Fig. 1. A sketch of the cylindrical ion channel of length L and two reservoirs at either end. An ion traverses from the source to the sink reservoir. The free ions can
occasionally bind reversibly with surface protein charges embedded in the channel’s wall.
Pandey, S. (2012). Analytical Modeling of the Ion Number Fluctuations in Biological Ion Channels. Journal of Nanoscience and Nanotechnology, 12(3), 2489–2495. https://doi.org/10.1166/jnn.2012.5771
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Fig. 2. The figure shows the diffusion-influenced time variation of the Green function from Eq. (8a). The channel was assumed to be 40 Å long and the initial pulse is applied
in the middle of the channel. The electric field is not applied here and the pulse decays with time as a result of diffusion.
Pandey, S. (2012). Analytical Modeling of the Ion Number Fluctuations in Biological Ion Channels. Journal of Nanoscience and Nanotechnology, 12(3), 2489–2495. https://doi.org/10.1166/jnn.2012.5771
https://www.ingentaconnect.com/content/asp/jnn/2012/00000012/00000003/art00106;jsessionid=9sa2eo64qp083.x-ic-live-02
Fig. 3. The figure shows the time diffusion and electric field-influenced variation of the Green function from Eq. (8b). The channel was assumed to be 40 Å long and the
initial pulse is applied in the middle of the channel. The pulse decays with time as a result of diffusion and also propagates to the right due to the applied electric field.
Pandey, S. (2012). Analytical Modeling of the Ion Number Fluctuations in Biological Ion Channels. Journal of Nanoscience and Nanotechnology, 12(3), 2489–2495. https://doi.org/10.1166/jnn.2012.5771
https://www.ingentaconnect.com/content/asp/jnn/2012/00000012/00000003/art00106;jsessionid=9sa2eo64qp083.x-ic-live-02
Fig. 4. Comparison of the potassium ion concentration in a cylindri- cal channel (40 Å long and 6 Å wide) obtained from this model and
Brownian dynamics12 in the absence of electric fields.
Pandey, S. (2012). Analytical Modeling of the Ion Number Fluctuations in Biological Ion Channels. Journal of Nanoscience and Nanotechnology, 12(3), 2489–2495. https://doi.org/10.1166/jnn.2012.5771
https://www.ingentaconnect.com/content/asp/jnn/2012/00000012/00000003/art00106;jsessionid=9sa2eo64qp083.x-ic-live-02
Fig. 5. In the presence of an electric field and increasing surface charge concentrations, the energy barrier is lowered and it is easier for ions to pass through the channel
region.
Pandey, S. (2012). Analytical Modeling of the Ion Number Fluctuations in Biological Ion Channels. Journal of Nanoscience and Nanotechnology, 12(3), 2489–2495. https://doi.org/10.1166/jnn.2012.5771
https://www.ingentaconnect.com/content/asp/jnn/2012/00000012/00000003/art00106;jsessionid=9sa2eo64qp083.x-ic-live-02
Fig. 6. The spectral density of particle number fluctuations obtained from Eq. (14) with fixed k a = 104 and values of k d varying
from bottom to top: infinity (free diffusion), 9.91 × 104 , 9.97 × 104 , 9.93 × 103 and 1.01 × 102 .
Pandey, S. (2012). Analytical Modeling of the Ion Number Fluctuations in Biological Ion Channels. Journal of Nanoscience and Nanotechnology, 12(3), 2489–2495. https://doi.org/10.1166/jnn.2012.5771
https://www.ingentaconnect.com/content/asp/jnn/2012/00000012/00000003/art00106;jsessionid=9sa2eo64qp083.x-ic-live-02
Fig. 7. The spectral density of particle number fluctuations obtained from Eq. (14) with fixed kd = 102 and values of ka varying from bottom to top:
infinity (free diffusion), 9.935 × 101 , 9.96 × 102 and 1.014 .
Pandey, S. (2012). Analytical Modeling of the Ion Number Fluctuations in Biological Ion Channels. Journal of Nanoscience and Nanotechnology, 12(3), 2489–2495. https://doi.org/10.1166/jnn.2012.5771
https://www.ingentaconnect.com/content/asp/jnn/2012/00000012/00000003/art00106;jsessionid=9sa2eo64qp083.x-ic-live-02