How does one optimally determine the diffusion coefficient of a diffusing particle from a single-time-lapse recorded trajectory of the particle? We answer this question with an explicit, unbiased, and practically optimal covariance-based estimator (CVE). This estimator is regression-free and is far superior to commonly used methods based on measured mean squared displacements. In experimentally relevant parameter ranges, it also outperforms the analytically intractable and computationally more demanding maximum likelihood estimator (MLE). For the case of diffusion on a flexible and fluctuating substrate, the CVE is biased by substrate motion. However, given some long time series and a substrate under some tension, an extended MLE can separate particle diffusion on the substrate from substrate motion in the laboratory frame. This provides benchmarks that allow removal of bias caused by substrate fluctuations in CVE. The resulting unbiased CVE is optimal also for short time series on a fluctuating substrate. We have applied our estimators to human 8-oxoguanine DNA glycolase proteins diffusing on flow-stretched DNA, a fluctuating substrate, and found that diffusion coefficients are severely overestimated if substrate fluctuations are not accounted for.

Empirical data on contacts between individuals in social contexts play an important role in providing information for models describing human behavior and how epidemics spread in populations. Here, we analyze data on face-to-face contacts collected in an office building. The statistical properties of contacts are similar to other social situations, but important differences are observed in the contact network structure. In particular, the contact network is strongly shaped by the organization of the offices in departments, which has consequences in the design of accurate agent-based models of epidemic spread. We consider the contact network as a potential substrate for infectious disease spread and show that its sparsity tends to prevent outbreaks of rapidly spreading epidemics. Moreover, we define three typical behaviors according to the fraction f of links each individual shares outside its own department: residents, wanderers and linkers. Linkers ( f ∼ 50%) act as bridges in the network and have large betweenness centralities. Thus, a vaccination strategy targeting linkers efficiently prevents large outbreaks. As such a behavior may be spotted a priori in the offices' organization or from surveys, without the full knowledge of the time-resolved contact network, this result may help the design of efficient, low-cost vaccination or social-distancing strategies.

Filopodia are dynamic, finger-like plasma membrane protrusions that sense the mechanical and chemical surroundings of the cell. Here, we show in epithelial cells that the dynamics of filopodial extension and retraction are determined by the difference between the actin polymerization rate at the tip and the retrograde flow at the base of the filopodium. Adhesion of a bead to the filopodial tip locally reduces actin polymerization and leads to retraction via retrograde flow, reminiscent of a process used by pathogens to invade cells. Using optical tweezers, we show that filopodial retraction occurs at a constant speed against counteracting forces up to 50 pN. Our measurements point toward retrograde flow in the cortex together with frictional coupling between the filopodial and cortical actin networks as the main retraction-force generator for filopodia. The force exerted by filopodial retraction, however, is limited by the connection between filopodial actin filaments and the membrane at the tip. Upon mechanical rupture of the tip connection, filopodia exert a passive retraction force of 15 pN via their plasma membrane. Transient reconnection at the tip allows filopodia to continuously probe their surroundings in a load-and-fail manner within a welldefined force range.cytoskeleton | mechanics | membrane-tension | pulling | lamellipodium