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Register a new userKey biology you should have learned in physics class: Using ideal-gas mixtures to understand biomolecular machines
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Daniel M. Zuckerman
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The biological cell exhibits a fantastic range of behaviors, but ultimately these are governed by a handful of physical and chemical principles. Here we explore simple theory, known for decades and based on the simple thermodynamics of mixtures of ideal gases, which illuminates several key functions performed within the cell. Our focus is the free-energy-driven import and export of molecules, such as nutrients and other vital compounds, via transporter proteins. Complementary to a thermodynamic picture is a description of transporters via mass-action chemical kinetics, which lends further insights into biological machinery and free energy use. Both thermodynamic and kinetic descriptions can shed light on the fundamental non-equilibrium aspects of transport. On the whole, our biochemical-physics discussion will remain agnostic to chemical details, but we will see how such details ultimately enter a physical description through the example of the cellular fuel ATP.
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One of the most intriguing results of single molecule experiments on proteins and nucleic acids is the discovery of functional heterogeneity: the observation that complex cellular machines exhibit multiple, biologically active conformations. The structural differences between these conformations may be subtle, but each distinct state can be remarkably long-lived, with random inter
A major challenge in molecular simulations is to describe denaturant-dependent folding of proteins order to make direct comparisons with {it in vitro} experiments. We use the molecular transfer model, which is currently the only method that accomplishes this goal albeit phenomenologically, to quantitatively describe urea-dependent folding of PDZ domain, which plays a significant role in molecular recognition and signaling. Experiments show that urea-dependent unfolding rates of the PDZ2 domain exhibit a downward curvature at high urea concentrations, which has been interpreted by invoking the presence of a sparsely populated high energy intermediate. Simulations using the MTM and a coarse-grained model of PDZ2 are used to show that the intermediate, which has some native-like character, is present in equilibrium both in the presence and absence of urea. The free energy profiles show that there are two barriers separating the folded and unfolded states. Structures of the transition state ensembles, ($TSE1$ separating the unfolded and $I_{EQ}$ and $TSE2$ separating $I_{EQ}$ and the native state), determined using the $P_{fold}$ method, show that $TSE1$ is expanded; $TSE2$ and native-like. Folding trajectories reveal that PDZ2 folds by parallel routes. In one pathway folding occurs exclusively through $I_1$, which resembles $I_{EQ}$. In a fraction of trajectories, constituting the second pathway, folding occurs through a combination of $I_{1}$ and a kinetic intermediate. The radius of gyration ($R_g^{U}$) of the unfolded state is more compact (by $sim$ 9%) under native conditions. Decrease in $R_g^{U}$ occurs on the time scale on the order of utmost $sim$ 20 $mu s$. The modest decrease in $R_g^{U}$ and the rapid collapse suggest that high spatial and temporal resolution are needed to detect compaction in finite-sized proteins.
Equilibrium sampling of biomolecules remains an unmet challenge after more than 30 years of atomistic simulation. Efforts to enhance sampling capability, which are reviewed here, range from the development of new algorithms to parallelization to novel uses of hardware. Special focus is placed on classifying algorithms -- most of which are underpinned by a few key ideas -- in order to understand their fundamental strengths and limitations. Although algorithms have proliferated, progress resulting from novel hardware use appears to be more clear-cut than from algorithms alone, partly due to the lack of widely used sampling measures.
Experiments indicate that unbinding rates of proteins from DNA can depend on the concentration of proteins in nearby solution. Here we present a theory of multi-step replacement of DNA-bound proteins by solution-phase proteins. For four different kinetic scenarios we calculate the depen- dence of protein unbinding and replacement rates on solution protein concentration. We find (1) strong effects of progressive rezipping of the solution-phase protein onto DNA sites liberated by unzipping of the originally bound protein; (2) that a model in which solution-phase proteins bind non-specifically to DNA can describe experiments on exchanges between the non specific DNA- binding proteins Fis-Fis and Fis-HU; (3) that a binding specific model describes experiments on the exchange of CueR proteins on specific binding sites.
The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.
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