The study of conformational states of proteins by nuclear magnetic resonance

Rapid prediction of full spin systems using uncertainty-aware machine learning

Accurate simulation of solution NMR spectra requires knowledge of all chemical shift and scalar coupling parameters, traditionally accomplished by heuristic-based techniques or ab initio computational chemistry methods. Here we present a novel machine learning technique which combines uncertainty-aware deep learning with rapid estimates of conformational geometries to generate Full Spin System Predictions with UnCertainty (FullSSPrUCe). We improve on previous state of the art in accuracy on chemical shift values, predicting protons to within 0.209 ppm and carbons to within 1.213 ppm. Further, we are able to predict all scalar coupling values, unlike previous GNN models, achieving 3JHH accuracies between 0.838 Hz and 1.392 Hz on small experimental datasets. Our uncertainty quantification shows a strong, useful correlation with accuracy, with the most confident predictions having significantly reduced error, including our top-80% most confident proton shift predictions having an average error of only 0.140 ppm. We also properly handle stereoisomerism and intelligently augment experimental data with ab initio data through disagreement regularization to account for deficiencies in training data.

A synthetic picture of intramolecular dynamics of proteins. Towards a contemporary statistical theory of biochemical processes

An increasing body of experimental evidence indicates the slow character of internal dynamics of native proteins. The important consequence of this is that theories of chemical reactions, used hitherto, appear inadequate for description of most biochemical reactions. Construction of a contemporary, truly advanced statistical theory of biochemical processes will need simple but realistic models of microscopic dynamics of biomolecules. In this review, intended to be a contribution towards this direction, three topics are considered. First, an intentionally simplified picture of dynamics of native proteins which emerges from recent investigations is presented. Fast vibrational modes of motion, of periods varying from 10(-14) to 10(-11) s, are contrasted with purely stochastic conformational transitions. Significant evidence is adduced that the relaxation time spectrum of the latter spreads in the whole range from 10(-11) to 10(5) s or longer, and up to 10(-7) s it is practically quasi-continuous. Next, the essential ideas of the theory of reaction rates based on stochastic models of intramolecular dynamics are outlined. Special attention is paid to reactions involving molecules in the initial conformational substrates confirmed to the transition state, which is realized in actual experimental situations. And finally, the two best experimentally justified classes of models of conformational transition dynamics, symbolically referred to as "protein glass" and "protein machine", are described and applied to the interpretation of a few simple biochemical processes, perhaps the most important result reported is the demonstration of the possibility of predominance of the short initial condition-dependent stage of protein involved reactions over the main stage described by the standard kinetics. This initial stage, and not the latter, is expected to be responsible for the coupling of component reactions in the complete enzymatic cycles as well as more complex processes of biological free energy transduction.

Conformational dynamics and enzyme activity

Conformational flexibility and structural fluctuations play an important role in enzyme activity. A great variety of internal motions ranging over different time scales and of different amplitudes are involved in the catalytic cycle. These different types of motions and their functional consequences are considered in the light of experimental data and theoretical analyses. The conformational changes upon substrate binding, and particularly the hinge-bending motion which occurs in enzymes made of two domains, are analyzed from several well documented examples. The conformational events accompanying the different steps of the catalytic cycle are discussed. The last section concerns the motions involved in the allosteric transition which regulates the enzyme activity.

19F NMR investigations of the catalytic mechanism of phosphoglucomutase using fluorinated substrates and inhibitors

The complexes of phosphoglucomutase with a number of fluorinated substrate analogues have been investigated by 19F NMR and the effects of the binding of Li+ and Cd2+ to these complexes determined. Very large downfield chemical shift changes (-14 to -19 ppm) accompanied binding of the inhibitors 6-deoxy-6-fluoro-alpha-D-glucopyranosyl phosphate and alpha-glucosyl fluoride 6-phosphate to the phosphoenzyme. Smaller shift changes were observed for ligands substituted with fluorine at other positions. Addition of Li+ to enzyme/fluorinated ligand complexes caused a 10(2)- to 10(3)-fold decrease in ligand dissociation constants as witnessed by the change from intermediate to slow-exchange conditions in the NMR spectra. Measurement of the 19F NMR spectra of complexes of the Li(+)-enzyme with each of the fluoroglucose 1-phosphates and 6-phosphates has provided some insight into the environment of each of these fluorines (thus also parent hydroxyls) in each of the complexes. Results obtained argue strongly against a single sugar binding mode for the glucose 1- and 6-phosphates. Two enzyme-bound species were detected in the 19F NMR spectra of the complexes formed by reaction of the Cd(2+)-phosphoenzyme complex with the 2- and 3-fluoroglucose phosphates. These are tentatively assigned as the fluoroglucose 1,6-bisphosphate species bound in two different modes to the dephosphoenzyme. Only one bound species was observed in the case of the 4-fluoroglucose phosphates.(ABSTRACT TRUNCATED AT 250 WORDS)

Peptide/antibody recognition: synthetic peptides derived from the E. coli tryptophan synthase beta 2 subunit interact with high affinity with an anti-beta 2 monoclonal antibody

Recent studies have shown that the antigenic determinant recognized by a monoclonal antibody (mAb 164-2) elicited against the beta 2 subunit of E. coli tryptophan synthase is localized between residues 276 and 297 of this protein. In order to delineate more precisely the epitope recognized by this antibody, peptides ranging in length from 11 to 29 amino acids and belonging to this region were synthesized, and their interactions with the antibody are described in this paper. The smallest peptide recognized with a high affinity by antibody 164-2 contains 11 residues (273-283). This peptide is recognized by antibody 164-2 with an affinity (KD = 7.5 x 10(-9) M) very close to that of the native beta 2 subunit, suggesting a high structural similarity of the epitope inside the protein and in the isolated peptide. The corresponding sequence of beta 2 is located in a region protruding from the protein surface that contains a beta-turn as unique element of secondary structure in the crystallographic model. The absence of interaction between antibody 164-2 and the octapeptide lacking the three residues at the C-terminal end of peptide 11 suggests that the beta-turn is important in the recognition by the antibody. Kinetic studies were performed to find out whether or not the binding of the antibody to the peptide involves any conformational adaptation. The dissociation equilibrium constant (KD), the dissociation rate constant (koff) and the association rate constant (kon) were measured for eight peptide/antibody complexes. The values obtained were compatible with a one-step reaction, suggesting that no important conformational adaptation is involved in the formation of the peptide/antibody complexes. Furthermore, it has been shown that differences in affinity of antibody 164-2 for the various peptides were mainly due to differences in the dissociation rate constants (koff) and not in the association rate constants (kon). The exceptional location of the epitope in the native protein and the unusually high affinity of the 11-residue peptide for mAb 164-2, makes this peptide a good model for studying the interaction between an antibody and a continuous epitope of a protein.

Theory of molecular machines. I. Channel capacity of molecular machines

Like macroscopic machines, molecular-sized machines are limited by their material components, their design, and their use of power. One of these limits is the maximum number of states that a machine can choose from. The logarithm to the base 2 of the number of states is defined to be the number of bits of information that the machine could "gain" during its operation. The maximum possible information gain is a function of the energy that a molecular machine dissipates into the surrounding medium (Py), the thermal noise energy which disturbs the machine (Ny) and the number of independently moving parts involved in the operation (dspace): Cy = dspace log2 [( Py + Ny)/Ny] bits per operation. This "machine capacity" is closely related to Shannon's channel capacity for communications systems. An important theorem that Shannon proved for communication channels also applies to molecular machines. With regard to molecular machines, the theorem states that if the amount of information which a machine gains is less than or equal to Cy, then the error rate (frequency of failure) can be made arbitrarily small by using a sufficiently complex coding of the molecular machine's operation. Thus, the capacity of a molecular machine is sharply limited by the dissipation and the thermal noise, but the machine failure rate can be reduced to whatever low level may be required for the organism to survive.

Studies of synthetic helical peptides using circular dichroism and nuclear magnetic resonance

We have designed a set of 17-residue synthetic peptides to be monomeric helices in aqueous solution. Circular dichrosim experiments indicate the presence of helical structure in aqueous solution at low temperature and low pH. The two-dimensional nuclear magnetic resonance results for one of the peptides show a segment of ten residues which clearly meets all of the criteria for the existence of helical structure at both 5 degrees C and 15 degrees C. The first four residues of the peptide are in a largely extended conformation. Calculations suggest that residues 5 through 14 are significantly helical at 5 degrees C. When the temperature is increased, circular dichroism spectra indicate that the helical content decreases. At 15 degrees C, the 3JN alpha coupling constants increase in the helical region, indicating an increase in motion or conformational averaging in the helical segment. None of the peptides has pH titration behavior consistent with salt bridge stabilization of helical conformation. Our data lend themselves to interpretation with the helix dipole model and specific side-chain interactions. When the N and C termini charges are removed the helical content of the peptides increases. The amount of helicity increases as the pH is lowered, due to the ionization of His16. Much of the helical stabilization appears to be due to a specific side-chain interaction between His16 and Tyr12.

Protein folding

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NMR studies of mobility within protein structure

NMR studies of dynamics within structure have revealed that a quite new approach to protein structure and its relation to function is necessary. This approach requires the consideration in detail of the following: 1. Local movements of groups and small segments to allow fast recognition and fitting. The motion concerns on/off rates as well as binding. The observations affect surface/surface recognition, e.g. of antigen/antibody as well as of substrate and protein. 2. Somewhat larger interdomain or N- and C-terminal segments which allow rearrangement. Cases in point are the movement of segments in blood-clotting proteins or in histones. 3. Relative motion of helices in hinges. These actions are likely in such enzymes as kinases and P-450 cytochromes. 4. Relative motion of helices within domains (relative to other helices or sheets) in mechanical devices (triggers) e.g. in calmodulin. 5. General motion in random proteins. Examples extend from rubber-like proteins (entropy sensors), some glycoproteins, to proteins carrying peptide hormones to be generated only after hydrolysis. 6. Order----disorder transitions locally as in osteocalcin and metallothionine. 7. Swinging arm motions associated with special sequences such as (Ala-Pro)n. 8. Of great interest is the power of NMR to look at proteins which are relatively large, up to 50 kDa proteins, and to isolate certain zones of interest. This needs careful temperature dependent studies and analysis of separated domains [72] as well as the use of a great variety of pulse sequences [15] and of nuclei other than protons. 9. In this article I have illustrated the different possibilities using work in my own group. This is done to lessen the burden of extensive review. I fully realise that the range of examples is now large. I would stress though that the production of the necessary technology was the endeavour of several of us within the Oxford Enzyme Group from 1970 to 1985, i.e. from 270-600 MHz Fourier-transform NMR spectroscopy. 10. While all of these features have been demonstrated by NMR methods there are parallel developments both using X-ray diffraction methods and theoretical approaches. All these procedures are changing the view of protein structure to one which incorporates dynamics all the way from conventional vibronic/rotational coupling to the disordered motions characteristic of random polymers. It is the understanding of dynamics that leads to an appreciation of function.

A comparison of the antioxidant requirements of proteins with those of synthetic polymers suggests an antioxidant function for clusters of aromatic and bivalent sulphur-containing amino acid residues

Many proteins which function in extracellular environments potentially rich in oxygen-derived free radicals contain clustered tyrosine and cysteine residues which, by analogy with the chemistry of antioxidants used with synthetic polymers, may provide an appreciable antioxidant and redox stabilization activity. Such proteins may function as antioxidants, and as ligand binding sites for free radicals and other active molecules employed in normal biochemical processes.

Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording

The lifetimes of the unitary currents from ion channels, as revealed from single-channel recording, are traditionally thought to follow exponential or multiexponential distributions. The interpretation of these event-time distributions is that the gating process follows Markov kinetics among a small number of states. There is recent evidence, however, that certain systems exhibit distributions that follow power laws or functions related to power laws. Likewise, it has been suggested that data sets that appear to be multiexponential may be fit to simple power laws as well. In this paper we propose a different view of ion-channel-gating kinetics that is consistent with these recent experimental observations. We retain the Markovian nature of the kinetics, but, in contrast to the traditional models, we suggest that ion-channel proteins have a very large number of states all of similar energy. Gating, therefore, resembles a diffusion process. We show that our simplest one-dimensional model exhibits single-channel distributions that follow power laws of the form t-a, where 1/2 less than or equal to a less than or equal to 3/2. Exponents determined from recent experiments approximately fall within this range. We believe that this model is consistent with modern views of protein dynamics and, thus, may provide a key to the molecular details of the gating process.

Anti-peptide antibodies detect steps in a protein conformational change: low-pH activation of the influenza virus hemagglutinin

At low pH, the hemagglutinin (HA) of influenza virus undergoes an irreversible conformational change that potentiates its essential membrane fusion function. We have probed the details of this conformational change using a panel of 14 anti-HA-peptide antibodies. Whereas some antibodies reacted equally well with both the neutral and low-pH HA conformations, others reacted to a significantly greater extent with the low-pH form. The locations of the peptides recognized by the latter antibodies in the three-dimensional HA structure indicated regions of the protein that change in response to low pH. Moreover, kinetic experiments suggested steps in the conformational change. In addition to their relevance to membrane fusion, our results show that anti-peptide antibodies can be used to study some types of biologically important protein conformational changes.

Conformations of intermediates in the folding of the pancreatic trypsin inhibitor

Intermediates in the folding pathway of the bovine pancreatic trypsin inhibitor (PTI) have been examined by 1H nuclear magnetic resonance (n.m.r.). The intermediates were trapped during the reoxidation and consequent refolding of reduced PTI by alkylating free thiols; each intermediate contained different disulphide linkages. The n.m.r. spectra reveal that conformational features of the native protein are present in the intermediate containing just one of the three normal disulphide linkages (30-51). As additional normal disulphide bonds are formed, the conformation becomes more similar to that of the native protein. Introduction of additional but incorrect disulphide bonds does not lead to an increase in observable globular structure. A description of the folding process in terms of the conformations of the different intermediates is proposed. The significance of these results for the general mechanism of protein folding is outlined.