Biological systems are often exposed to mechanical perturbations, which may modulate many biochemical processes. Ligand binding involves a wide range of structural changes in the receptor protein, from hinge movement of entire domains to minor sidechain rearrangements in the binding pocket residues. Hydrophobic ligand binding to protein alters the system’s vibrational free energy, allowing different conformational states of allosteric proteins. Excess hydrophobicity in protein–ligand binding generates mechanical force along the peptide backbone through the hydrophobic effect. We describe mechanically strained peptide structures involved in protein aggregation to determine the transition between the initial condensation of hydrophobic polypeptide chains into ordered fibrillar structures. This transition is due to the excess attractive hydrophobic force by ligand binding within proteins into fibrillar assemblies. The process of fibrillar formation has a mechanosensitive nature, which significantly influences the pathogenesis of several neurodegenerative diseases.

The physicochemical properties depend on the conformation changes in inbound and unbound forms of proteins to regulate physiological functions.1 The binding of a ligand to a protein can expose hydrophobic residues on the protein’s surface if the ligand has hydrophobic properties. In protein–ligand binding, a ligand produces a signal by binding to a site on a target protein initiating a downstream signaling cascade, where the signal is amplified through a series of protein–protein interactions. Signaling by the ligand binding provides chemical to mechanical energy transduction by generating molecular forces inside them.2 However, the mechanical energy alters the protein’s conformation and increases hydrophobicity for the protein to which it binds. Hydrophobicity affects a receptor protein’s three-dimensional shape and orientation, which ultimately impact the protein’s functional state.

In a peptide bond, the likely conformations for a polypeptide chain are quite restricted due to the limitation of rotational freedom at φ (Cα–N) and ψ (Cα–C) angles by steric hindrance between peptide backbone and sidechain, reducing correspondingly the available conformational space. The rotations around two other bonds linked to the Cα atom can rotate freely. Hence, each amino acid residue in the polypeptide chain has many possible confirmations. The polypeptide conformations do unfold at high temperatures, and thus, the hydrophobic amino acid sidechains are exposed to the surrounding aqueous environment (Fig. 1). Due to the mechanical nature of the unfolded state (more flexible),3 the total conformational entropy of the unfolded state is much greater than that of the folded state (more rigid). However, conformational entropy4 on protein unfolding5 involves hydrophobicity,6 as the hydrophobic sidechains are free to explore a large range of conformations in the aqueous environment.

FIG. 1.

Stretching of the unfolded protein.

FIG. 1.

Stretching of the unfolded protein.

Close modal

When a polypeptide chain is subjected to stretching force and cross-linking,7 the conformation of the chain can be decreased. The stretching force can pull a polypeptide chain into an extended conformation (Fig. 1), where it has fewer degrees of freedom than when it is in a more compact state. Similarly, cross-linking can physically restrict the range of motion of the polypeptide chain, reducing the number of possible conformations.

Assuming that ΓH is the maximum force applied to the α-helix of which elongation is ∆de (Fig. 1).

This force ΓH always considers higher than the mechanical stiffness12 of an α-helix hydrogen bond.

The stretching force on protein unfolding is described by the following equation:
ΓH=TΔSconfΔde=kBTlnWΔde.
The conformational energy8 T∆Sconf, which is the energy associated with changes in the conformation of a protein, is dissipated in the polypeptide thermal vibrations. Thermal vibration energy in a receptor protein can be stored as mechanical deformations in all microstates W.

If the conformational energy of a protein is higher than its enthalpy, then the protein’s conformation is likely to be highly dynamic and flexible. In this case, ligand binding to the protein provides unfolding free energy,9 ∆GU = −kBT ln κa (T = Temperature and κa = Binding association constant), which contributes to the stabilization of the protein’s structure. The unfolding free energy compensates for the protein’s own hydrophobicity deficiencies by exposing hydrophobic sidechains to a hydrophobic ligand for creating a favorable interaction between the protein and the ligand. On the other hand, the ligand’s excess hydrophobicity can be compensated by the protein’s unfolding free energy by exposing hydrophilic residues to the aqueous environment, thereby minimizing unfavorable interactions with water. Therefore, the excess hydrophobic force10,11 drives the ligand into a binding site in the protein (Fig. 2), where electrostatics and hydrogen bonding (e.g., salt bridges) govern specificity.

FIG. 2.

Ligand binding hydrophobicity.

FIG. 2.

Ligand binding hydrophobicity.

Close modal

The excess hydrophobic force can induce a mechanical deformation of a polypeptide chain13 by generating mechanical forces14 (Fig. 2). When a mechanical force15 is applied to a protein, it causes the protein to undergo mechanical unfolding, also known as the unfolding force or stretching force ΓH, which involves the conversion of the native protein conformation to a misfolded conformation.16 The misfolded protein initiates self-assembly and forms molten oligomers, which can be mechanically strained and stabilize charged residues and hydrophobic forces, leading to further self-assembly and the formation of larger aggregates. However, the mechanical force can work along the length of the unfolded domain17 to cause peptide stretching and ultimately result in an elongated state. Elongation can lead to changes in secondary structure that can affect the hydrophobicity of the protein. This hydrophobicity can trigger further misleading and the accumulation of other proteins aggregates or oligomers.

The hydrophobicity released during protein–ligand binding at a specific distance,18 ∆Ωb = 4 × 10−10 m, tends to stretch and orient geometrically bend peptides in the loading direction. The fully stretched polypeptide chain is less flexible due to the increased attraction among hydrophobic sidechains, which are energetically favorable and can contribute to the stability of the stretched conformation.

The strong attraction of polypeptide sidechains in water is reflected in the large interfacial energy of the protein–water interface. The hydrophobic sidechains in water have high surface tension and contact angle values. Hence, the hydrophobicity of a protein in contact with a hydrophobic surface will be dominated by van der Waals, long-range forces, and adhesion energy.

At a protein–water interface, the tendency of the hydrophobic protein–ligand complex is to minimize the contact area with water for maximizing hydrophobicity. The thermodynamics of protein self-assembly at a water interface can be described by the thermal aggregation parameter Πa. This parameter is a measure of unfolding free energy associated with the aggregation of protein–ligand binding complexes at the interface. It is defined as
Πa=ΞHδe2εHΔΩbkBTlnκa.
Since the protein aggregation parameter, Πa depends on the hydrophobicity of the peptide sequence19 σi, i.e., the number of hydrophobic peptide monomers. Thus, the characterization of hydrophobicity ΞH of a peptide sequence takes into account the number of hydrophobic peptide monomers normalized concerning the total number of hydrophobic sidechains ,
formula
The average hydrophobicity over a set of designing sequences of a given length can then be introduced as
formula
Peptide sequences that are symmetric under the reversal of hydrophobic sidechains only once in the statistics are known as palindromic sequences. Taking into account all peptide sequences of length , where each position can be occupied by any of the 20 standard amino acids, would lead to a binomial distribution for sin ce there are exactly sequences with hydrophobic peptide monomers.

The hydrophobic force, thermodynamic in nature and relatively stronger than dehydrons,20 is an average of a fluctuating force −∇εH, the average attractive force between hydrophobic groups being the negative gradient of free energy. The hydrophobic force, a force of mean-field normalized21 to 1 for ordered stable oligomers, relates to the energy δe∇εH involved in the salvation of hydrophobic sidechains that become exposed in the unfolded state22 (Fig. 1). However, the resultant attractive forces between water molecules tend to increase the area of the protein–water interface; the force is the negative gradient of the resultant free energy change −δe∇εH. The transfer of a protein sidechain from water to nonpolar solvent at a distance of {δe = 3.5 × 10−10 m}23 is thermodynamically favorable with a transfer-free energy change of −1.39 kJ/mol.

The thermal aggregation shows a linear relationship between Πa and the inverse of absolute temperature T, assuming ΞH, δ2, and Ωb are independent of temperature. If Πa is determined using ΞH = 1, δe = 3.5 × 10−10 m, ∇εH = 1, ∆Ωb = 4 × 10−10 m, {κa = 104},24 kB = 1.380 649 × 10−23 m2 kg s−2 K−1 at different temperatures, a linear plot of Πa vs 1/T can be obtained (Fig. 3).

FIG. 3.

Temperature dependence curves of aggregation parameter.

FIG. 3.

Temperature dependence curves of aggregation parameter.

Close modal

In Fig. 3, the curved function of temperature indicates the aggregation parameter changes with temperature, which is nonlinear and reaches an asymptotic value at high temperatures. The temperature increase enhances a critical α-helix to the random coil to β-sheet transitions, and thus, the rate of formation β-strand occurs through unfolding. In the α-helix to β-sheet transition, an increase in temperature (Tc > T) can disrupt the hydrogen bonding and van der Waals forces25 that stabilize the α-helix conformation, causing it to unfold into a random coil. As the temperature continues to increase, the random coil can form into β-sheet structures through the formation of inter-strand hydrogen bonds {T (α-Helix) > T (β-Sheet)}.25 The initial formation of a β-strand nucleus promotes the addition of more β-strands to form a stable β-sheet structure, which can lead to the formation of amyloid fibrils or other aggregates.

The derivative of Πa concerning temperature T (Fig. 3) determines a switch from α-helical to a β-strand. A sharp increase (Fig. 4) in the derivative of Πa with respect to temperature at a certain temperature indicates a transition from α-helical to β-strand conformations.

FIG. 4.

Graphs for temperature range 308–313 K, α value on the top of each graph, Tc assumed to be 311 K. When (Tc − T) is negative, it becomes a complex number for some values of α. In these graphs, the real part of complex numbers is considered.

FIG. 4.

Graphs for temperature range 308–313 K, α value on the top of each graph, Tc assumed to be 311 K. When (Tc − T) is negative, it becomes a complex number for some values of α. In these graphs, the real part of complex numbers is considered.

Close modal
Varying the temperature T of the system while keeping all other variables in thermal aggregation Πa fixed can lead to an unfolding-aggregation transition at critical temperature Tc. As the temperature increases toward Tc, the protein begins to unfold, exposing hydrophobic regions that can interact with other unfolded proteins to form aggregates. When T is near Tc, the thermal aggregation Πc has a power law behavior,
Πc=ΞHδe2εHΔΩbTcTαkBlnκa.
In Fig. 4, the critical parameter Πc of a polypeptide chain at Tc = 311 K has an aggregation-prone behavior near the unfolding-aggregation transition where the critical exponent α = 0.1 indicates a weakly first-order phase transition, which is not fixed above and below the critical temperature. As the temperature approaches Tc from below, Πc increases rapidly with decreasing temperature, consistent with a strong first-order phase transition. On the other hand, as the temperature approaches Tc from above, Πc increases more slowly, consistent with a weak first-order phase transition. The critical temperature Tc = 311 K represents the highest temperature at which a protein can aggregate through ligand binding as shown in Fig. 4. This result (Tc = 311 K) provides important insights into the protein’s thermal stability and aggregation behavior under these conditions. By comparing the critical temperatures from other techniques [Differential Titration Calorimetry (DSC), Isothermal Titration Calorimetry (ITC), Circular Dichroism (CD), etc.] with the value (Tc = 311 K) obtained from ligand binding, it may be possible to gain a complete understanding of the protein’s thermal stability and aggregation behavior.

The analysis of sidechain flexibility can provide valuable insights into the behavior and interactions of amino acid sidechains in proteins. The development of an index of amino-acid sidechain flexibility can be a powerful tool for predicting the behavior of proteins under different conditions, and for guiding the design of new proteins with desired properties. In this paper, we present molecular insights into the structure and the hydrophobicity of the β-sheet provides the aggregation process. However, protein aggregation is a complex phenomenon that is poorly understood at a molecular level. Hydrophobicity and apolarity are ubiquitous phenomena in protein aggregation. Quantifying the effect of the hydrophobic force on ligand-binding association has proven to be difficult because force is a vector magnitude and can act in different directions. This can result in the heterogeneous application of forces over uncontrolled reaction orientations, making it challenging to accurately quantify the contribution of hydrophobic forces to ligand binding. Minimization of the vector magnitude in ligand-protein association, the aggregation parameter is determined based on the hydrophobicity of dehydrated stretched polypeptides to sidechains. The aggregation parameter is measured by analyzing the physiochemical properties of the amino acids in the protein sequence. Protein aggregation results in the formation of oligomers from the mechanical conversion of unfolding proteins rich in β – sheets at the temperature Tc = 311 K. The temperature Tc = 311 K is significant because it is a physiological temperature close to the melting temperature of many proteins prone to aggregation. At this temperature, protein molecules are in a state of high energy and are more likely to undergo structural changes that can lead to aggregation. This provides a physical process of aggregation at a molecular level and suggests that the ligand-binding contacts control the observed amyloid fibril architectures. This is a valuable feature for understanding the structure and mechanical aspects of amyloid fibrils that might provide a solution to many therapies.

The authors have no conflicts to disclose.

Md. Mozzammel Haque: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Muhammad Abdul Kadir: Software (lead). Richard Bayford: Investigation (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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