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1.
J Laryngol Otol ; 134(6): 519-525, 2020 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-32613920

RESUMO

OBJECTIVE: To present our data evaluating the feasibility of simultaneous cochlear implantation with resection of acoustic neuroma. METHODS: This paper describes a case series of eight adult patients with a radiologically suspected acoustic neuroma, treated at a tertiary referral centre in Newcastle, Australia, between 2012 and 2015. Patients underwent cochlear implantation concurrently with removal of an acoustic neuroma. The approach was translabyrinthine, with facial nerve monitoring and electrically evoked auditory brainstem response testing. Standard post-implant rehabilitation was employed, with three and six months' follow-up data collected. The main outcome measures were: hearing, subjective benefit of implant, operative complications and tumour recurrence. RESULTS: Eight patients underwent simultaneous cochlear implantation with resection of acoustic neuroma over a 3-year period, and had 25-63 months' follow up. There were no major complications. All patients except one gained usable hearing and were daily implant users. CONCLUSION: Simultaneous cochlear implantation with resection of acoustic neuroma has been shown to be a safe treatment option, which will be applicable in a wide range of clinical scenarios as the indications for cochlear implantation continue to expand.


Assuntos
Implante Coclear/métodos , Terapia Combinada/métodos , Audição/fisiologia , Neuroma Acústico/cirurgia , Adolescente , Idoso , Austrália/epidemiologia , Terapia Combinada/estatística & dados numéricos , Potenciais Evocados Auditivos do Tronco Encefálico/fisiologia , Nervo Facial/cirurgia , Estudos de Viabilidade , Seguimentos , Testes Auditivos/métodos , Humanos , Pessoa de Meia-Idade , Recidiva Local de Neoplasia/epidemiologia , Neuroma Acústico/diagnóstico por imagem , Neuroma Acústico/patologia , Neuroma Acústico/reabilitação , Complicações Pós-Operatórias/epidemiologia , Estudos Retrospectivos , Centros de Atenção Terciária , Resultado do Tratamento
4.
Artigo em Inglês | MEDLINE | ID: mdl-24329301

RESUMO

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.


Assuntos
Canais de Cálcio/genética , Canais de Cálcio/metabolismo , Modelos Biológicos , Mutação , Canais de Sódio/genética , Canais de Sódio/metabolismo , Cálcio/metabolismo , Reprodutibilidade dos Testes , Sódio/metabolismo , Especificidade por Substrato , Termodinâmica
5.
Phys Biol ; 10(2): 026007, 2013 Apr.
Artigo em Inglês | MEDLINE | ID: mdl-23481350

RESUMO

We report self-consistent Brownian dynamics simulations of a simple electrostatic model of the selectivity filters (SF) of calcium ion channels. They reveal regular structure in the conductance and selectivity as functions of the fixed negative charge Qf at the SF. With increasing Qf, there are distinct regions of high conductance (conduction bands) M0, M1, M2 separated by regions of almost zero-conductance (stop-bands). Two of these conduction bands, M1 and M2, are related to the saturated calcium occupancies of P = 1 and P = 2, respectively and demonstrate self-sustained conductivity. Despite the model's limitations, its M1 and M2 bands show high calcium selectivity and prominent anomalous mole fraction effects and can be identified with the L-type and RyR calcium channels. The non-selective band M0 can be identified with a non-selective cation channel, or with OmpF porin.


Assuntos
Canais de Cálcio/metabolismo , Cálcio/metabolismo , Simulação por Computador , Modelos Biológicos , Canais de Cálcio/química , Condutividade Elétrica , Eletricidade Estática
6.
Aust Dent J ; 57(3): 379-87, 2012 Sep.
Artigo em Inglês | MEDLINE | ID: mdl-22924365

RESUMO

Dental surgeons may encounter in their clinical practice patients who present with aggressive pathologies that require early diagnosis and prompt treatment. This action may limit the extent of tissue damage and, where relevant, improve survival outcome. Clinicians should therefore be aware of the range of resective, reconstructive and rehabilitative options that are available in the management of these patients. We present our experience with the free fibula flap used for oromandibular reconstruction; this was undertaken in 21 patients following resective surgery for malignant pathology, cytologically benign but biologically aggressive odontogenic pathology and radiation induced osteonecrosis. We also review the history, surgical anatomy, surgical assessment and potential complications that are relevant to the free fibula flap.


Assuntos
Retalhos de Tecido Biológico , Doenças Maxilomandibulares/cirurgia , Mandíbula/cirurgia , Reconstrução Mandibular/métodos , Procedimentos Cirúrgicos Bucais/métodos , Adolescente , Adulto , Idoso , Carcinoma de Células Escamosas/cirurgia , Feminino , Retalhos de Tecido Biológico/efeitos adversos , Humanos , Masculino , Mandíbula/diagnóstico por imagem , Reconstrução Mandibular/efeitos adversos , Pessoa de Meia-Idade , Cistos Odontogênicos/cirurgia , Osteorradionecrose/cirurgia , Radiografia
7.
J Anal Toxicol ; 35(4): 199-204, 2011 May.
Artigo em Inglês | MEDLINE | ID: mdl-21513612

RESUMO

Imidocarb [N,N'-bis[3-(4,5-dihydro-1H-imidazol-2-yl)phenyl]urea, C(19)H(20)N(6)O(1), m.w. 348.41] is a symmetrical carbanilide derivative used to treat disease caused by protozoans of the Babesia genus. Imidocarb, however, is also considered capable of suppressing Babesia-specific immune responses, allowing Babesia-positive horses to pass a complement fixation test (CFT) without eliminating the infection. This scenario could enable Babesia-infected horses to pass CFT-based importation tests. It is imperative to unequivocally identify and quantify equine tissue residues of imidocarb by mass spectrometry to address this issue. As a pretext to development of sensitive tissue assays, we have investigated possibilities of mass spectrometric (MS) detection of imidocarb. Our analyses disclosed that an unequivocal mass spectral analysis of imidocarb is challenging because of its rapid fragmentation under standard gas chromatography (GC)-MS conditions. In contrast, solution chemistry of imidocarb is more stable but involves distribution into mono- and dicationic species, m/z 349 and 175, respectively, in acid owing to the compound's inherent symmetrical nature. Dicationic imidocarb was the preferred complex as viewed by either direct infusion-electrospray-MS or by liquid chromatography (LC)-MS. Dicationic imidocarb multiple reaction monitoring (MRM: m/z 175 → 162, 145, and 188) therefore offer the greatest opportunities for sensitive detection and LC-MS is more likely than GC-MS to yield a useful quantitative forensic analytical method for detecting imidocarb in horses.


Assuntos
Antiprotozoários/química , Imidocarbo/química , Espectrometria de Massas/métodos , Antiprotozoários/análise , Cromatografia Líquida , Cromatografia Gasosa-Espectrometria de Massas , Imidocarbo/análise
8.
Osteoporos Int ; 22(10): 2677-88, 2011 Oct.
Artigo em Inglês | MEDLINE | ID: mdl-21271340

RESUMO

UNLABELLED: Intra-and inter-reader reliability of semi-automated quantitative vertebral morphometry measurements was determined using lateral computed tomography (CT) scout views. The method requires less time than conventional morphometry. Reliability was excellent for vertebral height measurements, good for height ratios, and comparable to semi-quantitative grading by radiologists for identification of vertebral fractures. INTRODUCTION: Underdiagnosis and undertreatment of vertebral fracture (VFx) is a well-known problem worldwide. Thus, new methods are needed to facilitate identification of VFx. This study aimed to determine intra- and inter-reader reliability of semi-automated quantitative vertebral morphometry based on shape-based statistical modeling (SpineAnalyzer, Optasia Medical, Cheadle, UK). METHODS: Two non-radiologists independently assessed vertebral morphometry from CT lateral scout views at two time points in 96 subjects (50 men, 46 women, 70.3 ± 8.9 years) selected from the Framingham Heart Study Offspring and Third Generation Multi-Detector CT Study. VFxs were classified based solely on morphometry measurements using Genant's criteria. Intraclass correlation coefficients (ICCs), root mean squared coefficient of variation (RMS CV) and kappa (k) statistics were used to assess reliability. RESULTS: We analyzed 1,246 vertebrae in 96 subjects. The analysis time averaged 5.4 ± 1.7 min per subject (range, 3.2-9.1 min). Intra-and inter-reader ICCs for vertebral heights were excellent (>0.95) for all vertebral levels combined. Intra-and inter-reader RMS CV for height measurements ranged from 2.5% to 3.9% and 3.3% to 4.4%, respectively. Reliability of vertebral height ratios was good to fair. Based on morphometry measurements alone, readers A and B identified 51-52 and 46-59 subjects with at least one prevalent VFx, respectively, and there was a good intra-and inter-reader agreement (k = 0.59-0.69) for VFx identification. CONCLUSIONS: Semi-automated quantitative vertebral morphometry measurements from CT lateral scout views are convenient and reproducible, and may facilitate assessment of VFx.


Assuntos
Vértebras Lombares/diagnóstico por imagem , Fraturas da Coluna Vertebral/diagnóstico por imagem , Vértebras Torácicas/diagnóstico por imagem , Tomografia Computadorizada por Raios X/estatística & dados numéricos , Idoso , Idoso de 80 Anos ou mais , Algoritmos , Feminino , Humanos , Vértebras Lombares/anatomia & histologia , Masculino , Pessoa de Meia-Idade , Variações Dependentes do Observador , Reprodutibilidade dos Testes , Vértebras Torácicas/anatomia & histologia
9.
Phys Rev E Stat Nonlin Soft Matter Phys ; 80(2 Pt 1): 021925, 2009 Aug.
Artigo em Inglês | MEDLINE | ID: mdl-19792169

RESUMO

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the current-voltage characteristics obtained are in good quantitative agreement with experimental measurements.


Assuntos
Condutividade Elétrica , Ativação do Canal Iônico , Canais Iônicos/metabolismo , Modelos Biológicos , Difusão , Canais Iônicos/química , Modelos Lineares , Porosidade , Eletricidade Estática
10.
Ann Rheum Dis ; 67(12): 1724-31, 2008 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-18250115

RESUMO

OBJECTIVE: To study the effects in systemic lupus erythaematosus (SLE) of B cell directed therapy with rituximab, a chimeric monoclonal antibody directed at CD20+ B cells, without concomitant immunosuppressive therapy in mild to moderate SLE. METHODS: Patients (n=24) with active SLE and failure of >or=1 immunosuppressive were recruited from three university centres into this phase I/II prospective open-label study. Patients were followed for 1 year to assess safety, efficacy and biological effects. RESULTS: In total, 18 of the patients scheduled to receive the full lymphoma dose of rituximab were evaluable for B cell levels in peripheral blood. Of these, 17 had effective CD19+ B cell depletion (<5 cells/microl). However, six of the depleted patients showed B cell return before 24 weeks. A total of 70% of patients improved by week 55, as defined by an SLE Disease Activity Index (SLEDAI) score improvement of >or=2 units from baseline. The degree of CD19+ B cell depletion was correlated with SLEDAI improvement at week 15 (r=0.84). In general, rituximab infusions were well tolerated. Approximately a third of the patients developed human anti-chimeric antibody (HACA) titres, which correlated with poor B cell depletion. Most patients (9 of 14) did not respond to immunisations with Pneumovax and tetanus toxoid. CONCLUSIONS: Rituximab is a promising new therapy for SLE. The variability of responses in patients with SLE may be related to HACA formation. The failure to respond to immunisations is surprising, in view of the apparently low risk of infections. Better biological markers are necessary to follow these patients during treatment.


Assuntos
Anticorpos Monoclonais/uso terapêutico , Imunossupressores/uso terapêutico , Lúpus Eritematoso Sistêmico/tratamento farmacológico , Adulto , Anticorpos Monoclonais/efeitos adversos , Anticorpos Monoclonais Murinos , Antígenos CD20/imunologia , Linfócitos B/efeitos dos fármacos , Feminino , Humanos , Imunossupressores/efeitos adversos , Lúpus Eritematoso Sistêmico/imunologia , Contagem de Linfócitos , Depleção Linfocítica/métodos , Masculino , Pessoa de Meia-Idade , Estudos Prospectivos , Rituximab , Resultado do Tratamento , Adulto Jovem
11.
Eur J Appl Math ; 19(5): 541-569, 2008.
Artigo em Inglês | MEDLINE | ID: mdl-19809600

RESUMO

Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst-Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current-voltage (I-V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I-V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).

12.
Nature ; 447(7143): 376, 2007 May 24.
Artigo em Inglês | MEDLINE | ID: mdl-17522654
13.
Biosens Bioelectron ; 23(2): 183-90, 2007 Sep 30.
Artigo em Inglês | MEDLINE | ID: mdl-17507211

RESUMO

We demonstrate the microfabrication of a low-noise silicon based device with integrated silver/silver chloride electrodes used for the measurement of single ion channel proteins. An aperture of 150 microm diameter was etched in a silicon substrate using a deep silicon reactive ion etcher and passivated with 30 nm of polytetrafluoroethylene via chemical vapor deposition. The average recorded noise in measurements of lipid bilayers was reduced by a factor of four through patterning of a 75 microm thick SU-8 layer around the aperture. Integrated electrodes were fabricated on both sides of the device and used for repeatable, stable, giga-seal bilayer formations as well as characteristic measurements of the transmembrane protein OmpF porin.


Assuntos
Técnicas Biossensoriais/instrumentação , Eletroquímica/instrumentação , Canais Iônicos/química , Bicamadas Lipídicas/química , Microeletrodos , Porinas/química , Silício/química , Biomimética/instrumentação , Biomimética/métodos , Técnicas Biossensoriais/métodos , Eletroquímica/métodos , Desenho de Equipamento , Análise de Falha de Equipamento , Reprodutibilidade dos Testes , Sensibilidade e Especificidade , Integração de Sistemas
15.
Eur Biophys J ; 34(4): 314-22, 2005 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-15756588

RESUMO

The access resistance (AR) of a channel is an important component of the conductance of ion channels, particularly in wide and short channels, where it accounts for a substantial fraction of the total resistance to the movement of ions. The AR is usually calculated by using a classical and simple expression derived by Hall from electrostatics (J.E. Hall 1975 J. Gen. Phys. 66:531-532), though other expressions, both analytical and numerical, have been proposed. Here we report some numerical results for the AR of a channel obtained by solving the Poisson-Nernst-Planck equations at the entrance of a circular pore. Agreement is found between numerical calculations and analytical results from Hall's equation for uncharged pores in neutral membranes. However, for channels embedded in charged membranes, Hall's expression overestimates the AR, which is much lower and can even be neglected in some cases. The weak dependence of AR on the pore radius for charged membranes at low salt concentration can be exploited to separate the channel and the access contributions to the measured conductance.


Assuntos
Biologia Computacional/métodos , Transporte Biológico , Biofísica/métodos , Membrana Celular/metabolismo , Simulação por Computador , Difusão , Condutividade Elétrica , Impedância Elétrica , Transporte de Íons , Íons , Cinética , Modelos Biológicos , Modelos Moleculares , Modelos Estatísticos , Distribuição de Poisson , Sais/farmacologia , Cloreto de Sódio/farmacologia , Eletricidade Estática
16.
Phys Rev E Stat Nonlin Soft Matter Phys ; 70(5 Pt 1): 051912, 2004 Nov.
Artigo em Inglês | MEDLINE | ID: mdl-15600661

RESUMO

The ionic current flowing through a protein channel in the membrane of a biological cell depends on the concentration of the permeant ion, as well as on many other variables. As the concentration increases, the rate of arrival of bath ions to the channel's entrance increases, and typically so does the net current. This concentration dependence is part of traditional diffusion and rate models that predict Michaelis-Menten current-concentration relations for a single ion channel. Such models, however, neglect other effects of bath concentrations on the net current. The net current depends not only on the entrance rate of ions into the channel, but also on forces acting on ions inside the channel. These forces, in turn, depend not only on the applied potential and charge distribution of the channel, but also on the long-range Coulombic interactions with the surrounding bath ions. In this paper, we study the effects of bath concentrations on the average force on an ion in a single ion channel. We show that the force of the reaction field on a discrete ion inside a channel embedded in an uncharged lipid membrane contains a blocking (shielding) term that is proportional to the square root of the ionic bath concentration. We then show that different blocking strengths yield different behavior of the current-concentration and conductance-concentration curves. Our theory shows that at low concentrations, when the blocking force is weak, conductance grows linearly with concentration, as in traditional models, e.g., Michaelis-Menten formulations. As the concentration increases to a range of moderate shielding, conductance grows as the square root of concentration, whereas at high concentrations, with high shielding, conductance may actually decrease with increasing concentrations: the conductance-concentration curve can invert. Therefore, electrostatic interactions between bath ions and the single ion inside the channel can explain the different regimes of conductance-concentration relations observed in experiments.


Assuntos
Membrana Celular/química , Membrana Celular/fisiologia , Ativação do Canal Iônico/fisiologia , Canais Iônicos/química , Canais Iônicos/fisiologia , Modelos Biológicos , Modelos Químicos , Animais , Simulação por Computador , Humanos , Potenciais da Membrana/fisiologia
17.
Phys Rev E Stat Nonlin Soft Matter Phys ; 70(6 Pt 1): 061106, 2004 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-15697340

RESUMO

Flux between regions of different concentration occurs in nearly every device involving diffusion, whether an electrochemical cell, a bipolar transistor, or a protein channel in a biological membrane. Diffusion theory has calculated that flux since the time of Fick (1855), and the flux has been known to arise from the stochastic behavior of Brownian trajectories since the time of Einstein (1905), yet the mathematical description of the behavior of trajectories corresponding to different types of boundaries is not complete. We consider the trajectories of noninteracting particles diffusing in a finite region connecting two baths of fixed concentrations. Inside the region, the trajectories of diffusing particles are governed by the Langevin equation. To maintain average concentrations at the boundaries of the region at their values in the baths, a control mechanism is needed to set the boundary dynamics of the trajectories. Different control mechanisms are used in Langevin and Brownian simulations of such systems. We analyze models of controllers and derive equations for the time evolution and spatial distribution of particles inside the domain. Our analysis shows a distinct difference between the time evolution and the steady state concentrations. While the time evolution of the density is governed by an integral operator, the spatial distribution is governed by the familiar Fokker-Planck operator. The boundary conditions for the time dependent density depend on the model of the controller; however, this dependence disappears in the steady state, if the controller is of a renewal type. Renewal-type controllers, however, produce spurious boundary layers that can be catastrophic in simulations of charged particles, because even a tiny net charge can have global effects. The design of a nonrenewal controller that maintains concentrations of noninteracting particles without creating spurious boundary layers at the interface requires the solution of the time-dependent Fokker-Planck equation with absorption of outgoing trajectories and a source of ingoing trajectories on the boundary (the so called albedo problem).


Assuntos
Membrana Celular/química , Membrana Celular/fisiologia , Canais Iônicos/química , Canais Iônicos/fisiologia , Modelos Biológicos , Modelos Químicos , Transporte Biológico/fisiologia , Simulação por Computador , Difusão , Modelos Estatísticos , Tamanho da Partícula
18.
Phys Rev E Stat Nonlin Soft Matter Phys ; 68(2 Pt 1): 021905, 2003 Aug.
Artigo em Inglês | MEDLINE | ID: mdl-14525004

RESUMO

In an electrostatic problem with nonuniform geometry, a charge Q in one region induces surface charges [called dielectric boundary charges (DBC)] at boundaries between different dielectrics. These induced surface charges, in return, exert a force [called dielectric boundary force (DBF)] on the charge Q that induced them. The DBF is often overlooked. It is not present in standard continuum theories of (point) ions in or near membranes and proteins, such as Gouy-Chapman, Debye-Huckel, Poisson-Boltzmann or Poisson-Nernst- Planck. The DBF is important when a charge Q is near dielectric interfaces, for example, when ions permeate through protein channels embedded in biological membranes. In this paper, we define the DBF and calculate it explicitly for a planar dielectric wall and for a tunnel geometry resembling the ionic channel gramicidin. In general, we formulate the DBF in a form useful for continuum theories, namely, as a solution of a partial differential equation with boundary conditions. The DBF plays a crucial role in the permeation of ions through the gramicidin channel. A positive ion in the channel produces a DBF of opposite sign to that of the fixed charge force (FCF) produced by the permanent charge of the gramicidin polypeptide, and so the net force on the positive ion is reduced. A negative ion creates a DBF of the same sign as the FCF and so the net (repulsive) force on the negative ion is increased. Thus, a positive ion can permeate the channel, while a negative ion is excluded from it. In gramicidin, it is this balance between the FCF and DBF that allows only singly charged positive ions to move into and through the channel. The DBF is not directly responsible, however, for selectivity between the alkali metal ions (e.g., Li+, Na+, K+): we prove that the DBF on a mobile spherical ion is independent of the ion's radius.


Assuntos
Gramicidina/química , Fenômenos Biofísicos , Biofísica , Cálcio/química , Íons , Modelos Químicos
20.
Phys Rev E Stat Nonlin Soft Matter Phys ; 64(3 Pt 2): 036116, 2001 Sep.
Artigo em Inglês | MEDLINE | ID: mdl-11580403

RESUMO

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time averages over long times of the motion of a quasiparticle that diffuses with the same diffusion coefficient as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.


Assuntos
Íons , Modelos Moleculares , Eletrofisiologia , Modelos Estatísticos , Modelos Teóricos , Distribuição de Poisson , Eletricidade Estática
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