Isaac Klickstein

Afroza Shirin, Isaac Klickstein, Song Feng et al.

The effects of molecularly targeted drug perturbations on cellular activities and fates are difficult to predict using intuition alone because of the complex behaviors of cellular regulatory networks. An approach to overcoming this problem is to develop mathematical models for predicting drug effects. Such an approach beckons for co-development of computational methods for extracting insights useful for guiding therapy selection and optimizing drug scheduling. Here, we present and evaluate a generalizable strategy for identifying drug dosing schedules that minimize the amount of drug needed to achieve sustained suppression or elevation of an important cellular activity/process, the recycling of cytoplasmic contents through (macro)autophagy. Therapeutic targeting of autophagy is currently being evaluated in diverse clinical trials but without the benefit of a control engineering perspective. Using a nonlinear ordinary differential equation (ODE) model that accounts for activating and inhibiting influences among protein and lipid kinases that regulate autophagy (MTORC1, ULK1, AMPK and VPS34) and methods guaranteed to find locally optimal control strategies, we find optimal drug dosing schedules (open-loop controllers) for each of six classes of drugs and drug pairs. Our approach is generalizable to designing monotherapy and multi therapy drug schedules that affect different cell signaling networks of interest.

Afroza Shirin, Fabio Della Rossa, Isaac Klickstein et al.

The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.

Isaac Klickstein, Francesco Sorrentino

The control of complex networks has generated a lot of interest in a variety of fields from traffic management to neural systems. A commonly used metric to compare two particular control strategies that accomplish the same task is the control energy, the integral of the sum of squares of all control inputs. The minimum control energy problem determines the control input that lower bounds all other control inputs with respect to their control energies. Here, we focus on the infinite lattice graph with linear dynamics and analytically derive the expression for the minimum control energy in terms of the modified Bessel function. We then demonstrate that the control energy of the infinite lattice graph accurately predicts the control energy of finite lattice graphs.

Ishan Kafle, Sudarshan Bartaula, Afroza Shirin et al.

We consider the problem of a dynamical network whose dynamics is subject to external perturbations (`attacks') locally applied at a subset of the network nodes. We assume that the network has an ability to defend itself against attacks with appropriate countermeasures, which we model as actuators located at (another) subset of the network nodes. We derive the optimal defense strategy as an optimal control problem. We see that the network topology, as well as the distribution of attackers and defenders over the network affect the optimal control solution and the minimum control energy. We study the optimal control defense strategy for several network topologies, including chain networks, star networks, ring networks, and scale free networks.

Isaac Klickstein, Francesco Sorrentino

The control of dynamical, networked systems continues to receive much attention across the engineering and scientific research fields. Of particular interest is the proper way to determine which nodes of the network should receive external control inputs in order to effectively and efficiently control portions of the network. Published methods to accomplish this task either find a minimal set of driver nodes to guarantee controllability or a larger set of driver nodes which optimizes some control metric. Here, we investigate the control of lattice systems which provides analytical insight into the relationship between network structure and controllability. First we derive a closed form expression for the individual elements of the controllability Gramian of infinite lattice systems. Second, we focus on nearest neighbor lattices for which the distance between nodes appears in the expression for the controllability Gramian. We show that common control energy metrics scale exponentially with respect to the maximum distance between a driver node and a target node.