Rockets, gauges, and pendulums: applying engineering principles to cell biology

From flight to radar to Velcro, biological form and function have inspired engineers for centuries. It is equally valuable to consider whether concepts in engineering might provide insights into core biological processes. To explore this idea, cell cycle checkpoints, biological clocks, and signaling pathways are viewed here from an engineering perspective. Engineering concepts covered include gauge error, the distinction between precision and accuracy, and the Taguchi method of robust design. Also discussed is the Pareto principle, which describes the observation that, in complex systems, a minority of the components (or inputs) are responsible for a majority of the outputs. These concepts enable engineers to manage complexity, both in system design and in operation. Thus, with new techniques and large data sets revealing ever-increasing levels of biological complexity, an engineering mindset may be particularly valuable for the study of living systems.

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Engineering with Biomolecular Motors

Biomolecular motors, such as the motor protein kinesin, can be used as off-the-shelf components to power hybrid nanosystems. These hybrid systems combine elements from the biological and synthetic toolbox of the nanoengineer and can be used to explore the applications and design principles of active nanosystems.

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Low Efficiency Spotted in a Molecular Motor

Motor proteins are the engines of biology. They convert chemical energy into mechanical work to drive cell division, protein synthesis, muscle contraction, and other essential cellular processes. The motor protein kinesin carries vital cellular cargo through the cell by taking alternating steps along intracellular polymer tracks. A new study by Takayuki Ariga from Yamaguchi University, Japan, and colleagues has determined how much of the chemical energy is converted to mechanical work and how much is lost to heat for one type of kinesin called kinesin-1 [1]. The experiments, which use optical tweezers to exert an oscillating force on single motor proteins, show that kinesin-1 loses about 80% of its input energy to dissipation, or heat, within the molecule as it moves. Understanding the energy conversion by kinesin-1 compared to other motor proteins that are much more efficient could lead to insight into how the mechanochemistry of motor proteins is tuned for their specific cellular roles.

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Native-state fingerprint on the ubiquitin translocation across a nanopore

We study the translocation of the ubiquitin molecule (Ubq) across a channel with a double section which constitutes a general feature of several transmembrane nanopores such as the $\alpha$-hemolysin ($\alpha \mathrm{HL}$). Our purpose is to establish the structure-dependent character of the Ubq translocation pathway. This implies to find the correspondence, if any, between the translocational unfolding steps and the Ubq native state. For this reason, it is convenient to apply a coarse-grained computational approach, where the protein is described only by the backbone and the force field only exploits the information contained in the native state (in the spirit of Gō-like models, or native-centric models). The $\alpha \mathrm{HL}$-like pore is portrayed as two coaxial confining cylinders: a larger one for the vestibule and a narrower one for the barrel (or stem). Such simplified approach allows a large number of translocation events to be collected by limited computational resources. The co-translocational unfolding of Ubq is described via a few collective variables that characterize the translocation progress. We find two translocation intermediates (stalled conformations) that can be associated with specific unfolding stages. In particular, in the earliest step, the strand S5 unfolds and enters the pore. This step splits the native conformation into two structural clusters packing against each other in the Ubq fold. A second stall occurs when the hairpin of the N terminal engages the stem region.

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Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes

Membrane nanotubes are continuously assembled and disassembled by the cell to generate and dispatch transport vesicles, for instance, in endocytosis. While these processes crucially involve the ill-understood local mechanics of the nanotube, existing micromanipulation assays only give access to its global mechanical properties. Here we develop a new platform to study this local mechanics using atomic force microscopy (AFM). On a single coverslip we quickly generate millions of substrate-bound nanotubes, out of which dozens can be imaged by AFM in a single experiment. A full theoretical description of the AFM tip-membrane interaction allows us to accurately relate AFM measurements of the nanotube heights, widths, and rigidities to the membrane bending rigidity and tension, thus demonstrating our assay as an accurate probe of nanotube mechanics. We reveal a universal relationship between nanotube height and rigidity, which is unaffected by the specific conditions of attachment to the substrate. Moreover, we show that the parabolic shape of force-displacement curves results from thermal fluctuations of the membrane that collides intermittently with the AFM tip. We also show that membrane nanotubes can exhibit high resilience against extreme lateral compression. Finally, we mimic in vivo actin polymerization on nanotubes and use AFM to assess the induced changes in nanotube physical properties. Our assay may help unravel the local mechanics of membrane-protein interactions, including membrane remodeling in nanotube scission and vesicle formation.

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Motility and morphodynamics of confined cells

We introduce a minimal hydrodynamic model of polarization, migration, and deformation of a biological cell confined between two parallel surfaces. In our model, the cell is driven out of equilibrium by an active cytsokeleton force that acts on the membrane. The cell cytoplasm, described as a viscous droplet in the Darcy flow regime, contains a diffusive solute that actively transduces the applied cytoskeleton force. While fairly simple and analytically tractable, this quasi-two-dimensional model predicts a range of compelling dynamic behaviours. A linear stability analysis of the system reveals that solute activity first destabilizes a global polarization-translation mode, prompting cell motility through spontaneous symmetry breaking. At higher activity, the system crosses a series of Hopf bifurcations leading to coupled oscillations of droplet shape and solute concentration profiles. At the nonlinear level, we find traveling-wave solutions associated with unique polarized shapes that resemble experimental observations. Altogether, this model offers an analytical paradigm of active deformable systems in which viscous hydrodynamics are coupled to diffusive force transducers.

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Mechanosensitive self-assembly of myosin II minifilaments

Self-assembly and force generation are two central processes in biological systems that usually are considered in separation. However, the signals that activate nonmuscle myosin II molecular motors simultaneously lead to self-assembly into myosin II minifilaments as well as progression of the motor heads through the cross-bridge cycle. Here we investigate theoretically the possible effects of coupling these two processes. Our assembly model, which builds on a consensus architecture of the minifilament, predicts a critical aggregation concentration at which the assembly kinetics slows down dramatically. The combined model predicts that increasing actin filament concentration and force both lead to a decrease in the critical aggregation concentration. We suggest that due to these effects, myosin II minifilaments in a filamentous context might be in a critical state that reacts faster to varying conditions than in solution. We finally compare our model to experiments by simulating fluorescence recovery after photobleaching.

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Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum $\gamma$ oscillations have received particular attention due to their ubiquitous nature and their correlation with higher brain functions. Recently, it has been reported that $\gamma$ oscillations in the hippocampus of behaving rodents are segregated in two distinct frequency bands: slow and fast. These two $\gamma$ rhythms correspond to different states of the network, but their origin has been not yet clarified. Here we show theoretically and numerically that a single inhibitory population can give rise to coexisting slow and fast $\gamma$ rhythms corresponding to collective oscillations of a balanced spiking network. The slow and fast $\gamma$ rhythms are generated via two different mechanisms: the fast one being driven by the coordinated tonic neural firing and the slow one by endogenous fluctuations due to irregular neural activity. We show that almost instantaneous stimulations can switch the collective $\gamma$ oscillations from slow to fast and vice versa. Furthermore, to draw a connection with the experimental observations, we consider the modulation of the $\gamma$ rhythms induced by a slower ($\theta$) rhythm driving the network dynamics. In this context, depending on the strength of the forcing and the noise amplitude, we observe phase-amplitude and phase-phase coupling between the fast and slow $\gamma$ oscillations and the $\theta$ forcing. Phase-phase coupling reveals on average different $\theta$-phase preferences for the two coexisting $\gamma$ rhythms joined to a wide cycle-to-cycle variability.

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Explicit effect of stochastic reaction delay on gene expression

Apart from intrinsic stochastic variability, gene expression also involves stochastic reaction delay arising from heterogeneity and fluctuation processes, which can affect the efficiency of reactants (e.g., mRNA or protein) in exploring their environments. In contrast to the former that has been extensively investigated, the impact of the latter on gene expression remains not fully understood. Here, we analyze a non-Markovian model of bursty gene expression with general delay distribution. We analytically find that the effect of stochastic reaction delay is equivalent to the introduction of negative feedback, and stationary protein distribution only depends on the mean of the delay and is independent of its distribution. We numerically show that the stochastic reaction delay always slightly amplifies the mean protein level but remarkably reduces the protein noise (quantified by the ratio of the variance over the squared average). Our analysis indicates that stochastic reaction delay is an important factor affecting gene expression.

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Nonequilibrium physics in biology

Life is characterized by a myriad of complex dynamic processes allowing organisms to grow, reproduce, and evolve. Physical approaches for describing systems out of thermodynamic equilibrium have been increasingly applied to living systems, which often exhibit phenomena not found in those traditionally studied in physics. Spectacular advances in experimentation during the last decade or two, for example, in microscopy, single-cell dynamics, in the reconstruction of subcellular and multicellular systems outside of living organisms, and in high throughput data acquisition, have yielded an unprecedented wealth of data on cell dynamics, genetic regulation, and organismal development. These data have motivated the development and refinement of concepts and tools to dissect the physical mechanisms underlying biological processes. Notably, landscape and flux theory as well as active hydrodynamic gel theory have proven useful in this endeavor. Together with concepts and tools developed in other areas of nonequilibrium physics, significant progress has been made in unraveling the principles underlying efficient energy transport in photosynthesis, cellular regulatory networks, cellular movements and organization, embryonic development and cancer, neural network dynamics, population dynamics and ecology, as well as aging, immune responses, and evolution. Here recent advances in nonequilibrium physics are reviewed and their application to biological systems is surveyed. Many of these results are expected to be important cornerstones as the field continues to build our understanding of life.

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