Fig 1.
Steady-state activation and inactivation gating variables of Shaker in a Drosophila R1-6 photoreceptor.
A fraction of the conductance, ΞΎ = 0.13, fails to inactivate. Serotonin shifts Shaker activation and inactivation steady-state gating variables towards more depolarised potentials. The activation and inactivation curves are shown in bold blue and red lines, respectively. The shift in the activation and inactivation curves induced by serotonin is shown in thin lines.
Fig 2.
Steady-state activation and inactivation gating variables of Shab in a Drosophila R1-6 photoreceptor.
Serotonin shifts Shab activation and inactivation steady-state gating variables towards more depolarised potentials, while PIP2 depletion by light shifts activation towards hyperpolarised potentials. The activation and inactivation curves are shown in bold blue and red lines, respectively. The shifts in the activation and inactivation curves induced by serotonin or PIP2 depletion are shown in thin lines.
Fig 3.
Steady-state activation gating variable of the Novel conductance in a Drosophila R1-6 photoreceptor.
Fig 4.
Voltage responses of simulated Drosophila melanogaster R1-6 photoreceptors to 0.01 nA injected current pulses (a) Voltage response of a dark adapted membrane. Three curves are plotted. Continuous line shows the result of a simulation where all gating variables are allowed to change following Hodkgin-Huxley equations, and thus the voltage response shows both negative and positive feedback. Dotted line is the result of a simulation where inactivation gating variables of all conductances are kept fixed in their steady-state value, and thus there is negative feedback but no positive feedback. Dashed line shows the result of keeping all gating variables (activation and inactivation) fixed during simulation, or equivalently, the voltage response of a passive membrane with the same membrane resistance and capacitance. (b) Same as (a) but in a photoreceptor that has been depolarised by light to -59 mV. (c) Same as (a) and (b) but in a photoreceptor that has been depolarised by light to -41 mV.
Fig 5.
The effects of feedback produced by K+ conductances on a model photoreceptor, at dark resting potential and depolarised by light-induced current to four steady-state membrane potentials (a) Photoreceptor impedance in simulated photoreceptors depolarised by light to different voltages (solid lines). Dashed lines represent the membrane impedances of photoreceptors with frozen conductances, i.e. where the activation and inactivation gating variables are kept constant at each steady state when computing the impedance. They are RC membranes with the photoreceptor capacitance and true membrane capacitance fixed at the value taken in that particular voltage. The low frequency limits and values of the impedance at 2 Hz are represented in subfigures (b) and (c). (d) The bandwidth of simulated photoreceptors with active K+ conductances (solid line) depolarised by light to different voltages versus the bandwidth of photoreceptors with frozen conductances at each voltage (dashed line). (e) Photoreceptor energy consumption increases with depolarisation. At each depolarisation, the cost of an active fruit-fly photoreceptor (filled circles) is smaller than that of a passive photoreceptor with the same bandwidth and capacitance (empty circles).
Fig 6.
The contributions of the three voltage-dependent K+ conductances to the gain-bandwidth product (GBWP) of the photoreceptor membrane, over the range of depolarisation produced by the light induced current.
(a) GBWP of a fruit fly model photoreceptor across different light levels. Circles joined with black solid lines result from a model where only Shaker activation and inactivation gating variables are active, while the other two conductances are frozen, i.e. kept constant at each steady state when computing the impedance. Circles joined with grey solid lines are the result of the model with all active conductances, and circles joined with dashed lines are GBWP of the passive membrane, i.e. when all gating variables are frozen. (b) Same as (a) but keeping Shab activation and inactivation gating variables active, and freezing those of Shaker and Novel. (c) Same as (a) but keeping the Novel activation gating variable active, and freezing those of Shaker and Novel.
Fig 7.
Inactivation of the voltage-dependent K+ conductances affects the bandwidth and energy consumption of photoreceptors.
(a) Bandwidth at different membrane voltages of the photoreceptor (black line with colour circles) compared to that of photoreceptors where inactivation of the voltage-dependent conductances has been frozen, i.e. kept constant at the value corresponding to the circle of the same color. (b) As in (a), but plotting energy consumption against membrane voltage. (c) As in (a), but plotting energy consumption against bandwidth. (d) As in (c), but now the intact model (continuous line) is compared to a model in which the dynamics of inactivation have been accelerated so as to be the same as those of activation (dashed line).
Fig 8.
Voltage-dependent K+ conductances reduce contrast gain and increase contrast-gain-bandwidth product (cGBWP).
(a) Contrast gain of the active photoreceptors (solid line) compared to the contrast gain of passive photoreceptors with the same resistance, depolarising leak conductance and capacitance (dotted line). Photoreceptors depolarised by light-induced current (LiC) to steady-state values of membrane potential indicated by coloured points in (b). Contrast gain for the completely dark adapted photoreceptor does not appear in the log-log plot as it is 0 mV. (b) cGBWP of the active photoreceptors (solid line) compared to the cGBWP of passive photoreceptors with the same resistance, depolarising leak conductance and capacitance (coloured points joined with dashed line).
Fig 9.
When PIP2 depletion shifts the voltage activation ranges of Shab, membrane impedance decreases, and bandwidth and energy costs increase.
(a) Impedance with (solid lines) and without (dashed lines) the action of PIP2 depletion at four levels of depolarisation produced by changing the LiC. Dashed lines are the same as continuous lines in Fig 5a. (b) Bandwidth with (solid) and without (dashed) the action of PIP2 depletion. LiC fixed to values producing levels of depolarisation indicated by the key in (a). The leftward shift of coloured points indicates that PIP2 depletion hyperpolarises the membrane at rest, and at the 4 levels of LiC. (c) Energy cost, calculated as the rate of consumption of ATP, with (solid) and without (dashed) the action of PIP2 depletion on Shab.
Fig 10.
When serotonin shifts the voltage activation ranges of Shaker and Shab, membrane impedance increases, and bandwidth and energy costs decrease.
(a) Impedance with (solid curves) and without (dashed curves) the action of serotonin at four levels of depolarisation produced by fixing the LiC. (b) Bandwidth with (solid) and without (dashed) the action of serotonin. LiC fixed to values producing levels of depolarisation indicated by the key in (a). The rightward shift of coloured points indicates that serotonin depolarises the membrane at rest, and at the 4 levels of LiC. (c) Energy cost, calculated as the rate of consumption of ATP, with (solid) and without (dashed) the action of serotonin on Shaker and Shab.
Fig 11.
The contributions of different modulations to the gain-bandwidth product (GBWP) of the photoreceptor membrane, over the range of depolarisation produced by the light induced current.
(a) Circles joined with black solid lines result from a model where Shab and Shaker have been modulated by PIP2 depletion. Circles joined with grey solid lines are the GBWP of the unmodulated photoreceptors, and circles joined with dashed lines are GBWP of the passive membrane, i.e. when all gating variables are frozen. (b) Same as (a) but reducing Shab conductance by 50%. (c) Same as (a) but with serotonin shifting Shaker and Shab activation and inactivation curves.
Fig 12.
Contrast gain with (solid curves) and without (dashed curves) the modulator shift at four levels of depolarisation.
(a) Light-dependent modulation (b) Serotonin.
Fig 13.
Modulators shift bandwidth, peak contrast gain and energy consumption of photoreceptors (a) Bandwidth and contrast gain plotted against each other with (solid curves) and without (dashed curves) modulation at four levels of depolarisation produced by fixing the LiC. (b) Energy consumption and bandwidth plotted against each other with (solid curves) and without (dashed curves) modulation at four levels of depolarisation produced by fixing the LiC. (c) Energy consumption and peak contrast gain plotted against each other with (solid curves) and without (dashed curves) modulation at four levels of depolarisation produced by fixing the LiC.
Fig 14.
Shifts in voltage-dependent K+ conductances produced by modulators trade-off gain and bandwidth but have little influence on the cost of the contrast-gain-bandwidth product (cGBWP).
(a) Bandwidth and peak contrast gain for the model photoreceptor with unshifted conductances (dashed black line) where light-induced conductance has been increased to depolarise to four membrane potentials (colour circles). At each of these membrane potentials the light-induced conductance remained constant, and the photoreceptor was allowed to reach a new depolarisation (coloured circles on coloured lines). (b) The original (black dashed line) and shifted (coloured lines, colour code as in (a)) photoreceptors occupy a similar space in a cGBWP vs energy cost graph, illustrating that modulators changing channel properties have little effect in the cost of cGBWP.
Fig 15.
Neuromodulators trade-off photoreceptor gain and bandwidth.
The model photoreceptor is shown with unshifted conductances (dashed black line) or with conductances shifted by neuromodulators (coloured lines).