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Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called "drive," that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed within individual movements. For regularities across movements, drive conservation predicts a previously unidentified scaling law between the overall size and speed of various self-paced hand movements in the absence of any external tasks, which we confirmed with psychophysical experiments. Drive can be interpreted as a high-level control variable that sets the overall pace of movements and may be represented in the brain as the tonic levels of neuromodulators that control the level of internal motivation, thus providing insights into how internal states affect biological motor control.

In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the -1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the -1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and -2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.

Many RNAs, proteins, and organelles are present in such low numbers per cell that random segregation of individual copies causes large "partitioning errors" at cell division. Even symmetrically dividing cells can then by chance produce daughters with very different composition. The size of the errors depends on the segregation mechanism: Control systems can reduce low-abundance errors, but the segregation process can also be subject to upstream sources of randomness or spatial heterogeneities that create large errors despite high abundances. Here we mathematically demonstrate how partitioning errors arise for different types of segregation mechanisms and how errors can be greatly increased by upstream heterogeneity but remarkably hard to avoid through controlled partitioning. We also show that seemingly straightforward experiments cannot be straightforwardly interpreted because very different mechanisms produce identical fits and present an approach to deal with this problem by adding binomial counting noise and testing for convexity or concavity in the partitioning error as a function of the binomial thinning parameter. The results lay a conceptual groundwork for more effective studies of heterogeneity among growing and dividing cells, whether in microbes or in differentiating tissues.

To perform nontrivial, real-time computations on a sensory input stream, biological systems must retain a short-term memory trace of their recent inputs. It has been proposed that generic high-dimensional dynamical systems could retain a memory trace for past inputs in their current state. This raises important questions about the fundamental limits of such memory traces and the properties required of dynamical systems to achieve these limits. We address these issues by applying Fisher information theory to dynamical systems driven by time-dependent signals corrupted by noise. We introduce the Fisher Memory Curve (FMC) as a measure of the signal-to-noise ratio (SNR) embedded in the dynamical state relative to the input SNR. The integrated FMC indicates the total memory capacity. We apply this theory to linear neuronal networks and show that the capacity of networks with normal connectivity matrices is exactly 1 and that of any network of N neurons is, at most, N. A nonnormal network achieving this bound is subject to stringent design constraints: It must have a hidden feedforward architecture that superlinearly amplifies its input for a time of order N, and the input connectivity must optimally match this architecture. The memory capacity of networks subject to saturating nonlinearities is further limited, and cannot exceed square root N. This limit can be realized by feedforward structures with divergent fan out that distributes the signal across neurons, thereby avoiding saturation. We illustrate the generality of the theory by showing that memory in fluid systems can be sustained by transient nonnormal amplification due to convective instability or the onset of turbulence.

We describe a microfabricated airway system integrated with computerized air-liquid two-phase microfluidics that enables on-chip engineering of human airway epithelia and precise reproduction of physiologic or pathologic liquid plug flows found in the respiratory system. Using this device, we demonstrate cellular-level lung injury under flow conditions that cause symptoms characteristic of a wide range of pulmonary diseases. Specifically, propagation and rupture of liquid plugs that simulate surfactant-deficient reopening of closed airways lead to significant injury of small airway epithelial cells by generating deleterious fluid mechanical stresses. We also show that the explosive pressure waves produced by plug rupture enable detection of the mechanical cellular injury as crackling sounds.