Protein folding

Concept

Protein folding

T-092Home BU-306Threads structure · energy

Statement

The thermodynamics that select the native state.

Why it matters

protein-structure-levels describes the four levels of protein architecture as a static hierarchy; this result supplies the physical mechanism that actually selects one specific tertiary (and, where relevant, quaternary) structure out of the astronomical number of geometrically possible chain conformations, and does so reproducibly, in a biologically relevant timescale, using only the information encoded in the amino-acid sequence itself. Correct folding is a precondition for everything built on it later in the unit: x-ray-crystallography determines the folded structure this result explains the selection of, michaelis-menten-kinetics and allosteric-regulation both presuppose a stably folded active site and regulatory site, and molecular-motors presupposes folded, functional motor domains capable of undergoing large, reversible conformational changes.

Failure of this process, or of the systems (chaperones) that normally assist it, is directly implicated in human disease: several neurodegenerative conditions are associated with proteins that misfold or aggregate into an alternative, non-native structure, making the thermodynamics of folding a matter of direct medical, not merely structural, interest.

Hypotheses

Anfinsen's thermodynamic hypothesis: for many single-domain proteins, the native (functional) structure is the conformation of lowest Gibbs free energy accessible to that amino-acid sequence under physiological conditions.This is what makes folding a thermodynamic, sequence-determined problem rather than one requiring external, sequence-independent instructions: the primary sequence alone specifies the native structure, because that structure is simply wherever the free-energy landscape has its global minimum for that particular chain. Protein folding is driven predominantly, though not exclusively, by the hydrophobic effect.Burying nonpolar side chains away from water increases the entropy of the surrounding solvent (releasing ordered water molecules that had been caging the exposed hydrophobic surface), which is large enough in a typical globular protein to outweigh the loss of the unfolded chain's own conformational entropy; hydrogen bonding, van der Waals packing, and, for some proteins, disulfide bonds and metal coordination contribute additional, smaller stabilising terms. Folding proceeds via a funnel-shaped energy landscape, not by an exhaustive search of all possible conformations.Levinthal's paradox (Discussion) shows that a true random search of conformational space would take far longer than a protein actually takes to fold; the funnel picture resolves this by allowing many partially folded intermediates to already be lower in energy than the fully unfolded state, biasing the search strongly toward the native structure rather than requiring it to be found by chance.

Proof

\Delta G_{\text{fold}} = \Delta H_{\text{fold}} - T\Delta S_{\text{fold}}

Folding, like any spontaneous process at constant temperature and pressure, is governed by the Gibbs free-energy change; a conformation is thermodynamically favoured over the unfolded state exactly when \(\Delta G_{\text{fold}}<0\) for the transition from unfolded to that conformation. A

\Delta S_{\text{fold}} = \Delta S_{\text{chain}} + \Delta S_{\text{solvent}}, \qquad \Delta S_{\text{chain}}<0,\ \ \Delta S_{\text{solvent}}>0\ (\text{large})

Folding an extended chain into a single compact structure sharply reduces the chain's own conformational entropy (unfavourable), but burying nonpolar side chains releases the shell of ordered water molecules that had surrounded them in the unfolded state, raising solvent entropy by a larger amount for a typical globular protein; the hydrophobic effect (Hypotheses) is fundamentally this large, favourable solvent-entropy term. B

\Delta H_{\text{fold}} = \Delta H_{\text{H-bond}} + \Delta H_{\text{vdW}} + \Delta H_{\text{other}} < 0

Backbone hydrogen bonds (largely satisfied within \(\alpha\)-helices and \(\beta\)-sheets, protein-structure-levels), van der Waals packing in the buried hydrophobic core, and, in many proteins, disulfide bonds and salt bridges all contribute additional favourable (exothermic) enthalpy once the chain is compactly folded, reinforcing the entropically driven hydrophobic collapse of Step 2. B

\text{The free-energy landscape is funnel-shaped: many partially collapsed conformations lie at intermediate free energy between the unfolded ensemble and the single native-state minimum.}

Rather than requiring the chain to sample the entire conformational space at random before stumbling on the native structure, hydrophobic collapse can occur rapidly and non-specifically, producing a molten-globule-like intermediate that is already substantially lower in free energy than the unfolded state; from there, more specific packing and hydrogen-bonding interactions funnel the ensemble further downhill toward the single native structure at the funnel's base. B

\text{If no kinetic trap intervenes, the chain reaches the global free-energy minimum, i.e. the native structure, on a biologically relevant timescale.}

Because the funnel (Step 4) biases the search toward lower free energy at every stage rather than requiring exhaustive sampling, folding times for many small, single-domain proteins are microseconds to seconds — resolving Levinthal's paradox (Discussion) — though larger or more topologically complex proteins may require assistance from molecular chaperones to avoid becoming kinetically trapped in a local, non-native free-energy minimum along the way. A

Result

\text{Native structure} = \arg\min_{\text{conformation}} G(\text{conformation}), \qquad \Delta G_{\text{fold}} = \Delta H_{\text{fold}} - T\Delta S_{\text{fold}} < 0

Reading. The sequence-determined native structure is simply the conformation of lowest Gibbs free energy reachable by that chain; that minimum is reached efficiently because the underlying free-energy landscape is funnel-shaped, not flat, so the search is guided rather than exhaustive.

Scope. Holds well for many small, single-domain, globular proteins folding spontaneously in dilute solution (Anfinsen's experiment, Discussion). Larger multidomain proteins, membrane proteins, and many proteins inside the crowded cellular environment require assistance from molecular chaperones to reach the native state reliably and avoid aggregation, without this changing which structure is thermodynamically native.

Corollaries & converses

protein-structure-levels' four-level hierarchy (primary through quaternary) is the structural description of the single free-energy minimum this result explains the selection of; primary structure supplies the sequence, and secondary/tertiary/quaternary structure is the geometry that sequence's free-energy landscape happens to minimise at.
allosteric-regulation depends directly on this result: an allosteric protein possesses two (or more) distinct low-free-energy conformations of comparable stability, with ligand binding at one site shifting the free-energy balance between them — a controlled, reversible version of the same energy landscape described here, rather than a single unconditional global minimum.
Converse: if a protein's measured structure does not match the prediction from sequence alone, either the assumption of a single dominant free-energy minimum fails (multiple comparably stable states, as in some allosteric or chaperone-dependent proteins) or the protein has become kinetically trapped in a non-native local minimum rather than truly reaching thermodynamic equilibrium (Fails without).

Fails without

Drop Anfinsen's thermodynamic hypothesis (Hypotheses), i.e. assume the native structure requires external, sequence-independent instructions: Anfinsen's own experiment (Discussion) directly rules this out for the proteins he studied — a chemically denatured, disulfide-scrambled enzyme spontaneously refolds to full activity on simple removal of the denaturant, with no cellular machinery present at all, showing sequence alone is sufficient information for at least these cases.
Drop the funnel-shaped landscape (Step 4), i.e. assume folding genuinely requires an exhaustive random search of conformational space: this reproduces Levinthal's paradox exactly — a chain of even modest length has vastly more possible conformations than could be sampled at any plausible per-conformation rate within the actual observed folding time, so an unguided random search is physically inconsistent with how quickly real proteins are observed to fold.

Common errors

Treating protein folding as driven mainly by hydrogen bonding, by analogy with DNA base pairing; the dominant driving force for burying the hydrophobic core is the solvent-entropy gain of the hydrophobic effect (Step 2), with hydrogen bonding contributing an important but secondary enthalpic stabilisation (Step 3), largely already satisfied within regular secondary structure.
Assuming a lower-enthalpy structure is automatically the native one, ignoring the entropic (\(-T\Delta S\)) term in Step 1; a structure can be enthalpically very favourable yet not be the free-energy minimum once the (frequently large, unfavourable) loss of chain conformational entropy is included.
Believing chaperones supply the "folding instructions" or dictate the final structure; chaperones (Result's Scope) generally act by preventing aggregation and off-pathway kinetic traps, giving the chain more opportunity to find its own thermodynamically determined native structure, not by encoding an alternative, externally imposed structure.
Assuming Levinthal's paradox shows that protein folding cannot possibly be a thermodynamic, energy-minimisation process; it shows only that folding cannot be an unguided random search (Fails without) — the funnel landscape resolves the paradox without abandoning the thermodynamic picture.

Discussion

Christian Anfinsen's experiments on bovine pancreatic ribonuclease, published through the late 1950s and early 1960s, showed that fully denaturing and disulfide-reducing the enzyme, then simply removing the denaturant and allowing reoxidation, restored full enzymatic activity with no other cellular components present. This directly demonstrated that the amino-acid sequence alone contains sufficient information to specify the native structure, work recognised with a share of the 1972 Nobel Prize in Chemistry and now generally referred to as Anfinsen's thermodynamic hypothesis.

Cyrus Levinthal noted in 1969 that if a protein searched conformational space by randomly sampling torsion angles at each residue, even generously fast per-step rates would require folding times vastly longer than the seconds-to-milliseconds actually observed for many proteins — the paradox that motivated the funnel-shaped energy landscape picture (Hypotheses, Step 4) as the resolution: folding is a biased downhill search, not a random walk through an enormous, flat conformational space.

Not every protein finds its own native structure unassisted inside a living cell. Molecular chaperones (including the heat-shock protein families) bind partially folded or aggregation-prone intermediates and, in some cases using ATP hydrolysis, give the chain repeated opportunities to escape local, kinetically trapped, non-native minima and continue descending toward the true global free-energy minimum, without themselves specifying what that minimum structure is.

Common misconception: that misfolded or aggregated proteins (as implicated in several neurodegenerative diseases) contradict Anfinsen's hypothesis. They do not: misfolding reflects the chain becoming kinetically trapped in a non-native, locally stable conformation, or aggregating with other chains before reaching its own global minimum, rather than showing that the true native structure is not, in fact, the thermodynamic free-energy minimum for that sequence.

Worked examples

\text{Ribonuclease: denature with urea + a reducing agent (scrambling all four disulfide bonds); remove denaturant and reoxidant.}

On removal of urea and reintroduction of a mild oxidising environment, the fully unfolded, disulfide-scrambled chain refolds and reforms its four native disulfide bonds correctly (rather than any of the many other statistically possible, incorrect pairings), recovering full catalytic activity. This is Anfinsen's actual result: the sequence alone is guiding the chain to one specific low-free-energy structure out of many other geometrically possible ones. A

\text{Native, catalytically active ribonuclease is recovered with no external template or instruction present.}

Reading. Sequence information alone is sufficient to specify the native structure for this protein, exactly as the Result and Hypotheses assert.

Scope. The same logic (denature, then remove the denaturant and observe spontaneous, sequence-directed refolding) is the standard experimental test of whether a given protein folds thermodynamically, without assistance, in vitro.

Problems

A small, single-domain protein is found to fold reproducibly to its native, active structure in under a millisecond. Using Levinthal's paradox and the funnel picture, explain why this observation is not, in fact, physically surprising.
Solution
A truly random search of the chain's full conformational space would take far longer than a millisecond (Levinthal's paradox, Discussion), so a millisecond folding time would be surprising only under the (incorrect) assumption of an unguided random search. Under the funnel-shaped landscape (Step 4), the search is strongly biased downhill from the earliest stages of hydrophobic collapse onward, so folding times many orders of magnitude faster than a random search would predict are exactly what the funnel picture expects, not a contradiction of it.
Two mutant versions of the same protein are compared: mutant A has a substitution that removes one buried hydrophobic side chain and replaces it with a charged one; mutant B has a substitution on the protein's fully solvent-exposed surface, from one charged residue to another. Predict, using Step 2, which mutant is more likely to destabilise the native fold, and explain why.
Solution
Mutant A is far more likely to destabilise the fold. Burying a charged side chain in the hydrophobic core (Step 2) is energetically costly — it forfeits much of the favourable solvent-entropy gain that buries hydrophobic surface in the first place, and may leave an unsatisfied charge buried away from water entirely. Mutant B, a charge-to-charge substitution on an already solvent-exposed surface, changes essentially nothing about core packing or the hydrophobic effect and is expected to have little effect on the free energy of folding.
Explain, using the Result, why raising temperature substantially above physiological levels can cause a protein to denature (unfold), even though \(\Delta H_{\text{fold}}\) itself is favourable (negative) at physiological temperature.
Solution
\(\Delta G_{\text{fold}} = \Delta H_{\text{fold}} - T\Delta S_{\text{fold}}\) (Step 1), and folding's net entropy change \(\Delta S_{\text{fold}}\) is typically small and can be negative once solvent and chain contributions partially offset (Step 2). As \(T\) increases, the magnitude of the \(-T\Delta S_{\text{fold}}\) term grows; if \(\Delta S_{\text{fold}}\) is negative, this term becomes increasingly unfavourable with rising temperature until it exceeds the favourable \(\Delta H_{\text{fold}}\), flipping \(\Delta G_{\text{fold}}\) positive and making the unfolded state the new free-energy minimum — thermal denaturation.