Kinetics and Energetics of Biomolecular Folding and Binding

The ability of biomolecules to fold and to bind to other molecules is fundamental to virtually every living process. Advanced experimental techniques can now reveal how single biomolecules fold or bind against mechanical force, with the force serving as both the regulator and the probe of folding and binding transitions. Here, we present analytical expressions suitable for fitting the major experimental outputs from such experiments to enable their analysis and interpretation. The fit yields the key determinants of the folding and binding processes: the intrinsic on-rate and the location and height of the activation barrier.     

Kinetics and Energetics of Light-driven Chloroplast Glutamine Synthesis

Chloroplasts contain the enzyme glutamine synthetase. Formation of glutamine by isolated chloroplasts is light-dependent and requires an intact outer envelope. Addition of exogenous glutamic acid, as well as nitrogen donors such as nitrite or ammonium, stimulate the synthesis of this amide. Photosynthetic generation of ATP satisfies the light requirement of glutamine synthesis. The process is supported by cyclic as well as noncyclic photophosphorylation.     

Kinetics and Energetics of Producing Animal Manure-Based Biochar

Pyrolysis of animal manure produces biochar with multiple beneficial use potentials for improving soil quality and the environment. The kinetics and energetics of pyrolysis in producing manure-based biochar were reviewed and analyzed. Kinetic analysis of pyrolysis showed that the higher the temperature, the shorter the reaction time was needed for thermal decomposition and carbonization of animal manure. This kinetic information can assist in producing biochar with a desired proximate composition. Biochar with lower volatile matter (VM) content can be produced with either higher pyrolysis temperature or longer reaction time. Energetically, pyrolysis of wet manures is not sustainable due to high energy needed for drying moisture. However, co-pyrolysis with other high energy density wastes such as agricultural plastic wastes would produce not only energetically sustainable biochar but surplus energy as well. This could be used for local power generation.     

Folding/Unfolding Kinetics of Apomyoglobin

The equilibrium and kinetic folding/unfolding of apomyoglobin (ApoMb) were studied at pH 6.2, 11 °C by recording tryptophan fluorescence. The equilibrium unfolding of ApoMb in the presence of urea was shown to involve accumulation of an intermediate state, which had a higher fluorescence intensity as compared with the native and unfolded states. The folding proceeded through two kinetic phases, a rapid transition from the unfolded to the intermediate state and a slow transition from the intermediate to the native state. The accumulation of the kinetic intermediate state was observed in a wide range of urea concentrations. The intermediate was detected even in the region corresponding to the unfolding limb of the chevron plot. Urea concentration dependence was obtained for the observed folding/unfolding rate. The shape of the dependence was compared with that of two-state proteins characterized by a direct transition from the unfolded to the native state.     

Energetics and Location of Phosphoinositide Binding in Human Kir2.1 Channels

Kir2.1 channels are uniquely activated by phosphoinositide 4,5-bisphosphate (PI(4,5)P₂) and can be inhibited by other phosphoinositides (PIPs). Using biochemical and computational approaches, we assess PIP-channel interactions and distinguish residues that are energetically critical for binding from those that alter PIP sensitivity by shifting the open-closed equilibrium. Intriguingly, binding of each PIP is disrupted by a different subset of mutations. In silico ligand docking indicates that PIPs bind to two sites. The second minor site may correspond to the secondary anionic phospholipid site required for channel activation. However, 96–99% of PIP binding localizes to the first cluster, which corresponds to the general PI(4,5)P₂ binding location in recent Kir crystal structures. PIPs can encompass multiple orientations; each di- and triphosphorylated species binds with comparable energies and is favored over monophosphorylated PIPs. The data suggest that selective activation by PI(4,5)P₂ involves orientational specificity and that other PIPs inhibit this activation through direct competition.     

Uncoupling the Folding and Binding of an Intrinsically Disordered Protein

The relationship between helical stability and binding affinity was examined for the intrinsically disordered transactivation domain of the myeloblastosis oncoprotein, c-Myb, and its ordered binding partner, KIX. A series of c-Myb mutants was designed to either increase or decrease helical stability without changing the binding interface with KIX. This included a complimentary series of A, G, P, and V mutants at three non-interacting sites. We were able to use the glycine mutants as a reference state and show a strong correlation between binding affinity and helical stability. The intrinsic helicity of c-Myb is 21%, and helicity values of the mutants ranged from 8% to 28%. The c-Myb helix is divided into two conformationally distinct segments. The N-terminal segment, from K291–L301, has an average helicity greater than 60% and the C-terminal segment, from S304–L315, has an average helicity less than 10%. We observed different effects on binding when these two segments were mutated. Mutants in the N-terminal segment that increased helicity had no effect on the binding affinity to KIX, while helix destabilizing glycine and proline mutants reduced binding affinity by more than 1 kcal/mol. Mutants that either increased or decreased helical stability in the C-terminal segment had almost no effect on binding. However, several of the mutants reveal the presence of multiple conformations accessible in the bound state based on changes in enthalpy and linkage analysis of binding free energies. These results may explain the high level of sequence identity (> 90%), even at non-interacting sites, for c-Myb homologues.     

Predicting Secondary Structural Folding Kinetics for Nucleic Acids

We report a new computational approach to the prediction of RNA secondary structure folding kinetics. In this approach, each elementary kinetic step is represented as the transformation between two secondary structures that differ by a helix. Based on the free energy landscape analysis, we identify three types of dominant pathways and the rate constants for the kinetic steps: 1), formation; 2), disruption of a helix stem; and 3), helix formation with concomitant partial melting of a competing (incompatible) helix. The third pathway, termed the tunneling pathway, is the low-barrier dominant pathway for the conversion between two incompatible helices. Comparisons with experimental data indicate that this new method is quite reliable in predicting the kinetics for RNA secondary structural folding and structural rearrangements. The approach presented here may provide a robust first step for further systematic development of a predictive theory for the folding kinetics for large RNAs.     

Proteome Folding Kinetics Is Limited by Protein Halflife

How heterogeneous are proteome folding timescales and what physical principles, if any, dictate its limits? We answer this by predicting copy number weighted folding speed distribution – using the native topology – for E.coli and Yeast proteome. E.coli and Yeast proteomes yield very similar distributions with average folding times of 100 milliseconds and 170 milliseconds, respectively. The topology-based folding time distribution is well described by a diffusion-drift mutation model on a flat-fitness landscape in free energy barrier between two boundaries: i) the lowest barrier height determined by the upper limit of folding speed and ii) the highest barrier height governed by the lower speed limit of folding. While the fastest time scale of the distribution is near the experimentally measured speed limit of 1 microsecond (typical of barrier-less folders), we find the slowest folding time to be around seconds (8 seconds for Yeast distribution), approximately an order of magnitude less than the fastest halflife (approximately 2 minutes) in the Yeast proteome. This separation of timescale implies even the fastest degrading protein will have moderately high (96%) probability of folding before degradation. The overall agreement with the flat-fitness landscape model further hints that proteome folding times did not undergo additional major selection pressures – to make proteins fold faster – other than the primary requirement to “sufficiently beat the clock” against its lifetime. Direct comparison between the predicted folding time and experimentally measured halflife further shows 99% of the proteome have a folding time less than their corresponding lifetime. These two findings together suggest that proteome folding kinetics may be bounded by protein halflife.     

Insights into Coupled Folding and Binding Mechanisms from Kinetic Studies

Intrinsically disordered proteins (IDPs) are characterized by a lack of persistent structure. Since their identification more than a decade ago, many questions regarding their functional relevance and interaction mechanisms remain unanswered. Although most experiments have taken equilibrium and structural perspectives, fewer studies have investigated the kinetics of their interactions. Here we review and highlight the type of information that can be gained from kinetic studies. In particular, we show how kinetic studies of coupled folding and binding reactions, an important class of signaling event, are needed to determine mechanisms.     

Kinetics and Energetics of Light-enhanced Potassium Absorption by Corn Leaf Tissue

The effect of illumination on the absorption of K⁺ by leaf tissue of Zea mays was investigated. The rate of K⁺ absorption was enhanced by exposure of slices of corn leaf tissue to light, even of relatively low intensities. Potassium was transported inward, with virtually no efflux of previously accumulated K⁺. The evidence indicates that the transport mechanism for absorption of K⁺ is the same in the light as in the dark, but that the source of energy for absorption of K⁺ is different in the light from that in the dark. Various anti-metabolites were used to establish that the energy utilized for active ion transport in the light came partly from ATP supplied by cyclic photophosphorylation. Expenditure of ATP was required in the dark too, but this ATP was formed by oxidative phosphorylation. Establishing the ultimate source of energy for active ion uptake by higher plants might be facilitated by demonstration of an ion-transport process that is not linked directly with the transfer of electrons in the mitochondrial cytochrome chain.     

A Flexible Docking Scheme Efficiently Captures the Energetics of Glycan-Cyanovirin Binding

Cyanovirin-N (CVN), a cyanobacterial lectin, exemplifies a class of antiviral agents that inhibit HIV by binding to the highly glycosylated envelope protein gp120. Here, we investigate the energetics of glycan recognition using a computationally inexpensive flexible docking approach, backbone perturbation docking (BP-Dock). We benchmarked our method using two mutants of CVN: P51G-m4-CVN, which binds dimannose with high affinity through domain B, and CVN^(mutDB), in which binding to domain B has been abolished through mutation of five polar residues to small nonpolar side chains. We investigated the energetic contribution of these polar residues along with the additional position 53 by docking dimannose to single-point CVN mutant models. Analysis of the docking simulations indicated that the E41A/G and T57A mutations led to a significant decrease in binding energy scores due to rearrangements of the hydrogen-bond network that reverberated throughout the binding cavity. N42A decreased the binding score to a level comparable to that of CVN^(mutDB) by affecting the integrity of the local protein structure. In contrast, N53S resulted in a high binding energy score, similar to P51G-m4-CVN. Experimental characterization of the five mutants by NMR spectroscopy confirmed the binding affinity pattern predicted by BP-Dock. Despite their mostly conserved fold and stability, E41A, E41G, and T57A displayed dissociation constants in the millimolar range. N53S showed a binding constant in the low micromolar range, similar to that observed for P51G-m4-CVN. No binding was observed for N42A. Our results show that BP-Dock is a useful tool for rapidly screening the relative binding affinity pattern of in silico-designed mutants compared with wild-type, supporting its use to design novel mutants with enhanced binding properties.     

A Flexible Docking Scheme Efficiently Captures the Energetics of Glycan-Cyanovirin Binding

Cyanovirin-N (CVN), a cyanobacterial lectin, exemplifies a class of antiviral agents that inhibit HIV by binding to the highly glycosylated envelope protein gp120. Here, we investigate the energetics of glycan recognition using a computationally inexpensive flexible docking approach, backbone perturbation docking (BP-Dock). We benchmarked our method using two mutants of CVN: P51G-m4-CVN, which binds dimannose with high affinity through domain B, and CVN^(mutDB), in which binding to domain B has been abolished through mutation of five polar residues to small nonpolar side chains. We investigated the energetic contribution of these polar residues along with the additional position 53 by docking dimannose to single-point CVN mutant models. Analysis of the docking simulations indicated that the E41A/G and T57A mutations led to a significant decrease in binding energy scores due to rearrangements of the hydrogen-bond network that reverberated throughout the binding cavity. N42A decreased the binding score to a level comparable to that of CVN^(mutDB) by affecting the integrity of the local protein structure. In contrast, N53S resulted in a high binding energy score, similar to P51G-m4-CVN. Experimental characterization of the five mutants by NMR spectroscopy confirmed the binding affinity pattern predicted by BP-Dock. Despite their mostly conserved fold and stability, E41A, E41G, and T57A displayed dissociation constants in the millimolar range. N53S showed a binding constant in the low micromolar range, similar to that observed for P51G-m4-CVN. No binding was observed for N42A. Our results show that BP-Dock is a useful tool for rapidly screening the relative binding affinity pattern of in silico-designed mutants compared with wild-type, supporting its use to design novel mutants with enhanced binding properties.     

Computational Prediction of Alanine Scanning and Ligand Binding Energetics in G-Protein Coupled Receptors

Site-directed mutagenesis combined with binding affinity measurements is widely used to probe the nature of ligand interactions with GPCRs. Such experiments, as well as structure-activity relationships for series of ligands, are usually interpreted with computationally derived models of ligand binding modes. However, systematic approaches for accurate calculations of the corresponding binding free energies are still lacking. Here, we report a computational strategy to quantitatively predict the effects of alanine scanning and ligand modifications based on molecular dynamics free energy simulations. A smooth stepwise scheme for free energy perturbation calculations is derived and applied to a series of thirteen alanine mutations of the human neuropeptide Y1 receptor and series of eight analogous antagonists. The robustness and accuracy of the method enables univocal interpretation of existing mutagenesis and binding data. We show how these calculations can be used to validate structural models and demonstrate their ability to discriminate against suboptimal ones.     

Long Range Surface Plasmons for Observation of Biomolecular Binding Events at Metallic Surfaces

A long range surface plasmon (LRSP) is an electromagnetic wave propagating along a thin metal film with an order of magnitude lower damping than conventional surface plasmon (SP) waves. Thus, the excitation of LRSP is associated with a narrower resonance and it provides larger enhancement of intensity of the electromagnetic field. In surface plasmon resonance (SPR) biosensors, these features allow a more precise observation of the binding of biomolecules in the proximity to the metal surface by using the (label-free) measurement of refractive index (RI) variations and by SP-enhanced fluorescence spectroscopy. In this contribution, we investigate LRSPs excited on a layer structure consisting of a fluoropolymer buffer layer, a thin gold film, and an aqueous sample. By implementing such structure in an SPR sensor, we achieved a 2.4- and 4.4-fold improvement of the resolution in the label-free and fluorescence-based detection, respectively, of the binding of biomolecules in the close proximity to the surface. Moreover, we demonstrate that the sensor resolution can be improved by a factor of 14 and 12 for the label-free and fluorescence-based detection, respectively, if the biomolecular binding events occur within the whole evanescent field of LRSP.     

Slow,Reversible, Coupled Folding and Binding of the Spectrin Tetramerization Domain

Many intrinsically disordered proteins (IDPs) are significantly unstructured under physiological conditions. A number of these IDPs have been shown to undergo coupled folding and binding reactions whereby they can gain structure upon association with an appropriate partner protein. In general, these systems display weaker binding affinities than do systems with association between completely structured domains, with micromolar K_d values appearing typical. One such system is the association between α- and β-spectrin, where two partially structured, incomplete domains associate to form a fully structured, three-helix bundle, the spectrin tetramerization domain. Here, we use this model system to demonstrate a method for fitting association and dissociation kinetic traces where, using typical biophysical concentrations, the association reactions are expected to be highly reversible. We elucidate the unusually slow, two-state kinetics of spectrin assembly in solution. The advantages of studying kinetics in this regime include the potential for gaining equilibrium constants as well as rate constants, and for performing experiments with low protein concentrations. We suggest that this approach would be particularly appropriate for high-throughput mutational analysis of two-state reversible binding processes.