Clamping down on the “clamp”

In my last post, I discussed the cutting edge experimental technique known as dynamic clamp. Neuronal modelers often encounter the term “clamp” when looking at electrophysiology articles, but it may be difficult to reconcile the term in its various uses. In this post I will try to clarify what “clamp” really means. First, there are only two general electrical procedures you can perform on a neuron: (1) measure the voltage or (2) inject a current. Each of these involves different forms of a clamp. Measuring the membrane voltage (procedure #1) requires a basic technique called “patch clamp” which is described on this webpage. If you read that webpage carefully, hopefully you will realize where the “patch” part of patch clamp comes from. It involves isolating a small area (patch) of a cell membrane.

Now where does the “clamp” come into play? Measuring the voltage is a passive procedure where we simply observe what the cell is doing. Injecting a current (procedure #2 from above) is used to experiment with a cell. There are three different approaches to current injection, and each one is referred to as a different type of clamp.

1. Current clamp: This is simply direct current injection. It is the process of choosing a constant current and injecting it using an amplifier. Using the term “clamp” here can be confusing, but it is a common way to distinguish it from #2 below. It is sometimes explained that the amount of current is what is being clamped (fixed). Note that the experimenter can simultaneously measure the membrane voltage using the same electrode that is used for the current injection. So technically, just observing the cell without injecting current is a form of current clamp where the injected current is zero.

2. Voltage clamp: This is a more sophisticated form of current injection. In the 1940′s, voltage clamp was a new technique that changed everything. A particular ion conductance might be voltage-dependent, so you want to be able to measure that conductance at different voltages to see how they’re related. To measure the conductance at a particular voltage, it’s much like measuring the resistance of a resistor. One way is to inject a current, measure the resulting voltage, and compute the resistance. (Or do the reverse.) The problem with a neuron is that the voltage won’t sit still! Once the voltage changes, it may change one or more of the conductances which will add more current and change the voltage. In order to keep the voltage constant, you can use a differential amplifier to monitor the difference between the desired voltage and the actual voltage. Then you simply inject more or less current to counteract any changes in voltage. This is the reason for the term “voltage clamp”. A good diagram can be found here on the website by Dr. Michael Mann (it’s Fig 3-19).

3. Dynamic clamp: This is still basically current injection like #1 and #2. It’s very much like voltage clamp in that the injected current is continuously adjusted to achieve some result. The difference is that you can do things that are much more complicated than just clamping the voltage at a constant value. My last post explains more about this.

So what is a “patch clamp” again? It is a general term that encompasses all three of the techniques listed above. Hopefully you now have a firm mental clamp on the “clamp”.

Dynamic clamp: Single-cell cyborgs

I once talked some engineering students into learning about an electrophysiology technique known as “dynamic clamp”. In trying to explain the technique to them, I realized how poorly I understood it myself! Here I will explain the idea behind dynamic clamp like I did to those engineering students. Rather than discuss how it works, I want to address the reason why it is so useful. So to summarize the technique, dynamic clamp is a way of listening and talking to a neuron with a computer, sort of like a single-cell cyborg. To read about the technical side of it, I suggest some background reading on patch clamp technique and then this wonderful little summary on dynamic clamp. The enthusiastic reader might also attempt this more technical explanation.

So why is dynamic clamp useful? One answer is that it allows us to reverse-engineer a neuron with greater precision than we can do with other techniques. To reverse-engineer a neuron, we can’t unscrew the parts, so we either activate or deactivate individual parts one-at-a-time in order to figure out what each part does. The other techniques available include pharmacology and direct current injection. Pharmacology (drugs) can be used to turn all the ion channels in all the neurons on or off, but this is very imprecise because you can’t target a single neuron or know exactly how much of the drug actually reached it. Regular current injection can be used to raise or lower the membrane potential (voltage) of a single neuron, but this may affect more than one type of ion channel. Additionally, regular current injection is not dynamic because the computer/amplifier does not adjust the current flowing in and out of the cell based on the changing membrane voltage like a real neuron does. (For the electrophysiologists reading this, note that voltage clamp could be considered the most limited form of dynamic clamp possible. For others, you can read about voltage clamp on Wikipedia and Scholarpedia.)

Dynamic clamp is a dynamic form of current injection. Like regular current injection, it targets a single neuron. However the amount of injected current dynamically changes according to whatever rules you want to program into the computer. One application is to deactivate certain voltage-dependent ion channels on a single neuron. Why would anyone want to deactivate ion channels? Remember we are reverse-engineering the neuron here, so whatever happens without those channels will tell us something about what those channels actually do in the neuron. Suppose these channels open when the membrane potential exceeds a certain threshold but remain closed at lower potentials. In the dynamic clamp approach, we can use a mathematical model of the conductance for these channels to predict what they will do in real-time based on a continuous measurement the membrane potential. The key is that this programmed response is dynamic, meaning it can change in real-time just as the membrane potential of the neuron is changing in real-time.

So not only is it a real-life way to create a cyborg (on a small scale), but it has real scientific value.

Compromising: a lesson from coupled oscillators

In a recent paper about the neural control of breathing, we looked at the phenomenon of phase-locking in bursting neurons. We used a model (available on ModelDB) that consists of a network of bursting cells, each with an independent natural burst frequency. When the oscillators are coupled, their bursts can become phase-locked at a frequency that is somewhere between the smallest and largest natural burst frequencies of the individuals. This is known as the “compromise frequency”. We are currently working to understand this for bursting cells, and an obvious starting point is to consider the simpler case of complete synchronization in a pair of non-bursting oscillators.

The synchronization of two coupled oscillators is well understood. For example, see Chapter 8 in Synchronization: a universal concept in nonlinear sciences by Pikovsky, Rosenblum, and Kurths. The perspective from dynamical systems theory can be found in this nice article by Josic et al and in greater detail in Chapter 10 in Dynamical Systems in Neuroscience by Izhikevich (available free online). While looking for an explanation of the frequency of a coupled system, I was pleased to find a nice example in Nonlinear dynamics and chaos by Strogatz (section 8.6). In typical fashion, Strogatz makes everything crystal clear by combining a simple example with just the right amount of analysis. It is commonly known that two coupled oscillators will have a compromise frequency that lies somewhere between their respective natural frequencies. In his simple example, Strogatz shows how the resonant frequency is a function of the coupling strengths between the two oscillators and their natural frequencies. His derivation seems quite elegant to me.

My challenge now is to understand this for nonlinear oscillators, as discussed by Heath and Wiesenfeld in 1998. Bigger challenges lie in analyzing bursting neurons as well as different coupling architectures. The experimental results of our paper showed large phase differences (80 ms) between pairs of cells. To replicate this in our model, we defined clusters of cells such that connections within any given cluster were stronger than connections between clusters. The result is that all cells in the network become phase-locked, but the phase differences are significantly smaller between cells in the same cluster as compared to cells across two different clusters. In this case, each cluster becomes an oscillator, and even these populations find a compromise frequency between their own natural frequencies.

Just imagine if human society could master the science of the “compromise frequency”. If people are oscillators within clusters, what coupling strengths and architectures are necessary for synchronization? I wonder.

Numerical integration for novices

Numerical integration is an essential technique in computational neuroscience. Does that mean a student can’t do computational neuroscience without taking a course on differential equations? Certainly a formal course would help, but I think there is an alternative for learning how to work with something like the Hodgkin-Huxley model. I’ve had undergrads who wanted to work on neuronal simulations but had not yet had a course on differential equations or numerical methods. They have all been capable of understanding what the equations mean without knowing much about the theory. To deal with this, I put together a Crash Course on Numerical Integration. It uses an example from physics for the height of a falling object, which is something most students have seen before.

Generally, I believe the most effective way to teach is to build strong bridges from a student’s existing knowledge that connect with the new knowledge. Interestingly, I have found that most students are very capable of grasping the fundamentals of numerical integration as long as they have two prerequisites: (1) some exposure to calculus, and (2) a basic knowledge of computer programming. Luckily most freshman get both of these by the end of their first year in college.

The relevance of calculus is obvious, but how does a knowledge of computer programming help? I believe the experience of writing a loop in a computer program provides a very important bridge to understanding numerical methods. The way that the value of a variable changes inside a loop is remarkably similar to how state variables change in numerical integration. Because of this, my Crash Course uses this idea of repetition to create a bridge to the idea of integration. I have only recently started to use this approach for students interested computational neuroscience. It remains to be seen whether it can really provide a bridge to working effectively with something as complex as the Hodgkin-Huxley model.

Something in the air (environment and respiration)

My previous post discussed the importance of understanding the dynamical interaction between three components: brain, body, and environment. There I considered the lamprey model, but my own research deals with the respiratory control system which has its own interesting brain-body-environment dynamic. The central component of respiration involves the generation of a continuous rhythm of breathing, but this rhythm obviously is modulated by many factors, not the least of which is what is in the air that you breathe. Your body contains chemoreceptors that can detect changes in blood chemistry and modulates the respiratory rhythm to react.

Key properties that are monitored include levels of oxygen, carbon dioxide, and pH. Keep in mind that chemoreceptors do not monitor the air in your lungs. They monitor gases in your blood supply. So the circulatory system is the immediate environment, the chemoreceptors are the part of the body that translates an environmental effect to the nervous system, and the nervous system can respond to environmental changes. The repertoire of responses includes breathing faster, slower, or deeper.

I will surely delve into the nervous system component in later posts. Here I mainly want to point out how complex the situation is for such a lower-order function of the nervous system. Not only is there a complex process of chemoreception, but the respiratory rhythm is affected by other environment-body influences such as stretch receptors in the lungs and proprioceptive feedback from respiratory muscles. This helps to explain the difficulties in explaining and modeling even seemingly “simple” components of the nervous system. Even if the core central pattern generator for respiration were simple (a sensitive topic in itself for some of us), the dynamics become noticeably complex when this system is embedded within the body which is further embedded in an environment. OK, let’s all take breath.

Blood Suckers of Computational Neuroethology

There is a field known as computational neuroethology that looks at behavioral patterns and is closely related to computational neuroscience. It has been of particular interest to motor control enthusiasts like myself who study central pattern generation. In the modeling of sensorimotor integration, one usually considers the interaction of three systems: brain, body, and environment. The following quote summarizes the issue:

“The role of the nervous system is not so much to direct or to program behavior as to shape it and evoke the appropriate patterns of dynamics from the entire coupled system.” (Chiel HJ, Beer RD. The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment. Trends Neurosci. 1997 Dec;20(12):553-7.)

A striking example of such interactions is the change in dynamics that results when the environment is drastically changed, and I recently found some great video footage that demonstrates this. I was aware of the lamprey modeling work that was pioneered by Sten Grillner, and recently I came across some fascinating videos of lamprey-inspired robots on the website of the Lampetra project. While the lamprey family has a certain fame because of some bloodsucking family members, it is of interest to us modelers because of what we have learned from their locomotion dynamics. Watch any of the videos with the robots in water and you might start to think it’s just random wiggling without anything particularly dynamic. Then look at this one of a suspended robot out of the water and you should see a major difference. My understanding is that this is very similar to what a real lamprey will do out of the water. Clearly the environmental component is critical to the dynamical pattern evoked by the control system which was designed for a specific environment.

This robotic demonstration is interesting to me because it is a tangible example of the brain-body-environment connections. It highlights the value of considering more than just the nervous system when one is trying to model the nervous system. Also, the robots are pretty cute as compared to the bloodsuckers that inspired their creation.

The problem of synchrony in multiunit recordings

Extracellular multiunit recordings are great for analyzing the relationships between multiple neurons, but I wonder if their ubiquity belies a significant lack of understanding of the techniques involved. Any multiunit analysis requires the use of spike sorting which attempts to figure out which events correspond to which neurons. My background is primarily with intracellular recording, so I am a novice on the topic. I was curious last year when an experimentalist told me he did most of his spike sorting by hand, as opposed to trusting the automated software that was available with his recording equipment. This is interesting to me because of a fascinating 2000 article on sorting accuracy with tetrodes by Harris et al. One of the conclusions of the article was that operators generally do worse than software. Obviously this depends on the experiment, the equipment, the operator, and the software. One can easily understand that a generic algorithm might require significant tuning to be useful, so perhaps there are many who do not bother with that. However, it makes me wonder what types of significant mistakes might be lurking in the spike analysis literature.

One topic raised by the article is the identification of synchronous events. That is, what happens when synchronous spikes from multiple neurons are superimposed in a recording? The article is more concerned with operator error vs. software error, but it does estimate a possible software error rate of up to 30%! Unfortunately for me, this problem does not receive much treatment in the article. Yet it seems extremely important because of two reasons. First, this study involved the use of tetrodes which offer significantly better spatial resolution than larger multielectrode arrays. Therefore the problem must certainly become more significant with larger arrays. Second, one of the most common measures of interest in multiunit recordings is correlation and the phenomenon of spike synchrony.

I find this striking, but I’m aware that these authors are leaders in this field. A look through later articles that cite this one did not turn up any subsequent interest in this issue, so perhaps it’s not as serious of a problem as it seems. I certainly need to learn more about spike sorting.