Internal friction in enzyme reactions

Probing the Internal Dynamics and Shape of Simple Peptides in Urea, Guanidinium Hydrochloride, and Proline Solutions with Time-Resolved Fluorescence Anisotropy and Atomistic Cosolvent Simulations

Picosecond time-resolved fluorescence anisotropy was used to measure the effect of denaturants and osmolytes on the reorientation dynamics of the simplest dipeptide. The solvent denaturants guanidinium hydrochloride (gdm), urea, and the osmolyte proline were used at several concentrations. Analysis of the concentration dependence of denaturants at a fixed temperature showed faster and slower reorientation time in two different denaturants at a nearly identical solvent viscosity (η). The reorientation time τ significantly deviates from Kramers' theory (τ ∝ η¹) in the high friction limit for guanidinium and urea with r ≈ 0.4 and r ≈ 0.6 at pH 7.2, respectively. In proline, τ is nearly proportional to η. Atomistic molecular dynamics simulations of the dipeptide in identical cosolvents showed excellent agreement with the measured rotational orientation time. The dipeptide dihedral (ϕ, ψ) isomerization times in water and 6 M urea are almost identical and significantly slower in guanidinium. If a faster and slower reorientation time can be associated with the compact and expanded shapes, the fractional viscosity dependence for guanidinium and urea may result from the fact that internal dynamics of peptides in these cosolvents involve higher and lower internal friction within the dynamic elements.

Simulation of Gating Currents of the Shaker K Channel Using a Brownian Model of the Voltage Sensor

The physical mechanism underlying the voltage-dependent gating of K channels is usually addressed theoretically using molecular dynamics simulations. However, besides being computationally very expensive, this approach is presently unable to fully predict the behavior of fundamental variables of channel gating such as the macroscopic gating current, and hence, it is presently unable to validate the model. To fill this gap, here we propose a voltage-gating model that treats the S4 segment as a Brownian particle moving through a gating channel pore and adjacent internal and external vestibules. In our model, charges on the S4 segment are screened by charged residues localized on neighboring segments of the channel protein and by ions present in the vestibules, whose dynamics are assessed using a flux conservation equation. The electrostatic voltage spatial profile is consistently assessed by applying the Poisson equation to all the charges present in the system. The treatment of the S4 segment as a Brownian particle allows description of the dynamics of a single S4 segment using the Langevin stochastic differential equation or the behavior of a population of S4 segments-useful for assessing the macroscopic gating current-using the Fokker-Planck equation. The proposed model confirms the gating charge transfer hypothesis with the movement of the S4 segment among five different stable positions where the gating charges interact in succession with the negatively charged residues on the channel protein. This behavior produces macroscopic gating currents quite similar to those experimentally found.

Internal friction in an intrinsically disordered protein-Comparing Rouse-like models with experiments

Internal friction is frequently found in protein dynamics. Its molecular origin however is difficult to conceptualize. Even unfolded and intrinsically disordered polypeptide chains exhibit signs of internal friction despite their enormous solvent accessibility. Here, we compare four polymer theories of internal friction with experimental results on the intrinsically disordered protein ACTR (activator of thyroid hormone receptor). Using nanosecond fluorescence correlation spectroscopy combined with single-molecule Förster resonance energy transfer (smFRET), we determine the time scales of the diffusive chain dynamics of ACTR at different solvent viscosities and varying degrees of compaction. Despite pronounced differences between the theories, we find that all models can capture the experimental viscosity-dependence of the chain relaxation time. In contrast, the observed slowdown upon chain collapse of ACTR is not captured by any of the theories and a mechanistic link between chain dimension and internal friction is still missing, implying that the current theories are incomplete. In addition, a discrepancy between early results on homopolymer solutions and recent single-molecule experiments on unfolded and disordered proteins suggests that internal friction is likely to be a composite phenomenon caused by a variety of processes.

Origin of Internal Friction in Disordered Proteins Depends on Solvent Quality

Protein dynamics often exhibit internal friction; i.e., contributions to friction that cannot solely be attributed to the viscosity of the solvent. Remarkably, even unfolded and intrinsically disordered proteins (IDPs) exhibit this behavior, despite typically being solvent-exposed. Several competing molecular mechanisms have been suggested to underlie this phenomenon, in particular dihedral relaxation and intrachain interactions. It has also recently been shown that single-molecule data reflecting internal friction in the disordered protein ACTR cannot be explained using polymer models unless this friction is dependent on protein collapse. However, the connection between the collapse of the chain and the underlying mechanism of internal friction has been unclear. To address this issue, we combine molecular simulation and single-molecule experimental data to investigate how chain compaction affects protein dynamics in the context of ACTR. Chain reconfiguration times and internal friction estimated from all-atom simulations are in semiquantitative agreement with experimental data. We dissect the underlying molecular mechanism with all-atom and coarse-grained simulations and clearly identify both intrachain interactions and dihedral angle transitions as contributions to internal friction. However, their relative contribution is strongly dependent on the compactness of the IDP; while dihedral relaxation dominates internal friction in expanded configurations, intrachain interactions dominate for more compact chains. Our results thus imply a continuous transition between mechanisms and provide a link between internal friction in IDPs and that in more compact and folded states of proteins.

Cosolutes, Crowding, and Protein Folding Kinetics

Long accepted as the most important interaction, recent work shows that steric repulsions alone cannot explain the effects of macromolecular cosolutes on the equilibrium thermodynamics of protein stability. Instead, chemical interactions have been shown to modulate, and even dominate, crowding-induced steric repulsions. Here, we use 19F NMR to examine the effects of small and large cosolutes on the kinetics of protein folding and unfolding using the metastable 7 kDa N-terminal SH3 domain of the Drosophila signaling protein drk (SH3), which folds by a two-state mechanism. The small cosolutes consist of trimethylamine N-oxide and sucrose, which increase equilibrium protein stability, and urea, which destabilizes proteins. The macromolecules comprise the stabilizing sucrose polymer, Ficoll, and the destabilizing globular protein, lysozyme. We assessed the effects of these cosolutes on the differences in free energy between the folded state and the transition state and between the unfolded ensemble and the transition state. We then examined the temperature dependence to assess changes in activation enthalpy and entropy. The enthalpically mediated effects are more complicated than suggested by equilibrium measurements. We also observed enthalpic effects with the supposedly inert sucrose polymer, Ficoll, that arise from its macromolecular nature. Assessment of activation entropies shows important contributions from solvent and cosolute, in addition to the configurational entropy of the protein that, again, cannot be gleaned from equilibrium data. Comparing the effects of Ficoll to those of the more physiologically relevant cosolute lysozyme reveals that synthetic polymers are not appropriate models for understanding the kinetics of protein folding in cells.

Nodal versus Total Axonal Strain and the Role of Cholesterol in Traumatic Brain Injury

Traumatic brain injury (TBI) is a health threat that affects every year millions of people involved in motor vehicle and sporting accidents, and thousands of soldiers in battlefields. Diffuse axonal injury (DAI) is one of the most frequent types of TBI leading to death. In DAI, the initial traumatic event is followed by a cascade of biochemical changes that take time to develop in full, so that symptoms may not become apparent until days or weeks after the original injury. Hence, DAI is a dynamic process, and the opportunity exists to prevent its progression provided the initial trauma can be predicted at the molecular level. Here, we present preliminary evidence from micro-finite element (FE) simulations that the mechanical response of central nervous system myelinated fibers is dependent on the axonal diameter, the ratio between axon diameter and fiber diameter (g-ratio), the microtubules density, and the cholesterol concentration in the axolemma and myelin. A key outcome of the simulations is that there is a significant difference between the overall level of strain in a given axonal segment and the level of local strain in the Ranvier nodes contained in that segment, with the nodal strain being much larger than the total strain. We suggest that the acquisition of this geometric and biochemical information by means of already available high resolution magnetic resonance imaging techniques, and its incorporation in current FE models of the brain will enhance the models capacity to predict the site and magnitude of primary axonal damage upon TBI.

Crowding effects on the temperature and pressure dependent structure, stability and folding kinetics of Staphylococcal Nuclease

FT-IR spectroscopic, small-angle X-ray scattering and calorimetric measurements have been applied to explore the effect of the macromolecular crowder agent Ficoll on the temperature- and pressure-dependent stability diagram and folding reaction of the protein Staphylococcal Nuclease (SNase). Additionally, we compare the experimental data with approximate theoretical predictions. We found that temperature- and pressure-induced equilibrium unfolding of SNase is markedly shifted to higher temperatures and pressures in 30 wt% Ficoll solutions. The structure of the unfolded state ensemble does not seem to be strongly influenced in the presence of the crowder. Self-crowding effects have been found to become important at SNase concentrations above 10 wt% only. Our kinetic results show that the folding rate of SNase decreases markedly in the presence of Ficoll. These results indicate that besides the commonly encountered excluded volume effect, other factors need to be considered when assessing confinement effects on protein folding kinetics. Among those, crowder-induced viscosity changes seem to be prominent.

Synthetic biology for the directed evolution of protein biocatalysts: navigating sequence space intelligently

The amino acid sequence of a protein affects both its structure and its function. Thus, the ability to modify the sequence, and hence the structure and activity, of individual proteins in a systematic way, opens up many opportunities, both scientifically and (as we focus on here) for exploitation in biocatalysis. Modern methods of synthetic biology, whereby increasingly large sequences of DNA can be synthesised de novo, allow an unprecedented ability to engineer proteins with novel functions. However, the number of possible proteins is far too large to test individually, so we need means for navigating the 'search space' of possible protein sequences efficiently and reliably in order to find desirable activities and other properties. Enzymologists distinguish binding (Kd) and catalytic (kcat) steps. In a similar way, judicious strategies have blended design (for binding, specificity and active site modelling) with the more empirical methods of classical directed evolution (DE) for improving kcat (where natural evolution rarely seeks the highest values), especially with regard to residues distant from the active site and where the functional linkages underpinning enzyme dynamics are both unknown and hard to predict. Epistasis (where the 'best' amino acid at one site depends on that or those at others) is a notable feature of directed evolution. The aim of this review is to highlight some of the approaches that are being developed to allow us to use directed evolution to improve enzyme properties, often dramatically. We note that directed evolution differs in a number of ways from natural evolution, including in particular the available mechanisms and the likely selection pressures. Thus, we stress the opportunities afforded by techniques that enable one to map sequence to (structure and) activity in silico, as an effective means of modelling and exploring protein landscapes. Because known landscapes may be assessed and reasoned about as a whole, simultaneously, this offers opportunities for protein improvement not readily available to natural evolution on rapid timescales. Intelligent landscape navigation, informed by sequence-activity relationships and coupled to the emerging methods of synthetic biology, offers scope for the development of novel biocatalysts that are both highly active and robust.

Viscosity dependence of passage through a fluctuating bottleneck

We generalize the model of a rate process involving the passage of an object through a fluctuating bottleneck. The rate of passage is considered to be proportional to a power function of the radius of the bottleneck with exponent α > 0. The fluctuations of the bottleneck are coupled to the motion of the surrounding medium and governed by Langevin dynamics. We show numerically and also explain analytically that for slow bottleneck fluctuations the long time decay rate of the process has a fractional power law dependence on the solvent viscosity with exponent α/(α + 2). The results are consistent with the experimental data on ligand binding to myoglobin, and might also be relevant to other reactions for which exponents between 0 and 1 were reported.