Domitilla Del Vecchio

Modular cell biology: retroactivity and insulation

Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon interconnection. Just as electrical, hydraulic, and other physical systems often do not display modularity, nor do many biochemical systems, and specifically, genetic networks. Here, we study the effect of interconnections on the input–output dynamic characteristics of transcriptional components, focusing on a property, which we call ‘retroactivity’, that plays a role analogous to non‐zero output impedance in electrical systems. In transcriptional networks, retroactivity is large when the amount of transcription factor is comparable to, or smaller than, the amount of promoter‐binding sites, or when the affinity of such binding sites is high. To attenuate the effect of retroactivity, we propose a feedback mechanism inspired by the design of amplifiers in electronics. We introduce, in particular, a mechanism based on a phosphorylation–dephosphorylation cycle. This mechanism enjoys a remarkable insulation property, due to the fast timescales of the phosphorylation and dephosphorylation reactions.

Decomposition of human motion into dynamics-based primitives with application to drawing tasks

Using tools from dynamical systems and systems identification, we develop a framework for the study of primitives for human motion, which we refer to as movemes. The objective is understanding human motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet of dynamical systems. We develop a segmentation and classification algorithm in order to reduce a complex activity into the sequence of movemes that have generated it. We test our ideas on data sampled from five human subjects who were drawing figures using a computer mouse. Our experiments show that we are able to distinguish between movemes and recognize them even when they take place in activities containing an unspecified number of movemes.

Cooperative Collision Avoidance at Intersections: Algorithms and Experiments

In this paper, we leverage vehicle-to-vehicle (V2V) communication technology to implement computationally efficient decentralized algorithms for two-vehicle cooperative collision avoidance at intersections. Our algorithms employ formal control theoretic methods to guarantee a collision-free (safe) system, whereas overrides are only applied when necessary to prevent a crash. Model uncertainty and communication delays are explicitly accounted for by the model and by the state estimation algorithm. The main contribution of this work is to provide an experimental validation of our method on two instrumented vehicles engaged in an intersection collision avoidance scenario in a test track.

Signaling properties of a covalent modification cycle are altered by a downstream target

We used a model system of purified components to explore the effects of a downstream target on the signaling properties of a covalent modification cycle, an example of retroactivity. In the experimental system used, a bifunctional enzyme catalyzed the modification and demodification of its substrate protein, with both activities regulated by a small molecule stimulus. Here we examined how a downstream target for one or both forms of the substrate of the covalent modification cycle affected the steady-state output of the system, the sensitivity of the response to the stimulus, and the concentration of the stimulus required to provide the half-maximal response (S50). When both the modified and unmodified forms of the substrate protein were sequestered by the downstream target, the sensitivity of the response was dramatically decreased, but the S50 was only modestly affected. Conversely, when the downstream target only sequestered the unmodified form of the substrate protein, significant effects were observed on both system sensitivity and S50. Behaviors of the experimental systems were well approximated both by simple models allowing analytical solutions and by a detailed model based on the known interactions and enzymatic activities. Modeling and experimentation indicated that retroactivity may result in subsensitive responses, even if the covalent modification cycle displays significant ultrasensitivity in the absence of retroactivity. Thus, we provide examples of how a downstream target can alter the signaling properties of an upstream signal transduction covalent modification cycle.

Efficient algorithms for collision avoidance at intersections

We consider the problem of synthesising the least restrictive controller for collision avoidance of multiple vehicles at an intersection. The largest set of states for which there exists a control that avoids collisions is known as the maximal controlled invariant set. Exploiting results from the scheduling literature we prove that, for a general model of vehicle dynamics at an intersection, the problem of checking membership in the maximal controlled invariant set is NP-hard. We then describe an algorithm that solves this problem approximately and with provable error bounds. The approximate solution is used to design a supervisor for collision avoidance whose complexity scales polynomially with the number of vehicles. The supervisor is based on a hybrid algorithm that employs a dynamic model of the vehicles and periodically solves a scheduling problem.

Load-Induced Modulation of Signal Transduction Networks

The presence of downstream partners that interact with enzymatically modified or unmodified signaling proteins changes the dynamics of signal transduction. Modifying Signal Transduction Dynamics Signal transduction cascades exhibit complex dynamics, and theoretical studies have suggested that, like electrical and mechanical systems, the behavior of signaling modules can be affected by the presence of downstream targets, which act as “loads” on the system. Jiang et al. combined mathematical theory with an in vitro–reconstituted signaling network to show that the presence or absence of downstream targets that functioned as loads altered the dynamics of the system. Their work provides strong experimental evidence, backed by theory, that the bandwidth for information processing and the response time of the system are both affected by the presence of loads. This load-induced modulation of signaling dynamics may allow tuning of the signaling cascade to reduce the effects of noise or minimize crosstalk among pathways that share components. Biological signal transduction networks are commonly viewed as circuits that pass along information—in the process amplifying signals, enhancing sensitivity, or performing other signal-processing tasks—to transcriptional and other components. Here, we report on a “reverse-causality” phenomenon, which we call load-induced modulation. Through a combination of analytical and experimental tools, we discovered that signaling was modulated, in a surprising way, by downstream targets that receive the signal and, in doing so, apply what in physics is called a load. Specifically, we found that non-intuitive changes in response dynamics occurred for a covalent modification cycle when load was present. Loading altered the response time of a system, depending on whether the activity of one of the enzymes was maximal and the other was operating at its minimal rate or whether both enzymes were operating at submaximal rates. These two conditions, which we call “limit regime” and “intermediate regime,” were associated with increased or decreased response times, respectively. The bandwidth, the range of frequency in which the system can process information, decreased in the presence of load, suggesting that downstream targets participate in establishing a balance between noise-filtering capabilities and a circuit’s ability to process high-frequency stimulation. Nodes in a signaling network are not independent relay devices, but rather are modulated by their downstream targets.

Retroactivity Attenuation in Bio-Molecular Systems Based on Timescale Separation

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.

Development of a Scaled Vehicle With Longitudinal Dynamics of an HMMWV for an ITS Testbed

This paper applies Buckinghams pi theorem to the problem of building a scaled car whose longitudinal and power-train dynamics are similar to those of a full-size high-mobility multipurpose wheeled vehicle (HMMWV). The scaled vehicle uses hardware-in-the-loop (HIL) simulation to capture some of the scaled HMMWV dynamics physically, and simulates the remaining dynamics onboard in real time. This is performed with the ultimate goal of testing cooperative collision avoidance algorithms on a testbed comprising a number of these scaled vehicles. Both simulation and experimental results demonstrate the validity of this HIL-based scaling approach.

Least Restrictive Supervisors for Intersection Collision Avoidance: A Scheduling Approach

We consider a cooperative conflict resolution problem that finds application, for example, in vehicle intersection crossing. We seek to determine minimally restrictive supervisors, which allow agents to choose all possible control actions that keep the system safe, that is, conflict free. This is achieved by determining the maximal controlled invariant set, and then by determining control actions that keep the system state inside this set. By exploiting the natural monotonicity of the agents dynamics along their paths, we translate this problem into an equivalent scheduling problem. This allows us to leverage existing results in the scheduling literature to obtain both exact and approximate solutions. The approximate algorithms have polynomial complexity and can handle large problems with guaranteed approximation bounds. We illustrate the application of the proposed algorithms through simulations in which vehicles crossing an intersection are overridden by the supervisor only when necessary to maintain safety.

Isocost Lines Describe the Cellular Economy of Genetic Circuits

Genetic circuits in living cells share transcriptional and translational resources that are available in limited amounts. This leads to unexpected couplings among seemingly unconnected modules, which result in poorly predictable circuit behavior. In this study, we determine these interdependencies between products of different genes by characterizing the economy of how transcriptional and translational resources are allocated to the production of proteins in genetic circuits. We discover that, when expressed from the same plasmid, the combinations of attainable protein concentrations are constrained by a linear relationship, which can be interpreted as an isocost line, a concept used in microeconomics. We created a library of circuits with two reporter genes, one constitutive and the other inducible in the same plasmid, without a regulatory path between them. In agreement with the model predictions, experiments reveal that the isocost line rotates when changing the ribosome binding site strength of the inducible gene and shifts when modifying the plasmid copy number. These results demonstrate that isocost lines can be employed to predict how genetic circuits become coupled when sharing resources and provide design guidelines for minimizing the effects of such couplings.