a voltage sensor domain. Transient movements of these permanently charged arginines, caused by the change of transmembrane potential V, further drag the S4 segment and induce opening/closing of the ion conduction pore by moving the S4-S5 linker. This moving permanent charge induces capacitive current flow everywhere. Everything interacts with everything else in the voltage sensor and protein, and so it must also happen in its mathematical model. A Poisson-Nernst-Planck (PNP)-steric model of arginines and a mechanical model for the S4 segment are combined using energy variational methods in which all densities and movements of charge satisfy conservation laws, which are expressed as partial differential equations in space and time. The model computes gating current flowing in the baths produced by arginines moving in the voltage sensor. The model also captures the capacitive pile up of ions in the vestibules that link the bulk solution to the hydrophobic plug. Our model reproduces the signature properties of gating current: 1) equality of ON and OFF charge Q in integrals of gating current, 2) saturating voltage dependence in the Q(charge)-voltage curve, and 3) many (but not all) details of the shape of gating current as a function of voltage. Our results agree qualitatively with experiments and can be improved by adding more details of the structure and its correlated movements. The proposed continuum model is a promising tool to explore the dynamics and mechanism of the voltage sensor.

Numerical modeling of nanodrug distribution in tumors with heterogeneous vasculature.

The distribution and accumulation of nanoparticle dosage in a tumor are important in evaluating the effectiveness of cancer treatment. The cell survival rate can quantify the therapeutic effect, and the survival rates after multiple treatments are helpful to evaluate the efficacy of a chemotherapy plan. We developed a mathematical tumor model based on the governing equations describing the fluid flow and particle transport to investigate the drug transportation in a tumor and computed the resulting cumulative concentrations. The cell survival rate was calculated based on the cumulative concentration. The model was applied to a subcutaneous tumor with heterogeneous vascular distributions. Various sized dextrans and doxorubicin were respectively chosen as the nanodrug carrier and the traditional chemotherapeutic agent for comparison. The results showed that: 1) the largest nanoparticle drug in the current simulations yielded the highest cumulative concentration in the well vascular region, but second lowest in the surrounding normal tissues, which implies it has the best therapeutic effect to tumor and at the same time little harmful to normal tissue; 2) on the contrary, molecular chemotherapeutic agent produced the second lowest cumulative concentration in the well vascular tumor region, but highest in the surrounding normal tissue; 3) all drugs have very small cumulative concentrations in the tumor necrotic region, where drug transport is solely through diffusion. This might mean that it is hard to kill tumor stem cells hiding in it. The current model indicated that the effectiveness of the anti-tumor drug delivery was determined by the interplay of the vascular density and nanoparticle size, which governs the drug transport properties. The use of nanoparticles as anti-tumor drug carriers is generally a better choice than molecular chemotherapeutic agent because of its high treatment efficiency on tumor cells and less damage to normal tissues.

Simulation analysis of airflow alteration in the trachea following the vascular ring surgery based on CT images using the computational fluid dynamics method.

This study presents a computational fluid dynamics (CFD) model to simulate the three-dimensional airflow in the trachea before and after the vascular ring surgery (VRS). The simulation was based on CT-scan images of the patients with the vascular ring diseases. The surface geometry of the tracheal airway was reconstructed using triangular mesh by the Amira software package. The unstructured tetrahedral volume meshes were generated by the ANSYS ICEM CFD software package. The airflow in the tracheal airway was solved by the ESI CFD-ACE+ software package. Numerical simulation shows that the pressure drops across the tracheal stenosis before and after the surgery were 0.1789 and 0.0967 Pa, respectively, with the inspiratory inlet velocity 0.1 m/s. Meanwhile, the improvement percentage by the surgery was 45.95%. In the expiratory phase, by contrast, the improvement percentage was 40.65%. When the inspiratory velocity reached 1 m/s, the pressure drop became 4.988~Pa and the improvement percentage was 43.32%. Simulation results further show that after treatment the pressure drop in the tracheal airway was significantly decreased, especially for low inspiratory and expiratory velocities. The CFD method can be applied to quantify the airway pressure alteration and to evaluate the treatment outcome of the vascular ring surgery under different respiratory velocities.

Investigation of the spatiotemporal responses of nanoparticles in tumor tissues with a small-scale mathematical model.

The transport and accumulation of anticancer nanodrugs in tumor tissues are affected by many factors including particle properties, vascular density and leakiness, and interstitial diffusivity. It is important to understand the effects of these factors on the detailed drug distribution in the entire tumor for an effective treatment. In this study, we developed a small-scale mathematical model to systematically study the spatiotemporal responses and accumulative exposures of macromolecular carriers in localized tumor tissues. We chose various dextrans as model carriers and studied the effects of vascular density, permeability, diffusivity, and half-life of dextrans on their spatiotemporal concentration responses and accumulative exposure distribution to tumor cells. The relevant biological parameters were obtained from experimental results previously reported by the Dreher group. The area under concentration-time response curve (AUC) quantified the extent of tissue exposure to a drug and therefore was considered more reliable in assessing the extent of the overall drug exposure than individual concentrations. The results showed that 1) a small macromolecule can penetrate deep into the tumor interstitium and produce a uniform but low spatial distribution of AUC; 2) large macromolecules produce high AUC in the perivascular region, but low AUC in the distal region away from vessels; 3) medium-sized macromolecules produce a relatively uniform and high AUC in the tumor interstitium between two vessels; 4) enhancement of permeability can elevate the level of AUC, but have little effect on its uniformity while enhancement of diffusivity is able to raise the level of AUC and improve its uniformity; 5) a longer half-life can produce a deeper penetration and a higher level of AUC distribution. The numerical results indicate that a long half-life carrier in plasma and a high interstitial diffusivity are the key factors to produce a high and relatively uniform spatial AUC distribution in the interstitium.

PNP equations with steric effects: a model of ion flow through channels.

The flow of current through an ionic channel is studied using the energetic variational approach of Liu applied to the primitive (implicit solvent) model of ionic solutions. This approach allows the derivation of self-consistent (Euler-Lagrange) equations to describe the flow of spheres through channels. The partial differential equations derived involve the global interactions of the spheres and are replaced here with a local approximation that we call steric PNP (Poisson-Nernst-Planck) (Lin, T. C.; Eisenberg, B. To be submitted for publication, 2012). Kong combining rules are used and a range of values of steric interaction parameters are studied. These parameters change the energetics of steric interaction but have no effect on diffusion coefficients in models and simulations. Calculations are made for the calcium (EEEE, EEEA) and sodium channels (DEKA) previously studied in Monte Carlo simulations with comparable results. The biological function is quite sensitive to the steric interaction parameters, and we speculate that a wide range of the function of channels and transporters, even enzymes, might depend on such terms. We point out that classical theories of channels, transporters, and enzymes depend on ideal representations of ionic solutions in which nothing interacts with nothing, even in the enormous concentrations found near and in these proteins or near electrodes in electrochemical cells for that matter. We suggest that a theory designed to handle interactions might be more appropriate. We show that one such theory is feasible and computable: steric PNP allows a direct comparison with experiments measuring flows as well as equilibrium properties. Steric PNP combines atomic and macroscales in a computable formulation that allows the calculation of the macroscopic effects of changes in atomic scale structures (size ~/= 10(-10) meters) studied very extensively in channology and molecular biology.

d,l-Sotalol at therapeutic concentrations facilitates the occurrence of long-lasting non-stationary reentry during ventricular fibrillation in isolated rabbit hearts.

BACKGROUND: The effects of d,l-sotalol at therapeutic concentrations (

Effects of pulsatile blood flow in large vessels on thermal dose distribution during thermal therapy.

The aim of this study is to evaluate the effect of pulsatile blood flow in thermally significant blood vessels on the thermal lesion region during thermal therapy of tumor. A sinusoidally pulsatile velocity profile for blood flow was employed to simulate the cyclic effect of the heart beat on the blood flow. The evolution of temperature field was governed by the energy transport equation for blood flow together with Pennes' bioheat equation for perfused tissue encircling the blood vessel. The governing equations were numerically solved by a novel multi-block Chebyshev pseudospectral method and the accumulated thermal dose in tissue was computed. Numerical results show that pulsatile velocity profile, with various combinations of pulsatile amplitude and frequency, has little difference in effect on the thermal lesion region of tissue compared with uniform or parabolic velocity profile. However, some minor differences on the thermal lesion region of blood vessel is observed for middle-sized blood vessel. This consequence suggests that, in this kind of problem, we may as well do the simulation simply by a steady uniform velocity profile for blood flow.