Fibrils connect microtubule tips with kinetochores: a mechanism to couple tubulin dynamics to chromosome motion.

Kinetochores of mitotic chromosomes are coupled to spindle microtubules in ways that allow the energy from tubulin dynamics to drive chromosome motion. Most kinetochore-associated microtubule ends display curving "protofilaments," strands of tubulin dimers that bend away from the microtubule axis. Both a kinetochore "plate" and an encircling, ring-shaped protein complex have been proposed to link protofilament bending to poleward chromosome motion. Here we show by electron tomography that slender fibrils connect curved protofilaments directly to the inner kinetochore. Fibril-protofilament associations correlate with a local straightening of the flared protofilaments. Theoretical analysis reveals that protofilament-fibril connections would be efficient couplers for chromosome motion, and experimental work on two very different kinetochore components suggests that filamentous proteins can couple shortening microtubules to cargo movements. These analyses define a ring-independent mechanism for harnessing microtubule dynamics directly to chromosome movement.

Modulating binding affinity, specificity, and configurations by multivalent interactions.

Biological functions of proteins rely on their specific interactions with binding partners. Many proteins contain multiple domains, which can bind to their targets that often have more than one binding site, resulting in multivalent interactions. While it has been shown that multivalent interactions play a crucial role in modulating binding affinity and specificity, other potential effects of multivalent interactions are less explored. Here, we developed a broadly applicable transfer-matrix formalism and used it to investigate the binding of two-domain ligands to targets with multiple binding sites. We show that 1) ligands with two specific binding domains can drastically boost both the binding affinity and specificity and downshift the working concentration range, compared with single-domain ligands, 2) the presence of a positive domain-domain cooperativity or containing a nonspecific binding domain can downshift the working concentration range of ligands by increasing the binding affinity without compromising the binding specificity, and 3) the configuration of the bound ligands has a strong concentration dependence, providing important insights into the physical origin of phase-separation processes taking place in living cells. In line with previous studies, our results suggest that multivalent interactions are utilized by cells for highly efficient regulation of target binding involved in a diverse range of cellular processes such as signal transduction, gene transcription, and antibody-antigen recognition.

Nucleus size and its effect on nucleosome stability in living cells.

DNA architectural proteins play a major role in organization of chromosomal DNA in living cells by packaging it into chromatin, whose spatial conformation is determined by an intricate interplay between the DNA-binding properties of architectural proteins and physical constraints applied to the DNA by a tight nuclear space. Yet, the exact effects of the nucleus size on DNA-protein interactions and chromatin structure currently remain obscure. Furthermore, there is even no clear understanding of molecular mechanisms responsible for the nucleus size regulation in living cells. To find answers to these questions, we developed a general theoretical framework based on a combination of polymer field theory and transfer-matrix calculations, which showed that the nucleus size is mainly determined by the difference between the surface tensions of the nuclear envelope and the endoplasmic reticulum membrane as well as the osmotic pressure exerted by cytosolic macromolecules on the nucleus. In addition, the model demonstrated that the cell nucleus functions as a piezoelectric element, changing its electrostatic potential in a size-dependent manner. This effect has been found to have a profound impact on stability of nucleosomes, revealing a previously unknown link between the nucleus size and chromatin structure. Overall, our study provides new insights into the molecular mechanisms responsible for regulation of the nucleus size, as well as the potential role of nuclear organization in shaping the cell response to environmental cues.

Effects of size, cooperativity, and competitive binding on protein positioning on DNA.

Accurate positioning of proteins on chromosomal DNA is crucial for its proper organization as well as gene transcription regulation. Recent experiments revealed existence of periodic patterns of nucleoprotein complexes on DNA, which frequently cannot be explained by sequence-dependent binding of proteins. Previous theoretical studies suggest that such patterns typically emerge as a result of the proteins' volume-exclusion effect. However, the role of other physical factors in patterns' formation, such as the length of DNA, its sequence heterogeneity, and protein binding cooperativity/binding competition to DNA, remains unclear. To address these less understood yet important aspects, we investigated potential effects of these factors on protein positioning on finite-size DNA by using transfer-matrix calculations. It has been found that upon binding to DNA, proteins form oscillatory patterns that span over the length of up to ∼10 times the size of the protein binding site, with the shape of the patterns being strongly dependent on the length of DNA and the proteins' binding cooperativity to DNA. Furthermore, calculations showed that small variations in the proteins' affinity to DNA due to its sequence heterogeneity do not much change the main geometric characteristics of the observed protein patterns. Finally, competition between two different types of proteins for binding to DNA has been found to lead to formation of highly diverse and complex alternating positioning of the two proteins. Altogether, these results provide new insights into the roles of physicochemical properties of proteins, the DNA length, and DNA-binding competition between proteins in formation of protein positioning patterns on DNA.

Transfer-matrix calculations of the effects of tension and torque constraints on DNA-protein interactions.

Organization and maintenance of the chromosomal DNA in living cells strongly depends on the DNA interactions with a plethora of DNA-binding proteins. Single-molecule studies show that formation of nucleoprotein complexes on DNA by such proteins is frequently subject to force and torque constraints applied to the DNA. Although the existing experimental techniques allow to exert these type of mechanical constraints on individual DNA biopolymers, their exact effects in regulation of DNA-protein interactions are still not completely understood due to the lack of systematic theoretical methods able to efficiently interpret complex experimental observations. To fill this gap, we have developed a general theoretical framework based on the transfer-matrix calculations that can be used to accurately describe behaviour of DNA-protein interactions under force and torque constraints. Potential applications of the constructed theoretical approach are demonstrated by predicting how these constraints affect the DNA-binding properties of different types of architectural proteins. Obtained results provide important insights into potential physiological functions of mechanical forces in the chromosomal DNA organization by architectural proteins as well as into single-DNA manipulation studies of DNA-protein interactions.

Effects of Mechanical Stimuli on Profilin- and Formin-Mediated Actin Polymerization.

Self-assembling actin filaments not only form the basis of the cytoskeleton network in cells but also are utilized as nanosized building blocks to make novel active matter in which the dynamic polymerization and depolymerization of actin filaments play a key role. Formins belong to a main family of actin nucleation factors that bind to the barbed end of actin filaments and regulate actin polymerization through an interaction with profilin. Due to actomyosin contractility and relative rotation between formin and actin filaments, formin-dependent actin polymerization is subject to force and rotation constraints. However, it remains unclear how force and rotation constraints affect formin-dependent actin polymerization in the presence of profilin. Here, we show that for rotation-unconstrained actin filaments, elongation is accelerated by both force and profilin. The combined effect leads to surprisingly fast actin elongation that can approach the diffusion-limited rate at forces of a few piconewtons. The elongation of rotation-constrained filaments is also accelerated by profilin but is insensitive to applied force. We show that FH2, the main actin binding domain, plays the primary mechanosensing role. Together, the findings not only significantly advance our understanding of the mechanochemical regulation of formin-mediated actin polymerization in cells but also can potentially be utilized to make novel actin-based active matter.

Disturbance-free rapid solution exchange for magnetic tweezers single-molecule studies.

Single-molecule manipulation technologies have been extensively applied to studies of the structures and interactions of DNA and proteins. An important aspect of such studies is to obtain the dynamics of interactions; however the initial binding is often difficult to obtain due to large mechanical perturbation during solution introduction. Here, we report a simple disturbance-free rapid solution exchange method for magnetic tweezers single-molecule manipulation experiments, which is achieved by tethering the molecules inside microwells (typical dimensions-diameter (D): 40-50 µm, height (H): 100 µm; H:D∼2:1). Our simulations and experiments show that the flow speed can be reduced by several orders of magnitude near the bottom of the microwells from that in the flow chamber, effectively eliminating the flow disturbance to molecules tethered in the microwells. We demonstrate a wide scope of applications of this method by measuring the force dependent DNA structural transitions in response to solution condition change, and polymerization dynamics of RecA on ssDNA/SSB-coated ssDNA/dsDNA of various tether lengths under constant forces, as well as the dynamics of vinculin binding to α-catenin at a constant force (< 5 pN) applied to the α-catenin protein.

Delineating cooperative responses of processive motors in living cells.

Characterizing the collective functions of cytoskeletal motors is critical to understanding mechanisms that regulate the internal organization of eukaryotic cells as well as the roles various transport defects play in human diseases. Though in vitro assays using synthetic motor complexes have generated important insights, dissecting collective motor functions within living cells still remains challenging. Here, we show that the protein heterodimerization switches FKBP-rapalog-FRB can be harnessed in engineered COS-7 cells to compare the collective responses of kinesin-1 and myosinVa motors to changes in motor number and cargo size. The dependence of cargo velocities, travel distances, and position noise on these parameters suggests that multiple myosinVa motors can cooperate more productively than collections of kinesins in COS-7 cells. In contrast to observations with kinesin-1 motors, the velocities and run lengths of peroxisomes driven by multiple myosinVa motors are found to increase with increasing motor density, but are relatively insensitive to the higher loads associated with transporting large peroxisomes in the viscoelastic environment of the COS-7 cell cytoplasm. Moreover, these distinctions appear to be derived from the different sensitivities of kinesin-1 and myosinVa velocities and detachment rates to forces at the single-motor level. The collective behaviors of certain processive motors, like myosinVa, may therefore be more readily tunable and have more substantial roles in intracellular transport regulatory mechanisms compared with those of other cytoskeletal motors.

Transcriptional Repressor TrmBL2 from Thermococcus kodakarensis Forms Filamentous Nucleoprotein Structures and Competes with Histones for DNA Binding in a Salt- and DNA Supercoiling-dependent Manner.

Architectural DNA proteins play important roles in the chromosomal DNA organization and global gene regulation in living cells. However, physiological functions of some DNA-binding proteins from archaea remain unclear. Recently, several abundant DNA-architectural proteins including histones, Alba, and TrmBL2 have been identified in model euryarchaeon Thermococcus kodakarensis. Although histones and Alba proteins have been previously characterized, the DNA binding properties of TrmBL2 and its interplay with the other major architectural proteins in the chromosomal DNA organization and gene transcription regulation remain largely unexplored. Here, we report single-DNA studies showing that at low ionic strength (<300 mM KCl), TrmBL2 binds to DNA largely in non-sequence-specific manner with positive cooperativity, resulting in formation of stiff nucleoprotein filamentous patches, whereas at high ionic strength (>300 mM KCl) TrmBL2 switches to more sequence-specific interaction, suggesting the presence of high affinity TrmBL2-filament nucleation sites. Furthermore, in vitro assays indicate the existence of DNA binding competition between TrmBL2 and archaeal histones B from T. kodakarensis, which can be strongly modulated by DNA supercoiling and ionic strength of surrounding solution. Overall, these results advance our understanding of TrmBL2 DNA binding properties and provide important insights into potential functions of architectural proteins in nucleoid organization and gene regulation in T. kodakarensis.

Dynamics and stability of polymorphic human telomeric G-quadruplex under tension.

As critical DNA structures capping the human chromosome ends, the stability and structural polymorphism of human telomeric G-quadruplex (G4) have drawn increasing attention in recent years. This work characterizes the equilibrium transitions of single-molecule telomeric G4 at physiological K(+) concentration. We report three folded states of telomeric G4 with markedly different lifetime and mechanical stability. Our results show that the kinetically favored folding pathway is through a short-lived intermediate state to a longer-lived state. By examining the force dependence of transition rates, the force-dependent transition free energy landscape for this pathway is determined. In addition, an ultra-long-lived form of telomeric G4 structure with a much stronger mechanical stability is identified.

3D nanofabricated soft microrobots with super-compliant picoforce springs as onboard sensors and actuators.

Microscale organisms and specialized motile cells use protein-based spring-like responsive structures to sense, grasp and move. Rendering this biomechanical transduction functionality in an artificial micromachine for applications in single-cell manipulations is challenging due to the need for a bio-applicable nanoscale spring system with a large and programmable strain response to piconewton-scale forces. Here we present three-dimensional nanofabrication and monolithic integration, based on an acrylic elastomer photoresist, of a magnetic spring system with quantifiable compliance sensitive to 0.5 pN, constructed with customized elasticity and magnetization distributions at the nanoscale. We demonstrate the effective design programmability of these 'picospring' ensembles as energy transduction mechanisms for the integrated construction of customized soft micromachines, with onboard sensing and actuation functions at the single-cell scale for microrobotic grasping and locomotion. The integration of active soft springs into three-dimensional nanofabrication offers an avenue to create biocompatible soft microrobots for non-disruptive interactions with biological entities.

Collective dynamics of elastically coupled myosin V motors.

Characterization of the collective behaviors of different classes of processive motor proteins has become increasingly important to understand various intracellular trafficking and transport processes. This work examines the dynamics of structurally-defined motor complexes containing two myosin Va (myoVa) motors that are linked together via a molecular scaffold formed from a single duplex of DNA. Dynamic changes in the filament-bound configuration of these complexes due to motor binding, stepping, and detachment were monitored by tracking the positions of different color quantum dots that report the position of one head of each myoVa motor on actin. As in studies of multiple kinesins, the run lengths produced by two myosins are only slightly larger than those of single motor molecules. This suggests that internal strain within the complexes, due to asynchronous motor stepping and the resultant stretching of motor linkages, yields net negative cooperative behaviors. In contrast to multiple kinesins, multiple myosin complexes move with appreciably lower velocities than a single-myosin molecule. Although similar trends are predicted by a discrete state stochastic model of collective motor dynamics, these analyses also suggest that multiple myosin velocities and run lengths depend on both the compliance and the effective size of their cargo. Moreover, it is proposed that this unique collective behavior occurs because the large step size and relatively small stalling force of myoVa leads to a high sensitivity of motor stepping rates to strain.

Application of piconewton forces to individual filopodia reveals mechanosensory role of L-type Ca2+ channels.

Filopodia are ubiquitous membrane projections that play crucial role in guiding cell migration on rigid substrates and through extracellular matrix by utilizing yet unknown mechanosensing molecular pathways. As recent studies show that Ca2+ channels localized to filopodia play an important role in regulation of their formation and since some Ca2+ channels are known to be mechanosensitive, force-dependent activity of filopodial Ca2+ channels might be linked to filopodia's mechanosensing function. We tested this hypothesis by monitoring changes in the intra-filopodial Ca2+ level in response to application of stretching force to individual filopodia of several cell types using optical tweezers. Results show that stretching forces of tens of pN strongly promote Ca2+ influx into filopodia, causing persistent Ca2+ oscillations that last for minutes even after the force is released. Several known mechanosensitive Ca2+ channels, such as Piezo 1, Piezo 2 and TRPV4, were found to be dispensable for the observed force-dependent Ca2+ influx, while L-type Ca2+ channels appear to be a key player in the discovered phenomenon. As previous studies have shown that intra-filopodial transient Ca2+ signals play an important role in guidance of cell migration, our results suggest that the force-dependent activation of L-type Ca2+ channels may contribute to this process. Overall, our study reveals an intricate interplay between mechanical forces and Ca2+ signaling in filopodia, providing novel mechanistic insights for the force-dependent filopodia functions in guidance of cell migration.

The Dam1 ring binds microtubules strongly enough to be a processive as well as energy-efficient coupler for chromosome motion.

Accurate chromosome segregation during mitotic division of budding yeast depends on the multiprotein kinetochore complex, Dam1 (also known as DASH). Purified Dam1 heterodecamers encircle microtubules (MTs) to form rings that can function as "couplers," molecular devices that transduce energy from MT disassembly into the motion of a cargo. Here we show that MT depolymerization develops a force against a Dam1 ring that is sixfold larger than the force exerted on a coupler that binds only one side of an MT. Wild-type rings slow depolymerization fourfold, but rings that include a mutant Dam1p with truncated C terminus slow depolymerization less, consistent with the idea that this tail is part of a strong bond between rings and MTs. A molecular-mechanical model for Dam1-MT interaction predicts that binding between this flexible tail and the MT wall should cause a Dam1 ring to wobble, and Fourier analysis of moving, ring-attached beads corroborates this prediction. Comparison of the forces generated against wild-type and mutant complexes confirms the importance of tight Dam1-MT association for processive cargo movement under load.

Theoretical Methods for Studying DNA Structural Transitions under Applied Mechanical Constraints.

Recent progress in single-molecule manipulation technologies has made it possible to exert force and torque on individual DNA biopolymers to probe their mechanical stability and interaction with various DNA-binding proteins. It was revealed in these experiments that the DNA structure and formation of nucleoprotein complexes by DNA-architectural proteins can be strongly modulated by an intricate interplay between the entropic elasticity of DNA and its global topology, which is closely related to the mechanical constraints applied to the DNA. Detailed understanding of the physical processes underlying the DNA behavior observed in single-molecule experiments requires the development of a general theoretical framework, which turned out to be a rather challenging task. Here, we review recent advances in theoretical methods that can be used to interpret single-molecule manipulation experiments on DNA.

mDia1 senses both force and torque during F-actin filament polymerization.

Formins, an important family of force-bearing actin-polymerizing factors, function as homodimers that bind with the barbed end of actin filaments through a ring-like structure assembled from dimerized FH2 domains. It has been hypothesized that force applied to formin may facilitate transition of the FH2 ring from an inhibitory closed conformation to a permissive open conformation, speeding up actin polymerization. We confirm this hypothesis for mDia1 dependent actin polymerization by stretching a single-actin filament in the absence of profilin using magnetic tweezers, and observe that increasing force from 0.5 to 10 pN can drastically speed up the actin polymerization rate. Further, we find that this force-promoted actin polymerization requires torsionally unconstrained actin filament, suggesting that mDia1 also senses torque. As actin filaments are subject to complex mechanical constraints in living cells, these results provide important insights into how formin senses these mechanical constraints and regulates actin organization accordingly.

Transfer-matrix calculations of DNA polymer micromechanics under tension and torque constraints.

Recent development of single-molecule manipulation technologies has made it possible to exert constant force and torque on individual DNA biopolymers to probe their elastic characteristics and structural stability. It has been previously shown that depending on the nature of applied mechanical constraints, DNA can exist in several forms including B-, L-, and P-DNA. However, there is still a lack of understanding of how structural heterogeneity of DNA, which may naturally arise due to sequence-dependent DNA properties, protein binding, or DNA damage, influences local stability of the above DNA states. To provide a more complete and detailed description of the DNA mechanics, we developed a theoretical framework based on transfer-matrix calculations and demonstrated how it can be used to predict the DNA behavior upon application of a wide range of force and torque constraints. The resulting phase diagram shows DNA structural transitions that are in good agreement with previous experimental and theoretical studies. We further discuss how the constructed formalism can be extended to include local inhomogeneities in the DNA physical properties, thus making it possible to investigate the effect of DNA sequence as well as protein binding on DNA structural stability.

Force-dependent conformational switch of α-catenin controls vinculin binding.

Force sensing at cadherin-mediated adhesions is critical for their proper function. α-Catenin, which links cadherins to actomyosin, has a crucial role in this mechanosensing process. It has been hypothesized that force promotes vinculin binding, although this has never been demonstrated. X-ray structure further suggests that α-catenin adopts a stable auto-inhibitory conformation that makes the vinculin-binding site inaccessible. Here, by stretching single α-catenin molecules using magnetic tweezers, we show that the subdomains MI vinculin-binding domain (VBD) to MIII unfold in three characteristic steps: a reversible step at ~5 pN and two non-equilibrium steps at 10-15 pN. 5 pN unfolding forces trigger vinculin binding to the MI domain in a 1:1 ratio with nanomolar affinity, preventing MI domain refolding after force is released. Our findings demonstrate that physiologically relevant forces reversibly unfurl α-catenin, activating vinculin binding, which then stabilizes α-catenin in its open conformation, transforming force into a sustainable biochemical signal.