Moderate activity of RNA chaperone maximizes the yield of self-spliced pre-RNA in vivo.

CYT-19 is a DEAD-box protein whose adenosine-triphosphate (ATP)-dependent helicase activity facilitates the folding of group I introns in precursor RNA (pre-RNA) of Neurospora crassa (N. crassa). In the process, they consume a substantial amount of ATP. While much of the mechanistic insight into CYT-19 activity has been gained through the studies on the folding of Tetrahymena group I intron ribozyme, the more biologically relevant issue, namely the effect of CYT-19 on the self-splicing of pre-RNA, remains largely unexplored. Here, we employ a kinetic network model, based on the generalized iterative annealing mechanism (IAM), to investigate the relation between CYT-19 activity, rate of ribozyme folding, and the kinetics of the self-splicing reaction. The network rate parameters are extracted by analyzing the recent biochemical data for CYT-19-facilitated folding of Tetrahymena ribozyme. We then build extended models to explore the metabolism of pre-RNA. We show that the timescales of chaperone-mediated folding of group I ribozyme and self-splicing reaction compete with each other. As a consequence, in order to maximize the self-splicing yield of group I introns in pre-RNA, the chaperone activity must be sufficiently large to unfold the misfolded structures, but not too large to unfold the native structures prior to the self-splicing event. We discover that despite the promiscuous action on structured RNAs, the helicase activity of CYT-19 on group I ribozyme gives rise to self-splicing yields that are close to the maximum.

Hi-C-guided many-polymer model to decipher 3D genome organization.

We propose a high-throughput chromosome conformation capture data-based many-polymer model that allows us to generate an ensemble of multi-scale genome structures. We demonstrate the efficacy of our model by validating the generated structures against experimental measurements and employ them to address key questions regarding genome organization. Our model first confirms a significant correlation between chromosome size and nuclear positioning. Specifically, smaller chromosomes are distributed at the core region, whereas larger chromosomes are at the periphery, interacting with the nuclear envelope. The spatial distribution of A- and B-type compartments, which is nontrivial to infer from the corresponding high-throughput chromosome conformation capture maps alone, can also be elucidated using our model, accounting for an issue such as the effect of chromatin-lamina interaction on the compartmentalization of conventional and inverted nuclei. In accordance with imaging data, the overall shape of the 3D genome structures generated from our model displays significant variation. As a case study, we apply our method to the yellow fever mosquito genome, finding that the predicted morphology displays, on average, a more globular shape than the previously suggested spindle-like organization and that our prediction better aligns with the fluorescence in situ hybridization data. Our model has great potential to be extended to investigate many outstanding issues concerning 3D genome organization.

Water Hydrogen-Bond Mediated Layer by Layer Alignment of Lipid Rafts as a Precursor of Intermembrane Processes.

Lipid rafts, which are dynamic nanodomains in the plasma membrane, play a crucial role in intermembrane processes by clustering together and growing in size within the plane of the membrane while also aligning with each other across different membranes. However, the physical origin of layer by layer alignment of lipid rafts remains to be elucidated. Here, by using fluorescence imaging and synchrotron X-ray reflectivity in a phase-separated multilayer system, we find that the alignment of raft-mimicking Lo domains is regulated by the distance between bilayers. Molecular dynamics simulations reveal that the aligned state is energetically preferred when the intermembrane distance is small due to its ability to minimize the volume of surface water, which has fewer water hydrogen bonds (HBs) compared to bulk water. Our results suggest that water HB-driven alignment of lipid rafts plays a role as a precursor of intermembrane processes such as cell-cell fusion, virus entry, and signaling.

Location of the TEMPO moiety of TEMPO-PC in phosphatidylcholine bilayers is membrane phase dependent.

The (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) moiety tethered to the headgroup of phosphatidylcholine (PC) lipid is employed in spin labeling electron paramagnetic resonance spectroscopy to probe the water dynamics near lipid bilayer interfaces. Due to its amphiphilic character, however, TEMPO spin label could partition between aqueous and lipid phases, and may even be stabilized in the lipid phase. Accurate assessment of the TEMPO-PC configuration in bilayer membranes is essential for correctly interpreting the data from measurements. Here, we carry out all-atom molecular dynamics (MD) simulations of TEMPO-PC probe in single-component lipid bilayers at varying temperatures, using two standard MD force fields. We find that, for a dipalmitoylphosphatidylcholine (DPPC) membrane whose gel-to-fluid lipid phase transition occurs at 314 K, while the TEMPO spin label is stabilized above the bilayer interface in the gel phase, there is a preferential location of TEMPO below the membrane interface in the fluid phase. For bilayers made of unsaturated lipids, 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), which adopt the fluid phase at ambient temperature, TEMPO is unequivocally stabilized inside the bilayers. Our finding of membrane phase-dependent positioning of the TEMPO moiety highlights the importance of assessing the packing order and fluidity of lipids under a given measurement condition.

Dissecting the cosegregation probability from genome architecture mapping.

Genome architecture mapping (GAM) is a recently developed methodology that offers the cosegregation probability of two genomic segments from an ensemble of thinly sliced nuclear profiles, enabling us to probe and decipher three-dimensional chromatin organization. The cosegregation probability from GAM binned at 1 Mb, which thus probes the length scale associated with the genomic separation greater than 1 Mb, is, however, not identical to the contact probability obtained from Hi-C, and its correlation with interlocus distance measured with fluorescence in situ hybridization is not so good as the contact probability. In this study, by using a polymer-based model of chromatins, we derive a theoretical expression of the cosegregation probability as well as that of the contact probability and carry out quantitative analyses of how they differ from each other. The results from our study, validated with in silico GAM analysis on three-dimensional genome structures from fluorescence in situ hybridization, suggest that to attain strong correlation with the interlocus distance, a properly normalized version of cosegregation probability needs to be calculated based on a large number of nuclear slices (n>103).

Extracting multi-way chromatin contacts from Hi-C data.

There is a growing realization that multi-way chromatin contacts formed in chromosome structures are fundamental units of gene regulation. However, due to the paucity and complexity of such contacts, it is challenging to detect and identify them using experiments. Based on an assumption that chromosome structures can be mapped onto a network of Gaussian polymer, here we derive analytic expressions for n-body contact probabilities (n > 2) among chromatin loci based on pairwise genomic contact frequencies available in Hi-C, and show that multi-way contact probability maps can in principle be extracted from Hi-C. The three-body (triplet) contact probabilities, calculated from our theory, are in good correlation with those from measurements including Tri-C, MC-4C and SPRITE. Maps of multi-way chromatin contacts calculated from our analytic expressions can not only complement experimental measurements, but also can offer better understanding of the related issues, such as cell-line dependent assemblies of multiple genes and enhancers to chromatin hubs, competition between long-range and short-range multi-way contacts, and condensates of multiple CTCF anchors.

A unified framework for inferring the multi-scale organization of chromatin domains from Hi-C.

Chromosomes are giant chain molecules organized into an ensemble of three-dimensional structures characterized with its genomic state and the corresponding biological functions. Despite the strong cell-to-cell heterogeneity, the cell-type specific pattern demonstrated in high-throughput chromosome conformation capture (Hi-C) data hints at a valuable link between structure and function, which makes inference of chromatin domains (CDs) from the pattern of Hi-C a central problem in genome research. Here we present a unified method for analyzing Hi-C data to determine spatial organization of CDs over multiple genomic scales. By applying statistical physics-based clustering analysis to a polymer physics model of the chromosome, our method identifies the CDs that best represent the global pattern of correlation manifested in Hi-C. The multi-scale intra-chromosomal structures compared across different cell types uncover the principles underlying the multi-scale organization of chromatin chain: (i) Sub-TADs, TADs, and meta-TADs constitute a robust hierarchical structure. (ii) The assemblies of compartments and TAD-based domains are governed by different organizational principles. (iii) Sub-TADs are the common building blocks of chromosome architecture. Our physically principled interpretation and analysis of Hi-C not only offer an accurate and quantitative view of multi-scale chromatin organization but also help decipher its connections with genome function.

Revisiting the organization of Polycomb-repressed domains: 3D chromatin models from Hi-C compared with super-resolution imaging.

The accessibility of target gene, a factor critical for gene regulation, is controlled by epigenetic fine-tuning of chromatin organization. While there are multiple experimental techniques to study change of chromatin architecture with its epigenetic state, measurements from them are not always complementary. A qualitative discrepancy is noted between recent super-resolution imaging studies, particularly on Polycomb-group protein repressed domains in Drosophila cell. One of the studies shows that Polycomb-repressed domains are more compact than inactive domains and are segregated from neighboring active domains, whereas Hi-C and chromatin accessibility assay as well as the other super-resolution imaging studies paint a different picture. To examine this issue in detail, we analyzed Hi-C libraries of Drosophila chromosomes as well as distance constraints from one of the imaging studies, and modeled different epigenetic domains by employing a polymer-based approach. According to our chromosome models, both Polycomb-repressed and inactive domains are featured with a similar degree of intra-domain packaging and significant intermixing with adjacent active domains. The epigenetic domains explicitly visualized by our polymer model call for extra attention to the discrepancy of the super-resolution imaging with other measurements, although its precise physicochemical origin still remains to be elucidated.

Symmetry, Rigidity, and Allosteric Signaling: From Monomeric Proteins to Molecular Machines.

Allosteric signaling in biological molecules, which may be viewed as specific action at a distance due to localized perturbation upon binding of ligands or changes in environmental cues, is pervasive in biology. Insightful phenomenological Monod, Wyman, and Changeux (MWC) and Koshland, Nemethy, and Filmer (KNF) models galvanized research in describing allosteric transitions for over five decades, and these models continue to be the basis for describing the mechanisms of allostery in a bewildering array of systems. However, understanding allosteric signaling and the associated dynamics between distinct allosteric states at the molecular level is challenging and requires novel experiments complemented by computational studies. In this review, we first describe symmetry and rigidity as essential requirements for allosteric proteins or multisubunit structures. The general features, with MWC and KNF as two extreme scenarios, emerge when allosteric signaling is viewed from an energy landscape perspective. To go beyond the general theories, we describe computational tools that are either based solely on multiple sequences or their structures to predict the allostery wiring diagram. These methods could be used to predict the network of residues that carry allosteric signals. Methods to obtain molecular insights into the dynamics of allosteric transitions are briefly mentioned. The utility of the methods is illustrated by applications to systems ranging from monomeric proteins in which there is little conformational change in the transition between two allosteric states to membrane bound G-protein coupled receptors and multisubunit proteins. Finally, the role allostery plays in the functions of ATP-consuming molecular machines, bacterial chaperonin GroEL and molecular motors, is described. Although universal molecular principles governing allosteric signaling do not exist, we can draw the following general conclusions from a survey of different systems. (1) Multiple pathways connecting allosteric states are highly heterogeneous. (2) Allosteric signaling is exquisitely sensitive to the specific architecture of the system, which implies that the capacity for allostery is encoded in the structure itself. (3) The mechanical modes that connect distinct allosteric states are robust to sequence variations. (4) Extensive investigations of allostery in Hemoglobin and, more recently GroEL, show that to a large extent a network of salt bridge rearrangements serves as allosteric switches. In both these examples the dynamical changes in the allosteric switches are related to function.

Thermodynamic uncertainty relation to assess biological processes.

We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states and discuss how optimal these processes are in light of the universal bound set by the thermodynamic uncertainty relation (TUR). The values of the uncertainty product Q of TUR, which can be used as a measure of the precision of enzymatic processes realized for a given thermodynamic cost, are suboptimal when the substrate concentration is at the Michaelis constant, and some of the key biological processes are found to work around this condition. We illustrate the utility of Q in assessing how close the molecular motors and biomass producing machineries are to the TUR bound, and for the cases of biomass production (or biological copying processes), we discuss how their optimality quantified in terms of Q is balanced with the error rate in the information transfer process. We also touch upon the trade-offs in other error-minimizing processes in biology, such as gene regulation and chaperone-assisted protein folding. A spectrum of Q recapitulating the biological processes surveyed here provides glimpses into how biological systems are evolved to optimize and balance the conflicting functional requirements.

Polymer brush-induced depletion interactions and clustering of membrane proteins.

We investigate the effect of mobile polymer brushes on proteins embedded in biological membranes by employing both Asakura-Oosawa type of theoretical model and coarse-grained molecular dynamics simulations. The brush polymer-induced depletion attraction between proteins changes non-monotonically with the size of brush. The depletion interaction, which is determined by the ratio of the protein size to the grafting distance between brush polymers, increases linearly with the brush size as long as the polymer brush height is shorter than the protein size. When the brush height exceeds the protein size, however, the depletion attraction among proteins is slightly reduced. We also explore the possibility of the brush polymer-induced assembly of a large protein cluster, which can be related to one of many molecular mechanisms underlying recent experimental observations of integrin nanocluster formation and signaling.

Time-evolving genetic networks reveal a NAC troika that negatively regulates leaf senescence in Arabidopsis.

Senescence is controlled by time-evolving networks that describe the temporal transition of interactions among senescence regulators. Here, we present time-evolving networks for NAM/ATAF/CUC (NAC) transcription factors in Arabidopsis during leaf aging. The most evident characteristic of these time-dependent networks was a shift from positive to negative regulation among NACs at a presenescent stage. ANAC017, ANAC082, and ANAC090, referred to as a "NAC troika," govern the positive-to-negative regulatory shift. Knockout of the NAC troika accelerated senescence and the induction of other NACs, whereas overexpression of the NAC troika had the opposite effects. Transcriptome and molecular analyses revealed shared suppression of senescence-promoting processes by the NAC troika, including salicylic acid (SA) and reactive oxygen species (ROS) responses, but with predominant regulation of SA and ROS responses by ANAC090 and ANAC017, respectively. Our time-evolving networks provide a unique regulatory module of presenescent repressors that direct the timely induction of senescence-promoting processes at the presenescent stage of leaf aging.

Increased Confinement and Polydispersity of STIM1 and Orai1 after Ca2+ Store Depletion.

STIM1 (a Ca2+ sensor in the endoplasmic reticulum (ER) membrane) and Orai1 (a pore-forming subunit of the Ca2+-release-activated calcium channel in the plasma membrane) diffuse in the ER membrane and plasma membrane, respectively. Upon depletion of Ca2+ stores in the ER, STIM1 translocates to the ER-plasma membrane junction and binds Orai1 to trigger store-operated Ca2+ entry. However, the motion of STIM1 and Orai1 during this process and its roles to Ca2+ entry is poorly understood. Here, we report real-time tracking of single STIM1 and Orai1 particles in the ER membrane and plasma membrane in living cells before and after Ca2+ store depletion. We found that the motion of single STIM1 and Orai1 particles exhibits anomalous diffusion both before and after store depletion, and their mobility-measured by the radius of gyration of the trajectories, mean-square displacement, and generalized diffusion coefficient-decreases drastically after store depletion. We also found that the measured displacement distribution is non-Gaussian, and the non-Gaussian parameter drastically increases after store depletion. Detailed analyses and simulations revealed that single STIM1 and Orai1 particles are confined in the compartmentalized membrane both before and after store depletion, and the changes in the motion after store depletion are explained by increased confinement and polydispersity of STIM1-Orai1 complexes formed at the ER-plasma membrane junctions. Further simulations showed that this increase in the confinement and polydispersity after store depletion localizes a rapid increase of Ca2+ influx, which can facilitate the rapid activation of local Ca2+ signaling pathways and the efficient replenishing of Ca2+ store in the ER in store-operated Ca2+ entry.

Water-mediated biomolecular dynamics and allostery.

Dynamic coupling with water contributes to regulating the functional dynamics of a biomolecule. We discuss protein-water dynamics, with emphasis on water that is partially confined, and the role of protein-confined water dynamics in allosteric regulation. These properties are illustrated with two systems, a homodimeric hemoglobin from Scapharca inaequivalvis (HbI) and an A2A adenosine receptor (A2AAR). For HbI, water-protein interactions, long known to contribute to the thermodynamics of cooperativity, are seen to influence the dynamics of the protein not only around the protein-water interface but also into the core of each globule, where dynamic and entropic changes upon ligand binding are coupled to protein-water contact dynamics. Similarly, hydration waters trapped deep inside the core region of A2AAR enable the formation of an allosteric network made of water-mediated inter-residue contacts. Extending from the ligand binding pocket to the G-protein binding site, this allosteric network plays key roles in regulating the activity of the receptor.

Molecular chaperones maximize the native state yield on biological times by driving substrates out of equilibrium.

Molecular chaperones facilitate the folding of proteins and RNA in vivo. Under physiological conditions, the in vitro folding of Tetrahymena ribozyme by the RNA chaperone CYT-19 behaves paradoxically; increasing the chaperone concentration reduces the yield of native ribozymes. In contrast, the protein chaperone GroEL works as expected; the yield of the native substrate increases with chaperone concentration. The discrepant chaperone-assisted ribozyme folding thus contradicts the expectation that it operates as an efficient annealing machine. To resolve this paradox, we propose a minimal stochastic model based on the Iterative Annealing Mechanism (IAM) that offers a unified description of chaperone-mediated folding of both proteins and RNA. Our theory provides a general relation that quantitatively predicts how the yield of native states depends on chaperone concentration. Although the absolute yield of native states decreases in the Tetrahymena ribozyme, the product of the folding rate and the steady-state native yield increases in both cases. By using energy from ATP hydrolysis, both CYT-19 and GroEL drive their substrate concentrations far out of equilibrium, thus maximizing the native yield in a short time. This also holds when the substrate concentration exceeds that of GroEL. Our findings satisfy the expectation that proteins and RNA be folded by chaperones on biologically relevant time scales, even if the final yield is lower than what equilibrium thermodynamics would dictate. The theory predicts that the quantity of chaperones in vivo has evolved to optimize native state production of the folded states of RNA and proteins in a given time.

Compressing Θ-Chain in Slit Geometry.

When compressed in a slit of width D, a Θ-chain that displays the scaling of size R0 (diameter) with respect to the number of monomers N, R0 ∼ aN1/2, expands in the lateral direction as R|| ∼ aNν(a/D)2ν-1. Provided that the Θ condition is strictly maintained throughout the compression, the well-known scaling exponent of Θ-chain in two dimensions, ν = 4/7, is anticipated in a perfect confinement. However, numerics shows that upon increasing compression from R0/D < 1 to R0/D ≫ 1, ν gradually deviates from ν = 1/2 and plateaus at ν = 3/4, the exponent associated with the self-avoiding walk in two dimensions. Using both theoretical considerations and numerics, we argue that it is highly nontrivial to maintain the Θ condition under confinement because of two major effects. First, as the dimension is reduced from three to two dimensions, the contributions of higher order virial terms, which can be ignored in three dimensions at large N, become significant, making the perturbative expansion used in Flory-type approach inherently problematic. Second and more importantly, the geometrical confinement, which is regarded as an applied external field, alters the second virial coefficient (B2) changes from B2 = 0 (Θ condition) in free space to B2 > 0 (good-solvent condition) in confinement. Our study provides practical insight into how confinement affects the conformation of a single polymer chain.

Heterogeneous Loop Model to Infer 3D Chromosome Structures from Hi-C.

Adapting a well-established formalism in polymer physics, we develop a minimalist approach to infer three-dimensional folding of chromatin from Hi-C data. The three-dimensional chromosome structures generated from our heterogeneous loop model (HLM) are used to visualize chromosome organizations that can substantiate the measurements from fluorescence in situ hybridization, chromatin interaction analysis by paired-end tag sequencing, and RNA-seq signals. We demonstrate the utility of the HLM with several case studies. Specifically, the HLM-generated chromosome structures, which reproduce the spatial distribution of topologically associated domains from fluorescence in situ hybridization measurement, show the phase segregation between two types of topologically associated domains explicitly. We discuss the origin of cell-type-dependent gene-expression level by modeling the chromatin globules of α-globin and SOX2 gene loci for two different cell lines. We also use the HLM to discuss how the chromatin folding and gene-expression level of Pax6 loci, associated with mouse neural development, are modulated by interactions with two enhancers. Finally, HLM-generated structures of chromosome 19 of mouse embryonic stem cells, based on single-cell Hi-C data collected over each cell-cycle phase, visualize changes in chromosome conformation along the cell-cycle. Given a contact frequency map between chromatic loci supplied from Hi-C, HLM is a computationally efficient and versatile modeling tool to generate chromosome structures that can complement interpreting other experimental data.

Heterogeneity in kinesin function.

The kinesin family proteins are often studied as prototypical molecular motors; a deeper understanding of them can illuminate regulation of intracellular transport. It is typically assumed that they function identically. Here we find that this assumption of homogeneous function appears incorrect: variation among motors' velocities in vivo and in vitro is larger than the stochastic variation expected for an ensemble of "identical" motors. When moving on microtubules, slow and fast motors are persistently slow, and fast, respectively. We develop theory that provides quantitative criteria to determine whether the observed single-molecule variation is too large to be generated from an ensemble of identical molecules. To analyze such heterogeneity, we group traces into homogeneous sub-ensembles. Motility studies varying the temperature, pH and glycerol concentration suggest at least 2 distinct functional states that are independently affected by external conditions. We end by investigating the functional ramifications of such heterogeneity through Monte-Carlo multi-motor simulations.

Chain organization of human interphase chromosome determines the spatiotemporal dynamics of chromatin loci.

We investigate spatiotemporal dynamics of human interphase chromosomes by employing a heteropolymer model that incorporates the information of human chromosomes inferred from Hi-C data. Despite considerable heterogeneities in the chromosome structures generated from our model, chromatins are organized into crumpled globules with space-filling (SF) statistics characterized by a single universal scaling exponent (ν = 1/3), and this exponent alone can offer a quantitative account of experimentally observed, many different features of chromosome dynamics. The local chromosome structures, whose scale corresponds to that of topologically associated domains (∼ 0.1 - 1 Mb), display dynamics with a fast relaxation time (≲ 1 - 10 sec); in contrast, the long-range spatial reorganization of the entire chromatin ([Formula: see text] Mb) occurs on a much slower time scale (≳ hour), providing the dynamic basis of cell-to-cell variability and glass-like behavior of chromosomes. Biological activities, modeled using stronger isotropic white noises added to active loci, accelerate the relaxation dynamics of chromatin domains associated with the low frequency modes and induce phase segregation between the active and inactive loci. Surprisingly, however, they do not significantly change the dynamics at local scales from those obtained under passive conditions. Our study underscores the role of chain organization of chromosome in determining the spatiotemporal dynamics of chromatin loci.

Implications for human odor sensing revealed from the statistics of odorant-receptor interactions.

Binding of odorants to olfactory receptors (ORs) elicits downstream chemical and neural signals, which are further processed to odor perception in the brain. Recently, Mainland and colleagues have measured more than 500 pairs of odorant-OR interaction by a high-throughput screening assay method, opening a new avenue to understanding the principles of human odor coding. Here, using a recently developed minimal model for OR activation kinetics, we characterize the statistics of OR activation by odorants in terms of three empirical parameters: the half-maximum effective concentration EC50, the efficacy, and the basal activity. While the data size of odorants is still limited, the statistics offer meaningful information on the breadth and optimality of the tuning of human ORs to odorants, and allow us to relate the three parameters with the microscopic rate constants and binding affinities that define the OR activation kinetics. Despite the stochastic nature of the response expected at individual OR-odorant level, we assess that the confluence of signals in a neuron released from the multitude of ORs is effectively free of noise and deterministic with respect to changes in odorant concentration. Thus, setting a threshold to the fraction of activated OR copy number for neural spiking binarizes the electrophysiological signal of olfactory sensory neuron, thereby making an information theoretic approach a viable tool in studying the principles of odor perception.