HAT: Hypergraph analysis toolbox.

Recent advances in biological technologies, such as multi-way chromosome conformation capture (3C), require development of methods for analysis of multi-way interactions. Hypergraphs are mathematically tractable objects that can be utilized to precisely represent and analyze multi-way interactions. Here we present the Hypergraph Analysis Toolbox (HAT), a software package for visualization and analysis of multi-way interactions in complex systems.

Algorithm for cellular reprogramming.

The day we understand the time evolution of subcellular events at a level of detail comparable to physical systems governed by Newton's laws of motion seems far away. Even so, quantitative approaches to cellular dynamics add to our understanding of cell biology. With data-guided frameworks we can develop better predictions about, and methods for, control over specific biological processes and system-wide cell behavior. Here we describe an approach for optimizing the use of transcription factors (TFs) in cellular reprogramming, based on a device commonly used in optimal control. We construct an approximate model for the natural evolution of a cell-cycle-synchronized population of human fibroblasts, based on data obtained by sampling the expression of 22,083 genes at several time points during the cell cycle. To arrive at a model of moderate complexity, we cluster gene expression based on division of the genome into topologically associating domains (TADs) and then model the dynamics of TAD expression levels. Based on this dynamical model and additional data, such as known TF binding sites and activity, we develop a methodology for identifying the top TF candidates for a specific cellular reprogramming task. Our data-guided methodology identifies a number of TFs previously validated for reprogramming and/or natural differentiation and predicts some potentially useful combinations of TFs. Our findings highlight the immense potential of dynamical models, mathematics, and data-guided methodologies for improving strategies for control over biological processes.

Biomarker Selection for Adaptive Systems.

Biomarkers enable objective monitoring of a given cell or state in a biological system and are widely used in research, biomanufacturing, and clinical practice. However, identifying appropriate biomarkers that are both robustly measurable and capture a state accurately remains challenging. We present a framework for biomarker identification based upon observability guided sensor selection. Our methods, Dynamic Sensor Selection (DSS) and Structure-Guided Sensor Selection (SGSS), utilize temporal models and experimental data, offering a template for applying observability theory to unconventional data obtained from biological systems. Unlike conventional methods that assume well-known, fixed dynamics, DSS adaptively select biomarkers or sensors that maximize observability while accounting for the time-varying nature of biological systems. Additionally, SGSS incorporates structural information and diverse data to identify sensors which are resilient against inaccuracies in our model of the underlying system. We validate our approaches by performing estimation on high dimensional systems derived from temporal gene expression data from partial observations.

Nonholonomic double-bracket equations and the Gauss thermostat.

In this Rapid Communication we consider certain equations that arise from imposing a constant kinetic-energy constraint on a one-dimensional set of oscillators. This is a nonlinear nonholonomic constraint on these oscillators and the dynamics are consistent with Gauss's law of least constraint. Dynamics of this sort are of interest in nonequilibrium molecular dynamics. We show that under certain choices of external potential these equations give rise to a generalization of the so-called double-bracket equations which are of interest in studying gradient flows and integrable systems such as the Toda lattice. In the case of harmonic potentials the flow is described by a symmetric bracket and periodic solutions are obtained.

Optical mechanical analogy and nonlinear nonholonomic constraints.

In this paper we establish a connection between particle trajectories subject to a nonholonomic constraint and light ray trajectories in a variable index of refraction. In particular, we extend the analysis of systems with linear nonholonomic constraints to the dynamics of particles in a potential subject to nonlinear velocity constraints. We contrast the long time behavior of particles subject to a constant kinetic energy constraint (a thermostat) to particles with the constraint of parallel velocities. We show that, while in the former case the velocities of each particle equalize in the limit, in the latter case all the kinetic energies of each particle remain the same.

Optical mechanical analogy and Hamiltonization of a nonholonomic system.

It is well known that there is an analogy between optics and mechanics that prompted much of the classical theory of mechanics and indeed extended it to the theory of quantum mechanics. We develop here an optical mechanical analogy for a prototypical nonholonomic mechanical system, a knife edge moving on a plane under the influence of a potential. We show that this approach is related to but different from the classical theory of Hamiltonization of nonholonomic systems.

A new anterior cruciate ligament reconstruction fixation technique (quadrupled semitendinosus anterior cruciate ligament reconstruction with polyetheretherketone cage fixation).

Fixation of the graft during anterior cruciate ligament reconstruction surgery has been the subject of numerous technical innovations but still remains a challenge. This article describes a novel technique of graft fixation for hamstring tendon reconstruction: the Cage For One system (Sacimex, Aix-en-Provence, France). The technique uses only the semitendinosus tendon, which is looped to create a 4-strand graft. Leaving the gracilis tendon intact probably reduces the loss of knee flexion strength. The graft is indirectly anchored into both tunnels with polyetheretherketone cages by use of polyethylene terephthalate tape strips. Both cages and strips are magnetic resonance imaging compatible and do not create artifacts. The tunnels are drilled by an outside-in method with minimal incisions. This type of fixation creates a 360° bone contact at 1.5 cm in each tunnel and is compatible with double-bundle reconstruction. This easy-to-use novel technique of fixation for anterior cruciate ligament reconstruction produces a strong 4-strand graft while harvesting only the semitendinosus tendon and leaving the gracilis tendon intact to reduce flexion strength loss and preserve rotatory stability of the knee. It creates an immediate solid fixation that is independent of graft integration in the early postoperative period, allowing the patient to start immediate rehabilitation without the use of a brace.

Quantization of a nonholonomic system.

In this Letter, we consider the problem of quantizing a nonholonomic system. This is highly nontrivial since such a system, which is subject to nonholonomic constraints, is not variational (or Hamiltonian). Our approach is to couple the system to a field which enforces the constraint in a suitable limit. We consider a simple but representative nonholonomic system, the Chaplygin sleigh. We then quantize the full (Hamiltonian) system. This system exhibits a key complicating feature of some nonholonomic systems-internal dissipative dynamics.

Endpoint force fluctuations reveal flexible rather than synergistic patterns of muscle cooperation.

We developed a new approach to investigate how the nervous system activates multiple redundant muscles by studying the endpoint force fluctuations during isometric force generation at a multi-degree-of-freedom joint. We hypothesized that, due to signal-dependent muscle force noise, endpoint force fluctuations would depend on the target direction of index finger force and that this dependence could be used to distinguish flexible from synergistic activation of the musculature. We made high-gain measurements of isometric forces generated to different target magnitudes and directions, in the plane of index finger metacarpophalangeal joint abduction-adduction/flexion-extension. Force fluctuations from each target were used to calculate a covariance ellipse, the shape of which varied as a function of target direction. Directions with narrow ellipses were approximately aligned with the estimated mechanical actions of key muscles. For example, targets directed along the mechanical action of the first dorsal interosseous (FDI) yielded narrow ellipses, with 88% of the variance directed along those target directions. It follows the FDI is likely a prime mover in this target direction and that, at most, 12% of the force variance could be explained by synergistic coupling with other muscles. In contrast, other target directions exhibited broader covariance ellipses with as little as 30% of force variance directed along those target directions. This is the result of cooperation among multiple muscles, based on independent electromyographic recordings. However, the pattern of cooperation across target directions indicates that muscles are recruited flexibly in accordance with their mechanical action, rather than in fixed groupings.

Analysis of the effects of firing rate and synchronization on spike-triggered averaging of multidirectional motor unit torque.

Spike-triggered averaging (STA) of muscle force transients has often been used to estimate motor unit contractile properties, using the discharge of a motor unit within the muscle as the triggering events. For motor units that exert torque about multiple degrees-of-freedom, STA has also been used to estimate motor unit pulling direction. It is well known that motor unit firing rate and weak synchronization of motor unit discharges with other motor units in the muscle can distort STA estimates of contractile properties, but the distortion of STA estimates of motor unit pulling direction has not been thoroughly evaluated. Here, we derive exact equations that predict that STA decouples firing rate and synchronization distortion when used to estimate motor unit pulling direction. We derive a framework for analyzing synchronization, consider whether the distortion due to synchronization can be removed from STA estimates of pulling direction, and show that there are distributions of motor unit pulling directions for which STA is insensitive to synchronization. We conclude that STA may give insight into how motoneuronal synchronization is organized with respect to motor unit pulling direction.