Stress Analysis at the Molecular Level: A Forced Cucurbituril-Guest Dissociation Pathway

Dynamic Allostery of the Catabolite Activator Protein Revealed by Interatomic Forces

The Catabolite Activator Protein (CAP) is a showcase example for entropic allostery. For full activation and DNA binding, the homodimeric protein requires the binding of two cyclic AMP (cAMP) molecules in an anti-cooperative manner, the source of which appears to be largely of entropic nature according to previous experimental studies. We here study at atomic detail the allosteric regulation of CAP with Molecular dynamics (MD) simulations. We recover the experimentally observed entropic penalty for the second cAMP binding event with our recently developed force covariance entropy estimator and reveal allosteric communication pathways with Force Distribution Analyses (FDA). Our observations show that CAP binding results in characteristic changes in the interaction pathways connecting the two cAMP allosteric binding sites with each other, as well as with the DNA binding domains. We identified crucial relays in the mostly symmetric allosteric activation network, and suggest point mutants to test this mechanism. Our study suggests inter-residue forces, as opposed to coordinates, as a highly sensitive measure for structural adaptations that, even though minute, can very effectively propagate allosteric signals.

The Catabolite Activator Protein (CAP) is a well-studied example for how cellular catabolite levels are integrated into the gene regulation. Its affinity for a specific stretch of DNA can be switched on by the binding of two nucleotide molecules termed cAMP to its two protomers. Even though the nucleotides occupy structurally identical binding pockets, the second cAMP binding occurs at an affinity orders of magnitude lower than the first cAMP binding. The question arises how, in the absence of structural changes, the first binding can affect the second. An answer from experiments has been that the communication is largely of entropic nature, i.e. the second cAMP binding would lead to a pronounced reduction in atomic fluctuations of the protein without affecting the atomic mean positions. We here revisited this question by performing Molecular Dynamics simulations. By measuring correlations of forces, a newly derived method outperforming the more common coordinate-based approach, we could recover the previously determined entropic penalty. In addition, however, we observed unobtrusive structural changes of side-chain interactions leading to the occlusion of the second binding pocket that add a critical ‘enthalpic’ component hitherto overlooked. Our study provides a mechanistic view onto the intriguing anti-cooperativity of CAP.

Calculation and visualization of atomistic mechanical stresses in nanomaterials and biomolecules

Many biomolecules have machine-like functions, and accordingly are discussed in terms of mechanical properties like force and motion. However, the concept of stress, a mechanical property that is of fundamental importance in the study of macroscopic mechanics, is not commonly applied in the biomolecular context. We anticipate that microscopical stress analyses of biomolecules and nanomaterials will provide useful mechanistic insights and help guide molecular design. To enable such applications, we have developed Calculator of Atomistic Mechanical Stress (CAMS), an open-source software package for computing atomic resolution stresses from molecular dynamics (MD) simulations. The software also enables decomposition of stress into contributions from bonded, nonbonded and Generalized Born potential terms. CAMS reads GROMACS topology and trajectory files, which are easily generated from AMBER files as well; and time-varying stresses may be animated and visualized in the VMD viewer. Here, we review relevant theory and present illustrative applications.

Overcoming dissipation in the calculation of standard binding free energies by ligand extraction

This article addresses calculations of the standard free energy of binding from molecular simulations in which a bound ligand is extracted from its binding site by steered molecular dynamics (MD) simulations or equilibrium umbrella sampling (US). Host-guest systems are used as test beds to examine the requirements for obtaining the reversible work of ligand extraction. We find that, for both steered MD and US, marked irreversibilities can occur when the guest molecule crosses an energy barrier and suddenly jumps to a new position, causing dissipation of energy stored in the stretched molecule(s). For flexible molecules, this occurs even when a stiff pulling spring is used, and it is difficult to suppress in calculations where the spring is attached to the molecules by single, fixed attachment points. We, therefore, introduce and test a method, fluctuation-guided pulling, which adaptively adjusts the spring's attachment points based on the guest's atomic fluctuations relative to the host. This adaptive approach is found to substantially improve the reversibility of both steered MD and US calculations for the present systems. The results are then used to estimate standard binding free energies within a comprehensive framework, termed attach-pull-release, which recognizes that the standard free energy of binding must include not only the pulling work itself, but also the work of attaching and then releasing the spring, where the release work includes an accounting of the standard concentration to which the ligand is discharged.

Amyloid-β peptide structure in aqueous solution varies with fragment size

Various fragment sizes of the amyloid-β (Aβ) peptide have been utilized to mimic the properties of the full-length Aβ peptide in solution. Among these smaller fragments, Aβ16 and Aβ28 have been investigated extensively. In this work, we report the structural and thermodynamic properties of the Aβ16, Aβ28, and Aβ42 peptides in an aqueous solution environment. We performed replica exchange molecular dynamics simulations along with thermodynamic calculations for investigating the conformational free energies, secondary and tertiary structures of the Aβ16, Aβ28, and Aβ42 peptides. The results show that the thermodynamic properties vary from each other for these peptides. Furthermore, the secondary structures in the Asp1-Lys16 and Asp1-Lys28 regions of Aβ42 cannot be completely captured by the Aβ16 and Aβ28 fragments. For example, the β-sheet structures in the N-terminal region of Aβ16 and Aβ28 are either not present or the abundance is significantly decreased in Aβ42. The α-helix and β-sheet abundances in Aβ28 and Aβ42 show trends--to some extent--with the potential of mean forces but no such trend could be obtained for Aβ16. Interestingly, Arg5 forms salt bridges with large abundances in all three peptides. The formation of a salt bridge between Asp23-Lys28 is more preferred over the Glu22-Lys28 salt bridge in Aβ28 but this trend is vice versa for Aβ42. This study shows that the Asp1-Lys16 and Asp1-Lys28 regions of the full length Aβ42 peptide cannot be completely mimicked by studying the Aβ16 and Aβ28 peptides.

Force and Stress along Simulated Dissociation Pathways of Cucurbituril-Guest Systems

The field of host-guest chemistry provides computationally tractable yet informative model systems for biomolecular recognition. We applied molecular dynamics simulations to study the forces and mechanical stresses associated with forced dissociation of aqueous cucurbituril-guest complexes with high binding affinities. First, the unbinding transitions were modeled with constant velocity pulling (steered dynamics) and a soft spring constant, to model atomic force microscopy (AFM) experiments. The computed length-force profiles yield rupture forces in good agreement with available measurements. We also used steered dynamics with high spring constants to generate paths characterized by a tight control over the specified pulling distance; these paths were then equilibrated via umbrella sampling simulations and used to compute time-averaged mechanical stresses along the dissociation pathways. The stress calculations proved to be informative regarding the key interactions determining the length-force profiles and rupture forces. In particular, the unbinding transition of one complex is found to be a stepwise process, which is initially dominated by electrostatic interactions between the guest's ammoniums and the host's carbonyl groups, and subsequently limited by the extraction of the guest's bulky bicyclooctane moiety; the latter step requires some bond stretching at the cucurbituril's extraction portal. Conversely, the dissociation of a second complex with a more slender guest is mainly driven by successive electrostatic interactions between the different guest's ammoniums and the host's carbonyl groups. The calculations also provide information on the origins of thermodynamic irreversibilities in these forced dissociation processes.

Recognition properties of cucurbit[7]uril self-assembled monolayers studied with force spectroscopy

Specific (host-guest) and unspecific (substrate-guest) interactions between self-assembled monolayers of cucurbit[7]uril (CB[7]) on gold (Au) substrates and neutral adamantyl (Ad) guests were resolved by studying these interactions at the single molecule level using dynamic force spectroscopy. The dissociation rate constants of the Ad-Au and the Ad-CB[7] interactions were 0.3 s(-1) and 0.03 s(-1), respectively, indicating that the specific binding is more stable. The probability of observing a specific interaction (40 ± 9%) is similar to the reported surface coverages of CB[7] monolayers on Au substrates. The higher strength and stability of the Ad-CB[7] interactions explains why, although presenting an imperfect coverage, CB[n] monolayers can be used successfully as a platform for surface immobilization.