Abstract. In this work, we examine effects of permanent charges on ionic flows through ion channels via a quasi-one-dimensional classical Poisson-Nernst-Planck (PNP) model. The geometry of the three-dimensional channel is presented in this model to a certain extent, which is crucial for the study in this paper. Two ion species, one positively charged and one negatively charged, are considered with a simple profile of permanent charges: zeros at the two end regions and a constant Q 0 over the middle region. The classical PNP model can be viewed as a boundary value problem (BVP) of a singularly perturbed system. The singular orbit of the BVP depends on Q 0 in a regular way. Assuming |Q 0 | is small, a regular perturbation analysis is carried out for the singular orbit. Our analysis indicates that effects of permanent charges depend on a rich interplay between boundary conditions and the channel geometry. Furthermore, interesting common features are revealed: for Q 0 = 0, only an average quantity of the channel geometry plays a role; however, for Q 0 = 0, details of the channel geometry matter; in particular, to optimize effects of a permanent charge, the channel should have a short and narrow neck within which the permanent charge is confined. The latter is consistent with structures of typical ion channels.Key words. ionic flow, permanent charge, channel geometry AMS subject classifications. 34A26, 34B16, 34D15, 37D10, 92C35 DOI. 10.1137/140992527 Introduction.In this work, we analyze effects of permanent charges on ionic flows through ion channels, based on a quasi-one-dimensional classical PoissonNernst-Planck (PNP) model. The geometry of the three-dimensional channel is presented in this model to a certain extent, which is crucial for the study in this paper. We start with a brief discussion of the biological background of ion channel problems, a quasi-one-dimensional PNP model, and the main concern of our work in this paper.

In this work, we analyze a one-dimensional steady-state Poisson-Nernst-Planck-type model for ionic flow through a membrane channel with fixed boundary ion concentrations (charges) and electric potentials. We consider two ion species, one positively charged and one negatively charged, and assume zero permanent charge. A local hard-sphere potential that depends pointwise on ion concentrations is included in the model to account for ion size effects on the ionic flow. The model problem is treated as a boundary value problem of a singularly perturbed differential system. Our analysis is based on the geometric singular perturbation theory but, most importantly, on specific structures of this concrete model. The existence of solutions to the boundary value problem for small ion sizes is established and, treating the ion sizes as small parameters, we also derive an approximation of the I-V (current-voltage) relation and identify two critical potentials or voltages for ion size effects. Under electroneutrality (zero net charge) boundary conditions, each of these two critical potentials separates the potential into two regions over which the ion size effects are qualitatively opposite to each other. On the other hand, without electroneutrality boundary conditions, the qualitative effects of ion sizes will depend not only on the critical potentials but also on boundary concentrations. Important scaling laws of I-V relations and critical potentials in boundary concentrations are obtained. Similar results about ion size effects on the flow of matter are also discussed. Under electroneutrality boundary conditions, the results on the first order approximation in ion diameters of solutions, I-V relations, and critical potentials agree with those with a nonlocal hard-sphere potential examined by Ji and Liu [J. Dynam. Differential Equations, 24 (2012), pp. 955-983].

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Financial rewards and professional development were the two main predictors of job satisfaction. To improve CHS in China, policy-makers (especially the central government) need to consider the impact of current policies on job satisfaction in order to reduce job dissatisfaction.

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BackgroundHealth reform in China since 2009 has emphasized basic public health services to enhance the function of Community Health Services as a primary health care facility. A variety of studies have documented these efforts, and the challenges these have faced, yet up to now the experience of primary health care (PHC) providers in terms of how they have coped with these changes remains underdeveloped. Despite the abundant literature on psychological coping processes and mechanisms, the application of coping research within the context of human resources for health remains yet to be explored. This research aims to understand how PHC providers coped with the new primary health care model and the job characteristics brought about by these changes.MethodsSemi-structured interviews with primary health care workers were conducted in Jinan city of Shandong province in China. A maximum variation sampling method selected 30 PHC providers from different specialties. Thematic analysis was used drawing on a synthesis of theories related to the Job Demands-Resources model, work adjustment, and the model of exit, voice, loyalty and neglect to understand PHC providers’ coping strategies.ResultsOur interviews identified that the new model of primary health care significantly affected the nature of primary health work and triggered a range of PHC providers’ coping processes. The results found that health workers perceived their job as less intensive than hospital medical work but often more trivial, characterized by heavy workload, blurred job description, unsatisfactory income, and a lack of professional development. However, close relationship with community and low work pressure were satisfactory. PHC providers’ processing of job demands and resources displayed two ways of interaction: aggravation and alleviation. Processing of job demands and resources led to three coping strategies: exit, passive loyalty, and compromise with new roles and functions.ConclusionsPrimary health care providers employed coping strategies of exit, passive loyalty, and compromise to deal with changes in primary health work. In light of these findings, our paper concludes that it is necessary for the policymakers to provide further job resources for CHS, and involve health workers in policy-making. The introduction of particular professional training opportunities to support job role orientation for PHC providers is advocated.