The role of memory-dependent friction and solvent viscosity in isomerization kinetics in viscogenic media.

Molecular isomerization kinetics in liquid solvent depends on a complex interplay between the solvent friction acting on the molecule, internal dissipation effects (also known as internal friction), the viscosity of the solvent, and the dihedral free energy profile. Due to the absence of accurate techniques to directly evaluate isomerization friction, it has not been possible to explore these relationships in full. By combining extensive molecular dynamics simulations with friction memory-kernel extraction techniques we consider a variety of small, isomerising molecules under a range of different viscogenic conditions and directly evaluate the viscosity dependence of the friction acting on a rotating dihedral. We reveal that the influence of different viscogenic media on isomerization kinetics can be dramatically different, even when measured at the same viscosity. This is due to the dynamic solute-solvent coupling, mediated by time-dependent friction memory kernels. We also show that deviations from the linear dependence of isomerization rates on solvent viscosity, which are often simply attributed to internal friction effects, are due to the simultaneous violation of two fundamental relationships: the Stokes-Einstein relation and the overdamped Kramers prediction for the barrier-crossing rate, both of which require explicit knowledge of friction.

Stretch-shortening cycles protect against the age-related loss of power generation in rat single muscle fibres.

Aging is associated with impaired strength and power during isometric and shortening contractions, however, during lengthening (i.e., eccentric) contractions, strength is maintained. During daily movements, muscles undergo stretch-shortening cycles (SSCs). It is unclear whether the age-related maintenance of eccentric strength offsets age-related impairments in power generation during SSCs owing to the utilization of elastic energy or other cross-bridge based mechanisms. Here we investigated how aging influences SSC performance at the single muscle fibre level and whether performing active lengthening prior to shortening protects against age-related impairments in power generation. Single muscle fibres from the psoas major of young (∼8 months; n = 31 fibres) and old (∼32 months; n = 41 fibres) male F344BN rats were dissected and chemically permeabilized. Fibres were mounted between a force transducer and length controller and maximally activated (pCa 4.5). For SSCs, fibres were lengthened from average sarcomere lengths of 2.5 to 3.0 µm and immediately shortened back to 2.5 µm at both fast and slow (0.15 and 0.60 Lo/s) lengthening and shortening speeds. The magnitude of the SSC effect was calculated by comparing work and power during shortening to an active shortening contraction not preceded by active lengthening. Absolute isometric force was ∼37 % lower in old compared to young rat single muscle fibres, however, when normalized to cross-sectional area (CSA), there was no longer a significant difference in isometric force between age groups, meanwhile there was an ∼50 % reduction in absolute power in old as compared with young. We demonstrated that SSCs significantly increased power production (75-110 %) in both young and old fibres when shortening occurred at a fast speed and provided protection against power-loss with aging. Therefore, in older adults during everyday movements, power is likely 'protected' in part due to the stretch-shortening cycle as compared with isolated shortening contractions.

Accurate Memory Kernel Extraction from Discretized Time-Series Data.

Memory effects emerge as a fundamental consequence of dimensionality reduction when low-dimensional observables are used to describe the dynamics of complex many-body systems. In the context of molecular dynamics (MD) data analysis, accounting for memory effects using the framework of the generalized Langevin equation (GLE) has proven efficient, accurate, and insightful, particularly when working with high-resolution time series data. However, in experimental systems, high-resolution data are often unavailable, raising questions about the impact of the data resolution on the estimated GLE parameters. This study demonstrates that direct memory extraction from time series data remains accurate when the discretization time is below the memory time. To obtain memory functions reliably, even when the discretization time exceeds the memory time, we introduce a Gaussian Process Optimization (GPO) scheme. This scheme minimizes the deviation of discretized two-point correlation functions between time series data and GLE simulations and is able to estimate accurate memory kernels as long as the discretization time stays below the longest time scale in the data, typically the barrier crossing time.

Robust cytoplasmic partitioning by solving an intrinsic cytoskeletal instability.

Early development across vertebrates and insects critically relies on robustly reorganizing the cytoplasm of fertilized eggs into individualized cells. This intricate process is orchestrated by large microtubule structures that traverse the embryo, partitioning the cytoplasm into physically distinct and stable compartments. Despite the robustness of embryonic development, here we uncover an intrinsic instability in cytoplasmic partitioning driven by the microtubule cytoskeleton. We reveal that embryos circumvent this instability through two distinct mechanisms: either by matching the cell cycle duration to the time needed for the instability to unfold or by limiting microtubule nucleation. These regulatory mechanisms give rise to two possible strategies to fill the cytoplasm, which we experimentally demonstrate in zebrafish and Drosophila embryos, respectively. In zebrafish embryos, unstable microtubule waves fill the geometry of the entire embryo from the first division. Conversely, in Drosophila embryos, stable microtubule asters resulting from reduced microtubule nucleation gradually fill the cytoplasm throughout multiple divisions. Our results indicate that the temporal control of microtubule dynamics could have driven the evolutionary emergence of species-specific mechanisms for effective cytoplasmic organization. Furthermore, our study unveils a fundamental synergy between physical instabilities and biological clocks, uncovering universal strategies for rapid, robust, and efficient spatial ordering in biological systems.

Time course changes in in vivo muscle mechanical function and Ca2+ regulation of force following experimentally induced gradual ovarian failure in mice.

The abrupt cessation of ovarian hormone release is associated with declines in muscle contractile function, yet the impact of gradual ovarian failure on muscle contractility across peri-, early- and late-stage menopause remains unclear. In this study, a 4-vinylcyclohexene diepoxide (VCD)-induced ovarian failure mouse model was used to examine time course changes in muscle mechanical function. Plantar flexors of female mice (VCD: n = 10; CON: n = 8) were assessed at 40 (early perimenopause), 80 (late perimenopause), 120 (menopause onset) and 176 (late menopause) days post-initial VCD injection. A torque-frequency relationship was established across a range of frequencies (10-200 Hz). Isotonic dynamic contractions were elicited against relative loads (10-80% maximal isometric torque) to determine the torque-velocity-power relationship. Mice then performed a fatigue task using intermittent 100 Hz isometric contractions until torque dropped by 60%. Recovery of twitch, 10 Hz and 100 Hz torque were tracked for 10 min post-task failure. Additionally, intact muscle fibres from the flexor digitorum brevis underwent a fatigue task (50 repetitions at 70 Hz), and 10 and 100 Hz tetanic [Ca2+] were monitored for 10 min afterward. VCD mice exhibited 16% lower twitch torque than controls across all time points. Apart from twitch torque, 10 Hz torque and 10 Hz tetanic [Ca2+], where VCD showed greater values relative to pre-fatigue during recovery, no significant differences were observed between control and VCD mice during recovery. These results indicate that gradual ovarian failure has minimal detriments to in vivo muscle mechanical function, with minor alterations observed primarily for low-frequency stimulation during recovery from fatigue.

Fast protein folding is governed by memory-dependent friction.

When described by a low-dimensional reaction coordinate, the folding rates of most proteins are determined by a subtle interplay between free-energy barriers, which separate folded and unfolded states, and friction. While it is commonplace to extract free-energy profiles from molecular trajectories, a direct evaluation of friction is far more elusive and typically relies on fits of measured reaction rates to memoryless reaction-rate theories. Here, using memory-kernel extraction methods founded on a generalized Langevin equation (GLE) formalism, we directly calculate the time-dependent friction acting on the fraction of native contacts reaction coordinate Q, evaluated for eight fast-folding proteins, taken from a published set of large-scale molecular dynamics protein simulations. Our results reveal that, across the diverse range of proteins represented in this dataset, friction is more influential than free-energy barriers in determining protein folding rates. We also show that proteins fold in a regime where the finite decay time of friction significantly reduces the folding times, in some instances by as much as a factor of 10, compared to predictions based on memoryless friction.

The relationship between single muscle fibre and voluntary rate of force development in young and old males.

PURPOSE: It is suggested that the early phase (< 50 ms) of force development during a muscle contraction is associated with intrinsic contractile properties, while the late phase (> 50 ms) is associated with maximal force. There are no direct investigations of single muscle fibre rate of force development (RFD) as related to joint-level RFD METHODS: Sixteen healthy, young (n = 8; 26.4 ± 1.5 yrs) and old (n = 8; 70.1 ± 2.8 yrs) males performed maximal voluntary isometric contractions (MVC) and electrically evoked twitches of the knee extensors to assess RFD. Then, percutaneous muscle biopsies were taken from the vastus lateralis and chemically permeabilized, to assess single fibre function. RESULTS: At the joint level, older males were ~ 30% weaker and had ~ 43% and ~ 40% lower voluntary RFD values at 0-100 and 0-200 ms, respectively, than the younger ones (p ≤ 0.05). MVC torque was related to every voluntary RFD epoch in the young (p ≤ 0.001), but only the 0-200 ms epoch in the old (p ≤ 0.005). Twitch RFD was ~ 32% lower in the old compared to young (p < 0.05). There was a strong positive relationship between twitch RFD and voluntary RFD during the earliest time epochs in the young (≤ 100 ms; p ≤ 0.01). While single fibre RFD was unrelated to joint-level RFD in the young, older adults trended (p = 0.052-0.055) towards significant relationships between joint-level RTD and Type I single fibre RFD at the 0-30 ms (r2 = 0.48) and 0-50 ms (r2 = 0.49) time epochs. CONCLUSION: Electrically evoked twitches are good predictors of early voluntary RFD in young, but not older adults. Only the older adults showed a potential relationship between single fibre (Type I) and joint-level rate of force development.

No sex differences in evoked contractile properties after fatiguing isometric and isotonic exercise for the plantar flexors.

OBJECTIVES: Females tend to fatigue less than males after isometric exercise, but less is clear for isotonic exercise. Further, there have been relatively few sex comparisons for fatigability of the plantar flexors (PFs). We sought to investigate potential sex differences in contractile properties after a sustained maximal voluntary isometric contraction (MVIC) and isotonic contractions. METHODS: Twenty-seven physically active males (n=14; 22±2 yrs) and females (n=13; 21±2 yrs) randomly performed a 2 min MVIC and 120 concentric isotonic (30% MVIC) contractions for the PFs on separate visits. Before and after each fatiguing task, muscle activation was obtained from brief MVICs, which was followed (~2 sec) by tibial nerve stimulation at rest. Contractile properties including peak twitch, absolute and normalized time to peak twitch, and half relaxation time were calculated. RESULTS: No sex differences existed for fatigue-induced changes in muscle activation (p=0.09-0.41; d=0.33-0.69) or contractile properties (p=0.19-0.96; d=0.06-0.94). CONCLUSIONS: Peripheral fatigue, as indicated by contractile parameters, did not differ between sexes after isometric or isotonic exercise. The PFs similar fiber type proportions between sexes or greater fiber type heterogeneity may explain why sex differences in fatigability, though common in other muscle groups (e.g., knee extensors), were not expressed in this muscle group.

Generalized Langevin equation with a nonlinear potential of mean force and nonlinear memory friction from a hybrid projection scheme.

We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a generalized Langevin equation (GLE) for a general interacting many-body system. The resulting GLE includes (i) explicitly the potential of mean force (PMF) that describes the equilibrium distribution of the system in the chosen space of reaction coordinates, (ii) a random force term that explicitly depends on the initial state of the system, and (iii) a memory friction contribution that splits into two parts: a part that is linear in the past reaction-coordinate velocity and a part that is in general nonlinear in the past reaction coordinates but does not depend on velocities. Our hybrid scheme thus combines all desirable properties of the Zwanzig and Mori projection schemes. The nonlinear memory friction contribution is shown to be related to correlations between the reaction-coordinate velocity and the random force. We present a numerical method to compute all parameters of our GLE, in particular the nonlinear memory friction function and the random force distribution, from a trajectory in reaction coordinate space. We apply our method on the dihedral-angle dynamics of a butane molecule in water obtained from atomistic molecular dynamics simulations. For this example, we demonstrate that nonlinear memory friction is present and that the random force exhibits significant non-Gaussian corrections. We also present the derivation of the GLE for multidimensional reaction coordinates that are general functions of all positions in the phase-space of the underlying many-body system; this corresponds to a systematic coarse-graining procedure that preserves not only the correct equilibrium behavior but also the correct dynamics of the coarse-grained system.

Isometric versus isotonic contractions: Sex differences in the fatigability and recovery of isometric strength and high-velocity contractile parameters.

The purpose of this study was to investigate potential sex differences in the fatigue- and recovery-induced responses of isometric strength and power, as well as select dynamic contractile parameters after isometric and isotonic plantar flexor (PF) contractions. Healthy males (n = 12; age = 21.8 ± 2.2 years) and females (n = 14; age = 21.4 ± 2.5 years) performed a 2-min maximal voluntary isometric contraction and 120 concentric isotonic (30% peak isometric torque) contractions of the PFs on separate visits. Isometric strength, isotonic power, as well as torque- and velocity-related parameters were recorded before, immediately after, and throughout 10 min of recovery. Rate of EMG rise (RER) for the medial gastrocnemius (MG) and soleus was also obtained. All measures responded similarly between sexes after both fatiguing modalities (p > 0.05), except RER of the MG which, in males demonstrated both, a greater decrease during isotonic contractions (p = 0.038, ηp2  = 0.174) and more rapid recovery after isometric exercise (p = 0.043, ηp2  = 0.166). Although not significant, a nearly large effect size was demonstrated for the fatigue-induced decrease in isometric strength (p = 0.061; d = 0.77) due to relative decreases tending to be greater in males (-29% vs. -17%). Regardless of fatiguing modality, sex differences were minimal for fatigue and recovery-related responses in muscle function for the PFs, although the difference for RER may indicate a unique origin of fatigue. Further support for the disassociation between the response in isometric strength and power after fatiguing exercise was also demonstrated.

Fundamentals of the logarithmic measure for revealing multimodal diffusion.

We develop a theoretical foundation for a time-series analysis method suitable for revealing the spectrum of diffusion coefficients in mixed Brownian systems, for which no prior knowledge of particle distinction is required. This method is directly relevant for particle tracking in biological systems, in which diffusion processes are often nonuniform. We transform Brownian data onto the logarithmic domain, in which the coefficients for individual modes of diffusion appear as distinct spectral peaks in the probability density. We refer to the method as the logarithmic measure of diffusion, or simply as the logarithmic measure. We provide a general protocol for deriving analytical expressions for the probability densities on the logarithmic domain. The protocol is applicable for any number of spatial dimensions with any number of diffusive states. The analytical form can be fitted to data to reveal multiple diffusive modes. We validate the theoretical distributions and benchmark the accuracy and sensitivity of the method by extracting multimodal diffusion coefficients from two-dimensional Brownian simulations of polydisperse filament bundles. Bundling the filaments allows us to control the system nonuniformity and hence quantify the sensitivity of the method. By exploiting the anisotropy of the simulated filaments, we generalize the logarithmic measure to rotational diffusion. By fitting the analytical forms to simulation data, we confirm the method's theoretical foundation. An error analysis in the single-mode regime shows that the proposed method is comparable in accuracy to the standard mean-squared displacement approach for evaluating diffusion coefficients. For the case of multimodal diffusion, we compare the logarithmic measure against other, more sophisticated methods, showing that both model selectivity and extraction accuracy are comparable for small data sets. Therefore, we suggest that the logarithmic measure, as a method for multimodal diffusion coefficient extraction, is ideally suited for small data sets, a condition often confronted in the experimental context. Finally, we critically discuss the proposed benefits of the method and its information content.

Rate of Force Development as a Predictor of Mobility in Community-dwelling Older Adults.

BACKGROUND AND PURPOSE: Rate of force development (RFD) is influential, and possibly more influential than other muscular performance parameters, for mobility in older adults. However, only a few studies have investigated this matter, and this has not been examined for the plantar flexors (PFs). The purpose of this study was to examine the contribution of PF RFD and other common tests of muscular performance to Up-and-Go (UG) performance and walking speed (WS) in older adults. METHODS: Twenty-six (19 females) healthy, community-dwelling older adults (73.7 ± 4.9 years) were recruited from a senior citizen center for this observational study. Handgrip strength, UG performance, as well as preferred and maximal WS were obtained. Time taken to complete 5-chair rises and the number of chair rises completed in 30 seconds were recorded. Rate of force development of the PFs was obtained during a rapid, bilateral calf raise performed on a force plate. Hierarchical multiple linear regression was used to identify significant predictors, after adjusting for physical activity level and body mass index, of mobility (ie, UG, preferred and maximal WS). RESULTS AND DISCUSSION: No muscular performance variables correlated with preferred WS. Rate of force development (adjusted R2 = 0.356; P = .008) and handgrip strength (adjusted R2 = 0.293; P = .026) were the only predictors of maximal WS and accounted for a 21.7% and 16.1% change in R2, respectively, after accounting for physical activity level and body mass index. Rate of force development was the only predictor of UG performance (adjusted R2 = 0.212; P = .006) and accounted for a 29.2% change in R2 after adjustment variables were applied. CONCLUSIONS: Compared to common assessments of muscular performance, such as handgrip strength and chair rise performance, PF RFD was a greater predictor of mobility in older adults. These findings, in conjunction with recent reports, indicate that the assessment of RFD likely complements strength testing, thereby enabling a more robust assessment of functional decline in older adults.

Microbiopsy Sampling for Examining Age-Related Differences in Skeletal Muscle Fiber Morphology and Composition.

Introduction: The increasingly popular microbiopsy is an appealing alternative to the more invasive Bergström biopsy given the challenges associated with harvesting skeletal muscle in older populations. Parameters of muscle fiber morphology and composition derived from the microbiopsy have not been compared between young and older adults. Purpose: The purpose of this study was to examine muscle fiber morphology and composition in young (YM) and older (OM) males using the microbiopsy sampling technique. A secondary aim was to determine if specific strength is associated with serum levels of C-terminal agrin fragment [CAF; an indicator of neuromuscular junction (NMJ) degradation]. Methods: Thirty healthy, YM (n = 15, age = 20.7 ± 2.2 years) and OM (n = 15, age = 71.6 ± 3.9 years) underwent ultrasound imaging to determine whole-muscle cross-sectional area (CSA) of the vastus lateralis and rectus femoris as well as isometric and isokinetic (60°â‹…s-1 and 180°â‹…s-1) peak torque testing of the knee extensors. Microbiopsy samples of the vastus lateralis were collected from 13 YM and 11 OM, and immunofluorescence was used to calculate CSA and proportion of type I and type II fibers. Results: Peak torque was lower in OM at all velocities (p ≤ 0.001; d = 1.39-1.86) but only lower at 180°â‹…s-1 (p = 0.003; d = 1.23) when normalized to whole-muscle CSA. Whole-muscle CSA was smaller in OM (p = 0.001; d = 1.34), but atrophy was not present at the single fiber level (p > 0.05). Per individual, ∼900 fibers were analyzed, and type I fiber CSA was larger (p = 0.05; d = 0.94) in OM which resulted in a smaller type II/I fiber CSA ratio (p = 0.015; d = 0.95). CAF levels were not sensitive to age (p = 0.159; d = 0.53) nor associated with specific strength or whole-muscle CSA in OM. Conclusion: The microbiopsy appears to be a viable alternative to the Bergström biopsy for histological analyses of skeletal muscle in older adults. NMJ integrity was not influential for age-related differences in specific strength in our healthy, non-sarcopenic older sample.

Sit-to-Stand Kinetics and Correlates of Performance in Young and Older Males.

PURPOSE: To compare sit-to-stand (STS) kinetics in young (YM) and older (OM) males and determine correlates of STS performance. METHODS: YM (n = 15, age = 20.7 ±â€¯2.2 yrs) and OM (n = 15, age = 71.6 ±â€¯3.9 yrs) performed a single STS task as quickly as possible on a force plate and the vertical ground reaction force (VGRF) signal was analyzed. Peak VGRF, as well as peak (100 ms rolling average), early (minimum VGRF to 50% peak VGRF), late (50% peak VGRF to peak VGRF), and overall (minimum VGRF to peak VGRF) rate of force development (RFD) were calculated. Power (absolute and relative) and velocity parameters as well as rate of electromyography rise (RER) were also obtained. RESULTS: STS time, average power, early RFD, and lower limb lean mass were similar between groups (p > 0.05). All other power, velocity, RFD, and RER measures were lower in OM (p < 0.05; d = 0.41-2.19). Peak VGRF and all RFD measures, except late RFD, were strongly correlated with STS performance in OM, while peak VGRF and peak RFD were only moderately correlated with performance in YM. CONCLUSIONS: Most kinetic variables, except absolute average power, were diminished in OM, and there was a preferential decrease in late RFD compared to early RFD. Peak VGRF and RFD exhibited stronger correlations with STS time and power in OM compared to YM, and early RFD appears to be more influential for STS performance than late RFD. These findings may be useful for practitioners/clinicians involved in designing interventions aimed at optimizing STS performance in older adults.

Early and late rapid torque characteristics and select physiological correlates in middle-aged and older males.

PURPOSE: The purpose of this study was to compare early and late rapid torque parameters of the plantar flexors (PFs) in middle-aged (MM) and older (OM) males, and determine the effect of normalization to peak torque (PT) and muscle cross-sectional area (CSA). METHODS: Twenty-nine healthy, MM (n = 14; 45 ± 2 yrs) and OM (n = 15; 65 ± 3 yrs) performed rapid, maximal isometric contractions of the PFs. PT, as well as rate of torque development and impulse during the early (0-50 ms; RTD0-50, IMP0-50) and late (100-200 ms; RTD100-200, IMP100-200) contraction phases were calculated. Torque at 50 (TQ50), 100 (TQ100), and 200 (TQ200) ms was also obtained. CSA and echo-intensity (EI) of the gastrocnemii were acquired via ultrasonography. Torque variables were normalized to PT and CSA. Rate of EMG rise (RER) for the medial gastrocnemius was calculated at 30, 50 and 75 ms. RESULTS: TQ100 (MM = 69.71 ± 16.85 vs. OM = 55.99 ± 18.54 Nm; p = 0.046), TQ200 (MM = 114.76 ± 26.79 vs. OM = 91.56 ± 28.10 Nm; p = 0.031), and IMP100-200 (MM = 4.79 ± 1.11 vs. OM = 3.83 ± 1.17 Nm·s; p = 0.032) were lower in OM. PT, TQ50, RTD0-50, IMP0-50, RTD100-200, RER, CSA, and EI were similar between groups (p > 0.05). No differences were found for normalized torque variables (p > 0.05). EI was moderately associated with normalized torque parameters only (r = -0.38 --0.45). RER, at 75 ms, was moderately correlated with early, absolute torque measures and rapid torque variables made relative to PT and CSA (r = 0.41 --0.64). CONCLUSION: Late rapid torque parameters of the PFs were preferentially impaired in OM compared to MM, and PT as well as CSA appeared to mediate this result.

Neuromuscular function of the plantar flexors and predictors of peak power in middle-aged and older males.

Little evidence exists regarding the contribution of torque and velocity to the age-related decrease in peak power (PP) for the plantar flexors (PFs). A comprehensive assessment of PF neuromuscular function is necessary to elucidate age-related changes, especially between middle-aged and older adults, in order to identify early, age-related decrements. Thus, the purpose of this study was to examine neuromuscular function of the PFs in middle-aged and older males, and identify predictors of PP. Twenty-eight healthy, middle-aged (n = 13; 45.1 ±â€¯2.7 yrs) and older (n = 15; 65.3 ±â€¯3.2 yrs) males performed concentric isotonic PF contractions ranging in intensity from 20% to 70% isometric strength using a dynamometer. PP in addition to velocity and torque at the moment in time PP occurred, as well as the rate of velocity, torque (RTD), and power (RPD) development were recorded. The rate of electromyography rise (RER) was derived from the linear slope of the normalized electromyography signal. Isometric and concentric dynamic strength were assessed, as well as cross-sectional area and muscle quality (i.e., echo intensity) of the PFs via panoramic ultrasonography. The relationship between serum c-terminal agrin levels and select variables was examined to explore the potential role of neuromuscular junction deterioration. Appendicular lean mass and physical activity level were similar between groups (p > 0.05), and only PP (p = 0.046; d = 0.79), RPD (p = 0.026; d = 0.90), RTD (p = 0.022; d = 0.91), and RER (p = 0.010; d = 1.04) were lower in older males. When groups were collapsed, RTD was the only significant predictor of PP, while c-terminal agrin levels were not associated with any variables. Our findings indicate that PP and time-dependent parameters of muscle activation and contractile function of the PFs are dramatically diminished in older adults compared to middle-aged adults. PP is produced at the same velocity and relative intensity in middle-aged and older males, and RTD is most influential for PP. The inability of the PFs to be rapidly activated appeared to be influential for the age-related impairment in PP and time-dependent contractile parameters.

Autocatalytic microtubule nucleation determines the size and mass of Xenopus laevis egg extract spindles.

Regulation of size and growth is a fundamental problem in biology. A prominent example is the formation of the mitotic spindle, where protein concentration gradients around chromosomes are thought to regulate spindle growth by controlling microtubule nucleation. Previous evidence suggests that microtubules nucleate throughout the spindle structure. However, the mechanisms underlying microtubule nucleation and its spatial regulation are still unclear. Here, we developed an assay based on laser ablation to directly probe microtubule nucleation events in Xenopus laevis egg extracts. Combining this method with theory and quantitative microscopy, we show that the size of a spindle is controlled by autocatalytic growth of microtubules, driven by microtubule-stimulated microtubule nucleation. The autocatalytic activity of this nucleation system is spatially regulated by the limiting amounts of active microtubule nucleators, which decrease with distance from the chromosomes. This mechanism provides an upper limit to spindle size even when resources are not limiting.

Nonlocal response functions for predicting shear flow of strongly inhomogeneous fluids. II. Sinusoidally driven shear and multisinusoidal inhomogeneity.

We use molecular-dynamics computer simulations to investigate the density, strain-rate, and shear-pressure responses of a simple model atomic fluid to transverse and longitudinal external forces. We have previously introduced a response function formalism for describing the density, strain-rate, and shear-pressure profiles in an atomic fluid when it is perturbed by a combination of longitudinal and transverse external forces that are independent of time and have a simple sinusoidal spatial variation. In this paper, we extend the application of the previously introduced formalism to consider the case of a longitudinal force composed of multiple sinusoidal components in combination with a single-component sinusoidal transverse force. We find that additional harmonics are excited in the density, strain-rate, and shear-pressure profiles due to couplings between the force components. By analyzing the density, strain-rate, and shear-pressure profiles in Fourier space, we are able to evaluate the Fourier coefficients of the response functions, which now have additional components describing the coupling relationships. Having evaluated the Fourier coefficients of the response functions, we are then able to accurately predict the density, velocity, and shear-pressure profiles for fluids that are under the influence of a longitudinal force composed of two or three sinusoidal components combined with a single-component sinusoidal transverse force. We also find that in the case of a multisinusoidal longitudinal force, it is sufficient to include only pairwise couplings between different longitudinal force components. This means that it is unnecessary to include couplings between three or more force components in the case of a longitudinal force composed of many Fourier components, and this paves the way for a highly accurate but tractable treatment of nonlocal transport phenomena in fluids with density and strain-rate inhomogeneities on the molecular length scale.

Nonlocal response functions for predicting shear flow of strongly inhomogeneous fluids. I. Sinusoidally driven shear and sinusoidally driven inhomogeneity.

We present theoretical expressions for the density, strain rate, and shear pressure profiles in strongly inhomogeneous fluids undergoing steady shear flow with periodic boundary conditions. The expressions that we obtain take the form of truncated functional expansions. In these functional expansions, the independent variables are the spatially sinusoidal longitudinal and transverse forces that we apply in nonequilibrium molecular-dynamics simulations. The longitudinal force produces strong density inhomogeneity, and the transverse force produces sinusoidal shear. The functional expansions define new material properties, the response functions, which characterize the system's nonlocal response to the longitudinal force and the transverse force. We find that the sinusoidal longitudinal force, which is mainly responsible for the generation of density inhomogeneity, also modulates the strain rate and shear pressure profiles. Likewise, we find that the sinusoidal transverse force, which is mainly responsible for the generation of sinusoidal shear flow, can also modify the density. These cross couplings between density inhomogeneity and shear flow are also characterized by nonlocal response functions. We conduct nonequilibrium molecular-dynamics simulations to calculate all of the response functions needed to describe the response of the system for weak shear flow in the presence of strong density inhomogeneity up to the third order in the functional expansion. The response functions are then substituted directly into the truncated functional expansions and used to predict the density, velocity, and shear pressure profiles. The results are compared to the directly evaluated profiles from molecular-dynamics simulations, and we find that the predicted profiles from the truncated functional expansions are in excellent agreement with the directly computed density, velocity, and shear pressure profiles.

Effects of nanoscale density inhomogeneities on shearing fluids.

It is well known that density inhomogeneities at the solid-liquid interface can have a strong effect on the velocity profile of a nanoconfined fluid in planar Poiseuille flow. However, it is difficult to control the density inhomogeneities induced by solid walls, making this type of system unsuitable for a comprehensive study of the effect on density inhomogeneity on nanofluidic flow. In this paper, we employ an external force compatible with periodic boundary conditions to induce the density variation, which greatly simplifies the problem when compared to flow in nonperiodic nanoconfined systems. Using the sinusoidal transverse force method to produce shearing velocity profiles and the sinusoidal longitudinal force method to produce inhomogeneous density profiles, we are able to observe the interactions between the two property inhomogeneities at the level of individual Fourier components. This gives us a method for direct measurement of the coupling between the density and velocity fields and allows us to introduce various feedback control mechanisms which customize fluid behavior in individual Fourier components. We briefly discuss the role of temperature inhomogeneity and consider whether local thermal expansion due to nonuniform viscous heating is sufficient to account for shear-induced density inhomogeneities. We also consider the local Newtonian constitutive relation relating the shear stress to the velocity gradient and show that the local model breaks down for sufficiently large density inhomogeneities over atomic length scales.