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.

Abstract-As with several engineering systems, bio-molecular systems display impedance-like effects at interconnections, called retroactivity. In this paper, we propose a mechanism that exploits the natural timescale separation present in bio-molecular systems to attenuate retroactivity. Retroactivity enters the dynamics of a bio-molecular system as a state dependent disturbance multiplied by gains that can be very large. By virtue of the system structure, retroactivity can be arbitrarily attenuated by internal system gains even when these are much smaller than the gains multiplying retroactivity terms. This result is obtained by employing a suitable change of coordinates and a nested application of the singular perturbation theorem on the finite time interval. As an application example, we show that two modules extracted from natural signal transduction pathways have a remarkable capability of attenuating retroactivity, which is certainly desirable in any (engineered or natural) signal transmission system.

For modern Time-Of-Flight 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 sub-sampled 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.