Folding protein models with a simple hydrophobic energy function: The fundamental importance of monomer inside/outside segregation

The present study explores a “hydrophobic” energy function for folding simulations of the protein lattice model. The contribution of each monomer to conformational energy is the product of its “hydrophobicity” and the number of contacts it makes, i.e., E(h⃗, c⃗) = −Σi=1N cihi = −(h⃗.c⃗) is the negative scalar product between two vectors in N-dimensional cartesian space: h⃗ = (h1, … , hN), which represents monomer hydrophobicities and is sequence-dependent; and c⃗ = (c1, … , cN), which represents the number of contacts made by each monomer and is conformation-dependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for protein-like behavior is to be satisfied. Given a conformation with vector c⃗, the best sequence is a vector h⃗ on the direction upon which the projection of c⃗ − c̄⃗ is maximal, where c̄⃗ is the diagonal vector with components equal to c̄, the average number of contacts per monomer in the unfolded state. Best native conformations are suggested to be not maximally compact, as assumed in many studies, but the ones with largest variance of contacts among its monomers, i.e., with monomers tending to occupy completely buried or completely exposed positions. This inside/outside segregation is reflected on an apolar/polar distribution on the corresponding sequence. Monte Carlo simulations in two dimensions corroborate this general scheme. Sequences targeted to conformations with large contact variances folded cooperatively with thermodynamics of a two-state transition. Sequences targeted to maximally compact conformations, which have lower contact variance, were either found to have degenerate ground state or to fold with much lower cooperativity.

Protein folding kinetics exhibit an Arrhenius temperature dependence when corrected for the temperature dependence of protein stability

The anomalous temperature dependence of protein folding has received considerable attention. Here we show that the temperature dependence of the folding of protein L becomes extremely simple when the effects of temperature on protein stability are corrected for; the logarithm of the folding rate is a linear function of 1/T on constant stability contours in the temperature–denaturant plane. This convincingly demonstrates that the anomalous temperature dependence of folding derives from the temperature dependence of the interactions that stabilize proteins, rather than from the super Arrhenius temperature dependence predicted for the configurational diffusion constant on a rough energy landscape. However, because of the limited temperature range accessible to experiment, the results do not rule out models with higher order temperature dependences. The significance of the slope of the stability-corrected Arrhenius plots is discussed.

Stability and dynamics in a hyperthermophilic protein with melting temperature close to 200°C

The rubredoxin protein from the hyperthermophilic archaebacterium Pyrococcus furiosus was examined by a hydrogen exchange method. Even though the protein does not exhibit reversible thermal unfolding, one can determine its stability parameters—free energy, enthalpy, entropy, and melting temperature—and also the distribution of stability throughout the protein, by using hydrogen exchange to measure the reversible cycling of the protein between native and unfolded states that occurs even under native conditions.

Semirational design of active tumor suppressor p53 DNA binding domain with enhanced stability

We have designed a p53 DNA binding domain that has virtually the same binding affinity for the gadd45 promoter as does wild-type protein but is considerably more stable. The design strategy was based on molecular evolution of the protein domain. Naturally occurring amino acid substitutions were identified by comparing the sequences of p53 homologues from 23 species, introducing them into wild-type human p53, and measuring the changes in stability. The most stable substitutions were combined in a multiple mutant. The advantage of this strategy is that, by substituting with naturally occurring residues, the function is likely to be unimpaired. All point mutants bind the consensus DNA sequence. The changes in stability ranged from +1.27 (less stable Q165K) to −1.49 (more stable N239Y) kcal mol−1, respectively. The changes in free energy of unfolding on mutation are additive. Of interest, the two most stable mutants (N239Y and N268D) have been known to act as suppressors and restored the activity of two of the most common tumorigenic mutants. Of the 20 single mutants, 10 are cancer-associated, though their frequency of occurrence is extremely low: A129D, Q165K, Q167E, and D148E are less stable and M133L, V203A and N239Y are more stable whereas the rest are neutral. The quadruple mutant (M133LV203AN239YN268D), which is stabilized by 2.65 kcal mol−1 and Tm raised by 5.6°C is of potential interest for trials in vivo.

Peptide interfacial adsorption is kinetically limited by the thermodynamic stability of self association

We present a study of the adsorption of two peptides at the octane–water interface. The first peptide, Lac21, exists in mixed monomer–tetramer equilibrium in bulk solution with an appreciable monomer concentration. The second peptide, Lac28, exists as a tetramer in solution, with minimal exposed hydrophobic surface. A kinetic limitation to interfacial adsorption exists for Lac28 at moderate to high surface coverage that is not observed for Lac21. We estimate the potential energy barrier for Lac28 adsorption to be 42 kJ/mol and show that this is comparable to the expected free energy barrier for tetramer dissociation. This finding suggests that, at moderate to high surface coverage, adsorption is kinetically limited by the availability of interfacially active monomeric “domains” in the subinterfacial region. We also show how the commonly used empirical equation for protein adsorption dynamics can be used to estimate the potential energy barrier for adsorption. Such an approach is shown to be consistent with a formal description of diffusion–adsorption, provided a large potential energy barrier exists. This work demonstrates that the dynamics of interfacial adsorption depend on protein thermodynamic stability, and hence structure, in a quantifiable way.

Single-molecule protein folding: Diffusion fluorescence resonance energy transfer studies of the denaturation of chymotrypsin inhibitor 2

We report single-molecule folding studies of a small, single-domain protein, chymotrypsin inhibitor 2 (CI2). CI2 is an excellent model system for protein folding studies and has been extensively studied, both experimentally (at the ensemble level) and theoretically. Conformationally assisted ligation methodology was used to synthesize the proteins and site-specifically label them with donor and acceptor dyes. Folded and denatured subpopulations were observed by fluorescence resonance energy transfer (FRET) measurements on freely diffusing single protein molecules. Properties of these subpopulations were directly monitored as a function of guanidinium chloride concentration. It is shown that new information about different aspects of the protein folding reaction can be extracted from such subpopulation properties. Shifts in the mean transfer efficiencies are discussed, FRET efficiency distributions are translated into potentials, and denaturation curves are directly plotted from the areas of the FRET peaks. Changes in stability caused by mutation also are measured by comparing pseudo wild-type CI2 with a destabilized mutant (K17G). Current limitations and future possibilities and prospects for single-pair FRET protein folding investigations are discussed.

Stability of nonrelativistic quantum mechanical matter coupled to the (ultraviolet cutoff) radiation field

We announce a proof of H-stability for the quantized radiation field, with ultraviolet cutoff, coupled to arbitrarily many non-relativistic quantized electrons and static nuclei. Our result holds for arbitrary atomic numbers and fine structure constant. We also announce bounds for the energy of many electrons and nuclei in a classical vector potential and for the eigenvalue sum of a one-electron Pauli Hamiltonian with magnetic field.

Transition-state structure as a unifying basis in protein-folding mechanisms: Contact order, chain topology, stability, and the extended nucleus mechanism

I attempt to reconcile apparently conflicting factors and mechanisms that have been proposed to determine the rate constant for two-state folding of small proteins, on the basis of general features of the structures of transition states. Φ-Value analysis implies a transition state for folding that resembles an expanded and distorted native structure, which is built around an extended nucleus. The nucleus is composed predominantly of elements of partly or well-formed native secondary structure that are stabilized by local and long-range tertiary interactions. These long-range interactions give rise to connecting loops, frequently containing the native loops that are poorly structured. I derive an equation that relates differences in the contact order of a protein to changes in the length of linking loops, which, in turn, is directly related to the unfavorable free energy of the loops in the transition state. Kinetic data on loop extension mutants of CI2 and α-spectrin SH3 domain fit the equation qualitatively. The rate of folding depends primarily on the interactions that directly stabilize the nucleus, especially those in native-like secondary structure and those resulting from the entropy loss from the connecting loops, which vary with contact order. This partitioning of energy accounts for the success of some algorithms that predict folding rates, because they use these principles either explicitly or implicitly. The extended nucleus model thus unifies the observations of rate depending on both stability and topology.

Novel role of phosphorylation in Fe–S cluster stability revealed by phosphomimetic mutations at Ser-138 of iron regulatory protein 1

Animals regulate iron metabolism largely through the action of the iron regulatory proteins (IRPs). IRPs modulate mRNA utilization by binding to iron-responsive elements (IRE) in the 5′ or 3′ untranslated region of mRNAs encoding proteins involved in iron homeostasis or energy production. IRP1 is also the cytosolic isoform of aconitase. The activities of IRP1 are mutually exclusive and are modulated through the assembly/disassembly of its [4Fe–4S] cluster, reversibly converting it between an IRE-binding protein and cytosolic aconitase. IRP1 is also phosphoregulated by protein kinase C, but the mechanism by which phosphorylation posttranslationally increases IRE binding activity has not been fully defined. To investigate this, Ser-138 (S138), a PKC phosphorylation site, was mutated to phosphomimetic glutamate (S138E), aspartate (S138D), or nonphosphorylatable alanine (S138A). The S138E IRP1 mutant and, to a lesser extent, the S138D IRP1 mutant were impaired in aconitase function in yeast when grown aerobically but not when grown anaerobically. Purified wild-type and mutant IRP1s could be reconstituted to active aconitases anaerobically. However, when exposed to oxygen, the [4Fe–4S] cluster of the S138D and S138E mutants decayed 5-fold and 20-fold faster, respectively, than was observed for wild-type IRP1. Our findings suggest that stability of the Fe–S cluster of IRP1 can be regulated by phosphorylation and reveal a mechanism whereby the balance between the IRE binding and [4Fe–4S] forms of IRP1 can be modulated independently of cellular iron status. Furthermore, our results show that IRP1 can function as an oxygen-modulated posttranscriptional regulator of gene expression.

Solvent effects on the energy landscapes and folding kinetics of polyalanine

The effect of a solvation on the thermodynamics and kinetics of polyalanine (Ala12) is explored on the basis of its energy landscapes in vacuum and in an aqueous solution. Both energy landscapes are characterized by two basins, one associated with α-helical structures and the other with coil and β-structures of the peptide. In both environments, the basin that corresponds to the α-helical structure is considerably narrower than the basin corresponding to the β-state, reflecting their different contributions to the entropy of the peptide. In vacuum, the α-helical state of Ala12 constitutes the native state, in agreement with common helical propensity scales, whereas in the aqueous medium, the α-helical state is destabilized, and the β-state becomes the native state. Thus solvation has a dramatic effect on the energy landscape of this peptide, resulting in an inverted stability of the two states. Different folding and unfolding time scales for Ala12 in hydrophilic and hydrophobic chemical environments are caused by the higher entropy of the native state in water relative to vacuum. The concept of a helical propensity has to be extended to incorporate environmental solvent effects.

Site-specifically located 8-amino-2′-deoxyguanosine: thermodynamic stability and mutagenic properties in Escherichia coli

2-Nitropropane (2-NP), an important industrial solvent and a component of cigarette smoke, is mutagenic in bacteria and carcinogenic in rats. 8-Amino-2′-deoxyguanosine (8-amino-dG) is one of the types of DNA damage found in liver, the target organ in 2-NP-treated rats. To investigate the thermodynamic properties of 8-amino-dG opposite each of the four DNA bases, we have synthesized an 11mer, d(CCATCG*CTACC), in which G* represents the modified base. By annealing a complementary DNA strand to this modified 11mer, four sets of duplexes were generated each containing one of the four DNA bases opposite the lesion. Circular dichroism studies indicated that 8-amino-dG did not alter the global helical properties of natural right-handed B-DNA. The thermal stability of each duplex was examined by UV melting measurements and compared with its unmodified counterpart. For the unmodified 11mer, the relative stability of the complementary DNA bases opposite G was in the order C > T > G > A, as determined from their –ΔG° values. The free energy change of each modified duplex was lower than its unmodified counterpart, except for the G*:G pair that exhibited a higher melting transition and a larger –ΔG° than the G:G duplex. Nevertheless, the stability of the modified 11mer duplex also followed the order C > T > G > A when placed opposite 8-amino-dG. To explore if 8-amino-dG opposite another 8-amino-dG has any advantage in base pairing, a G*:G* duplex was evaluated, which showed that the stability of this duplex was similar to the G*:G duplex. Mutagenesis of 8-amino-dG in this sequence context was studied in Escherichia coli, which showed that the lesion is weakly mutagenic (mutation frequency ∼10–3) but still can induce a variety of targeted and semi-targeted mutations.

Altered stability of pulmonary surfactant in SP-C-deficient mice

The surfactant protein C (SP-C) gene encodes an extremely hydrophobic, 4-kDa peptide produced by alveolar epithelial cells in the lung. To discern the role of SP-C in lung function, SP-C-deficient (−/−) mice were produced. The SP-C (−/−) mice were viable at birth and grew normally to adulthood without apparent pulmonary abnormalities. SP-C mRNA was not detected in the lungs of SP-C (−/−) mice, nor was mature SP-C protein detected by Western blot of alveolar lavage from SP-C (−/−) mice. The levels of the other surfactant proteins (A, B, D) in alveolar lavage were comparable to those in wild-type mice. Surfactant pool sizes, surfactant synthesis, and lung morphology were similar in SP-C (−/−) and SP-C (+/+) mice. Lamellar bodies were present in SP-C (−/−) type II cells, and tubular myelin was present in the alveolar lumen. Lung mechanics studies demonstrated abnormalities in lung hysteresivity (a term used to reflect the mechanical coupling between energy dissipative forces and tissue-elastic properties) at low, positive-end, expiratory pressures. The stability of captive bubbles with surfactant from the SP-C (−/−) mice was decreased significantly, indicating that SP-C plays a role in the stabilization of surfactant at low lung volumes, a condition that may accompany respiratory distress syndrome in infants and adults.

Unraveling principles of lead discovery: from unfrustrated energy landscapes to novel molecular anchors.

The search for novel leads is a critical step in the drug discovery process. Computational approaches to identify new lead molecules have focused on discovering complete ligands by evaluating the binding affinity of a large number of candidates, a task of considerable complexity. A new computational method is introduced in this work based on the premise that the primary molecular recognition event in the protein binding site may be accomplished by small core fragments that serve as molecular anchors, providing a structurally stable platform that can be subsequently tailored into complete ligands. To fulfill its role, we show that an effective molecular anchor must meet both the thermodynamic requirement of relative energetic stability of a single binding mode and its consistent kinetic accessibility, which may be measured by the structural consensus of multiple docking simulations. From a large number of candidates, this technique is able to identify known core fragments responsible for primary recognition by the FK506 binding protein (FKBP-12), along with a diverse repertoire of novel molecular cores. By contrast, absolute energetic criteria for selecting molecular anchors are found to be promiscuous. A relationship between a minimum frustration principle of binding energy landscapes and receptor-specific molecular anchors in their role as "recognition nuclei" is established, thereby unraveling a mechanism of lead discovery and providing a practical route to receptor-biased computational combinatorial chemistry.

Prediction of the stability of DNA triplexes.

We present rules that allow one to predict the stability of DNA pyrimidine.purine.pyrimidine (Y.R.Y) triple helices on the basis of the sequence. The rules were derived from van't Hoff analysis of 23 oligonucleotide triplexes tested at a variety of pH values. To predict the enthalpy of triplex formation (delta H degrees), a simple nearest-neighbor model was found to be sufficient. However, to accurately predict the free energy of the triplex (delta G degrees), a combination model consisting of five parameters was needed. These parameters were (i) the delta G degrees for helix initiation, (ii) the delta G degrees for adding a T-A.T triple, (iii) the delta G degrees for adding a C(+)-G.C triple, (iv) the penalty for adjacent C bases, and (v) the pH dependence of the C(+)-G.C triple's stability. The fitted parameters are highly consistent with thermodynamic data from the basis set, generally predicting both delta H degrees and delta G degrees to within the experimental error. Examination of the parameters points out several interesting features. The combination model predicts that C(+) -G.C. triples are much more stabilizing than T-A.T triples below pH 7.0 and that the stability of the former increases approximately equal to 1 kcal/mol per pH unit as the pH is decreased. Surprisingly though, the most stable sequence is predicted to be a CT repeat, as adjacent C bases partially cancel the stability of one another. The parameters successfully predict tm values from other laboratories, with some interesting exceptions.

Direct measurement of salt-bridge solvation energies using a peptide model system: implications for protein stability.

The solvation energies of salt bridges formed between the terminal carboxyl of the host pentapeptide AcWL- X-LL and the side chains of Arg or Lys in the guest (X) position have been measured. The energies were derived from octanol-to-buffer transfer free energies determined between pH 1 and pH 9. 13C NMR measurements show that the salt bridges form in the octanol phase, but not in the buffer phase, when the side chains and the terminal carboxyl group are charged. The free energy of salt-bridge formation in octanol is approximately -4 kcal/mol (1 cal = 4.184 J), which is equal to or slightly larger than the sum of the solvation energies of noninteracting pairs of charged side chains. This is about one-half the free energy that would result from replacing a charge pair in octanol with a pair of hydrophobic residues of moderate size. Therefore, salt bridging in octanol can change the favorable aqueous solvation energy of a pair of oppositely charged residues to neutral or slightly unfavorable but cannot provide the same free energy decrease as hydrophobic residues. This is consistent with recent computational and experimental studies of protein stability.