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.

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.

Myosin IIA and formin dependent mechanosensitivity of filopodia adhesion

Filopodia, dynamic membrane protrusions driven by polymerization of an actin filament core, can adhere to the extracellular matrix and experience both external and cell-generated pulling forces. The role of such forces in filopodia adhesion is however insufficiently understood. Here, we study filopodia induced by overexpression of myosin X, typical for cancer cells. The lifetime of such filopodia positively correlates with the presence of myosin IIA filaments at the filopodia bases. Application of pulling forces to the filopodia tips through attached fibronectin-coated laser-trapped beads results in sustained growth of the filopodia. Pharmacological inhibition or knockdown of myosin IIA abolishes the filopodia adhesion to the beads. Formin inhibitor SMIFH2, which causes detachment of actin filaments from formin molecules, produces similar effect. Thus, centripetal force generated by myosin IIA filaments at the base of filopodium and transmitted to the tip through actin core in a formin-dependent fashion is required for filopodia adhesion.

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.

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.

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.

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.

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.

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.

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.

Analysis of Cooperative Behavior in Multiple Kinesins Motor Protein Transport by Varying Structural and Chemical Properties

Intracellular transport is a fundamental biological process during which cellular materials are driven by enzymatic molecules called motor proteins. Recent optical trapping experiments and theoretical analysis have uncovered many features of cargo transport by multiple kinesin motor protein molecules under applied loads. These studies suggest that kinesins cooperate negatively under typical transport conditions, although some productive cooperation could be achieved under higher applied loads. However, the microscopic origins of this complex behavior are still not well understood. Using a discrete-state stochastic approach we analyze factors that affect the cooperativity among kinesin motors during cargo transport. Kinesin cooperation is shown to be largely unaffected by the structural and mechanical parameters of a multiple motor complex connected to a cargo, but much more sensitive to biochemical parameters affecting motor-filament affinities. While such behavior suggests the net negative cooperative responses of kinesins will persist across a relatively wide range of cargo types, it is also shown that the rates with which cargo velocities relax in time upon force perturbations are influenced by structural factors that affect the free energies of and load distributions within a multiple kinesin complex. The implications of these later results on transport phenomena where loads change temporally, as in the case of bidirectional transport, are discussed.

How the interplay between mechanical and nonmechanical interactions affects multiple kinesin dynamics

Intracellular transport is supported by enzymes called motor proteins that are often coupled to the same cargo and function collectively. Recent experiments and theoretical advances have been able to explain certain behaviors of multiple motor systems by elucidating how unequal load sharing between coupled motors changes how they bind, step, and detach. However, nonmechanical interactions are typically overlooked despite several studies suggesting that microtubule-bound kinesins interact locally via short-range nonmechanical potentials. This work develops a new stochastic model to explore how these types of interactions influence multiple kinesin functions in addition to mechanical coupling. Nonmechanical interactions are assumed to affect kinesin mechanochemistry only when the motors are separated by less than three microtubule lattice sites, and it is shown that relatively weak interaction energies (~2 k(B)T) can have an appreciable influence over collective motor velocities and detachment rates. In agreement with optical trapping experiments on structurally defined kinesin complexes, the model predicts that these effects primarily occur when cargos are transported against loads exceeding single-kinesin stalling forces. Overall, these results highlight the interdependent nature of factors influencing collective motor functions, namely, that the way the bound configuration of a multiple motor system evolves under load determines how local nonmechanical interactions influence motor cooperation.

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.

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.

Force production by depolymerizing microtubules: a theoretical study

Chromosome movement during mitosis is powered in part by energy released through the depolymerization of kinetochore microtubules (MTs). Strong but indirect evidence suggests the existence of a specialized coupling between kinetochores and MT plus ends that enables this transduction of chemical energy into mechanical work. Analysis of this phenomenon is important for learning how energy is stored within the MT lattice, how it is transduced, and how efficient the process can be, given coupling devices of different designs. Here we use a recently developed molecular-mechanical model of MTs to examine the mechanism of disassembly dependent force generation. Our approach is based on changes in tubulin dimer conformation that occur during MT disassembly. We find that all of the energy of polymerization-associated GTP hydrolysis can be stored as deformations of the longitudinal bonds between tubulin dimers, and its optimal use does not require the weakening of lateral bonds between dimers. Maximum utilization of this stored energy and, hence, the generation of the strongest possible force, is achieved by a protofilament power-stroke mechanism, so long as the coupling device does not restrict full dissociation of the lateral bonds between tubulin dimers.