Self-consistent theory of transcriptional control in complex regulatory architectures.

Individual regulatory proteins are typically charged with the simultaneous regulation of a battery of different genes. As a result, when one of these proteins is limiting, competitive effects have a significant impact on the transcriptional response of the regulated genes. Here we present a general framework for the analysis of any generic regulatory architecture that accounts for the competitive effects of the regulatory environment by isolating these effects into an effective concentration parameter. These predictions are formulated using the grand-canonical ensemble of statistical mechanics and the fold-change in gene expression is predicted as a function of the number of transcription factors, the strength of interactions between the transcription factors and their DNA binding sites, and the effective concentration of the transcription factor. The effective concentration is set by the transcription factor interactions with competing binding sites within the cell and is determined self-consistently. Using this approach, we analyze regulatory architectures in the grand-canonical ensemble ranging from simple repression and simple activation to scenarios that include repression mediated by DNA looping of distal regulatory sites. It is demonstrated that all the canonical expressions previously derived in the case of an isolated, non-competing gene, can be generalised by a simple substitution to their grand canonical counterpart, which allows for simple intuitive incorporation of the influence of multiple competing transcription factor binding sites. As an example of the strength of this approach, we build on these results to present an analytical description of transcriptional regulation of the lac operon.

The transcription factor titration effect dictates level of gene expression.

Models of transcription are often built around a picture of RNA polymerase and transcription factors (TFs) acting on a single copy of a promoter. However, most TFs are shared between multiple genes with varying binding affinities. Beyond that, genes often exist at high copy number-in multiple identical copies on the chromosome or on plasmids or viral vectors with copy numbers in the hundreds. Using a thermodynamic model, we characterize the interplay between TF copy number and the demand for that TF. We demonstrate the parameter-free predictive power of this model as a function of the copy number of the TF and the number and affinities of the available specific binding sites; such predictive control is important for the understanding of transcription and the desire to quantitatively design the output of genetic circuits. Finally, we use these experiments to dynamically measure plasmid copy number through the cell cycle.

Scaling of gene expression with transcription-factor fugacity.

The proteins associated with gene regulation are often shared between multiple pathways simultaneously. By way of contrast, models in regulatory biology often assume these pathways act independently. We demonstrate a framework for calculating the change in gene expression for the interacting case by decoupling repressor occupancy across the cell from the gene of interest by way of a chemical potential. The details of the interacting regulatory architecture are encompassed in an effective concentration, and thus, a single scaling function describes a collection of gene expression data from diverse regulatory situations and collapses it onto a single master curve.

Optical fluid and biomolecule transport with thermal fields.

A long standing goal is the direct optical control of biomolecules and water for applications ranging from microfluidics over biomolecule detection to non-equilibrium biophysics. Thermal forces originating from optically applied, dynamic microscale temperature gradients have shown to possess great potential to reach this goal. It was demonstrated that laser heating by a few Kelvin can generate and guide water flow on the micrometre scale in bulk fluid, gel matrices or ice without requiring any lithographic structuring. Biomolecules on the other hand can be transported by thermal gradients, a mechanism termed thermophoresis, thermal diffusion or Soret effect. This molecule transport is the subject of current research, however it can be used to both characterize biomolecules and to record binding curves of important biological binding reactions, even in their native matrix of blood serum. Interestingly, thermophoresis can be easily combined with the optothermal fluid control. As a result, molecule traps can be created in a variety of geometries, enabling the trapping of small biomolecules, like for example very short DNA molecules. The combination with DNA replication from thermal convection allows us to approach molecular evolution with concurrent replication and selection processes inside a single chamber: replication is driven by thermal convection and selection by the concurrent accumulation of the DNA molecules. From the short but intense history of applying thermal fields to control fluid flow and biological molecules, we infer that many unexpected and highly synergistic effects and applications are likely to be explored in the future.

An optical conveyor for molecules.

Trapping single ions under vacuum allows for precise spectroscopy in atomic physics. The confinement of biological molecules in bulk water is hindered by the lack of comparably strong forces. Molecules have been immobilized to surfaces, however often with detrimental effects on their function. Here, we optically trap molecules by creating the microscale analogue of a conveyor belt: a bidirectional flow is combined with a perpendicular thermophoretic molecule drift. Arranged in a toroidal geometry, the conveyor accumulates a hundredfold excess of 5-base DNA within seconds. The concentrations of the trapped DNA scale exponentially with length, reaching trapping potential depths of 14 kT for 50 bases. The mechanism does not require microfluidics, electrodes, or surface modifications. As a result, the trap can be dynamically relocated. The optical conveyor can be used to enhance diffusion-limited surface reactions, redirect cellular signaling, observe individual biomolecules over a prolonged time, or approach single-molecule chemistry in bulk water.

Observation of slip flow in thermophoresis.

Two differing theories aim to describe fluidic thermophoresis, the movement of particles along a temperature gradient. While thermodynamic approaches rely on local equilibrium, hydrodynamic descriptions assume a quasi-slip-flow boundary condition at the particle's surface. Evidence for slip flow is presented for the case of thermal gradients exceeding (aS_(T)(-1) with particle radius a and Soret coefficient S_(T). Thermophoretic slip flow at spheres near a surface attracts or repels tracer particles perpendicular to the thermal gradient. Moreover, particles mutually attract and form colloidal crystals. Fluid dynamic slip explains the latter quantitatively.

Microscale fluid flow induced by thermoviscous expansion along a traveling wave.

The thermal expansion of a fluid combined with a temperature-dependent viscosity introduces nonlinearities in the Navier-Stokes equations unrelated to the convective momentum current. The couplings generate the possibility for net fluid flow at the microscale controlled by external heating. This novel thermomechanical effect is investigated for a thin fluid chamber by a numerical solution of the Navier-Stokes equations and analytically by a perturbation expansion. A demonstration experiment confirms the basic mechanism and quantitatively validates our theoretical analysis.

Extreme accumulation of nucleotides in simulated hydrothermal pore systems.

We simulate molecular transport in elongated hydrothermal pore systems influenced by a thermal gradient. We find extreme accumulation of molecules in a wide variety of plugged pores. The mechanism is able to provide highly concentrated single nucleotides, suitable for operations of an RNA world at the origin of life. It is driven solely by the thermal gradient across a pore. On the one hand, the fluid is shuttled by thermal convection along the pore, whereas on the other hand, the molecules drift across the pore, driven by thermodiffusion. As a result, millimeter-sized pores accumulate even single nucleotides more than 10(8)-fold into micrometer-sized regions. The enhanced concentration of molecules is found in the bulk water near the closed bottom end of the pore. Because the accumulation depends exponentially on the pore length and temperature difference, it is considerably robust with respect to changes in the cleft geometry and the molecular dimensions. Whereas thin pores can concentrate only long polynucleotides, thicker pores accumulate short and long polynucleotides equally well and allow various molecular compositions. This setting also provides a temperature oscillation, shown previously to exponentially replicate DNA in the protein-assisted PCR. Our results indicate that, for life to evolve, complicated active membrane transport is not required for the initial steps. We find that interlinked mineral pores in a thermal gradient provide a compelling high-concentration starting point for the molecular evolution of life.