physics

Internal Coordinate Mechanics

Internal Coordinate Mechanics is a physics 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 Internal Coordinate Mechanics rather than just read about it. In short: Internal Coordinate Mechanics (ICM) is a software program and algorithm to predict low-energy conformations of molecules by sampling the space of internal coordinates (bond lengths, bond angles and dihedral angles) defining molecular geometry. In ICM each molecule is constructed as a tree from an entry atom where each next atom is built iteratively from the preceding three atoms via three internal variables.

Key takeaways

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

Reference excerpt

Internal Coordinate Mechanics (ICM) is a software program and algorithm to predict low-energy conformations of molecules by sampling the space of internal coordinates (bond lengths, bond angles and dihedral angles) defining molecular geometry. In ICM each molecule is constructed as a tree from an entry atom where each next atom is built iteratively from the preceding three atoms via three internal variables. The rings kept rigid or imposed via additional restraints. ICM is used for modelling peptides and interactions with substrates and coenzymes.

Software ICM also is a programming environment for various tasks in computational chemistry and computational structural biology, sequence analysis and rational drug design. The original goal was to develop algorithms for energy optimization of several biopolymers with respect to an arbitrary subset of internal coordinates such as bond lengths, bond angles torsion angles and phase angles. The efficient and general global optimization method which evolved from the original ICM method is still the central piece of the program. It is this basic algorithm which is used for peptide prediction, homology modeling and loop simulations, flexible macromolecular docking and energy refinement. However the complexity of problems related to structure prediction and analysis, as well as the desire for perfection, compactness and consistency, led to the program's expansion into neighboring areas such as graphics, chemistry, sequence analysis and database searches, mathematics, statistics and plotting. The original meaning became too narrow, but the name was kept. The current integrated ICM shell contains hundreds of variables, functions, commands, database and web tools, novel algorithms for structure prediction and analysis into a powerful, yet compact program which is still called ICM. The seven principal areas are centered on a general core of shell-language and data analysis and visualization.

References

Abagyan, R; Totrov, M (January 1994). "Biased probability Monte Carlo conformational searches and electrostatic calculations for peptides and proteins". J. Mol. Biol. 235: 983–1002. doi:10.1006/jmbi.1994.1052. PMID 8289329. Abagyan, R.A.; Totrov, M.M.; Kuznetsov, D.A. (1994). "ICM: A New Method For Protein Modeling and Design: Applications To Docking and Structure Prediction From The Distorted Native Conformation". J. Comput. Chem. 15: 488–506. doi:10.1002/jcc.540150503. Totrov, M.M.; Abagyan, R.A. (1994). "Efficient Parallelization of The Energy, Surface and Derivative Calculations For internal Coordinate Mechanics". J. Comput. Chem. 15: 1105–1112. doi:10.1002/jcc.540151006.

External links www.molsoft.com iSee (interactive Structurally enhanced experience) EDS (Electron Density Server) Archived 2017-07-02 at the Wayback Machine (ICM supports electron density visualization)

Worked examples

Example 1 — a first encounter with Internal Coordinate Mechanics

Start with the simplest possible case. Write down what Internal Coordinate Mechanics claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, 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 Internal Coordinate Mechanics 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 Internal Coordinate Mechanics 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 Internal Coordinate Mechanics

In research: Internal Coordinate Mechanics appears in physics 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 Internal Coordinate Mechanics 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: Internal Coordinate Mechanics is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computational chemistry software, so understanding it makes those chapters shorter.
In everyday life: Look for Internal Coordinate Mechanics 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 Internal Coordinate Mechanics in 20 minutes

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

Frequently asked questions

What is Internal Coordinate Mechanics in simple terms?

Why does Internal Coordinate Mechanics matter?

Because it connects several physics 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 Internal Coordinate Mechanics?

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 Internal Coordinate Mechanics.