Design of Oscillatory Networks through Post-Translational Control of Network Components.

Many essential functions in biological systems, including cell cycle progression and circadian rhythm regulation, are governed by the periodic behaviors of specific molecules. These periodic behaviors arise from the precise arrangement of components in biomolecular networks that generate oscillatory output signals. The dynamic properties of individual components of these networks, such as maturation delays and degradation rates, often play a key role in determining the network's oscillatory behavior. In this study, we explored the post-translational modulation of network components as a means to generate genetic circuits with oscillatory behaviors and perturb the oscillation features. Specifically, we used the NanoDeg platform-A bifunctional molecule consisting of a target-specific nanobody and a degron tag-to control the degradation rates of the circuit's components and predicted the effect of NanoDeg-mediated post-translational depletion of a key circuit component on the behavior of a series of proto-oscillating network topologies. We modeled the behavior of two main classes of oscillators, namely relaxation oscillator topologies (the activator-repressor and the Goodwin oscillator) and ring oscillator topologies (repressilators). We identified two main mechanisms by which non-oscillating networks could be induced to oscillate through post-translational modulation of network components: an increase in the separation of timescales of network components and mitigation of the leaky expression of network components. These results are in agreement with previous findings describing the effect of timescale separation and mitigation of leaky expression on oscillatory behaviors. This work thus validates the use of tools to control protein degradation rates as a strategy to modulate existing oscillatory signals and construct oscillatory networks. In addition, this study provides the design rules to implement such an approach based on the control of protein degradation rates using the NanoDeg platform, which does not require genetic manipulation of the network components and can be adapted to virtually any cellular protein. This work also establishes a framework to explore the use of tools for post-translational perturbations of biomolecular networks and generates desired behaviors of the network output.

Retroactivity controls the temporal dynamics of gene transcription.

Just like in many engineering systems, impedance-like effects, called retroactivity, arise at the interconnection of biomolecular circuits, leading to unexpected changes in a circuit's behavior. In this paper, we provide a combined experimental and theoretical study to characterize the effects of retroactivity on the temporal dynamics of a gene transcription module in vivo. The response of the module to an inducer was measured both in isolation and when the module was connected to downstream clients. The connected module, when compared to the isolated module, responded selectively to the introduction of the inducer versus its withdrawal. Specifically, a "sign-sensitive delay" appeared, in which the connected module displayed a time delay in the response to induction and anticipation in the response to de-induction. The extent of these effects can be made larger by increasing the amounts of downstream clients and/or their binding affinity to the output protein of the module. Our experimental results and mathematical formulas make it possible to predict the extent of the change in the dynamic behavior of a module after interconnection. They can be employed to both recover the predictive power of a modular approach to understand systems or as an additional design tool to shape the temporal behavior of gene transcription.

Tuning genetic clocks employing DNA binding sites.

Periodic oscillations play a key role in cell physiology from the cell cycle to circadian clocks. The interplay of positive and negative feedback loops among genes and proteins is ubiquitous in these networks. Often, delays in a negative feedback loop and/or degradation rates are a crucial mechanism to obtain sustained oscillations. How does nature control delays and kinetic rates in feedback networks? Known mechanisms include proper selection of the number of steps composing a feedback loop and alteration of protease activity, respectively. Here, we show that a remarkably simple means to control both delays and effective kinetic rates is the employment of DNA binding sites. We illustrate this design principle on a widely studied activator-repressor clock motif, which is ubiquitous in natural systems. By suitably employing DNA target sites for the activator and/or the repressor, one can switch the clock "on" and "off" and precisely tune its period to a desired value. Our study reveals a design principle to engineer dynamic behavior in biomolecular networks, which may be largely exploited by natural systems and employed for the rational design of synthetic circuits.

Efficient 3-D TOF PET reconstruction using view-grouped histo-images: DIRECT-direct image reconstruction for TOF.

For modern time-of-flight (TOF) positron emission tomography (PET) systems, in which the number of possible lines of response and TOF bins is much larger than the number of acquired events, the most appropriate reconstruction approaches are considered to be list-mode methods. However, their shortcomings are relatively high computational costs for reconstruction and for sensitivity matrix calculation. Efficient treatment of TOF data within the proposed DIRECT approach is obtained by 1) angular (azimuthal and co-polar) grouping of TOF events to a set of views as given by the angular sampling requirements for the TOF resolution, and 2) deposition (weighted-histogramming) of these grouped events, and correction data, into a set of "histo-images," one histo-image per view. The histo-images have the same geometry (voxel grid, size and orientation) as the reconstructed image. The concept is similar to the approach involving binning of the TOF data into angularly subsampled histo-projections-projections expanded in the TOF directions. However, unlike binning into histo-projections, the deposition of TOF events directly into the image voxels eliminates the need for tracing and/or interpolation operations during the reconstruction. Together with the performance of reconstruction operations directly in image space, this leads to a very efficient implementation of TOF reconstruction algorithms. Furthermore, the resolution properties are not compromised either, since events are placed into the image elements of the desired size from the beginning. Concepts and efficiency of the proposed data partitioning scheme are demonstrated in this work by using the DIRECT approach in conjunction with the row-action maximum-likelihood (RAMLA) algorithm.