I’m telling this story to explore choice and to present some research I did in college. The research will be after the story and it’s really heady – I’ve learned how to internalize information and present it in a way that would make sense to me easily since writing the research paper, so please forgive my young brain. Pun intended as you’ll see.
I remember the smell of that delicious blackberry coffee steam hitting me in the face as my friend’s Camel Lites were sitting on the metal table outside where we were discussing our high school philosophy of the world. As we sat in our shorts that sunny school day afternoon, the beautiful essence of tobacco crept into my nostrils through the coffee particles.
It was time to finally ask him for one. I smoked it, and almost fell over. Relatable? Those nicotine-highs after not smoking for a while are wild. I was into it.
When I was in college I was taking a class called Mathematical Modeling in Physiology and Medicine – yes, I’m a dork at times. The professor was a fucking awesome dude who was the interim director of the Biomedical Engineering Department at the time, and one day he saw me outside smoking a hand-rolled cigy-butt. He said, “I didn’t know you smoked. You’re going to mathematically model the effects of nicotine on the brain for this class.” I said, “Fuck”, but was excited about the challenge and got after it. (The research is below, and I never got around to publishing it – more on that in other posts)
For 15 years I’ve been smoking cigarettes on and off. I’ve quit for short periods and long stretches. Most notable being a nine-month period where half of it was when I lived in Japan. The cigs there cost $2.50. Most recently I quit for two weeks and started again after I got a series of really heavy and hard situations that I took the responsibility to work on.
In any case, I’ve been having an existential argument with myself about smoking after picking them up again most recently. Was I showing a sign of weakness? Did I not have the willpower to get over presumed stress? Why does it matter?
Here is my argument to quitting: Why should I value my life so much to quit? We will all die. Dust to dust. I try not to smoke offensively – bothering people with the second-hand. I’m a healthy human, and I enjoy smoking for many reasons – pleasure, highs, social aspects, getting outside, mini-breaks from tedium.
Essentially I came to the conclusion that I enjoy it, I take care of myself well, I don’t try to offend other people with it, and the long-term effects are arguable. Lot’s of people smoke till they die of natural causes. Lot’s of people die because they smoke. I will die at some point, so why care about how it happens?
Presenting this question to friends opened my eyes a bit. Again, I am being selfish. The real reason to quit may be to save the people around me who may have to take care of my old and/or sick ass. Eye opener. Again, this is arguable as some people get sick from it and some don’t. The choice is real, and I’m asking that you put your two-cents, or more, into the discussion. I’d love to hear thoughts.
Below is the research. It basically says that having constant nicotine in a particular brain cell is better for the cell than having none, and then spiking it. Consistency over intensity
🙂
The one I thought about publishing is more involved and I’ll put that up next week hopefully.
Nicotinic Effects on a Single Basal Ganglia Cell Simulation by Adding Identical Potassium Channels to the Hodgkin-Huxley Model.
Abstract:
Electrical activity in individual neurons (called single-unit activity) was simulated using a derivation of the Hodgkin-Huxley model for a neuronal membrane under the addition of multiple identical potassium channels to model a portion of the effect caused by dopamine released from the consumption of nicotine. MATLAB was utilized as the simulating program. Implementation of the 1952 paper “A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve” by Alan Hodgkin and Andrew Huxley along with “Interactions of Glutamate and Dopamine in a Computational Model of the Striatum” by Rolf Kotter and Jeff Wickens, 1995 will be exercised to compare theoretical data. The simulation related a linear growth in the amplitude of response by the addition of Na+ and K+ channels with fluctuations at .1s and .7s.
Introduction:
Nicotine, among many other things, causes a rapid release of the neurotransmitter dopamine, often represented by Da, or DA. Through DA, nicotine has been known to decrease the amount of sodium, Na+, within neurons located in the striatum. Liu et al was the first to investigate how nicotine, being an alkaloid, affected sodium channels. When taken into the body, it produces a myriad of physiological actions that occur primarily through the activation of neuronal nicotinic acetylcholine receptors (nAChRs). [1] Traditionally dynamical systems are used to assess brain functions such as the one being presented here, but that is beyond the scope of this paper. Therefore the system to be modeled is how nicotine affects Na channels within the striatum.
The striatum is a portion of the brain located ventromedial to the cerebral cortex and is thought to be concerned with motor and cognitive planning. It is said that the striatum is used by the mind and brain to map context to action. The striatum is also the location of many diseases including: Parkinson’s, Huntington’s, Tourette’s, and dystonia. The anatomy of the corpus striatum and the surrounding tissues can be found in Fig 1.
Figure 1 The Corpus Striatum and surrounding tissue
Figure 2 Gutkin et al. hypothesized that there were three main pathways involving actions set forth by the striatum. This is a diagram of their idea.
Nicotine effects on the VTA (ventral tegmental area) DA signaling initiate a cascade of molecular changes that, in turn, bias glutamatergic learning processes in the dorsal striatal structures responsible for behavioral choice, leading to the onset of stable self-administration. (Gutkin, Dehaene, and Changeux 2006) Their hypothesis can be seen in Fig 2.
Nicotine usually elicits its actions through the activation of specific neuronal nicotinic acetylcholine receptors (nAChRs) (Lindstrom 1977; Role and Berg 1996). To gain a better understanding of the physiological process through which dopamine interacts with a neuron see Figure 3. In regard to peripheral anesthetic mechanisms, in vagal nerve neurons, nicotine (0.6 mM) was shown to reduce the amplitude of action potentials (Armett and Ritchie 1961) suggesting that it may block voltage-gated sodium channels. (Liu et al 2003). Consequently this study focuses on the effect of adding multiple identical potassium channels to the Hodgkin Huxley model proposed in 1952.
Figure 3 A picture of a striatal synapse involving dopamine and the accompanying receptors and transporters.
Current Methods and Techniques:
Kotter and Wickens, 1995, modeled 400 principal neurons to describe the passive and active behavior of their membrane compartments by using equivalent electrical circuits. Dopaminergic signals are simulated as time-dependent variations in specific membrane conductances (Kotter and Wickens 1995). Relevant data for this experiment was extracted from their table given below in Table 1 to compare to previous results run on the Hodgkin Huxley model simulations.
Table 1 Parameter values of Striatal Neuron Model: Source: (KÖtter and Wickens, 1995).
| Parameter | Value | Reference |
| Soma cylinder length (um) | 15 | Bishop et al. 1982 |
| Soma cylinder diameter (um) | 15 | Bishop et al. 1982 |
| Dendrite cylinder length (um) | 400 | Bishop et al. 1982 |
| Dendrite cylinder diameter (um) | 15 | Bishop et al. 1982 |
| Membrane capacity (uF cm-1) | 1 | Rall et al., 1992 |
| Membrane resistivity (k? cm2) | 10 | Wilson,1990 |
| Axial Resistivity (k? cm) | 0.3 | Rail et al., 1992 |
| Leakage equlibrium potential (mV) | -90 | Jiang and North, 1991 |
| Excitatory equilibrium potential (mV) | 0 | Jiang and North, 1991 |
| Peak excitatory conductance (nS) | 50 | Ryan et al., 1986 |
| Time constant of excitation (ms) | 2 | Akalke et al., 1988 |
| Inhibitory equilibrium potential (mV) | -60 | Jiang and North, 1991 |
| Peak inhibitory conductance (nS) | 80 | Misgelde et al., 1982 |
| Time constant of inhibition (ms) | 10 | Misgelde t al., 1982 |
| AHP equilibrium potential (mV) | -90 | Rutherford et al., 1988 |
| Peak fast AHP conductance (nS) | 25 | Galarragaet al., 1989 |
| Time constant of fast AHP (ms) | 5 | Calabresei t al., 1987a |
| Peak slow AHP conductance (nS) | 0.5 | Rutherford et al., 1988 |
| Time constant of slow AHP (ms) | 250 | Rutherford et al., 1988 |
| Action potential threshold (mV) | -45 | Misgelde t al., 1982 |
| Inhibitory conduction velocity (m/s) | 0.1 | Bishope t al., 1982 |
The values given by Kotter and Wickens were shown to follow standard membrane parameters. This model adds two different types of K+ conductances to its mathematical model.
The application of 1 mM nicotine to a CS neuron decreases the amplitude of the AP. On average, 1 mM nicotine decreased the AP amplitude 5.3 mV from 130 ± 5 to 125 ±5 mV (n ± 6, paired P 0.01) that recovered to 132 ± 4 mV (n ±6) after a 3-min wash. They also tested the effect of nicotine using a current- ramp protocol. After a 3-min incubation period, the number of evoked APs was reduced by nicotine from 25±14 to 12±7 (n±5, P 0.05 paired), and after a 3-min wash, 21 ± 8 APs were evoked. Both of the reduction in AP amplitude and decrease in the number of evoked responses are consistent with nicotine inhibiting voltage gated sodium channels.
Figure 4. Nicotine decreases AP amplitude in capsaicin-sensitive neuron. A: current-clamp measurements. A 20-ms injection of –200 pA produced an action potential (AP) having a hump on the repolarization phase. Holding potential _ –80 mV. In the presence of 1 mM nicotine, the amplitude of the AP decreased and the threshold potentials increased (arrows). After a 3-min wash these effects were partially reversible. Inset: in the same neuron the application of 1 _M capsaicin produced a depolarization that generated of a burst of APs. B: the effect of 10 mM nicotine on the generation of APs was measured by current ramps 0 to _2 nA of 1.5-s duration. After a 3-min incubation, the number of AP triggered by the ramp was reduced from 24 to 14, and after 3-min wash, 25 APs were evoked.
Kotter and Wickens modeled the potassium current as:
IK(t) = GK(t)(EK – V) (1)
In order to calculate the membrane potential they summed the potassium currents as:
(2)
Where Va/Ra is an adjoining compartment. This paper focuses on a single neuron and the possible effects on surrounding neurons, but this is not a concern for a single neuron and will be neglected. Their resting membrane potential was set at -90mV and threshold for an AP at -45mV.
Implementation and Verification:
In running simulations, it was fitting to implement MATLAB 7.0. This program was used in earlier simulations with the equations proposed by the Hodgkin-Huxley model of a squid giant axon. In running these simulations variations in membrane voltage, Na+ and K+ and leak currents, and activation and inactivation particles m, h, and n were examined after injecting a current pulse of 0.2308 nA 10Hz/ 0.5 duty cycle simulating a patch clamp experiment similar in style to the experiments carried out by Kotter and Wickens, 1995.
Modeling the action potential of the HH equations and the altered equations showed no difference in amplitude, time to peak, or time to settle as can be seen in Figure 5 A,B.
Figure 5 Action potential of a neuron generated by the Hodgkin-Huxley model (A) and altered states after adding additional K+ channels (B). Notice that there is no difference between the AP’s.
(A) (B)
Initial simulations were run using two different sodium channels. One of which was found directly from experiments carried out in class whereas the second was determined through data found in other references. Later experiments were run using identical potassium channels. If the potassium current can be said to be (1) then multiple identical IK currents can be said be a multiple of this equation. In other words equation (3) can be said to be any number, n, of identical K+ currents:
Simulations were run using this technique to model the effects hypothesized as stated above. Experiments with one channel (Fig 6A) two channels (Fig 6B) and ten channels (Fig 6C) were carried out and found to increase the amplitude of the potassium response by the respective number of channels.
Figure 6 Current responses of sodium and potassium. (A) Single Na and K current each. (B) Two identical K currents with one Na. (C) Ten identical K currents and a single Na current. Notice how the time to peak stays the same whereas the amplitude of the responses increases linearly.
(A) (B) (C)
Discussion:
This implementation of the data taken from the stated sources [1,2,3,4,5] versus the previous testing of the HH model proved to be beneficial in understanding how Na and K currents affect the AP and responses of Na and K of a striatal neuron.
After running the simulation for an extended period of time it is evident that the effect of adding a second K+ channel to the HH model caused an end point of the amplitude of the action potential. This is to say that there were no action potentials generated after a .7s period and the variance in peaks was only significant at .1s. This may imply, and therefore describe, the effect of chronic nicotinic use on the desensitization of reward centers of neurons and thus the brain forcing neurons through neurotransmitters to remain in homeostatic imbalance until nicotine is consumed again after an initial use. Figure 7 gives a brief description of what was discovered.
Figure 7 (A) Current response of K and Na from the HH model for 1s. (B) Response of Vm(t) from HH after 1s. (C) Current response of K and Na after adding an identical K channel for 1s. (D) Response of Vm(t) after adding an identical K channel for 1s. Note that the response of Vm(t) did not change in the simulation. However, there was a spike in amplitude at .1s and at .7s the AP generation discontinued in both simulations.
It is apparent through experiments carried out that adding identical K+ channels to the original Hodgkin Huxley model did not alter the time to peak or the settling time of the Vm(t) response. There was a significant difference in the response of K+. The difference doubled the amplitude of the potassium response. Adding 10 identical K+ channels accounted for a ten-fold magnification of the amplitude of the response. Thus it can be assumed that for every identical K+ channel added the response’s amplitude will continuously increase linearly.
The amplitude of the sub-K increased as well though the amount was difficult to assess and is beyond the scope of this paper. When adding more than one identical channel the amplitude continues to grow.
Problems arose when it was assumed that dopamine increased the amount of Na+ ions when further research confirmed that it inhibited them. Therefore the bias of this paper was written to address another non-identical sodium channel when in reality it needed to be negated. Some of the results of adding a second Na channel can be seen in Figures 4 & 5. To overcome this fatal flaw, less time was allowed, thus less information was gained and presented. Fortunately, when adding single identical channels to the HH model there is not much manual labor that needs to be done.
Though much information was gained through these simulations, it is apparent that there is much more to learn about the processes through which nicotine affects neurons, and the pathways that are affected. Further studies may include a comprehensive study of multiple additions of channels and a theoretical formulation of an affected neuronal membrane.
Appendix C
Figure 8 Current responses of K and 10 identical Na channels.
References:
- Liu, L., W. Zhu, Z.-S. Zhang, T. Yang, A. Grant, G. Oxford, and S. A. Simon. Nicotine Inhibits Voltage-Dependant Sodium Channels and Sensitizes Vanilloid Receptors. Journal of Neurophysiology, 91: 1482–1491, 2004.
- Boris S. Gutkin, Stanislas Dehaene, and Jean-Pierre Changeux. A Neurocomputational Hypothesis for Nicotine Addiction. Proceedings of the National Academy of the Sciences of the United States of America, 2006;103;1106-1111; Jan 13, 2006.
- Rolf Kotter, Jeff Wickens. Interactions of Glutamate and Dopamine in a Computational Model of the Striatum. Journal of Computational Neuroscience, 2, 195-214 (1995).
- L. Hodgkin, A.F. Huxley. A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve. Journal of Physiology, (1952) 117, 500-544.
- Christof Koch. Biophysics of Computation; Information Processing in Single Neurons. Oxford University Press, Inc. 1999
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