Dr. Hoi Fung CHAU
Department of Physics, The University of Hong Kong

Biological ideas do not solely come from biologists. In fact, scientific ideas and concepts can often be applied to more than one discipline. Specifically, a lot of physical concepts are required in the study of animals and plants. For example, our lung can inhale air because of the pressure difference between the interior and the exterior of the lung. Mineral absorption in plants involves diffusion and osmosis. We are able to stand upright because our bones are strong enough to bear our body weight without breaking. All these examples tell us that physical laws are required to understand certain aspects of biological functions; and the study of physical processes in biological systems is called biophysics.

In this short article, I am going to tell you more about a specific subject biophysicists have been studying --- neurons. You may recall from your biology class that neurons are special kinds of highly elongated cells. (Figure 1 shows a typical neuron.) Interconnection of neurons in our brain enables us to think. In fact, neuron acts like a messenger by transmitting information from one part of the body to the other. For instance, when you walk, your brain somehow sends a message to the neurons connecting your brain and your legs. Upon receiving the message, electrical signals in the form of voltage pulse are then transmitted through these elongated neurons until reaching the legs. The voltage pulse typically ranges from about 0.01V to 0.1V and travels along the neuron at a speed of about 10m/s. In a copper wire, electrical current is the result of the motion of free electrons. Ohm’s law tells us that such an electrical current leads to a potential difference along the copper wire. Of course there is little free electron in a neuron. In contrast, the electrical current and hence potential difference in a neuron is the result of motion of primarily sodium and potassium ions within the neuron as well as across the cell membrane. The flow of sodium and potassium ions across cell membrane is controlled by special structures on the membrane known as ion channels. Before stimulation, the interior of a neuron has a higher concentration of chloride ions and a lower concentration of sodium ions. This makes the neuron slightly negatively charged compared with the extracellular space and hence the voltage of the neuron interior is negative compared with extracellular space (see figure 2). Upon stimulation, a voltage pulse in the neuron will generated as a result of the opening of sodium ion channel. Once the sodium ion channel is fully opened, extracellular sodium ions rapidly flow into the neuron making it slightly positively charged. Thus, the voltage of the neuron increases (see figure 2). At a later time, the sodium ion channel is closed while the potassium ion channel opens. This allows the potassium ions inside the neuron to move out across the cell membrane thereby making the neuron slightly negatively charged again. Consequently, the voltage of the neuron decreases (see figure 2). Finally, potassium ions are pumped in and sodium ions are pumped out of the neuron via protein transport molecules until the original concentrations of sodium and potassium ions are restored. In this way, a voltage pulse is formed; and such pulse travels along a neuron. Once the leg muscles receive the voltage pulse, they contract and hence you are able to walk.

(Figure 1 A typical neuron)

(Figure 2 Relationship between ion channels and voltage)

Due to the presence of resistance in the interior of a neuron, known as intracellular resistance, current flowing along the interior of a neuron is accompanied by a potential drop. In addition, the electrical resistance across the cell membrane, known as the membrane resistance, is high but not infinite. Therefore, a small but non-zero electrical current will flow across the cell membrane. These two factors limit the distance a voltage pulse can travel and hence the (operational) length of a neuron.

To study how the current and voltage pulse travel along a neuron in detail, biophysicists consider a very simple-minded model of resistor network as shown in figure 3. The bottom wire represents the voltage level outside the neuron while the top wire represents the voltage level inside the neuron. The resistors on the top wire represent the intracellular resistance while the resistors connecting the top and the bottom wire represent the membrane resistance. Given the potential differences between the top and the bottom wires in the far left and the far right in figure 3, biophysicists use Ohm’s law to setup a system of equations relating the potential difference between different points on the wires and the current passing through each resistor. Such system of equations is a special case of the so-called cable equation used by physicists and electrical engineers to study of potential difference drop along an electric cable. (To tell you the truth, the actual model as well as the equations used by biophysicists are far more complex, involving batteries and capacitors. The batteries are used to model the pumping action of protein transport molecules while the capacitors are used to model the ion channels. But the simplified version I have introduced here is sufficient to illustrate the physics discussed in this article.)

In spite of its simplicity, this simple-minded resistance network model is already able to explain a few facts. For example, upon eating excessive common salt, extracellular sodium ion concentration will drastically increase. Therefore, more sodium ions will flow into neurons once the sodium ion channel is opened. In this case, the potential difference between the top and the bottom wires in the far left of figure 3 is increased. Thus, the voltage pulse is stronger and can travel a longer distance along a neuron. This is the reason why excessive sodium intake may cause hyperactivity. More strikingly, recent experiments find that membrane resistance in neurons of the brain of an Alzheimer’s disease patient is much lower than that of a normal healthy person. (Alzheimer is a disease usually occurring in middle-aged person. This disease is associated with the degradation of neurons in the brain. Typical syndrome includes gradual loss of memory and the ability to control ones motion.) The resistor network model we have just come across predicts that the voltage pulse cannot travel too far along the neurons of an Alzheimer patient. (Do you know why?) Hence, communication amongst neurons in the brain of an Alzheimer patient is greatly impaired. This may be one of the reasons why Alzheimer patients become forgetful.

(Figure 3 Model of resistor network)