All fundamental self-sustaining processes of living organisms are based on their ability to receive, process, create and transmit signals. Human sensory systems receive a vast variety of signals, including photonic, acoustic, thermal, mechanical, and chemical ones. All of these signals must be converted into electric signals for the brain to process. Ion channels are the devices that transform all kind of mechanical, physical, and chemical signals into electric signals, which are transferred to the brain via neurons. Ion channels control a wide variety of important physiological processes, ranging from nerve and muscle excitation, muscle contraction, action potential generation and resting, sensory transduction, cell volume and blood pressure regulation, cell proliferation, hormone secretion, fertilization, maintenance of salt and water balance, metabolism of certain viruses, neurotoxicology, learning and memory, to programmed cell death. Some genetic diseases (channelopathies) are directly linked to malfunctioning of ion channel components. The impact of trauma or chronic traumatic encephalopathy on cell membranes, ion channels of axons and neurons and astrocytes is an active research front. Ion channel aggregation and collective motion play a significant role in synaptic plasticity and memory. Due to their paramount importance, there is a huge ion-channel community in contemporary biology. About 40% of all drugs target ion channels. Similarly, gap junctions are intercellular channels that allow various molecules and ions to pass between cells. Transmembrane brushes and transmembrane transporters are important for maintaining a proper material balance in cells. Ion channels, gap junctions and transmembrane transporters can vary two orders in their spatial and time scales. Currently, the study of ion channels, gap junctions and transmembrane transporters is an underrepresented field in the mathematical biology community. Apparently, a major barrier for mathematical scientists to work in this exciting field is the lack of knowledge concerning recent experiments on ion channels and gap junctions, while a major barrier for biologists in formulating sophisticated computational models is their lack of knowledge concerning the development in the last couple decades of modern mathematical tools and techniques. This workshop is designed to help bridge gaps between biologists and mathematicians. This workshop will cover a wide range of topics in mathematical modeling of ion channels and gap junctions, and their applications to specific research problems. The specific range will of course depend on the ultimate list of participants and speakers, but example topics are ion channels structures; ion channel-membrane interaction; ion channel gating mechanism; ion channel-neuron interfaces; Brownian dynamics; Langevin dynamics; stochastic models; rare event analysis; Markov process and master equation; molecular dynamics; mean field models; generalized Poisson-Nernst-Planck equations; electro-elastic models; fluid-electro-elastic models; complex fluid; inverse design; micro-macro models; continuum-discrete models; electrohydrodynamics of ion channel systems; and differential geometry based multiscale models. Emphasis will be placed on the application of the aforementioned models, theories, methods and algorithms to the better understanding of the structure, dynamics and transport of ion channels and gap junctions. This workshop will take the advantage of recently mathematical advances in stochastic and stochastic-hybrid systems for ion channel analysis. This workshop will significantly strengthen the existing collaborations between mathematicians and biologists, broaden their horizons to higher synergies, and further stimulate information flow "from biology to mathematics", i.e., to introduce new bio-inspired mathematical models, such as partial differential equations (PDEs), molecular manifolds, molecular Euler characteristics, etc, to graduate students and recent doctoral recipients.