We derive general equations of motions for highly-confined particles that perform quasi-two-dimensional motion in Hele-Shaw channels, which we solve analytically, aiming to derive design principles for self-steering particles. Based on symmetry properties of a particle, its equations of motion can be simplified, where we retrieve an earlier-known equation of motion for the orientation of dimer particles consisting of disks (Uspal et al 2013 Nat. Commun. 4), but now in full generality. Subsequently, these solutions are compared with particle trajectories that are obtained numerically. For mirror-symmetric particles, excellent agreement between the analytical and numerical solutions is found. For particles lacking mirror symmetry, the analytic solutions provide means to classify the motion based on particle geometry, while we find that taking the side-wall interactions into account is important to accurately describe the trajectories.

We combine theory and numerical calculations to accurately predict the motion of anisotropic particles in shallow microfluidic channels, in which the particles are strongly confined in the vertical direction. We formulate an effective quasi-two-dimensional description of the Stokes flow around the particle via the Brinkman equation, which can be solved in a time that is two orders of magnitude faster than the three-dimensional problem. The computational speedup enables us to calculate the full trajectories of particles in the channel. To validate our scheme, we study the motion of dumbbell-shaped particles that are produced in a microfluidic channel using ‘continuous-flow lithography’. Contrary to what was reported in earlier work (Uspal et al. in Nat Commun 4:2666, 2013 ), we find that the reorientation time of a dumbbell particle in an external flow exhibits a minimum as a function of its disk size ratio. This finding is in excellent agreement with new experiments, thus confirming the predictive power of our scheme. Electronic supplementary material The online version of this article (10.1007/s10404-018-2092-y) contains supplementary material, which is available to authorized users.

Comprehensive understanding of particle motion in microfluidic devices is essential to unlock additional technologies for shape-based separation and sorting of microparticles like microplastics, cells, and crystal polymorphs. Such particles interact hydrodynamically with confining surfaces, thus altering their trajectories. These hydrodynamic interactions are shape dependent and can be tuned to guide a particle along a specific path. We produce strongly confined particles with various shapes in a shallow microfluidic channel via stop flow lithography. Regardless of their exact shape, particles with a single mirror plane have identical modes of motion: in-plane rotation and cross-stream translation along a bell-shaped path. Each mode has a characteristic time, determined by particle geometry. Furthermore, each particle trajectory can be scaled by its respective characteristic times onto two master curves. We propose minimalistic relations linking these timescales to particle shape. Together these master curves yield a trajectory universal to particles with a single mirror plane.

The ability of cells to respond to external stimuli, by up and down regulation of genes, is a key strategy for survival in changing environmental conditions. Models based on equilibrium statistical mechanics have been able to successfully predict in vivo fold changes in gene expression by computing weights of configurational states of the promoter where genes can be expressed. These models are based on the same, perhaps unintuitive, assumption that transcription initiation-an inherently nonequilibrium process-can indeed be effectively described by the equilibrium binding of transcription factors (TFs) and polymerases to the promoter. The few earlier studies that independently test this assumption [P. H. von Hippel et al., Proc. Natl. Acad. Sci. USA 71, 4808 (1974)], were published before much of our modern day understanding of molecular biology was established, and their models fail to explain more recent experimental results. As such, it is not obvious that the original conclusions remain valid. Equilibrium models depend on fitted free energy differences between binding of TFs to specific operator sites versus nonspecific DNA. In this article we compare the fitted binding free energy of the well-studied LacI repressor to equilibrium binding constants measured in independent in vitro experiments. To make this comparison we take into account the distribution of binding energies of the transcription factor to the nonspecific DNA, and we adjust LacI binding constants to a common set of physiological conditions. We find that the fitted binding energies of the LacI repressor in vivo indeed agree with in vitro measured equilibrium binding constants, reestablishing the idea that equilibrium statistical mechanical models of transcriptional regulation should be viewed not merely as mathematical tools, but also as informative physical representations of underlying TF-DNA interactions.