Steady-State Description of Cell Membrane Potential and IV Curves

Driving force on ions across membranes- generate simple IV curves

I've already mentioned IV curves in a previous post, but here's a couple more random tidbits about them:

• The x-intercept of the curve is where the current = 0 (i.e. no flow of that ion into or out of the cell). If the concentrations of the two ions are equal to each other, the x-intercept will occur when V_m = 0. Otherwise, the x-intercept will occur somewhere else.
• The x-intercept is also called the reversal potential (I think). This is because this is the point where the current reverses direction (if you go slightly past the reversal potential in one direction, current is going out of the cell, and if you go in the other direction, current is going into the cell).

Describe the steady state situation for multiple ion permeability

In my first post for PHYL3001, I talked about electrochemical equilibrium. Unfortunately, membrane potentials are actually more complicated than that, as there are multiple ions moving back and forth across the membrane. This results in a "steady state," rather than true equilibrium.

Aside from K⁺, another important ion involved in the "steady state" potential is Na⁺. At first glance, Na⁺ has a lot going for it: it has a concentration gradient going into the cell (there is more Na⁺ outside than inside the cell) and an electrical gradient going in the same direction (it is more negative inside than outside of the cell, and the negative charge attracts Na⁺. However, permeability to Na⁺ is much less than permeability to K⁺. Hence, the flow of Na⁺ into the cell more or less balances out the flow of K⁺ out of the cell, resulting in a "steady state."

An important caveat to note is that, if this was allowed to proceed without any intervention, eventually the concentrations of these ions would be out of whack. That's why the Na⁺/K⁺ pump, which you've probably heard of a lot, exists: it helps to maintain ion concentrations and thus also helps maintain steady state.

Explain principles of derivation of the steady state (Goldman) equation for membrane potential

Nernst-Planck Electrodiffusion Theory

The first thing I'm going to cover here is the Nernst-Planck Electrodiffusion Theory, which, to my understanding, suggests the parameters that govern the rate of ion movement through the membrane. Essentially, the main factors that control the rate of ion movement through the membrane are concentration gradient, V_m and P_x, which is the permeability coefficient for ion x. P_x can be calculated with the following equation:

P_x = D_xβ/a where D_x is the diffusion constant, β is the partition coefficient (the ability of the ion to dissolve in the membrane) and a is the membrane thickness.

This model relies on a few assumptions: that the membrane is homogenous throughout, the transmembrane voltage changes linearly across the membrane, ions move independently of each other and the permeability coefficient is constant.

Goldman-Hodgkin-Katz (GHK) Equation

Anyway now that you know what a permeability coefficient is, we're going to move on to the Goldman-Hodgkin-Katz current equation, which I'm not going to write here because a) we don't need to memorise it (thank goodness) and b) it's kinda complicated and would probably be more of a distraction than a help. Essentially, it defines the current of an ion in terms of valency, voltage, permeability coefficient, temperature and so on. This creates a curved line, unlike the linear IV curves that I've been talking about up until now.

One cool thing about this curve is that the outward current and inward current appear to be affected by the concentrations in different areas. Generally, outward currents of the ion tend to be more reflective of intracellular concentration of that ion, and vice versa.

Goldman Equation

Now we're finally on to talking about the Goldman equation! I've talked for a bit about current and steady states and so forth, and now it finally comes together with this equation. In the steady state, the net membrane current is zero, but there is still movement of some ions because the membrane isn't at equilibrium. However, these currents cancel each other out, so the sum of all of the ionic currents equals zero.

A little bit of equation rearranging later, and you end up with the Goldman equation:

V_m = -60log₁₀[(P_KK_in + P_NaNa_in + P_ClCl_out)/(P_KK_out + P_NaNa_out + P_ClCl_in)]

You might notice this as an extended version of the Nernst equation in which multiple ions, as well as the permeability for each ion, are included.

Illustrate use of the Goldman equation

There is also a variant of this equation in which the relative membrane permeability between two ions, rather than the absolute permeability, is considered:

V_m = -60log₁₀[(K_in + αNa_in)/(K_out + αNa_out)]

where α = relative membrane permeability of Na to K (i.e. an α value of 0.1 means that the membrane is 10x more permeable to K than to Na).

You can fiddle around with different values of α to try and find a value that fits your data points the best, and I think there are also computer programs that can do that for you too.

Vascular Reactivity

First post for PHYL3002! This one's later than the others, because the first lecture was just an introduction lecture, and the second lecture basically went through a semester's worth of stats in 45 minutes (far too much information for me to try and explain adequately in a single blog post). This post will hopefully be short, as it touches on a lot of things that were covered in PHYL2001.

Describe the main features of the vascular system and how they influence blood flow and BP.

See earlier post: The Vascular System. One thing that I don't think is covered in that post is the concept of axial streaming. Basically, the faster the flow, the more blood vessels line up bang smack in the centre of the vessel (as opposed to taking up the entire width of the vessel, as in slower flow).

Understand how the features are affected by age and disease.

As we get older, many of our blood vessels stiffen. This causes systolic blood pressure to increase, diastolic blood pressure to decrease and pulse pressure to increase. Disease isn't actually mentioned in the slides, but I can think of several examples: diabetes can cause stiffening of the blood vessels (if I remember correctly), and atherosclerotic plaques effectively narrow the diameter of the blood vessel.

Explain flow-mediated vasodilation and the role of NO as a signalling molecule in the cardiovascular system.

Flow-mediated vasodilation (FMD) is, simply put, vasodilation in response to increased flow. Blood flow through a vessel exerts a shear stress on the vessel wall, and the reason why it's a shear stress is because blood flow is actually slightly slower right against the vessel wall (due to friction) than slightly further away. This stress is sensed by mechanosensitive Ca2+ channels, which activate eNOS (endothelial nitric oxide synthase). eNOS catalyses the production of NO (nitric oxide) from L-arginine, which goes to smooth muscle cells and increases the formation of cGMP, thereby inducing vasodilation. FMD can be measured by using ultrasound images of blood vessels.

Age and smoking habits can decrease FMD. Age decreases FMD because production of NO is reduced due to down-regulation of eNOS, reduced availability of L-arginine (which gets converted to NO) and increased levels of ADMA (an inhibitor of eNOS). Age also increases the breakdown of NO via increased production of superoxide anions.

Explain the roles of endothelial cells, myogenic regulation and tissue metabolism in regulating blood flow.

Endothelial cells: see above- you need an intact endothelium for FMD as that's where NO is produced.
Myogenic regulation: Special Circulations and Temperature Regulation
Tissue metabolism: Microcirculation and Blood Flow

Describe how the distribution of blood flow changes during exercise.

See Special Circulations and Temperature Regulation, it'll tell you more than you need to know.

Metabolic Syndrome and Fat Metabolism

This post is basically what it says in the title: an overview of metabolic syndrome and fat metabolism!

Metabolic Syndrome

1. What is metabolic syndrome?

Metabolic syndrome is a group of conditions associated with the development of cardiovascular disease and diabetes.

2. What are the risk factors used to define metabolic syndome?

Metabolic syndrome is defined as having central obesity, as well as at least two of the following four factors:

1. Raised triglyceride level or specific treatment for this abnormality
2. Reduced HDL levels or specific treatment for this abnormality
3. Raised blood pressure or previously diagnosed hypertension
4. Raised fasting plasma glucose (FPG) or previously diagnosed type 2 diabetes

3. What are the key lifestyle diseases associated with metabolic syndrome?

The key lifestyle diseases associated with metabolic syndrome are type 2 diabetes and atherosclerosis (as well as diseases that often result from atherosclerosis, such as coronary heart disease, heart attack and stroke).

4. Which groups are likely to have metabolic syndrome?

People with obesity, insulin resistance or reduced physical activity are the most likely to have metabolic syndrome.

Dietary Fat

1. Why is fat required in the diet?

Fat is required in the diet in order to make cell and organelle membranes, steroid hormones, bile salts and so on. They are also required in order to transport fat-soluble vitamins (A, D, E and K) as well as carotenoids. Aside from these functions, fatty acids are a good source of energy. Our body can manufacture many fatty acids, but there are two that we must take in our diet (and are thus known as "essential fatty acids"). These are linoleic acid and α-linolenic acid.

2. How are fatty acids metabolised?

There are several different metabolic pathways for fatty acids in the liver:

1. Can be stored as fat
2. Can be broken down to Acetyl-CoA via the process of beta-oxidation (see here for more details). Acetyl-CoA can then help out in two main ways:
1. Conversion into cholesterol, which can become incorporated in cell membranes. Cholesterol can also be broken down to form bile salts or steroid hormones.
2. Entrance into the citric acid cycle, which ultimately results in the production of ATP.

3. What are the different types of fats?

The different types of fats include:

• saturated fats (SFA), which contain only single C-C bonds;
• monounsaturated fats (MUFA), which contain one double C=C bond (all other C-C bonds are single);
• polyunsaturated fats (PUFA), which contain multiple double C=C bonds;
• trans fats, which are essentially MUFAs or PUFAs in which the double bonds are in the trans- (rather than cis-) conformation); and
• cholesterol, which has a characteristic four-ring structure

4. Describe the terminology for fatty acids.

The terminology for fatty acids was discussed in a post for CHEM1004. (Yup, first-year stuff is still relevant.)

5. Describe the differences in quality between different fats. What are the benefits of unsaturated fatty acids?

Not all fats are created equal. The different fats have different effects on our health:

• Saturated fatty acids (SFA), found in animal fats, coconut oil, palm oil and other places, tend to be cholesterol-raising. They also form solids more easily (as I'll explain in a bit), allowing them to clog up arteries and so forth. It is generally advised that you keep your saturated fat intake to 10% of your total calories or less.
• Monounsaturated fatty acids (MUFA), such as oleic acid, decrease blood cholesterol levels.
• Polyunsaturated fats (PUFA) include linoleic acid and α-linolenic acid which, as I said above, are essential fatty acids (i.e. they can't be made by the body). Polyunsaturated fats also include omega-6 and omega-3 fatty acids, which weren't covered in any more detail in this lecture, but are often touted as being beneficial to your health.
• Trans fats, as I'll explain below, are somewhat similar to saturated fats in that they can easily form solids. The advantage of this is that solids are easier to transport and are more resistant to spoilage, but the obvious disadvantages lie in what they do to your arteries.
• Cholesterol is an essential part of cell membranes, as well as a precursor for steroid hormones and bile acids. There is no evidence for a particular dietary requirement surrounding cholesterol, as our body makes quite a bit of it anyway. In the past, people were advised to avoid dietary cholesterol; however, now we know that dietary cholesterol is really a drop in the bucket compared to the cholesterol that our bodies make. As such, you don't need to be too concerned about overconsumption.

6. Why are saturated fats solid at room temperature?

Saturated fatty acids tend to be more linear (as opposed to cis-unsaturated fatty acids, which have "kinks" in them due to the double bond). This linear conformation allows the molecules to get closer together, which helps them solidify.

Note that trans fats, despite having double bonds, are also somewhat linear (the trans configuration doesn't create a "kink"). This means that trans fats often have somewhat similar properties to saturated fats.

Single Cell Electrophysiology Techniques

Second post for PHYL3001! Here we will learn about the different methods used to measure membrane potential and voltage across the membrane.

In vitro (cell free) systems- artificial membranes

Artificial membranes are a useful way of finding out how altering the ionic composition on either side can affect the membrane potential. These thin membranes, which can contain membrane proteins, are "painted" across a small diameter hole. The solutions on either side of the artificial membrane can have their composition altered, and their voltage measured by the use of Ag/AgCl electrodes.

In vivo systems- glass micropipette electrodes

Glass micropipette electrodes, which can be poked through a cell membrane without damaging it, can be used to measure membrane potentials in vivo. These cone-shaped electrodes, which have a small opening at the bottom, are filled with a solution such as KCl and are connected to a pre-amplifier by an Ag/AgCl wire. A second wire connected to the pre-amplifier, called the reference wire, sits in the bathing medium surrounding the cell. This allows the potential difference between the inside and outside of the cell to be measured.

While glass micropipettes can be useful in helping us record the inside of the cell, they do have disadvantages. They have a high electrical resistance, resulting in lots of noise and interference. Special electronics are also required due to the high resistance.

How are ionic currents passing through membranes measured?

Ionic currents passing through the membrane can be measured by means of the voltage clamp method. Two electrodes are used in this method: one to measure the membrane potential and the other to inject a current into the cell. The electrode measuring membrane potential feeds back to a feedback amplifier, which adjusts the current to keep the membrane potential constant.

The voltage clamp method relies on the logic that to keep the membrane potential constant, the current going into the cell must be equal to the current going out of the cell. Hence, when we adjust the current to keep the membrane potential the same, we are really adjusting the inward current to be equal to the outward current. In this way, we can measure the outward membrane current. (Or at least that's my understanding of how this works :P)

How is single channel behaviour measured?

The behaviour of single channels can be measured by use of the patch clamp technique, which uses blunt glass micropipettes. Unlike those used in the electrode technique above, these pipettes do not impale the membrane. Instead, they suck up a small portion, such that only a small number of ion channels are contained within the "sucked up" part. The current in this small section can be measured.

There are a few variations on the patch clamp method. If a strong suction is used, the cell membrane can rupture, allowing the pipette to directly access the cytoplasm. The pipette can then be retracted and the broken ends of the membrane allowed to anneal, forming a loop of membrane in an "outside-out configuration." (If the pipette is retracted when using normal suction as above, then an "inside-out configuration" is created instead.)

The Epidemiology and History of Cardiovascular Disease

First post for PHAR3303! This is basically a "background information" type lecture- or at least I hope it is because I'll admit that I didn't pay close attention to all of the details :P

Be able to define the term "epidemiology" and appreciate its value in studying causes of human disease on a population scale

"Epidemiology" is the study of health and disease in populations, as opposed to just studying the mechanisms of disease in some cells, organs or individuals. It is useful in letting us know the prevalence of a disease, as well as in coming up with approaches to tackle them on a wider scale (e.g. policy measures to combat tobacco consumption).

Identify the major types of cardiovascular disease (CVD), and demonstrate awareness for how epidemiological approaches help us address the toll CVD takes on the health of human societies

Many cardiovascular diseases occur due to atherosclerosis. These include ischaemic heart disease, coronary artery disease, cerebrovascular disease, hypertension and peripheral vascular disease. Other heart diseases include congenital heart disease, rheumatic heart disease, cardiomyopathies and arrhythmias. If you want more details, I wrote a few posts on cardiovascular diseases for PHGY350 (a unit I took while on exchange).

Be able to describe the significance and contributions large scale multi-generational, community-based observational studies such as the Framingham Study have made to our ability to diagnose, treat and prevent CVD

Following the death of President Roosevelt from a cerebral haemorrhage related to high blood pressure, there was increased interest in risk factors for CVD. A long-term cohort study, called the Framingham Study (after the town that the original cohort came from), was conducted. The large number of participants and the length of time of the study allowed researchers to identify many different risk factors for CVD, such as hypertension, diabetes and so on. This is knowledge that we take for granted now, but in the past it did help dispel many myths, as well as open up new therapeutic approaches (e.g. working to lower blood pressure).

Identify the major insights that have emerged from descriptive, analytical and interventional studies of CVD

Descriptive epidemiology describes the distribution of cardiovascular disease in terms of characteristics such as age, gender, place and so on. Some of the major insights from descriptive epidemiology studies of CVD include the following:

• Global distribution patterns: CVD accounts for ~1/3 of global deaths, but the majority of these deaths take place in low- and middle-income countries (due to less access to medical care, less expenditure on public health campaigns and so on).
• Age: The percentage of deaths attributable to CVD increases as age increases.
• Sex: Contrary to popular belief, CVD affects nearly as many women as men, though usually women are affected at an older age. There are also sex-specific risk factors for CVD, such as oral contraceptives, hormone replacement therapy and so on.
• Global changes in CVD mortality: In many developed countries, CVD deaths have declined due to increased awareness of risk factors and improved medical care. However, in many developing countries, there are opposing trends due to increased longevity, as well as the wider availability of fatty foods etc.

Analytic epidemiology examines risk factors for CVD. Many risk factors have been identified, but only a handful are attributed to the majority of cases. Some of these risk factors are modifiable, such as obesity, physical inactivity and tobacco use, whereas others are not modifiable such as age or ethnicity.

Experimental epidemiology looks at interventions that can be used to prevent CVD. There are several different levels of prevention:

• Primordial prevention tends to look at legal and other widespread interventions. An example of primordial prevention would be banning smoking in many public areas so as to prevent CVD, lung cancer and other issues.
• Primary prevention also involves widespread interventions (though maybe less widespread than the legal interventions in primordial prevention). These interventions include health education programs, sports programs, regular blood pressure checks, and so on.
• Secondary prevention involves taking care of patients who are showing some symptoms of CVD. Screening and treatment of these patients are done.
• Tertiary prevention involves taking care of patients who have already had a heart attack or some other complication of CVD. The aim of tertiary prevention is to prevent recurrence of such events.

Nutrition and Lifestyle Diseases

First lecture for BIOC3004! The content in this lecture isn't particularly exciting (unless "eat a healthy diet" is news to you), so I'll try and keep this relatively short and painless.

Be able to give an example of a lifestyle disease.

Cardiovascular disease is a prime example: many lifestyle factors, such as obesity, low physical activity and tobacco use can predispose to this. Another example is type 2 diabetes, in which poor diet and low physical activity are also lifestyle-related factors.

Know the risk factors for Cardiovascular Disease and Diabetes.

See above.

Know the difference between a micronutrient and a macronutrient.

Macronutrients are the bulk of what we need for energy. The main macronutrients are proteins, fats and carbohydrates. Micronutrients include pretty much everything else, such as vitamins and trace minerals (iron, cobalt, copper etc.).

Know what factors can affect nutrient reference values.

Age and gender, as well as whether or not you are pregnant or lactating.

Be able to explain RDI

RDI stands for "Recommended Daily Intake." This is essentially the amount of a nutrient that we are recommended to take in each day.

Know the Australian and USA guidelines for diet.

This is going to be pretty much a straight copypasta, except with some changes here and there so that I don't get sued for breaking copyright or something like that.

Australian guidelines:

1. Be physically active and consume nutritious stuff that will meet your energy needs
2. Eat a variety of foods from the following food groups: vegetables, fruit, grains, meats (and/or tofu, nuts, seeds, legumes etc.) and dairy. Drink lots of water.
3. Limit saturated fat, alcohol and added salt and sugars
4. Breastfeed (young children and babies, that is. It doesn't explicitly say that you cannot breastfeed your adult children, but I think that's implied.)
5. Prepare and store food safely

USA guidelines:

1. Eat healthily, no matter how old or young you are
2. Focus on variety, nutrient density and amount
3. Limit saturated fats, salt and sugar
4. Choose healthier foods and beverages
5. EVERYONE EAT HEALTHY OK (obvious paraphrase is obvious)

Be able to explain what nutrient dense means.

"Nutrient dense" basically refers to the proportion of food that has nutritious stuff in it, as opposed to the bits that just have added fats, sugars or salts. An example of a food that is definitely not nutrient dense are fries- the potato might have had some nutrients in it, but the bucketloads of oil used to turn that potato into fries do not.

Be aware of the differences in consumption relative to recommendations.

As you are well aware, we're not always good at doing what's best for us. In America, at least, the 2010 guidelines showed that the "typical American diet" has much more sodium, saturated fat, refined grains, solid fats and so forth than is recommended, and far less whole grains, vegetables, fruits, dairy and so on. Now, this might be in America, but don't assume that Australia is any better! After all, we did manage to beat them once in the title of "World's Fattest Country!"

Single Cell Physiology: Concepts and Methods

First post of the new academic year! This one is for PHYL3001: Physiology of Membranes, Muscles and Signalling.

This post is supposedly revision if you did PHYL2002: Physiology of Cells. I didn't do that unit, and I also didn't do physics in year 11/12, so some of this is new to me.

Review of membrane properties

Yay, a section that isn't particularly new to me! Main things you need to know are that the membrane is a lipid bilayer that lets through some things more easily than others, but there are also channels that can help carry through stuff that won't readily diffuse through the membrane (mainly ions and larger polar molecules).

Here are some posts that you can read for more information:

• Cell Membrane Structure
• Membrane Diffusion and Osmosis
• Lipids- Membranes as Dynamic Molecular Barriers

I did write other stuff on membranes back when I was doing CHEM1004/SCIE1106, but those three posts are the most relevant ones.

Importance of electrical phenomena for all cells

The movement of ions and other charged particles is pretty important. Aside from controlling phenomena such as signalling, enzyme cascades and so forth, ions are the most abundant dissolved solutes, so their concentrations in different compartments can contribute greatly to the osmotic balance in cells. This, in turn, can lead to the control of fluid flow, such as in the reabsorption processes in the kidney.

Principles of membrane potential generation

Membrane potential relies on different concentrations of ions on either side of the cell membrane. (My understanding of "potential" is all of that energy that those ions could produce if they could just smash through the membrane and move down their concentration gradients, but I could be wrong. Despite my dad being a lecturer of electronic engineering, electrical stuff was never my strong suit.) This, in turn, relies on the membrane being selectively permeable to ions (if the membrane was 100% permeable, then ions would just diffuse across until there were equal amounts on either side of the membrane). As I alluded to in the first section, this permeability is helped along by channels and so forth that can help carry some ions (but not others) across the cell membrane.

There are several different types of channels. Uniports only bring one substance across the membrane. A symport can bring two substances across at once: sometimes one that is moving up its concentration gradient, coupled with one that is moving down its concentration gradient (so that no energy is required). An antiport works similarly to a symport, but the two substances are moving in opposite directions across the membrane.

As well as channels, there are also pumps, which use ATP in order to move solutes against the concentration gradient. The most well-known example of a pump is the Na⁺-K⁺ ATPase, which moves 3 Na⁺ ions out for every 2 K⁺ ions in.

Concept of electrochemical equilibrium

Electrochemical equilibrium is probably a bit easier to explain with an example. Due to the action of the Na⁺-K⁺ ATPase, there is usually more K⁺ inside a cell than outside of it. When a K⁺ channel opens, K⁺ begins to move down its concentration gradient. However, it never gets to the stage where there are equal amounts of K⁺ inside and outside of the cell. This is because the outward movement of K⁺ makes the outside more positive than the inside, and K⁺, being a positive ion, is drawn towards the negative charges. Eventually the electrical force pulling K⁺ into the cell balances out the chemical force pulling K⁺ out of the cell, so there is no further net movement of K⁺. When this happens, K⁺ is in electrochemical equilibrium.

Driving force on ions across membranes- generate simple IV curves

Before I go any further, I'm going to go through some definitions. These should be revision from high school physics (I say "should be," because back when we did electricity in year 9 physics, I had a teacher with an accent that I couldn't understand).

• Charge (Q): The imbalance between positively- and negatively-charged particles. Measured in coulombs (C).
• Avogadro's number (N): The number of protons (or whatever) in one mole of a substance. Equal to 6.02*10^23.
• Faraday's constant (F): The magnitude of electric charge in one mole of protons. This is equal to the charge on one proton (1.6*10^(-19)C) multiplied by the number of protons in a mole (which is simply Avogadro's number), giving a Faraday's constant of ~96 500 C/mole.
• Valence (z): The charge on an ion.
• Current (I): The movement of charge over a certain amount of time (I = Q/t). Measured in amperes (amps).
• Voltage (V): The difference in electrical potential between two points. (And it has to be more than one point, because you can't have a difference over one point, unless you're Donald Trump.) Measured in volts.
• Resistance (R): A quantity that measures how a material reduces the flow of current. Measured in ohms (Ω). Cell membranes have a high resistance, so good thing that they have a shit ton of ion channels.
• Conductance (G): The reciprocal of resistance (i.e. 1/R), conductance is the ease with which an electric current passes. Measured in siemens (S).
• Capacitance (C): The ability to store charges of opposite sign on opposite sides of an insulating layer. Measured in farads (F). Capacitance is proportional to the surface area of the membrane and inversely proportional to the thickness. Cell membranes are thin and thus have a high capacitance.

You also need to learn (or remember, if you've learned this in the past), some of the relationships between the quantities above.

Firstly, voltage developed due to storage of different charges across a membrane (i.e. capacitance) is proportional to the amount of charge separated (Q) and inversely proportional to capacitance (C). This relationship can be written as V = Q/C, which can also be rearranged to Q = CV or C = Q/V.

A possibly more important relationship to know, however, is Ohm's Law, which relates current, voltage and resistance. This is V = IR, which can be rearranged to I = V/R or R = V/I.

Electrochemical driving force and the Nernst equation

I'm going to take a bit of a hiatus here to talk about the electrochemical potential energy difference, which is the main driving force behind ion movement. This ties in with the concept of electrochemical equilibrium, as discussed above. Essentially, if the electrical and chemical forces are not in balance, there's an electrochemical potential energy difference, which causes ions to move. The electrochemical potential energy difference can be summed up in an equation:

Δμ_x = RT ln(([X]_i)/([X]_o)) + z_xF(ψ_i - ψ_o)

That looks really scary, so let's break it down. The Δμ_x refers to the electrochemical potential energy difference. This is essentially just the sum of the chemical potential energy difference (RT ln(([X]_i)/([X]_o))) and the electrical potential energy difference (z_xF(ψ_i - ψ_o)). R is the gas constant, which is around 8.3 J/mol/K, T is the absolute temperature in Kelvin, the two terms in the natural log refer to the concentration of the ion in question inside and outside of the cell, z_x refers to the valency of the ion, F is Faraday's constant and (ψ_i - ψ_o) is the voltage across the membrane (which can also be abbreviated as V_m).

The Nernst equation can be derived from the above. It uses the fact that, at equilibrium, Δμ_x should be equal to 0. This allows us to do the following rearrangements:

0 = RT ln(([X]_i)/([X]_o)) + z_xFV_m
-RT ln(([X]_i)/([X]_o)) = z_xFV_m

V_m = -(RT/z_xF) ln(([X]_i)/([X]_o))
V_m = -2.303(RT/z_xF) log(([X]_i)/([X]_o)) (the -2.303 comes from turning the natural log into a base 10 log)
V_m = E_x =  -2.303(RT/z_xF) log(([X]_i)/([X]_o))

E_x is the theoretical membrane potential at which the ion in question is in equilibrium. I say "theoretical" because in reality there are a whole lot of ions that are trying to get themselves into equilibrium, and a perfect solution is pretty much never reached. If V_m = E_x then there is no net flow of the ion, but if they are different then there is a net flow in some direction. This can be expressed by the following equation:

I_x = G_x(V_m - E_x) where I_x is the current and G_x is the membrane conductance.

If you think about it, this equation is similar to Ohm's Law. Remember, V = IR can be rearranged to I = V/R, or I = (V)(1/R). Conductance is equal to 1/R, so this can be simplified to I = VG (or I = GV if you want to keep the terms in the same order as the equation above).

Oh, Ohm's Law! That goes nicely with my next part...

IV Curve

Nope, this has nothing to do with intravenous medication, which is what I thought of first when I saw "IV curve" on the lecture outcomes slide. In this case, IV simply stands for current and voltage. It is a graph in which the voltage is on the x-axis, and the current is on the y-axis. Since I = V/R (from Ohm's Law), this produces a linear curve which is steeper if R is lowered. Positive values of I generally indicate flow of the ion out of the cell, whereas negative values generally indicate flow into the cell.