Dynamin1 long- and short-tail isoforms exploit distinct recruitment and spatial patterns to form endocytic nanoclusters.

Endocytosis requires a coordinated framework of molecular interactions that ultimately lead to the fission of nascent endocytic structures. How cytosolic proteins such as dynamin concentrate at discrete sites that are sparsely distributed across the plasma membrane remains poorly understood. Two dynamin-1 major splice variants differ by the length of their C-terminal proline-rich region (short-tail and long-tail). Using sptPALM in PC12 cells, neurons and MEF cells, we demonstrate that short-tail dynamin-1 isoforms ab and bb display an activity-dependent recruitment to the membrane, promptly followed by their concentration into nanoclusters. These nanoclusters are sensitive to both Calcineurin and dynamin GTPase inhibitors, and are larger, denser, and more numerous than that of long-tail isoform aa. Spatiotemporal modelling confirms that dynamin-1 isoforms perform distinct search patterns and undergo dimensional reduction to generate endocytic nanoclusters, with short-tail isoforms more robustly exploiting lateral trapping in the generation of nanoclusters compared to the long-tail isoform.

Temporal control by cofactors prevents kinetic trapping in retroviral Gag lattice assembly.

For retroviruses like HIV to proliferate, they must form virions shaped by the self-assembly of Gag polyproteins into a rigid lattice. This immature Gag lattice has been structurally characterized and reconstituted in vitro, revealing the sensitivity of lattice assembly to multiple cofactors. Due to this sensitivity, the energetic criterion for forming stable lattices is unknown, as are their corresponding rates. Here, we use a reaction-diffusion model designed from the cryo-ET structure of the immature Gag lattice to map a phase diagram of assembly outcomes controlled by experimentally constrained rates and free energies, over experimentally relevant timescales. We find that productive assembly of complete lattices in bulk solution is extraordinarily difficult due to the large size of this ∼3700 monomer complex. Multiple Gag lattices nucleate before growth can complete, resulting in loss of free monomers and frequent kinetic trapping. We therefore derive a time-dependent protocol to titrate or "activate" the Gag monomers slowly within the solution volume, mimicking the biological roles of cofactors. This general strategy works remarkably well, yielding productive growth of self-assembled lattices for multiple interaction strengths and binding rates. By comparing to the in vitro assembly kinetics, we can estimate bounds on rates of Gag binding to Gag and the cellular cofactor IP6. Our results show that Gag binding to IP6 can provide the additional time delay necessary to support smooth growth of the immature lattice with relatively fast assembly kinetics, mostly avoiding kinetic traps. Our work provides a foundation for predicting and disrupting formation of the immature Gag lattice via targeting specific protein-protein binding interactions.

Structure of the HIV immature lattice allows for essential lattice remodeling within budded virions.

For HIV virions to become infectious, the immature lattice of Gag polyproteins attached to the virion membrane must be cleaved. Cleavage cannot initiate without the protease formed by the homo-dimerization of domains linked to Gag. However, only 5% of the Gag polyproteins, termed Gag-Pol, carry this protease domain, and they are embedded within the structured lattice. The mechanism of Gag-Pol dimerization is unknown. Here, we use spatial stochastic computer simulations of the immature Gag lattice as derived from experimental structures, showing that dynamics of the lattice on the membrane is unavoidable due to the missing 1/3 of the spherical protein coat. These dynamics allow for Gag-Pol molecules carrying the protease domains to detach and reattach at new places within the lattice. Surprisingly, dimerization timescales of minutes or less are achievable for realistic binding energies and rates despite retaining most of the large-scale lattice structure. We derive a formula allowing extrapolation of timescales as a function of interaction free energy and binding rate, thus predicting how additional stabilization of the lattice would impact dimerization times. We further show that during assembly, dimerization of Gag-Pol is highly likely and therefore must be actively suppressed to prevent early activation. By direct comparison to recent biochemical measurements within budded virions, we find that only moderately stable hexamer contacts (-12kBT<∆G<-8kBT) retain both the dynamics and lattice structures that are consistent with experiment. These dynamics are likely essential for proper maturation, and our models quantify and predict lattice dynamics and protease dimerization timescales that define a key step in understanding formation of infectious viruses.

Secretion-Catalyzed Assembly of Protein Biomaterials on a Bacterial Membrane Surface.

Protein-based biomaterials have played a key role in tissue engineering, and additional exciting applications as self-healing materials and sustainable polymers are emerging. Over the past few decades, recombinant expression and production of various fibrous proteins from microbes have been demonstrated; however, the resulting proteins typically must then be purified and processed by humans to form usable fibers and materials. Here, we show that the Gram-positive bacterium Bacillus subtilis can be programmed to secrete silk through its translocon via an orthogonal signal peptide/peptidase pair. Surprisingly, we discover that this translocation mechanism drives the silk proteins to assemble into fibers spontaneously on the cell surface, in a process we call secretion-catalyzed assembly (SCA). Secreted silk fibers form self-healing hydrogels with minimal processing. Alternatively, the fibers retained on the membrane provide a facile route to create engineered living materials from Bacillus cells. This work provides a blueprint to achieve autonomous assembly of protein biomaterials in useful morphologies directly from microbial factories.

Large self-assembled clathrin lattices spontaneously disassemble without sufficient adaptor proteins.

Clathrin-coated structures must assemble on cell membranes to internalize receptors, with the clathrin protein only linked to the membrane via adaptor proteins. These structures can grow surprisingly large, containing over 20 clathrin, yet they often fail to form productive vesicles, instead aborting and disassembling. We show that clathrin structures of this size can both form and disassemble spontaneously when adaptor protein availability is low, despite high abundance of clathrin. Here, we combine recent in vitro kinetic measurements with microscopic reaction-diffusion simulations and theory to differentiate mechanisms of stable vs unstable clathrin assembly on membranes. While in vitro conditions drive assembly of robust, stable lattices, we show that concentrations, geometry, and dimensional reduction in physiologic-like conditions do not support nucleation if only the key adaptor AP-2 is included, due to its insufficient abundance. Nucleation requires a stoichiometry of adaptor to clathrin that exceeds 1:1, meaning additional adaptor types are necessary to form lattices successfully and efficiently. We show that the critical nucleus contains ~25 clathrin, remarkably similar to sizes of the transient and abortive structures observed in vivo. Lastly, we quantify the cost of bending the membrane under our curved clathrin lattices using a continuum membrane model. We find that the cost of bending the membrane could be largely offset by the energetic benefit of forming curved rather than flat structures, with numbers comparable to experiments. Our model predicts how adaptor density can tune clathrin-coated structures from the transient to the stable, showing that active energy consumption is therefore not required for lattice disassembly or remodeling during growth, which is a critical advance towards predicting productive vesicle formation.

A common chemomechanical coupling model for orphan and conventional kinesin molecular motors.

Orphan and conventional kinesin dimers represent two families of the kinesin superfamily molecular motors. Conventional kinesin, having a 14-residue neck linker (NL) in each head, can step processively on microtubule (MT), with an ATP hydrolysis being coupled with a mechanical stepping under no load. Orphan kinesin phragmoplast-associated kinesin-related protein 2 (PAKRP2) dimer, despite having a NL of 32 residues in each head, can also step processively on MT and exhibits tight chemomechanical coupling under no load. However, the dynamic properties of the wild type PAKRP2 and the mutant one with each NL truncated to 14 residues are very different from those of the wild type conventional kinesin and the mutant one with each NL being replaced by the 32-residue NL from PAKRP2. Here, based on a common chemomechanical coupling model we study computationally the dynamics of the two families of the kinesin dimers, with the simulated results explaining quantitatively the available experimental data. The large differences in the dynamics between the two families of kinesin dimers arise mainly from different rate constants of NL docking and ATPase activity and different weak affinities of the head in ADP state for MT. The studies indicate that both the orphan kinesin PAKRP2 and conventional kinesin use the same mechanism for processive motility.

All-atom molecular dynamics simulations reveal how kinesin transits from one-head-bound to two-heads-bound state.

Kinesin dimer walks processively along a microtubule (MT) protofilament in a hand-over-hand manner, transiting alternately between one-head-bound (1HB) and two-heads-bound (2HB) states. In 1HB state, one head bound by adenosine diphosphate (ADP) is detached from MT and the other head is bound to MT. Here, using all-atom molecular dynamics simulations we determined the position and orientation of the detached ADP-head relative to the MT-bound head in 1HB state. We showed that in 1HB state when the MT-bound head is in ADP or nucleotide-free state, with its neck linker being undocked, the detached ADP-head and the MT-bound head have the high binding energy, and after adenosine triphosphate (ATP) binds to the MT-bound head, with its neck linker being docked, the binding energy between the two heads is reduced greatly. These results reveal how the kinesin dimer retains 1HB state before ATP binding and how the dimer transits from 1HB to 2HB state after ATP binding. Key residues involved in the head-head interaction in 1HB state were identified.

Run length distribution of dimerized kinesin-3 molecular motors: comparison with dimeric kinesin-1.

Kinesin-3 and kinesin-1 molecular motors are two families of the kinesin superfamily. It has been experimentally revealed that in monomeric state kinesin-3 is inactive in motility and cargo-mediated dimerization results in superprocessive motion, with an average run length being more than 10-fold longer than that of kinesin-1. In contrast to kinesin-1 showing normally single-exponential distribution of run lengths, dimerized kinesin-3 shows puzzlingly Gaussian distribution of run lengths. Here, based on our proposed model, we studied computationally the dynamics of kinesin-3 and compared with that of kinesin-1, explaining quantitatively the available experimental data and revealing the origin of superprocessivity and Gaussian run length distribution of kinesin-3. Moreover, predicted results are provided on ATP-concentration dependence of run length distribution and force dependence of mean run length and dissociation rate of kinesin-3.

A Generalized Kinetic Model for Coupling between Stepping and ATP Hydrolysis of Kinesin Molecular Motors.

A general kinetic model is presented for the chemomechanical coupling of dimeric kinesin molecular motors with and without extension of their neck linkers (NLs). A peculiar feature of the model is that the rate constants of ATPase activity of a kinesin head are independent of the strain on its NL, implying that the heads of the wild-type kinesin dimer and the mutant with extension of its NLs have the same force-independent rate constants of the ATPase activity. Based on the model, an analytical theory is presented on the force dependence of the dynamics of kinesin dimers with and without extension of their NLs at saturating ATP. With only a few adjustable parameters, diverse available single molecule data on the dynamics of various kinesin dimers, such as wild-type kinesin-1, kinesin-1 with mutated residues in the NLs, kinesin-1 with extension of the NLs and wild-type kinesin-2, under varying force and ATP concentration, can be reproduced very well. Additionally, we compare the power production among different kinesin dimers, showing that the mutation in the NLs reduces the power production and the extension of the NLs further reduces the power production.

Force dependence of unbinding rate of kinesin motor during its processive movement on microtubule.

Kinesin is a biological molecular motor that can move continuously on microtubule until it unbinds. Here, we studied computationally the force dependence of the unbinding rate of the motor. Our results showed that while the unbinding rate under the forward load has the expected characteristic of "slip bond", with the unbinding rate increasing monotonically with the increase of the forward load, the unbinding rate under the backward load shows counterintuitive characteristic of "slip-catch-slip bond": as the backward load increases, the unbinding rate increases exponentially firstly, then drops rapidly and then increases again. Our calculated data are in agreement with the available single-molecule data from different research groups. The mechanism of the slip-catch-slip bond was revealed.

Dynamics of cooperative cargo transport by two elastically coupled kinesin motors.

Intracellular transport is performed often by multiple motor proteins bound to the same cargo. Here, we study theoretically collective transport of the cargo by two kinesin motors. We propose that the motor has only the elastic interaction with the cargo via the linker connecting them and has no interaction with another motor. With parameters values for single motors from the available single-molecule data, we show that at linker's elastic strength [Formula: see text] pN/nm the theoretical data of both velocity and run length of the two-motor assembly under no load are identical to the available experimental data. The run length distribution is single exponential. The single-motor-bound state of the assembly dominates the transport. Both the force dependence of the velocity of the cargo driven by single load-bearing motor and that by two load-bearing motors in the assembly are consistent with the experimental data. The stall force of the assembly is larger than the sum of stall forces of two uncoupled motors. Moreover, we predict that the stall force increases with the increase of K and becomes saturated at large K, with the saturated value being 1.5-fold larger than the sum of stall forces of the two uncoupled motors.

Force Dependence of Velocity and Run Length of Kinesin-1, Kinesin-2 and Kinesin-5 Family Molecular Motors.

Kinesin-1, kinesin-2 and kinesin-5 are three families of a superfamily of motor proteins; which can walk processively on microtubule filaments by hydrolyzing ATP. It was experimentally shown that while the three kinesin dimers show similar feature on the force dependence of velocity, they show rather different features on the force dependence of run length. However, why the three families of kinesins show these rather different features is unclear. Here, we computationally studied the movement dynamics of the three dimers based on our proposed model. The simulated results reproduce well the available experimental data on the force dependence of velocity and run length. Moreover, the simulated results on the velocity and run length for the three dimers with altered neck linker lengths are also in quantitative agreement with the available experimental data. The studies indicate that the three families of kinesins show much similar movement mechanism and the rather different features on the force dependence of run length arise mainly from the difference in rate constants of the ATPase activity and neck linker docking. Additionally, the asymmetric (limping) movement dynamics of the three families of homodimers with and without altered neck linker lengths are studied, providing predicted results.

ATP-Concentration- and Force-Dependent Chemomechanical Coupling of Kinesin Molecular Motors.

A model is presented for the chemomechanical coupling of kinesin motors, which proposes that the rate constants of the chemical reaction are independent of the external force. On the basis of the model, we study theoretically the movement dynamics of the motors under varying external force and ATP concentration, such as the forward to backward stepping ratio, velocity, dwell time between two mechanical steps, stall force, and so on. The theoretical results reproduce quantitatively the diverse and even contradictory available single-molecule experimental data for different species of the motors. Furthermore, we study the dependence of the chemomechanical coupling ratio on ATP concentration and external force, with both ATP concentration and external force having large effects on the chemomechanical coupling.

Processivity of dimeric kinesin-1 molecular motors.

Kinesin-1 is a homodimeric motor protein that can move along microtubule filaments by hydrolyzing ATP with a high processivity. How the two motor domains are coordinated to achieve such high processivity is not clear. To address this issue, we computationally studied the run length of the dimer with our proposed model. The computational data quantitatively reproduced the puzzling experimental data, including the dramatically asymmetric character of the run length with respect to the direction of external load acting on the coiled-coil stalk, the enhancement of the run length by addition of phosphate, and the contrary features of the run length for different types of kinesin-1 with extensions of their neck linkers compared with those without extension of the neck linker. The computational data on other aspects of the movement dynamics such as velocity and durations of one-head-bound and two-head-bound states in a mechanochemical coupling cycle were also in quantitative agreement with the available experimental data. Moreover, predicted results are provided on dependence of the run length upon external load acting on one head of the dimer, which can be easily tested in the future using single-molecule optical trapping assays.

Investigating role of conformational changes of microtubule in regulating its binding affinity to kinesin by all-atom molecular dynamics simulation.

Changes of affinity of kinesin head to microtubule regulated by changes in the nucleotide state are essential to processive movement of kinesin on microtubule. Here, using all-atom molecular dynamics simulations we show that besides the nucleotide state, large conformational changes of microtubule-tubulin heterodimers induced by strong interaction with the head in strongly binding state are also indispensable to regulate the affinity of the head to the tubulin. In strongly binding state the high affinity of the head to microtubule arises largely from mutual conformational changes of the microtubule and head induced by the specific interaction between them via an induced-fit mechanism. Moreover, the ADP-head has a much weaker affinity to the local microtubule-tubulin, whose conformation is largely altered by the interaction with the head in strongly binding state, than to other unperturbed tubulins. This indicates that upon Pi release the ADP-head temporarily has a much weaker affinity to the local tubulin than to other tubulins.

Dynamics of dimeric kinesins: Limping, effect of longitudinal force, effects of neck linker extension and mutation, and comparison between kinesin-1 and kinesin-2.

Conventional kinesin (kinesin-1) can walk on microtubule filaments in an asymmetric hand-over-hand manner, exhibiting a marked alternation in the mean dwell time in successive steps. Here, we study computationally the asymmetric stepping dynamics of the kinesin-1 homodimer, revealing its origin and providing quantitative explanations of the available experimental data. The alternation in the mean dwell time in successive steps arises from the alternation in the mechanochemical coupling ratio, which is in turn caused by the alternation in the slight variation of the stretched neck linker length. Both the vertical and backward longitudinal forces can enhance the asymmetric ratio. Additionally, other aspects of the stepping dynamics of the dimer such as the velocity versus longitudinal force, extended neck linker, etc., are also studied. In particular, the conflicting experimental data, with some showing that the velocity does not change with the forward longitudinal load while others showing that the velocity increases largely with the forward longitudinal load, are explained quantitatively and consistently. The intriguing experimental data showing that cysteine-light Drosophila and human kinesin-1 mutants have different load-dependent velocity from the wild-type cases as well as that kinesin-2 dimers have different load-dependent velocity from the kinesin-1 are also explained consistently and quantitatively.

A model of processive movement of dimeric kinesin.

Dimeric kinesin can move processively on microtubule filaments by hydrolyzing ATP. Diverse aspects of its movement dynamics have been studied extensively by using various experimental methods. However, the detailed molecular mechanism of the processive movement is still undetermined and a model that can provide a consistent and quantitative explanation of the diverse experimental data is still lacking. Here, we present such a model, with which we study the movement dynamics of the dimer under variations of solution viscosity, external load, ATP concentration, neck linker length, effect of neck linker docking, effect of a large-size particle attached to one kinesin head, etc., providing consistent and quantitative explanations of the available diverse experimental data. Moreover, predicted results are also provided.