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Goldman equation

Goldman equation is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Goldman equation rather than just read about it. In short: The Goldman–Hodgkin–Katz voltage equation, sometimes called the Goldman equation, is used in cell membrane physiology to determine the resting potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane. The discoverers of this are David E.

Key takeaways

  • Goldman equation belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Goldman equation to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Goldman equation from memory before moving on to harder problems.

Reference excerpt

The Goldman–Hodgkin–Katz voltage equation, sometimes called the Goldman equation, is used in cell membrane physiology to determine the resting potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane. The discoverers of this are David E. Goldman of Columbia University, and the Medicine Nobel laureates Alan Lloyd Hodgkin and Bernard Katz.

Equation for monovalent ions The GHK voltage equation for n {\displaystyle n} monovalent positive ionic species M i {\displaystyle M_{i}} and m {\displaystyle m} negative species A j {\displaystyle A_{j}} :

E m = R T F ln ⁡ ( ∑ i n P M i + [ M i + ] o u t + ∑ j m P A j − [ A j − ] i n ∑ i n P M i + [ M i + ] i n + ∑ j m P A j − [ A j − ] o u t ) {\displaystyle E_{m}={\frac {RT}{F}}\ln {\left({\frac {\sum _{i}^{n}P_{M_{i}^{+}}[M_{i}^{+}]_{\mathrm {out} }+\sum _{j}^{m}P_{A_{j}^{-}}[A_{j}^{-}]_{\mathrm {in} }}{\sum _{i}^{n}P_{M_{i}^{+}}[M_{i}^{+}]_{\mathrm {in} }+\sum _{j}^{m}P_{A_{j}^{-}}[A_{j}^{-}]_{\mathrm {out} }}}\right)}}

This results in the following if we consider a membrane separating two K x N a 1 − x C l {\displaystyle \mathrm {K} _{x}\mathrm {Na} _{1-x}\mathrm {Cl} } -solutions:

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Goldman equation

Start with the simplest possible case. Write down what Goldman equation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Goldman equation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Goldman equation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Goldman equation

In research
Goldman equation appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Goldman equation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Goldman equation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Electrochemical equations, Membrane physiology, Physical chemistry, so understanding it makes those chapters shorter.
In everyday life
Look for Goldman equation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Goldman equation in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Goldman equation means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Goldman equation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Goldman equation in simple terms?

The Goldman–Hodgkin–Katz voltage equation, sometimes called the Goldman equation, is used in cell membrane physiology to determine the resting potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane. The discoverers of this are David E.

Why does Goldman equation matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Goldman equation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Goldman equation.

Tags

  • Electrochemical equations
  • Membrane physiology
  • Physical chemistry

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