Amino Acid Stabilization of Nucleic Acid Secondary Structure: Kinetic Insights from Single-Molecule Studies

Kinetic and Thermodynamic Control of G-Quadruplex Polymorphism by Na+ and K+ Cations

G-Quadruplexes (G4s) are ubiquitous nucleic acid folding motifs that exhibit structural diversity that is dependent on cationic conditions. In this work, we exploit temperature-controlled single-molecule fluorescence resonance energy transfer (smFRET) to elucidate the kinetic and thermodynamic mechanisms by which monovalent cations (K+ and Na+) impact folding topologies for a simple G-quadruplex sequence (5'-GGG-(TAAGGG)3-3') with a three-state folding equilibrium. Kinetic measurements indicate that Na+ and K+ influence G4 formation in two distinctly different ways: the presence of Na+ modestly enhances an antiparallel G4 topology through an induced fit (IF) mechanism with a low affinity (Kd = 228 ± 26 mM), while K+ drives G4 into a parallel/hybrid topology via a conformational selection (CS) mechanism with much higher affinity (Kd = 1.9 ± 0.2 mM). Additionally, temperature-dependent studies of folding rate constants and equilibrium ratios reveal distinctly different thermodynamic driving forces behind G4 binding to K+ (ΔH°bind > 0, ΔS°bind > 0) versus Na+ (ΔH°bind < 0, ΔS°bind < 0), which further illuminates the diversity of the possible pathways for monovalent facilitation of G-quadruplex folding.

Ionic Cooperativity between Lysine and Potassium in the Lysine Riboswitch: Single-Molecule Kinetic and Thermodynamic Studies

Functionality in many biological systems, including proteins and nucleic acid structures, including protein and nucleic acid riboswitch structures, can depend on cooperative kinetic behavior between multiple small molecule ligands. In this work, single-molecule FRET data on the Bacillus subtilis lysine riboswitch reveals that affinity for the cognate lysine ligand increases significantly with K⁺, providing evidence for synergism between lysine/K⁺ binding to the aptamer and successful folding of the riboswitch. To describe/interpret this more complex kinetic scenario, we explore the conventional 4-state ("square") model for aptamer binding as a function of K⁺. Extension into this additional dimension generates a novel "cube" model for riboswitch folding dynamics with respect to lysine/K⁺ binding, revealing that riboswitch folding (k_fold) and unfolding (k_unfold) rate constants increase and decrease dramatically with K⁺, respectively. Furthermore, temperature-dependent single-molecule kinetic studies indicate that the presence of K⁺ entropically enhances the transition state barrier to folding but partially compensates for this by increasing the overall exothermicity for lysine binding. We rationalize this behavior as evidence that K⁺ facilitates hydrogen bonding between the negatively charged carboxyl group of lysine and the RNA, increasing structural rigidity and lowering entropy in the binding pocket. Finally, we explore the effects of cation size with Na⁺ and Cs⁺ studies to demonstrate that K⁺ is optimally suited for bridging interactions between lysine and the riboswitch aptamer domain. Regulation of lysine production and transport, dictated by the riboswitch's ability to recognize and bind lysine, is therefore intimately tied to the presence of K⁺ in the binding pocket and is strongly modulated by local cation conditions. The results suggest an increase in lysine riboswitch functionality by sensitivity to additional species in the cellular riboswitch environment.

Lysine-Dependent Entropy Effects in the B. subtilis Lysine Riboswitch: Insights from Single-Molecule Thermodynamic Studies

Riboswitches play an important role in RNA-based sensing/gene regulation control for many bacteria. In particular, the accessibility of multiple conformational states at physiological temperatures allows riboswitches to selectively bind a cognate ligand in the aptamer domain, which triggers secondary structural changes in the expression platform, and thereby "switching" between on or off transcriptional or translational states for the downstream RNA. The present work exploits temperature-controlled, single-molecule total internal reflection fluorescence (TIRF) microscopy to study the thermodynamic landscape of such ligand binding/folding processes, specifically for the Bacillus subtilis lysine riboswitch. The results confirm that the riboswitch folds via an induced-fit (IF) mechanism, in which cognate lysine ligand first binds to the riboswitch before structural rearrangement takes place. The transition state to folding is found to be enthalpically favored (ΔH_fold^‡ < 0), yet with a free-energy barrier that is predominantly entropic (-TΔS_fold^‡ > 0), which results in folding (unfolding) rate constants strongly dependent (independent) of lysine concentration. Analysis of the single-molecule kinetic "trajectories" reveals this rate constant dependence of k_fold on lysine to be predominantly entropic in nature, with the additional lysine conferring preferential advantage to the folding process by the presence of ligands correctly oriented with respect to the riboswitch platform. By way of contrast, van't Hoff analysis reveals enthalpic contributions to the overall folding thermodynamics (ΔH⁰) to be surprisingly constant and robustly independent of lysine concentration. The results demonstrate the crucial role of hydrogen bonding between the ligand and riboswitch platform but with only a relatively modest fraction (45%) of the overall enthalpy change needed to access the transition state and initiate transcriptional switching.

Effects of Molecular Crowders on Single-Molecule Nucleic Acid Folding: Temperature-Dependent Studies Reveal True Crowding vs Enthalpic Interactions

Biomolecular folding in cells can be strongly influenced by spatial overlap/excluded volume interactions (i.e., "crowding") with intracellular solutes. As a result, traditional in vitro experiments with dilute buffers may not accurately recapitulate biomolecule folding behavior in vivo. In order to account for such ubiquitous excluded volume effects, biologically inert polyethylene glycol (PEG) and polysaccharides (dextran and Ficoll) are often used as in vitro crowding agents to mimic in vivo crowding conditions, with a common observation that high concentrations of these polymers stabilize the more compact biomolecule conformation. However, such an analysis can be distorted by differences in polymer interactions with the folded vs unfolded conformers, requiring temperature-dependent analysis of the thermodynamics to reliably assess competing enthalpic vs entropic contributions and thus the explicit role of excluded volume. In this work, temperature-controlled single-molecule fluorescence resonance energy transfer (smFRET) is used to characterize the thermodynamic interaction between nucleic acids and common polymer crowders PEG, dextran, and Ficoll. The results reveal that PEG promotes secondary and tertiary nucleic acid folding by simultaneously increasing the folding rate while decreasing the unfolding rate, with temperature-dependent studies confirming that the source of PEG stabilization is predominantly entropic and consistent with a true excluded volume crowding mechanism. By way of contrast, neither dextran nor Ficoll induces any significant concentration-dependent change in nucleic acid folding stability at room temperature, but instead, stabilization effects gradually appear with a temperature increase. Such a thermal response indicates that both folding enthalpies and entropies are impacted by dextran and Ficoll. A detailed thermodynamic analysis of the kinetics suggests that, instead of true entropic molecular crowding, dextran and Ficoll associate preferentially with the unfolded vs folded nucleic acid conformer as a result of larger solvent accessible surface area, thereby skewing the free energy landscapes through both significant entropic/enthalpic contributions that compete and fortuitously cancel near room temperature.

Codon Usage Bias in Autophagy-Related Gene 13 in Eukaryotes: Uncovering the Genetic Divergence by the Interplay Between Nucleotides and Codon Usages

Synonymous codon usage bias is a universal characteristic of genomes across various organisms. Autophagy-related gene 13 (atg13) is one essential gene for autophagy initiation, yet the evolutionary trends of the atg13 gene at the usages of nucleotide and synonymous codon remains unexplored. According to phylogenetic analyses for the atg13 gene of 226 eukaryotic organisms at the nucleotide and amino acid levels, it is clear that their nucleotide usages exhibit more genetic information than their amino acid usages. Specifically, the overall nucleotide usage bias quantified by information entropy reflected that the usage biases at the first and second codon positions were stronger than those at the third position of the atg13 genes. Furthermore, the bias level of nucleotide ‘G’ usage is highest, while that of nucleotide ‘C’ usage is lowest in the atg13 genes. On top of that, genetic features represented by synonymous codon usage exhibits a species-specific pattern on the evolution of the atg13 genes to some extent. Interestingly, the codon usages of atg13 genes in the ancestor animals (Latimeria chalumnae, Petromyzon marinus, and Rhinatrema bivittatum) are strongly influenced by mutation pressure from nucleotide composition constraint. However, the distributions of nucleotide composition at different codon positions in the atg13 gene display that natural selection still dominates atg13 codon usages during organisms’ evolution.

Measuring Excess Heat Capacities of Deoxyribonucleic Acid (DNA) Folding at the Single-Molecule Level

Measurements of the thermodynamic properties of biomolecular folding (ΔG°, ΔH°, ΔS°, etc.) provide a wealth of information on the folding process and have long played a central role in biophysical investigation. In particular, the excess heat capacity of folding (ΔC_P) is crucial, as typically measured in bulk ensemble studies by differential scanning calorimetry (DSC) and isothermal titration calorimetry (ITC). Here, we report the first measurements of ΔC_P at the single-molecule level using the single-molecule fluorescence resonance energy transfer (smFRET) as well as the very first measurements of the heat capacity change associated with achieving the transition state (ΔC^‡_P) for nucleic acid folding. The deoxyribonucleic acid (DNA) hairpin used in these studies exhibits an excess heat capacity for hybridization (ΔC_P = -340 ± 60 J/mol/K per base pair) consistent with the range of literature expectations (ΔC_P = -100 to -420 J/mol/K per base pair). Furthermore, the measured activation heat capacities (ΔC^‡_P) for such hairpin unfolding are consistent with a folding transition state containing few fully formed base pairs, in agreement with prevailing models of DNA hybridization.

Functional Roles of Chelated Magnesium Ions in RNA Folding and Function

RNA regulates myriad cellular events such as transcription, translation, and splicing. To perform these essential functions, RNA often folds into complex tertiary structures in which its negatively charged ribose-phosphate backbone interacts with metal ions. Magnesium, the most abundant divalent metal ion in cells, neutralizes the backbone, thereby playing essential roles in RNA folding and function. This has been known for more than 50 years, and there are now thousands of in vitro studies, most of which have used ≥10 mM free Mg²⁺ ions to achieve optimal RNA folding and function. In the cell, however, concentrations of free Mg²⁺ ions are much lower, with most Mg²⁺ ions chelated by metabolites. In this Perspective, we curate data from a number of sources to provide extensive summaries of cellular concentrations of metabolites that bind Mg²⁺ and to estimate cellular concentrations of metabolite-chelated Mg²⁺ species, in the representative prokaryotic and eukaryotic systems Escherichia coli, Saccharomyces cerevisiae, and iBMK cells. Recent research from our lab and others has uncovered the fact that such weakly chelated Mg²⁺ ions can enhance RNA function, including its thermodynamic stability, chemical stability, and catalysis. We also discuss how metabolite-chelated Mg²⁺ complexes may have played roles in the origins of life. It is clear from this analysis that bound Mg²⁺ should not be simply considered non-RNA-interacting and that future RNA research, as well as protein research, could benefit from considering chelated magnesium.

Pushing Camera-Based Single-Molecule Kinetic Measurements to the Frame Acquisition Limit with Stroboscopic smFRET

Single-molecule fluorescence resonance energy transfer (smFRET) experiments permit detailed examination of microscopic dynamics. However, kinetic rate constants determined by smFRET are susceptible to systematic underestimation when the rate constants are comparable to the data acquisition rate. We demonstrate how such systematic errors in camera-based total internal reflection fluorescence microscopy experiments can be greatly reduced by using stroboscopic illumination/detection, allowing accurate rate constant determination up to the data sampling rate and yielding an order of magnitude increase in the dynamic range. Implementation of these stroboscopic smFRET ideas is straightforward, and the stroboscopically obtained data are compatible with multiple trajectory analysis methods, including dwell-time analysis and hidden Markov modeling. Such stroboscopic methods therefore offer a remarkably simple yet valuable addition to the smFRET toolkit, requiring only relatively modest modification to the normal data collection and analysis procedures.

Chirality-Dependent Amino Acid Modulation of RNA Folding

The preponderance of a specific d- or l-chirality in fats, sugars, amino acids, nucleic acids, and so on is ubiquitous in nature, yet the biological origin of such chiral dominance (i.e., with one enantiomer overwhelmingly present) remains an open question. One plausible proposal for the predominance of l-chirality in amino acids could be through evolutionary templating of chiral RNA-folding via chaperone activity. To help evaluate this possibility, single molecule fluorescence experiments have been performed that measure the chiral dependence of chaperone folding dynamics for the simple tetraloop-tetraloop receptor (TL-TLR) tertiary binding motif in the presence of a series of chiral amino acids. Specifically, d- vs l-arginine is found to accelerate the unfolding of this RNA motif in a chirally selective fashion, with temperature-dependent studies of the kinetics performed to extract free energy, enthalpy, and entropy landscapes for the underlying thermodynamics. Furthermore, all-atom molecular dynamics (MD) simulations are pursued to provide additional physical insight into this chiral sensitivity, which reveal enantiomer-specific sampling of nucleic acid surfaces by d- vs l-arginine and support a putative mechanism for chirally specific denaturation of RNA tertiary structure by arginine but not other amino acids.

High pressure single-molecule FRET studies of the lysine riboswitch: cationic and osmolytic effects on pressure induced denaturation

Deep sea biology is known to thrive at pressures up to ≈1 kbar, which motivates fundamental biophysical studies of biomolecules under such extreme environments. In this work, the conformational equilibrium of the lysine riboswitch has been systematically investigated by single molecule FRET (smFRET) microscopy at pressures up to 1500 bar. The lysine riboswitch preferentially unfolds with increasing pressure, which signals an increase in free volume (ΔV0 > 0) upon folding of the biopolymer. Indeed, the effective lysine binding constant increases quasi-exponentially with pressure rise, which implies a significant weakening of the riboswitch-ligand interaction in a high-pressure environment. The effects of monovalent/divalent cations and osmolytes on folding are also explored to acquire additional insights into cellular mechanisms for adapting to high pressures. For example, we find that although Mg2+ greatly stabilizes folding of the lysine riboswitch (ΔΔG0 < 0), there is negligible impact on changes in free volume (ΔΔV0 ≈ 0) and thus any pressure induced denaturation effects. Conversely, osmolytes (commonly at high concentrations in deep sea marine species) such as the trimethylamine N-oxide (TMAO) significantly reduce free volumes (ΔΔV0 < 0) and thereby diminish pressure-induced denaturation. We speculate that, besides stabilizing RNA structure, enhanced levels of TMAO in cells might increase the dynamic range for competent riboswitch folding by suppressing the pressure-induced denaturation response. This in turn could offer biological advantage for vertical migration of deep-sea species, with impacts on food searching in a resource limited environment.

Unprecedented tunability of riboswitch structure and regulatory function by sub-millimolar variations in physiological Mg2

Riboswitches are cis-acting regulatory RNA biosensors that rival the efficiency of those found in proteins. At the heart of their regulatory function is the formation of a highly specific aptamer–ligand complex. Understanding how these RNAs recognize the ligand to regulate gene expression at physiological concentrations of Mg²⁺ ions and ligand is critical given their broad impact on bacterial gene expression and their potential as antibiotic targets. In this work, we used single-molecule FRET and biochemical techniques to demonstrate that Mg²⁺ ions act as fine-tuning elements of the amino acid-sensing lysC aptamer's ligand-free structure in the mesophile Bacillus subtilis. Mg²⁺ interactions with the aptamer produce encounter complexes with strikingly different sensitivities to the ligand in different, yet equally accessible, physiological ionic conditions. Our results demonstrate that the aptamer adapts its structure and folding landscape on a Mg²⁺-tunable scale to efficiently respond to changes in intracellular lysine of more than two orders of magnitude. The remarkable tunability of the lysC aptamer by sub-millimolar variations in the physiological concentration of Mg²⁺ ions suggests that some single-aptamer riboswitches have exploited the coupling of cellular levels of ligand and divalent metal ions to tightly control gene expression.

Single-molecule kinetic studies of DNA hybridization under extreme pressures

Pressure-responsive dynamics of DNA hairpin hybridization/dehybridization is directly visualized at the single molecule level.

DNA Hairpin Hybridization under Extreme Pressures: A Single-Molecule FRET Study

Organisms have evolved to live in a variety of complex environments, which clearly has required cellular biology to accommodate to extreme conditions of hydraulic pressure and elevated temperature. In this work, we exploit single-molecule Forster resonance energy transfer (FRET) spectroscopy to probe structural changes in DNA hairpins as a function of pressure and temperature, which allows us to extract detailed thermodynamic information on changes in free energy (ΔG°), free volume (ΔV°), enthalpy (ΔH°), and entropy (ΔS°) associated with DNA loop formation and sequence-dependent stem hybridization. Specifically, time-correlated single-photon counting experiments on freely diffusing 40A DNA hairpin FRET constructs are performed in a 50 μm × 50 μm square quartz capillary cell pressurized from ambient pressure up to 3 kbar. By pressure-dependent van't Hoff analysis of the equilibrium constants, ΔV° for hybridization of the DNA hairpin can be determined as a function of stem length (n_stem = 7-10) with single base-pair resolution, which further motivates a simple linear deconstruction into additive stem (ΔV°_stem = ΔV°_bp x n_stem) and loop (ΔV°_loop) contributions. We find that increasing pressure destabilizes the DNA hairpin stem region [ΔV°_bp = +1.98(16) cm³/(mol bp)], with additional positive free volume changes [ΔV°_loop = +7.0(14) cm³/mol] we ascribe to bending and base stacking disruption of the 40-dA loop. From a van't Hoff temperature-dependent analysis of the DNA 40A hairpin equilibria, the data support a similar additive loop/stem deconstruction of enthalpic (ΔH° = ΔH°_loop + ΔH°_stem) and entropic (ΔS° = ΔS°_loop + ΔS°_stem) contributions, which permits insightful comparison with predictions from nearest-neighbor thermodynamic models for DNA duplex formation. In particular, the stem thermodynamics is consistent with exothermically favored (ΔH°_stem < 0) and entropically penalized (ΔS°_stem < 0) hydrogen bonding but with additional enthalpic (ΔH°_loop > 0) and entropic (ΔS°_loop > 0) contributions due to loop bending effects consistent with distortion of dA base stacking in the 40-dA linker.

Algorithmic and Stochastic Representations of Gene Regulatory Networks and Protein-Protein Interactions

BACKGROUND

Latest studies reveal the importance of Protein-Protein interactions on physiologic functions and biological structures. Several stochastic and algorithmic methods have been published until now, for the modeling of the complex nature of the biological systems.

OBJECTIVE

Biological Networks computational modeling is still a challenging task. The formulation of the complex cellular interactions is a research field of great interest. In this review paper, several computational methods for the modeling of GRN and PPI are presented analytically.

METHODS

Several well-known GRN and PPI models are presented and discussed in this review study such as: Graphs representation, Boolean Networks, Generalized Logical Networks, Bayesian Networks, Relevance Networks, Graphical Gaussian models, Weight Matrices, Reverse Engineering Approach, Evolutionary Algorithms, Forward Modeling Approach, Deterministic models, Static models, Hybrid models, Stochastic models, Petri Nets, BioAmbients calculus and Differential Equations.

RESULTS

GRN and PPI methods have been already applied in various clinical processes with potential positive results, establishing promising diagnostic tools.

CONCLUSION

In literature many stochastic algorithms are focused in the simulation, analysis and visualization of the various biological networks and their dynamics interactions, which are referred and described in depth in this review paper.