Optimal Control Strategies for Complex Biological Systems

To better understand and to improve therapies for complex diseases such as cancer or diabetes, it is not sufficient to identify and characterize the interactions between molecules and pathways in complex biological systems, such as cells, tissues, and the human body. It also is necessary to characterize the response of a biological system to externally supplied agents (e.g., drugs, insulin), including a proper scheduling of these drugs, and drug combinations in multi drugs therapies. This obviously becomes important in applications which involve control of physiological processes, such as controlling the number of autophagosome vesicles in a cell, or regulating the blood glucose level in patients affected by diabetes. A critical consideration when controlling physiological processes in biological systems is to reduce the amount of drugs used, as in some therapies drugs may become toxic when they are overused. All of the above aspects can be addressed by using tools provided by the theory of optimal control, where the externally supplied drugs or hormones are the inputs to the system. Another important aspect of using optimal control theory in biological systems is to identify the drug or the combination of drugs that are effective in regulating a given therapeutic target, i.e., a biological target of the externally supplied stimuli. The dynamics of the key features of a biological system can be modeled and described as a set of nonlinear differential equations. For the implementation of optimal control theory in complex biological systems, in what follows we extract \textit{a network} from the dynamics. Namely, to each state variable $x_i$ we will assign a network node $v_i$ ($i=1,...,N$) and a network directed edge from node $v_i$ to another node $v_j$ will be assigned every time $x_j$ is present in the time derivative of $x_i$. The node which directly receives an external stimulus is called a \emph{driver nodes} in a network. The node which directly connected to an output sensor is called a \emph{target node}. %, and it has a prescribed final state that we wish to achieve in finite time. From the control point of view, the idea of controllability of a system describes the ability to steer the system in a certain time interval towards thea desired state with a suitable choice of control inputs. However, defining controllability of large complex networks is quite challenging, primarily because of the large size of the network, its complex structure, and poor knowledge of the precise network dynamics. A network can be controllable in theory but not in practice when a very large control effort is required to steer the system in the desired direction. This thesis considers several approaches to address some of these challenges. Our first approach is to reduce the control effort is to reduce the number of target nodes. We see that by controlling the states of a subset of the network nodes, rather than the state of every node, while holding the number of control signals constant, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. We call this strategy \emph{target control}. As our second approach is based on reducing the control efforts by allowing the prescribed final states are satisfied approximately rather than strictly. We introduce a new control strategy called \textit{balanced control} for which we set our objective function as a convex combination of two competitive terms: (i) the distance between the output final states at a given final time and given prescribed states and (ii) the total control efforts expenditure over the given time period. Based on the above two approaches, we propose an algorithm which provides a locally optimal control technique for a network with nonlinear dynamics. We also apply pseudo-spectral optimal control, together with the target and balance control strategies previously described, to complex networks with nonlinear dynamics. These optimal control techniques empower us to implement the theoretical control techniques to biological systems evolving with very large, complex and nonlinear dynamics. We use these techniques to derive the optimal amounts of several drugs in a combination and their optimal dosages. First, we provide a prediction of optimal drug schedules and combined drug therapies for controlling the cell signaling network that regulates autophagy in a cell. Second, we compute an optimal dual drug therapy based on administration of both insulin and glucagon to control the blood glucose level in type I diabetes. Finally, we also implement the combined control strategies to investigate the emergence of cascading failures in the power grid networks

Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon

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.Comment: Accepted for publication in PLOS ON

Host-directed therapies for tuberculosis: quantitative systems pharmacology approaches

Host-directed therapies (HDTs) that modulate host-pathogen interactions offer an innovative strategy to combat Mycobacterium tuberculosis (Mtb) infections. When combined with tuberculosis (TB) antibiotics, HDTs could contribute to improving treatment outcomes, reducing treatment duration, and preventing resistance development. Translation of the interplay of host-pathogen interactions leveraged by HDTs towards therapeutic outcomes in patients is challenging. Quantitative understanding of the multifaceted nature of the host-pathogen interactions is vital to rationally design HDT strategies. Here, we (i) provide an overview of key Mtb host-pathogen interactions as basis for HDT strategies; and (ii) discuss the components and utility of quantitative systems pharmacology (QSP) models to inform HDT strategies. QSP models can be used to identify and optimize treatment targets, to facilitate preclinical to human translation, and to design combination treatment strategies.Animal science

Circadian Genes as Therapeutic Targets in Pancreatic Cancer

JL was supported by the Nicolás Monardes Program from the Andalusian Health Service (C-0033-2015). This work was supported by a research grant from the Instituto de Salud Carlos III-FEDER (PI18/01947).Pancreatic cancer is one of the most lethal cancers worldwide due to its symptoms, early metastasis, and chemoresistance. Thus, the mechanisms contributing to pancreatic cancer progression require further exploration. Circadian rhythms are the daily oscillations of multiple biological processes regulated by an endogenous clock. Several evidences suggest that the circadian clock may play an important role in the cell cycle, cell proliferation and apoptosis. In addition, timing of chemotherapy or radiation treatment can influence the efficacy and toxicity treatment. Here, we revisit the studies on circadian clock as an emerging target for therapy in pancreatic cancer. We highlight those potential circadian genes regulators that are commonly affected in pancreatic cancer according to most recent reports.Nicolás Monardes Program from the Andalusian Health Service (C-0033-2015)Instituto de Salud Carlos III-FEDER (PI18/01947

Adjusting the molecular clock: The importance of circadian rhythms in the development of glioblastomas and its intervention as a therapeutic strategy

Gliomas are solid tumors of the central nervous system (CNS) that originated from differentglial cells. The World Health Organization (WHO) classifies these tumors into four groups (I-IV)with increasing malignancy. Glioblastoma (GBM) is the most common and aggressive type of braintumor classified as grade IV. GBMs are resistant to conventional therapies with poor prognosis after diagnosis even when the Stupp protocol that combines surgery and radiochemotherapy is applied.Nowadays, few novel therapeutic strategies have been used to improve GBM treatment, lookingfor higher efficiency and lower side effects, but with relatively modest results. The circadian timingsystem temporally organizes the physiology and behavior of most organisms and daily regulatesseveral cellular processes in organs, tissues, and even in individual cells, including tumor cells. Thepotentiality of the function of the circadian clock on cancer cells modulation as a new target for novel treatments with a chronobiological basis offers a different challenge that needs to be considered in further detail. The present review will discuss state of the art regarding GBM biology, the role of the circadian clock in tumor progression, and new chrono-chemotherapeutic strategies applied for GBM treatment.Fil: Wagner, Paula Micaela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Química Biológica de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Centro de Investigaciones en Química Biológica de Córdoba; ArgentinaFil: Prucca, Cesar German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Química Biológica de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Centro de Investigaciones en Química Biológica de Córdoba; ArgentinaFil: Caputto, Beatriz Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Química Biológica de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Centro de Investigaciones en Química Biológica de Córdoba; ArgentinaFil: Guido, Mario Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Química Biológica de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Centro de Investigaciones en Química Biológica de Córdoba; Argentin