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.

Gating of the MlotiK1 potassium channel involves large rearrangements of the cyclic nucleotide-binding domains.

Cyclic nucleotide-regulated ion channels are present in bacteria, plants, vertebrates, and humans. In higher organisms, they are closely involved in signaling networks of vision and olfaction. Binding of cAMP or cGMP favors the activation of these ion channels. Despite a wealth of structural and studies, there is a lack of structural data describing the gating process in a full-length cyclic nucleotide-regulated channel. We used high-resolution atomic force microscopy (AFM) to directly observe the conformational change of the membrane embedded bacterial cyclic nucleotide-regulated channel MlotiK1. In the nucleotide-bound conformation, the cytoplasmic cyclic nucleotide-binding (CNB) domains of MlotiK1 are disposed in a fourfold symmetric arrangement forming a pore-like vestibule. Upon nucleotide-unbinding, the four CNB domains undergo a large rearrangement, stand up by ∼1.7 nm, and adopt a structurally variable grouped conformation that closes the cytoplasmic vestibule. This fully reversible conformational change provides insight into how CNB domains rearrange when regulating the potassium channel.

Quantitative imaging of the electrostatic field and potential generated by a transmembrane protein pore at subnanometer resolution.

Elucidating the mechanisms by which proteins translocate small molecules and ions through transmembrane pores and channels is of great interest in biology, medicine, and nanotechnology. However, the characterization of pore forming proteins in their native state lacks suitable methods that are capable of high-resolution imaging (~1 nm) while simultaneously mapping physical and chemical properties. Here we report how force-distance (FD) curve-based atomic force microscopy (AFM) imaging can be applied to image the native pore forming outer membrane protein F (OmpF) at subnanometer resolution and to quantify the electrostatic field and potential generated by the transmembrane pore. We further observe the electrostatic field and potential of the OmpF pore switching "on" and "off" in dependence of the electrolyte concentration. Because electrostatic field and potential select for charged molecules and ions and guide them to the transmembrane pore the insights are of fundamental importance to understand the pore function. These experimental results establish FD-based AFM as a unique tool to image biological systems to subnanometer resolution and to quantify their electrostatic properties.

Mechanoenzymatics of titin kinase.

Biological responses to mechanical stress require strain-sensing molecules, whose mechanically induced conformational changes are relayed to signaling cascades mediating changes in cell and tissue properties. In vertebrate muscle, the giant elastic protein titin is involved in strain sensing via its C-terminal kinase domain (TK) at the sarcomeric M-band and contributes to the adaptation of muscle in response to changes in mechanical strain. TK is regulated in a unique dual autoinhibition mechanism by a C-terminal regulatory tail, blocking the ATP binding site, and tyrosine autoinhibition of the catalytic base. For access to the ATP binding site and phosphorylation of the autoinhibitory tyrosine, the C-terminal autoinhibitory tail needs to be removed. Here, we use AFM-based single-molecule force spectroscopy, molecular dynamics simulations, and enzymatics to study the conformational changes during strain-induced activation of human TK. We show that mechanical strain activates ATP binding before unfolding of the structural titin domains, and that TK can thus act as a biological force sensor. Furthermore, we identify the steps in which the autoinhibition of TK is mechanically relieved at low forces, leading to binding of the cosubstrate ATP and priming the enzyme for subsequent autophosphorylation and substrate turnover.

Primary steps of pH-dependent insulin aggregation kinetics are governed by conformational flexibility.

Insulin aggregation critically depends on pH. The underlying energetic and structural determinants are, however, unknown. Here, we measure the kinetics of the primary aggregation steps of the insulin monomer in vitro and relate it to its conformational flexibility. To assess these primary steps the monomer concentration was monitored by mass spectrometry at various pH values and aggregation products were imaged by atomic force microscopy. Lowering the pH from 3 to 1.6 markedly accelerated the observed aggregation kinetics. The influence of pH on the monomer structure and dynamics in solution was studied by molecular dynamics simulations, with the protonation states of the titrable groups obtained from electrostatic calculations. Reduced flexibility was observed for low pH values, mainly in the C terminus and in the helix of the B chain; these corresponded to an estimated entropy loss of 150 J mol(-1) K(-1). The striking correlation between entropy loss and pH value is consistent with the observed kinetic traces. In analogy to the well-known Phi value analysis, this result allows the extraction of structural information about the rate determining transition state of the primary aggregation steps. In particular, we suggest that the residues in the helix of the B chain are involved in this transition state.

Adaptive anisotropic kernels for nonparametric estimation of absolute configurational entropies in high-dimensional configuration spaces.

The quasiharmonic approximation is the most widely used estimate for the configurational entropy of macromolecules from configurational ensembles generated from atomistic simulations. This method, however, rests on two assumptions that severely limit its applicability, (i) that a principal component analysis yields sufficiently uncorrelated modes and (ii) that configurational densities can be well approximated by Gaussian functions. In this paper we introduce a nonparametric density estimation method which rests on adaptive anisotropic kernels. It is shown that this method provides accurate configurational entropies for up to 45 dimensions thus improving on the quasiharmonic approximation. When embedded in the minimally coupled subspace framework, large macromolecules of biological interest become accessible, as demonstrated for the 67-residue coldshock protein.

How To Minimize Artifacts in Atomistic Simulations of Membrane Proteins, Whose Crystal Structure Is Heavily Engineered: ß2-Adrenergic Receptor in the Spotlight.

Atomistic molecular dynamics (MD) simulations are used extensively to elucidate membrane protein properties. These simulations are based on three-dimensional protein structures that in turn are often based on crystallography. The protein structures resolved in crystallographic studies typically do not correspond to pristine proteins, however. Instead the crystallized proteins are commonly engineered, including structural modifications (mutations, replacement of protein sequences by antibodies, bound ligands, etc.) whose impact on protein structure and dynamics is largely unknown. Here we explore this issue through atomistic MD simulations (∼5 µs in total), focusing on the ß2-adrenergic receptor (ß2AR) that is one of the most studied members of the G-protein coupled receptor superfamily. Starting from an inactive-state crystal structure of ß2AR, we remove the many modifications in ß2AR systematically one at a time, in six consecutive steps. After each step, we equilibrate the system and simulate it quite extensively. The results of this step-by-step approach highlight that the structural modifications used in crystallization can affect ligand and G-protein binding sites, packing at the transmembrane-helix interface region, and the dynamics of connecting loops in ß2AR. When the results of the systematic step-by-step approach are compared to an all-at-once technique where all modifications done on ß2AR are removed instantaneously at the same time, it turns out that the step-by-step method provides results that are superior in terms of maintaining protein structural stability. The results provide compelling evidence that for membrane proteins whose 3D structure is based on structural engineering, the preparation of protein structure for atomistic MD simulations is a delicate and sensitive process. The results show that most valid results are found when the structural modifications are reverted slowly, one at a time.

Macromolecular Entropy Can Be Accurately Computed from Force.

A method is presented to evaluate a molecule's entropy from the atomic forces calculated in a molecular dynamics simulation. Specifically, diagonalization of the mass-weighted force covariance matrix produces eigenvalues which in the harmonic approximation can be related to vibrational frequencies. The harmonic oscillator entropies of each vibrational mode may be summed to give the total entropy. The results for a series of hydrocarbons, dialanine and a ß hairpin are found to agree much better with values derived from thermodynamic integration than results calculated using quasiharmonic analysis. Forces are found to follow a harmonic distribution more closely than coordinate displacements and better capture the underlying potential energy surface. The method's accuracy, simplicity, and computational similarity to quasiharmonic analysis, requiring as input force trajectories instead of coordinate trajectories, makes it readily applicable to a wide range of problems.

Mechanistic explanation of different unfolding behaviors observed for transmembrane and soluble ß-barrel proteins.

In response to mechanical stress, membrane proteins progress through sequences of major unfolding barriers, whereas soluble proteins usually must overcome only one major unfolding barrier. To gain insight into these markedly different unfolding behaviors, we applied force-probe molecular dynamics simulations and unfolded two ß-barrel proteins, the transmembrane outer membrane protein G (OmpG) and the water-soluble green fluorescent protein (GFP). The simulations mimic with high precision the unfolding experiments and show that OmpG in the absence of a membrane and GFP circumvent high unfolding barriers by rotations and explore alternative unfolding pathways. Embedding OmpG in the lipid membrane restricts this search for pathways and forces the protein to cross high unfolding barriers. Likewise, restricting the rotation forces GFP to traverse high unfolding barriers in a similar manner to membrane-embedded OmpG. These results indicate that mechanically stressed proteins search alternative unfolding pathways by rotations and explain why membrane proteins generally show higher mechanical stability compared to water-soluble proteins.

Exploring protein dynamics space: the dynasome as the missing link between protein structure and function.

Proteins are usually described and classified according to amino acid sequence, structure or function. Here, we develop a minimally biased scheme to compare and classify proteins according to their internal mobility patterns. This approach is based on the notion that proteins not only fold into recurring structural motifs but might also be carrying out only a limited set of recurring mobility motifs. The complete set of these patterns, which we tentatively call the dynasome, spans a multi-dimensional space with axes, the dynasome descriptors, characterizing different aspects of protein dynamics. The unique dynamic fingerprint of each protein is represented as a vector in the dynasome space. The difference between any two vectors, consequently, gives a reliable measure of the difference between the corresponding protein dynamics. We characterize the properties of the dynasome by comparing the dynamics fingerprints obtained from molecular dynamics simulations of 112 proteins but our approach is, in principle, not restricted to any specific source of data of protein dynamics. We conclude that: 1. the dynasome consists of a continuum of proteins, rather than well separated classes. 2. For the majority of proteins we observe strong correlations between structure and dynamics. 3. Proteins with similar function carry out similar dynamics, which suggests a new method to improve protein function annotation based on protein dynamics.

Estimating absolute configurational entropies of macromolecules: the minimally coupled subspace approach.

We develop a general minimally coupled subspace approach (MCSA) to compute absolute entropies of macromolecules, such as proteins, from computer generated canonical ensembles. Our approach overcomes limitations of current estimates such as the quasi-harmonic approximation which neglects non-linear and higher-order correlations as well as multi-minima characteristics of protein energy landscapes. Here, Full Correlation Analysis, adaptive kernel density estimation, and mutual information expansions are combined and high accuracy is demonstrated for a number of test systems ranging from alkanes to a 14 residue peptide. We further computed the configurational entropy for the full 67-residue cofactor of the TATA box binding protein illustrating that MCSA yields improved results also for large macromolecular systems.