Entropic control of the free-energy landscape of an archetypal biomolecular machine.

Biomolecular machines are complex macromolecular assemblies that utilize thermal and chemical energy to perform essential, multistep, cellular processes. Despite possessing different architectures and functions, an essential feature of the mechanisms of action of all such machines is that they require dynamic rearrangements of structural components. Surprisingly, biomolecular machines generally possess only a limited set of such motions, suggesting that these dynamics must be repurposed to drive different mechanistic steps. Although ligands that interact with these machines are known to drive such repurposing, the physical and structural mechanisms through which ligands achieve this remain unknown. Using temperature-dependent, single-molecule measurements analyzed with a time-resolution-enhancing algorithm, here, we dissect the free-energy landscape of an archetypal biomolecular machine, the bacterial ribosome, to reveal how its dynamics are repurposed to drive distinct steps during ribosome-catalyzed protein synthesis. Specifically, we show that the free-energy landscape of the ribosome encompasses a network of allosterically coupled structural elements that coordinates the motions of these elements. Moreover, we reveal that ribosomal ligands which participate in disparate steps of the protein synthesis pathway repurpose this network by differentially modulating the structural flexibility of the ribosomal complex (i.e., the entropic component of the free-energy landscape). We propose that such ligand-dependent entropic control of free-energy landscapes has evolved as a general strategy through which ligands may regulate the functions of all biomolecular machines. Such entropic control is therefore an important driver in the evolution of naturally occurring biomolecular machines and a critical consideration for the design of synthetic molecular machines.

Increasing the accuracy of single-molecule data analysis using tMAVEN.

Time-dependent single-molecule experiments contain rich kinetic information about the functional dynamics of biomolecules. A key step in extracting this information is the application of kinetic models, such as hidden Markov models (HMMs), which characterize the molecular mechanism governing the experimental system. Unfortunately, researchers rarely know the physicochemical details of this molecular mechanism a priori, which raises questions about how to select the most appropriate kinetic model for a given single-molecule data set and what consequences arise if the wrong model is chosen. To address these questions, we have developed and used time-series modeling, analysis, and visualization environment (tMAVEN), a comprehensive, open-source, and extensible software platform. tMAVEN can perform each step of the single-molecule analysis pipeline, from preprocessing to kinetic modeling to plotting, and has been designed to enable the analysis of a single-molecule data set with multiple types of kinetic models. Using tMAVEN, we have systematically investigated mismatches between kinetic models and molecular mechanisms by analyzing simulated examples of prototypical single-molecule data sets exhibiting common experimental complications, such as molecular heterogeneity, with a series of different types of HMMs. Our results show that no single kinetic modeling strategy is mathematically appropriate for all experimental contexts. Indeed, HMMs only correctly capture the underlying molecular mechanism in the simplest of cases. As such, researchers must modify HMMs using physicochemical principles to avoid the risk of missing the significant biological and biophysical insights into molecular heterogeneity that their experiments provide. By enabling the facile, side-by-side application of multiple types of kinetic models to individual single-molecule data sets, tMAVEN allows researchers to carefully tailor their modeling approach to match the complexity of the underlying biomolecular dynamics and increase the accuracy of their single-molecule data analyses.

Insights on heterogeneity in blinking mechanisms and non-ergodicity using sub-ensemble statistical analysis of single quantum-dots.

Photo-luminescence (P-L) intermittency (or blinking) in semiconductor nanocrystals (NCs), a phenomenon ubiquitous to single-emitters, is generally considered to be temporally random intensity fluctuations between "bright" ("On") and "dark" ("Off") states. However, individual quantum-dots (QDs) rarely exhibit such telegraphic signals, and yet, a vast majority of single-NC blinking data are analyzed using a single fixed threshold which generates binary trajectories. Furthermore, while blinking dynamics can vary dramatically over NCs in the ensemble, the extent of diversity in the exponents (mOn/Off) of single-particle On-/Off-time distributions (P(tOn/Off)), often used to validate mechanistic models of blinking, remains unclear due to a lack of statistically relevant data sets. Here, we subclassify an ensemble of QDs based on the emissivity of each emitter and subsequently compare the (sub)ensembles' behaviors. To achieve this, we analyzed a large number (>1000) of blinking trajectories for a model system, Mn+2 doped ZnCdS QDs, which exhibits diverse blinking dynamics. An intensity histogram dependent thresholding method allowed us to construct distributions of relevant blinking parameters (such as mOn/Off). Interestingly, we find that single QD P(tOn/Off)s follow either truncated power law or power law, and their relative proportion varies over subpopulations. Our results reveal a remarkable variation in mOn/Off amongst as well as within subensembles, which implies multiple blinking mechanisms being operational amongst various QDs. We further show that the mOn/Off obtained via cumulative single-particle P(tOn/Off) is distinct from the weighted mean value of all single-particle mOn/Off, evidence for the lack of ergodicity. Thus, investigation and analyses of a large number of QDs, albeit for a limited time span of a few decades, are crucial to characterize the spatial heterogeneity in possible blinking mechanisms.

Increasing the accuracy of single-molecule data analysis using tMAVEN.

Time-dependent single-molecule experiments contain rich kinetic information about the functional dynamics of biomolecules. A key step in extracting this information is the application of kinetic models, such as hidden Markov models (HMMs), which characterize the molecular mechanism governing the experimental system. Unfortunately, researchers rarely know the physico-chemical details of this molecular mechanism a priori, which raises questions about how to select the most appropriate kinetic model for a given single-molecule dataset and what consequences arise if the wrong model is chosen. To address these questions, we have developed and used time-series Modeling, Analysis, and Visualization ENvironment (tMAVEN), a comprehensive, open-source, and extensible software platform. tMAVEN can perform each step of the single-molecule analysis pipeline, from pre-processing to kinetic modeling to plotting, and has been designed to enable the analysis of a single-molecule dataset with multiple types of kinetic models. Using tMAVEN, we have systematically investigated mismatches between kinetic models and molecular mechanisms by analyzing simulated examples of prototypical single-molecule datasets exhibiting common experimental complications, such as molecular heterogeneity, with a series of different types of HMMs. Our results show that no single kinetic modeling strategy is mathematically appropriate for all experimental contexts. Indeed, HMMs only correctly capture the underlying molecular mechanism in the simplest of cases. As such, researchers must modify HMMs using physico-chemical principles to avoid the risk of missing the significant biological and biophysical insights into molecular heterogeneity that their experiments provide. By enabling the facile, side-by-side application of multiple types of kinetic models to individual single-molecule datasets, tMAVEN allows researchers to carefully tailor their modeling approach to match the complexity of the underlying biomolecular dynamics and increase the accuracy of their single-molecule data analyses.

RNA adapts its flexibility to efficiently fold and resist unfolding.

Recent studies have demonstrated that the mechanisms through which biopolymers like RNA interconvert between multiple folded structures are critical for their cellular functions. A major obstacle to elucidating these mechanisms is the lack of experimental approaches that can resolve these interconversions between functionally relevant biomolecular structures. Here, using a nano-electronic device with microsecond time resolution, we dissect the complete set of structural rearrangements executed by an ultra-stable RNA, the UUCG stem-loop, at the single-molecule level. We show that the stem-loop samples at least four conformations along two folding pathways leading to two distinct folded structures, only one of which has been previously observed. By modulating its flexibility, the stem-loop can adaptively select between these pathways, enabling it to both fold rapidly and resist unfolding. This paradigm of stabilization through compensatory changes in flexibility broadens our understanding of stable RNA structures and is expected to serve as a general strategy employed by all biopolymers.

Inferring the shape of data: a probabilistic framework for analysing experiments in the natural sciences.

A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional molecular spectra or emitters in fluorescence microscopy images. Identifying such features involves determining if the overall shape of the data is consistent with an expected shape; however, it is generally unclear how to quantitatively make this determination. In practice, many analysis methods employ subjective, heuristic approaches, which complicates the validation of any ensuing results-especially as the amount and dimensionality of the data increase. Here, we present a probabilistic solution to this problem by using Bayes' rule to calculate the probability that the data have any one of several potential shapes. This probabilistic approach may be used to objectively compare how well different theories describe a dataset, identify changes between datasets and detect features within data using a corollary method called Bayesian Inference-based Template Search; several proof-of-principle examples are provided. Altogether, this mathematical framework serves as an automated 'engine' capable of computationally executing analysis decisions currently made by visual inspection across the sciences.

Bayesian Inference: The Comprehensive Approach to Analyzing Single-Molecule Experiments.

Biophysics experiments performed at single-molecule resolution provide exceptional insight into the structural details and dynamic behavior of biological systems. However, extracting this information from the corresponding experimental data unequivocally requires applying a biophysical model. In this review, we discuss how to use probability theory to apply these models to single-molecule data. Many current single-molecule data analysis methods apply parts of probability theory, sometimes unknowingly, and thus miss out on the full set of benefits provided by this self-consistent framework. The full application of probability theory involves a process called Bayesian inference that fully accounts for the uncertainties inherent to single-molecule experiments. Additionally, using Bayesian inference provides a scientifically rigorous method of incorporating information from multiple experiments into a single analysis and finding the best biophysical model for an experiment without the risk of overfitting the data. These benefits make the Bayesian approach ideal for analyzing any type of single-molecule experiment.

Investigation of Structural Heterogeneity in Individual Amyloid Fibrils Using Polarization-Resolved Microscopy.

Amyloid fibrils are structurally heterogeneous protein aggregates that are implicated in a wide range of neurodegenerative and other proteopathic diseases. These fibrils exist in a variety of different tertiary and higher-level structures, and this exhibited polymorphism greatly complicates any structural study of amyloid fibrils. In this work, we demonstrate a method of using polarization-resolved microscopy to directly observe the structural heterogeneity of individual amyloid fibrils using amyloid-bound fluorophores. We formulate a mathematical quantity, helical anisotropy, which utilizes the polarized emission of amyloid-bound fluorophores to report on the local structure of individual fibrils. Using this method, we show how model amyloid fibrils generated from short peptides exhibit diverse structural properties both between different fibrils and within a single fibril, in a manner that is replicated for fibrils assembled from longer proteins. Our method represents an accessible and easily adaptable technique by which polymorphism in the structure of amyloid fibrils can be probed. Additionally, the methodology we describe here can be easily extended to the study of other fibrillar and otherwise ordered supramolecular structures.

Mathematical Characterization of Protein Sequences Using Patterns as Chemical Group Combinations of Amino Acids.

Comparison of amino acid sequence similarity is the fundamental concept behind the protein phylogenetic tree formation. By virtue of this method, we can explain the evolutionary relationships, but further explanations are not possible unless sequences are studied through the chemical nature of individual amino acids. Here we develop a new methodology to characterize the protein sequences on the basis of the chemical nature of the amino acids. We design various algorithms for studying the variation of chemical group transitions and various chemical group combinations as patterns in the protein sequences. The amino acid sequence of conventional myosin II head domain of 14 family members are taken to illustrate this new approach. We find two blocks of maximum length 6 aa as 'FPKATD' and 'Y/FTNEKL' without repeating the same chemical nature and one block of maximum length 20 aa with the repetition of chemical nature which are common among all 14 members. We also check commonality with another motor protein sub-family kinesin, KIF1A. Based on our analysis we find a common block of length 8 aa both in myosin II and KIF1A. This motif is located in the neck linker region which could be responsible for the generation of mechanical force, enabling us to find the unique blocks which remain chemically conserved across the family. We also validate our methodology with different protein families such as MYOI, Myosin light chain kinase (MLCK) and Rho-associated protein kinase (ROCK), Na+/K+-ATPase and Ca2+-ATPase. Altogether, our studies provide a new methodology for investigating the conserved amino acids' pattern in different proteins.