A simple electrostatic criterion for predicting the thermal stability of proteins

The use of vector formalism in the analysis of hydrophobic and electric driving forces in biological assemblies

Hydrophobic forces are known to have a crucial part not only in the conformation of the three-dimensional structure of proteins, but also in the build-up of DNA–protein complexes. Electric forces also play an important role both in the tertiary as well in the quaternary structure of macromolecular associations. Sometimes both hydrophobic and electric interactions add up their strengths to accomplish these structures but in most cases they act in opposite directions. This fact, together with being overall interactions with different ranges, provides a nuanced equilibrium also modulated by the need to comply with steric hindrances and geometric frustration effects. This review focuses on the utility of using the hydrophobic and electrical dipole moment vectors to describe the interactions that give rise to the structures of biological macromolecules. Although different definitions of both electric dipole and hydrophobic moments have been described in the literature, results obtained in biological assemblies demonstrate the principle of the biological membrane model. According to this model, postulated by our group, biological macromolecules tend to associate by aligning their hydrophobic moments in a similar manner to phospholipids in a membrane. Examples of both closed and open structures are used to assess the predictability of our model. We seek agreement between our results with those described in the current literature. The review ends with possible future projections using this formalism.

The importance of hydrophobic interactions in the structure of transcription systems

Hydrophobic forces play a crucial role in both the stability of B DNA and its interactions with proteins. In the present study, we postulate that the hydrophobic effect is an essential component in establishing specificity in the interaction transcription factor proteins with their consensus DNA sequence partners. The PDB coordinates of more than 50 transcription systems have been used to analyze the hydrophobic attraction of proteins towards their DNA consensus. This analysis includes computing the hydrophobic energy of the interacting molecules by means of their hydrophobic moments. Hydrophobic moments have successfully been used in previous studies involving self-assembly protein systems. In the present case, in spite of some variability, we found specificity in transcription factors when interacting with their respective consensus DNA sequences. By applying our model of biological membrane pattern for hydrophobic interactions, we postulate that hydrophobic forces constitute the necessary intermediate interaction between the unspecific electrostatic attraction for DNA phosphate groups and the very short-range interaction promoting hydrogen bonds. We conclude that hydrophobic interactions serve as the intermediate force guiding transcriptions factors towards the proper hydrogen bonds to their DNAs.

Insights on protein thermal stability: a graph representation of molecular interactions

Motivation

Understanding the molecular mechanisms of thermal stability is a challenge in protein biology. Indeed, knowing the temperature at which proteins are stable has important theoretical implications, which are intimately linked with properties of the native fold, and a wide range of potential applications from drug design to the optimization of enzyme activity.

Results

Here, we present a novel graph-theoretical framework to assess thermal stability based on the structure without any a priori information. In this approach we describe proteins as energy-weighted graphs and compare them using ensembles of interaction networks. Investigating the position of specific interactions within the 3D native structure, we developed a parameter-free network descriptor that permits to distinguish thermostable and mesostable proteins with an accuracy of 76% and area under the receiver operating characteristic curve of 78%.

Availability and implementation

Code is available upon request to edoardo.milanetti@uniroma1.it

Supplementary information

Supplementary data are available at Bioinformatics online.

Simulated Epidemics in 3D Protein Structures to Detect Functional Properties

The outcome of an epidemic is closely related to the network of interactions between individuals. Likewise, protein functions depend on the 3D arrangement of their residues and the underlying energetic interaction network. Borrowing ideas from the theoretical framework that has been developed to address the spreading of real diseases, we study for the first time the diffusion of a fictitious epidemic inside the protein nonbonded interaction network, aiming to study network features and properties. Our approach allows us to probe the overall stability and the capability of propagating information in complex 3D structures, proving to be very efficient in addressing different problems, from the assessment of thermal stability to the identification of functional sites.

A protein self-assembly model guided by electrostatic and hydrophobic dipole moments

Protein self-assembling is studied under the light of the Biological Membrane model. To this purpose we define a simplified formulation of hydrophobic interaction energy in analogy with electrostatic energy stored in an electric dipole. Self-assembly is considered to be the result of the balanced influence of electrostatic and hydrophobic interactions, limited by steric hindrance as a consequence of the relative proximity of their components. Our analysis predicts the type of interaction that drives an assembly. We study the growth of both electrostatic and hydrophobic energies stored by a protein system as it self-assembles. Each type of assembly is studied by using two examples, PDBid 2OM3 (hydrophobic) and PDBid 3ZEE (electrostatic). Other systems are presented to show the application of our procedure. We also study the relative orientation of the monomers constituting the first dimer of a protein assembly to check whether their relative position provides the optimal interaction energy (energy minimum). It is shown that the inherent orientation of the dimers corresponds to the optimum energy (energy minimum) of assembly compatible with steric limitations. These results confirm and refine our Biological Membrane model of protein self-assembly valid for all open and closed systems.

Role of simple descriptors and applicability domain in predicting change in protein thermostability

The melting temperature (Tm) of a protein is the temperature at which half of the protein population is in a folded state. Therefore, Tm is a measure of the thermostability of a protein. Increasing the Tm of a protein is a critical goal in biotechnology and biomedicine. However, predicting the change in melting temperature (dTm) due to mutations at a single residue is difficult because it depends on an intricate balance of forces. Existing methods for predicting dTm have had similar levels of success using generally complex models. We find that training a machine learning model with a simple set of easy to calculate physicochemical descriptors describing the local environment of the mutation performed as well as more complicated machine learning models and is 2-6 orders of magnitude faster. Importantly, unlike in most previous publications, we perform a blind prospective test on our simple model by designing 96 variants of a protein not in the training set. Results from retrospective and prospective predictions reveal the limited applicability domain of each model. This study highlights the current deficiencies in the available dTm dataset and is a call to the community to systematically design a larger and more diverse experimental dataset of mutants to prospectively predict dTm with greater certainty.

Choreography of the Reductase and P450BM3 Domains Toward Electron Transfer Is Instigated by the Substrate

The driving force for the electron transfer (ET) step in the catalytic cycle of cytochrome P450_BM3 is investigated using three sets of 1 μs molecular dynamic simulations for the resting state of P450 in complex with the flavin (FMN) in the reductase domain. These sets involve the following: (i) substrate-free (SF), (ii) substrate (N-palmitoyl glycine, i.e., NPG)-bound (SB), and (iii) SB with the semiquinone radical anion (SQ^-) of FMN. Starting from the X-ray structure of the SF heme domain, we observe that the α1-helix (of the reductase) and the C-helix (of the heme) undergo reorientation to a parallel orientation, which is the thermochemically stable form. The reorientation of the helices pushes away the FMN to a distance of 18.4 Å from the heme's center. When the substrate binds it causes the I-helix of the heme domain to kink and push the C-helix toward the α1-helix, thereby locking the latter two into a stabilized perpendicular conformation, wherein the FMN-heme distance is 12 Å. The distance drops further in the SQ^- form, and upon QM/MM geometry optimization the two moieties approach 8.8 Å, which enhances the ET rate (by 10⁴-10⁶ fold) to the heme's Fe³⁺ ion. These motions are driven by hydrogen bond strengthening between the C- and the α1-helices. Finally, substrate binding leads to formation of an organized water chain connecting the FMN and heme moieties. The water channel assists the ET and couples it to the proton transfer steps that should activate O₂ and create the oxo-iron active species.

A model of protein association based on their hydrophobic and electric interactions

The propensity of many proteins to oligomerize and associate to form complex structures from their constituent monomers, is analyzed in terms of their hydrophobic (H), and electric pseudo-dipole (D) moment vectors. In both cases these vectors are defined as the product of the distance between their positive and negative centroids, times the total hydrophobicity or total positive charge of the protein. Changes in the magnitudes and directions of H and D are studied as monomers associate to form larger complexes. We use these descriptors to study similarities and differences in two groups of associations: a) open associations such as polymers with an undefined number of monomers (i.e. actin polymerization, amyloid and HIV capsid assemblies); b) closed symmetrical associations of finite size, like spherical virus capsids and protein cages. The tendency of the hydrophobic moments of the monomers in an association is to align in parallel arrangements following a pattern similar to those of phospholipids in a membrane. Conversely, electric dipole moments of monomers tend to align in antiparallel associations. The final conformation of a given assembly is a fine-tuned combination of these forces, limited by steric constraints. This determines whether the association will be open (indetermined number of monomers) or closed (fixed number of monomers). Any kinetic, binding or molecular peculiarities that characterize a protein assembly, comply with the vector rules laid down in this paper. These findings are also independent of protein size and shape.

LogitBoost classifier for discriminating thermophilic and mesophilic proteins

A novel classifier, the so-called LogitBoost classifier, was introduced to discriminate the thermophilic and mesophilic proteins according to their primary structures. When the 20-amino acid composition was chosen as the feature vector, the overall accuracy of the self-consistency check and a five-fold cross-validation procedure was 97.0% and 86.6%, respectively. To test if the method was also applicable to a wide range of biological targets, an independent testing dataset was also used. The method based on LogitBoost algorithm has achieved an overall classification accuracy of 88.9%. According to the three different validation check approaches, it was demonstrated that LogitBoost outperformed AdaBoost and performed comparably with RBF neural network and support vector machine. The influence of protein size on discrimination was addressed.

Hydrophobicity Density Profiles to Predict Thermal Stability Enhancement in Proteins

A hydrophobicity density is defined for a protein through its hydrophobicity tensor (similar to the inertia tensor), by using the Eisenberg hydrophobicity scale of the hydrophobic amino acids of a protein. This allows calculation of the radii of the corresponding hydrophobic ellipsoid of a protein and thus subsequently of its hydrophobic density. A hydrophobicity density profile is then obtained by simulating point mutations of each amino acid of a protein either to a high hydrophobicity value or to zero hydrophobicity. It is found that an increase in the hydrophobic density of the protein correlates with an increase of its mid-point transition temperature. From this profile it is possible to determine the amino acids or domain stretches in a protein that are most amenable to mutation in order to increase the thermal stability. The model is tested to predict the thermostabilisation effects of two mutations in a beta-glucanase: M29G and M29F. This model is compared with other hydrophobicity-related profiles described by other authors.

The Mechanism of TC230′s Thermostability: A Molecular Dynamics Simulation Study

The quasielastic neutron scattering index beta and the modulus of a protein's quasi-electric dipole moment were utilized to quantitate the thermostability of wildtype TC23O and its mutants. Charged residues Arg314, Glu246, Glu291, and some prolines near the C-terminus of the sequence (Pro228, Pro296, and Pro308) were identified to be critical for the thermostability of wildtype TC23O according to these two criteria. By analyzing the molecular conformation changes during the simulation, it was demonstrated how the mutant P228S was destabilized by disrupting two salt-bridges Asp116OD1-Lys215N and Glu210OE1-Lys217N at an adjacent beta-turn. The destabilization of P296S also shown to be intimate correlated with the break down of ion pair Lys188N-Glu291OE1. The sensitivity of its electrostatic network to the local structure is an important feature. It reveals that the 'proline effect' and electrostatic interactions together influences the thermostability of TC23O a lot.

Study of the influence of temperature on the dynamics of the catalytic cleft in 1,3-1,4-β-glucanase by molecular dynamics simulations

The dependence of some molecular motions in the enzyme 1,3-1,4-beta-glucanase from Bacillus licheniformis on temperature changes and the role of the calcium ion in them were explored. For this purpose, two molecular dynamics simulated trajectories along 4 ns at low (300 K) and high (325 K) temperatures were generated by the GROMOS96 package. Several structural and thermodynamic parameters were calculated, including entropy values, solvation energies, and essential dynamics (ED). In addition, thermoinactivation experiments to study the influence of the calcium ion and some residues on the activity were conducted. The results showed the release of the calcium ion, which, in turn, significantly affected the movements of loops 1, 2, and 3, as shown by essential dynamics. These movements differ at low and high temperatures and affect dramatically the activity of the enzyme, as observed by thermoinactivation studies.

How to improve nature: study of the electrostatic properties of the surface of alpha-lactalbumin

It was recently shown that alpha-lactalbumin interacts with histones and simple models of histone proteins such as positively charged polyamino acids, suggesting that some fundamental aspects of the protein surface electrostatics may come into play. In the present work, the energies of charge-charge interaction in apo- and Ca(2+)-loaded alpha-lactalbumin were calculated using a Tanford-Kirkwood algorithm with either solvent accessibility correction or using a finite difference Poisson-Boltzmann method. The analysis revealed two major regions of alpha-lactalbumin that possessed highly unfavorable electrostatic potentials: (a) the Ca(2+)-binding loop and its neighboring residues and (b) the N-terminal region of the protein. Several individual mutants were prepared to neutralize specific individual surface acidic amino acids at both the N-terminus and Ca(2+)-binding loop of bovine alpha-lactalbumin. These mutants were characterized by intrinsic fluorescence, differential scanning microcalorimetry and circular dichroism. The structural and thermodynamic data agree in every case with the theoretical predictions, confirming that the N-terminal region is very sensitive to changes in charge. For example, desMet D14N mutation destabilizes protein and decreases its calcium affinity. On the other hand, desMet E1M and desMet D37N substitutions increase the thermal stability and calcium affinity. The Met E1Q is characterized by a marked increase in protein stability, whereas desMet E7Q and desMet E11L display a slight increase in calcium affinity and thermal stability. Examination of the unfavorable energy contributed by Glu1 and the energetically favorable consequences of neutralizing this residue suggests that nature may have made an error with bovine alpha-lactalbumin from the viewpoint of stabilizing structure and conformation.

Role of the surface charges D72 and K8 in the function and structural stability of the cytochrome c6 from Nostoc sp. PCC 7119

We investigated the role of electrostatic charges at positions D72 and K8 in the function and structural stability of cytochrome c6 from Nostoc sp. PCC 7119 (cyt c6). A series of mutant forms was generated to span the possible combinations of charge neutralization (by mutation to alanine) and charge inversion (by mutation to lysine and aspartate, respectively) in these positions. All forms of cyt c6 were functionally characterized by laser flash absorption spectroscopy, and their stability was probed by urea-induced folding equilibrium relaxation experiments and differential scanning calorimetry. Neutralization or inversion of the positive charge at position K8 reduced the efficiency of electron transfer to photosystem I. This effect could not be reversed by compensating for the change in global charge that had been introduced by the mutation, indicating a specific role for K8 in the formation of the electron transfer complex between cyt c6 and photosystem I. Replacement of D72 by asparagine or lysine increased the efficiency of electron transfer to photosystem I, but destabilized the protein. D72 apparently participates in electrostatic interactions that stabilize the structure of cyt c6. The destabilizing effect was reduced when aspartate was replaced by the small amino acid alanine. Complementing the mutation D72A with a charge neutralization or inversion at position K8 led to mutant forms of cyt c6 that were more stable than the wild-type under all tested conditions.

Stabilization of the Cold Shock Protein CspB from Bacillus subtilis by Evolutionary Optimization of Coulombic Interactions

The bacterial cold shock proteins (Csp) are used by both experimentalists and theoreticians as model systems for analyzing the Coulombic contributions to protein stability. We employ Proside, a method of directed evolution, to identify stabilized variants of Bs-CspB from Bacillus subtilis. Proside links the increased protease resistance of stabilized protein variants to the infectivity of a filamentous phage. Here, three cspB libraries were used for in vitro selections to explore the stabilizing potential of charged amino acids in Bs-CspB. In the first library codons for nine selected surface residues were partially randomized, in the second one random mutations were introduced non-specifically by error-prone PCR, and in the third one the spontaneous mutation rate of the phage in Escherichia coli was used. Stabilizing mutations were found at the surface positions 1, 3, 46, 48, 65, and 66. The contributions of these mutations to stability were characterized by analyzing them individually and in combination. The best combination (M1R, E3K, K65I, and E66L) increased the midpoint of thermal unfolding of Bs-CspB from 53.8 to 85.0 degrees C. The effects of most mutations are strongly context dependent. A good example is provided by the E3R mutation. It is strongly stabilizing (DeltaDeltaGD=11.1kJ mol(-1)) in the wild-type protein, but destabilizing (DeltaDeltaGD=-4.0kJ mol(-1)) in the A46K/S48R/E66L variant. The stabilizations by charge mutations did not correlate well with the corresponding changes in the protein net charge, and they could not be ascribed to the formation of ion pairs. Previous theoretical analyses did not identify the stabilization caused by the mutations at positions 1, 46, and 48. Also, electrostatics calculations based on protein net charge or charge asymmetry did not predict well the stability changes that occur when charged residues in Bs-CspB are mutated. It remains a challenge to model the Coulombic interactions of charged residues in a protein and to determine their contributions to the Gibbs free energy of protein folding.

An electrostatic basis for the stability of thermophilic proteins

Two factors provide key contributions to the stability of thermophilic proteins relative to their mesophilic homologues: electrostatic interactions of charged residues in the folded state and the dielectric response of the folded protein. The dielectric response for proteins in a "thermophilic series" globally modulates the thermal stability of its members, with the calculated dielectric constant for the protein increasing from mesophiles to hyperthermophiles. This variability results from differences in the distribution of charged residues on the surface of the protein, in agreement with structural and genetic observations. Furthermore, the contribution of electrostatic interactions to the stability of the folded state is more favorable for thermophilic proteins than for their mesophilic homologues. This leads to the conclusion that electrostatic interactions play an important role in determining the stability of proteins at high temperatures. The interplay between electrostatic interactions and dielectric response also provides further rationalization for the enhanced stability of thermophilic proteins with respect to cold-denaturation. Taken together, the distribution of charged residues and their fluctuations have been shown to be factors in modulating protein stability over the entire range of biologically relevant temperatures.