We intend to build an artificial neuron using materials and principles of non-living science. We build ’Maxwell-demon’-like objects into the separating membrane: gated ion channels, see Fig. (2.12). The ion channels operate as demons (from the point of view of the segments and the observer). Some power opens them, they autonomously transfer ions in a potential-accelerated operating mode, and then that power puts the cap back on the top of the channel. Let us separate our volume with a semipermeable membrane having capped ion channels inserted into its material. As long as the caps of the ion channels are closed and the ion concentration on the two sides of the membrane are the same, we do not see any change in the state of the solutions. However, our construction ’looks like a duck’.
Although the channels can stochastically open, close, and re-open, they transmit more or less well defined charge quanta. Even the channels can recognize the ions’ chemical nature and transmit only a selected ion type. The channels are passive during those processes, although the enormous voltage gradient can rearrange their structure and change their behavior through that. The demons also concert their actions using the layer containing charges as a communication medium; their population maintains a well defined macroscopic current across the membrane. Our construction swims like a ’duck’.
”Voltage sensing by ion channels is the key event enabling the generation and propagation of electrical activity in excitable cells.”[130] How voltage gating of channels works is still a mystery; one of the worst consequences that Hodgkin and Huxley separated the potential from ions and their current. It is not easy to investigate it experimentally: ”the structural basis of voltage gating is uncertain because the resting state exists only at deeply negative membrane potentials” [131]. Usually, a ”sliding helix” (structural) model is assumed.
Under certain conditions, an ion channel can be opened in only one direction and only for a limited period, and this way the membrane becomes semipermeable. We imagine an ion channel as a simple hole (a cylinder) between the high and low-concentration segments with a cap on its top (on the side of the low-concentration segment). Until the cap is removed/lifted (the channel gets open), practically nothing changes. At the points where the ion channels are located the ions cannot penetrate the membrane. Unlike the original Maxwell demon, our demon does not have information in advance about which particle should be transmitted: it is passive in selecting the particle. (Passive here means that no biologically produced energy is used: the electric potential energy from the voltage difference across the membrane moves the ions to the other side of the membrane.) It only keeps one way closed for part of the time, and the voltage performs selecting the ions.
We can easily interpret why our voltage-controlled ion channel model gets opened and closed due to purely electrostatic reasons. It works as the two-plate simple nano-scale electrometer (of type quadrant, Lindermann, Hoffman, and Wulf) similar to the ones used to measure the small electrical potential between charged elements (e.g., plates or fine quartz fibers). Given that the membrane and the cap in their resting state are isolators, no electrical repulsion is evoked between them and the adhesion sticks them firmly to each other, representing a permanent force. The van der Waals force is inversely proportional to the squared distance between the dipoles in the cap and the membrane, respectively, and is linearly proportional to the perimeter of the channel.
However, when a slow ion current flows into the surface layer in the proximity of the cap, charges appear in the layer proximal to the membrane; the membrane and the cap get covered by a very thin electrical skin. The charge on the cap is proportional to the surface of the cap and similarly inversely proportional to the squared distance between the cap and the membrane. A local voltage gradient is generated by the local gradient of the slow ion current (see below), and the force acting on the cap is proportional to the product of the voltage gradient and the area of the cap. Given that the cap is slightly elevated, the repulsion force may have a component in the direction of lifting the cap. Since the van der Waals force is of fixed size, the electrical repulsion exceeds it at a critical voltage gradient value and the channel opens. The gate remains open as long as the local charge distribution enables it. The cap is connected to the membrane only at one point, so it cannot fly away and also cannot close again until the charge on the surface is present. In the absense of charge, the cap makes a random movement and the short-distance van der Waals force may eventually fix the cap again to the membrane, this way closing the channel. The voltage sensing electrometer opens the channel and the lack of charge on the surface enables to close it, but the closing is not immediate (the mass of the cap is by orders of magnitude larger than the mass of an ion that can pass the channel). The fluctuation of the voltage gradient due to the gradient of the slow current in the layer in the proximity of the membrane near the ion channel’s exit opens, closes, and re-opens the channel in an apparently stochastic way (actually, as the repulsion of charges due to the fluctuating current on the cap and the membrane regulates it), as observed. Having gates (caps) is needed only for the synchronized operation of the channels: opening and closing work also in the absence of caps, as discussed.
When one cap is removed, the rushed-in ions in the proximity of the channel’s exit suddenly increase the local potential (produce fast transient changes [81]) proximal to the spot centered at the exit in the layer on the membrane’s surface. The surface outside the spot remains at a lower potential, so the ions in the layer start moving toward other channel exits, delivering potential to those channel exits. Given that they are voltage-controlled, they get open, and the process continues in an avalanche-like way [82]. The avalanche, as explained, needs a sufficiently large voltage gradient; which can be triggered by several synaptic inputs if they sum up appropriately. Alternatively, a single spike with sufficiently steep front slope [63] can be sufficient; providing a simple way of synchronizing neuronal assemblies (and proving that not the voltage, but the voltage gradient, single of summed, controls the operation).
The operation of the ion channel, alone, cannot explain that the channel closes after a given number of ions passed the channel; that number is not (entirely) random. Actually, the local behavior of the membrane’s surface layers regulate the number of ions.
The segments are no longer mechanically separated when the cap is removed. The charged ions are enabled to rush into the lower concentration segment. They experience an enormous accelerating gradient: ”an electrical potential difference about … exists across a plasma membrane only about thick, so that the resulting voltage gradient is about ” [107]. That enormous gradient, comparable to that of electrostratic particle accelerators, ”snorts” the ions from the high-concentration side into the low-concentration side and causes a process ”like a flee hopping in a breeze”. Consequently, ”transport efficiency of ion channels is times greater than the fastest rate of transport mediated by any known carrier protein” [107]. Recall that, in physics, the drift speed, the electrical repulsion-assisted speed, and the electrical potential-accelerated speed of ions differ by several orders of magnitude (for visibility, the ratio of the gradients in Fig. 2.12 is not proportional).
The snorted ions ”hop” into the layer from the another layer. In the beginning, with their voltage-accelerated speed, it could take less than to pass the channel (simulation [132] uses a representative time interval), in the end, they may slow down to the voltage-assisted level as the potential gradually decreases (which is still ), so we can omit that time when calculating the charged layer formation. Due to the enormous speed difference between the accelerated and assisted speeds, the passage is practically instant. The accelerating field through the hole across the layers persists, although it decreases; see Fig. 2.14. On the high-concentration segment, only the ions in the layer in the immediate proximity of the entrance can feel the accelerating potential and move with the potential-accelerated speed. The after-diffusion with the potential-assisted speed from the next neighboring layer in the high potential segment is by orders of magnitude slower than the passage through the hole with the potential-accelerated speed. Depending on the process parameters, the local potential can rise above the high-concentration segment’s potential for a short period due to the accelerated current’s ’ram pressure’ (or ’impact pressure’). Due to their electrical repulsion, the ions induce a similar change on the opposite segment.
The accelerating potential around the channel’s exit gradually (but quickly) disappears when the particle exits the ion channel (see the green ion in the figure), and the ion arrives at the bulk potential. It practically stops: it can continue only with its potential-assisted (later with drift) speed, which is several orders of magnitude lower. However, the rest of the ions are still accelerated through the channel, and somewhat later, they also land in the formerly low-concentration layer, further increasing its potential and concentration. The passed-through ions increase the local potential in the layer in the low-concentration segment and decrease the local potential in the layer in the high-concentration segment. Given that the after-diffusion speeds in the layers are limited, ”as ion concentrations are increased, the flux of ions through a channel increases proportionally but then levels off (saturates) at a maximum rate” [107].
Here the efect of the finite resources, see section 2.2.2, explicitly appears. As we discuss in sections 2.5.7 and 2.11.1, about ions are transferred per channel. These ions are snorted from one layer in the high-concentration segment into another layer in the low-concentration layer. The driving force gradually decreases, see Fig. 2.8.2, because ions leave the first layer and they appear in the second mentioned layer. The potential-assisted speed to replace the leaving ions into the first segment from the bulk as well as diffusing out from the second segment without appropriate driving forces is by orders of magnitude slower, so we can approximate the process that a gradually decreasing accelerating force drives the ions. The process leads to a special reversal of concentrations and potentials. In a very short period, in the layer on the formerly low-concentration side a very thin high-potential layer is formed that prevents further ions from entering the formerly high-concentration layer: the process of transferring ions through the channel closes the door behind the needed amount of ions. Now the gradient diminished and the van der Waals force can close the channel again.
The commonly used picture about the operation of ion channels [133] is definitely wrong.
the potential generated across the membrane is entirely neglected
the ions have no driving force and the hypothesized protein carriers are too slow [107]
the considered van der Waaals force is too weak to be noticed by the ions (the ’cation-attractive negative ends’ of the Alpha helices are too far)
the assumed force by the ’cation-attractive negative ends’ destabilize the ion path: as the deviation from the central path increases, so increases the deviating driving force
even if the weak van der Waaals force would work for a single ion, the next ion would be rejected by the strong Coulomb-force due to the first ion
The passage is too quick to affect the bulk (see also the discussion in section 3.5.1), given that the ions can only use a potential-assisted speed to reach distant places in both segments. Again, the charge and mass conservation works: the ions pass suddenly from the high-concentration side to the low-concentration side, only from one layer to another. The mentioned layers on the two sides will actively initiate and terminate the ion transfer through the ion channels, but the ions can only pass through an open channel. One layer saturates, and the other empties. After a while, the source of ions will be exhausted. Those layers’ existence suggests revisiting the idea of describing neuronal operation by two single potentials of the bulks on the two sides of the membrane.
Following their arrival, the driving force perpendicular to the membrane’s voltage disappears, and the ions form a thin ”hot spot” in the layer. The electric repulsion acts in parallel with the membrane’s surface and leads to distributing the ions (decreasing the gradient by distributing the charge locally) around the channel’s exit. The ions saturate the layer on the membrane’s surface with a time constant between () at the beginning and at the end of their arrival period (we assumed average distance between ion channel exits on the membrane). We shall take the longer time, so that we can expect a time constant for the saturation current around the ion channel’s exit in the order of . When charging up the membrane in an avalanche-like way, the ions must pass on average a distance of about from its center to its farthest point, so we expect a () time until the membrane’s slow current charges up the membrane to its maximum potential. The created charge must flow out from the farthest point in the neuron membrane of size in time of order at or below (); see the length of the pulse measured at the beginning of the AIS [117], see Fig. 3.13, which time is prolonged up to by the neuronal circuit; the ions are slow when the voltage on the AIS is low, see Eq. (2.30). Assuming those distances and speeds, including the potential-assisted speed of the slow current, we are on a time scale matching the available observations.
Maybe the mechanism of channel passing can also contribute to explaining ion selectivity. ”The normal selectivity cannot be explained by pore size, because is smaller than [107]”. The two ions have the same charge, but is nearly 70% heavier than , a definite disadvantage when accelerated by a vast electrical gradient. When the layer on the arrival side gets saturated, its potential reaches the potential of the bulk on the high concentration side (this is necessary to decelerate the accelerated ions), and so the channel gets closed (the accelerating potential disappears for a short period until the ions from the layer flow away toward the drain or they diffuse toward the bulk). We assume that the ions continuously accelerate, then decelerate, due to the potential gradient (which we assume to be constant for a moment). When ions stopped after passing the channel and built up a repulsive layer proximal to the channel’s exit, the ions passed only about 60% of the channel’s length. The ions, which started from the departure layer with a handicap of , will arrive earlier than the ions from the thick charged layer proximal to the channel’s entrance. That is, this handicap results in a strong enrichment of ions. For the detailed calculations see section 2.5.7.
Given that the potential reverses, the late ions are decelerated and then accelerated in the reverse direction (recall that the layer they started from is still empty and attractive), they simply go back to the departure side. The ions also repulse each other while being accelerated (the accelerating gradient acts on a distance of while the ions may approach each other to a distance of , so the mutual repulsion can be significant). In this way, the heavier ions help their competitors and vice versa. (The different ions can also connect to different, heavy-weight components of the solution, drastically changing the picture.) The result is that only the lighter ions can pass the channel from an ion mixture when the cup is suddenly removed. The passage is super-fast; it is in the region (with a voltage-accelerated speed compared to the voltage-assisted speed of after-loading ions from the next layer), and the created potential quickly decays by diffusion.
The commonly used picture about the operation of selectivity filters is surely wrong. The assumed mechanical operation of the pores is simply too slow: the assument structural change needs and the ions passage time is about (furthermore, it must be repeated about times per passage). If a wrong ion is catched, it must be transported back to its departure side, through the right ions (against their repulsion), and the right ions must retry. Neither for moving forward nor backward an appropriate driving force is present in that picture.