Control Theory and Systems Biology: Potential Applications in Neurodegeneration and Search for Therapeutic Targets

Abstract

Control theory, a well-established discipline in engineering and mathematics, has found novel applications in systems biology. This interdisciplinary approach leverages the principles of feedback control and regulation to gain insights into the complex dynamics of cellular and molecular networks underlying chronic diseases, including neurodegeneration. By modeling and analyzing these intricate systems, control theory provides a framework to understand the pathophysiology and identify potential therapeutic targets. Therefore, this review examines the most widely used control methods in conjunction with genomic-scale metabolic models in the steady state of the multi-omics type. According to our research, this approach involves integrating experimental data, mathematical modeling, and computational analyses to simulate and control complex biological systems. In this review, we find that the most significant application of this methodology is associated with cancer, leaving a lack of knowledge in neurodegenerative models. However, this methodology, mainly associated with the Minimal Dominant Set (MDS), has provided a starting point for identifying therapeutic targets for drug development and personalized treatment strategies, paving the way for more effective therapies.

Keywords: control theory; genome-scale metabolic networks; neurodegenerative diseases; systems biology.

Figure 1

The systems biology approach to genomic-scale model reconstruction. The letters A–F represent the metabolists included in the system.

Figure 2

Flow balance analysis (FBA) scheme and representation of the flow coupling graph. (A) The metabolic network consists of a list of stoichiometrically balanced biochemical reactions (R1, R2, R3, Rn). This type of reconstruction can be represented mathematically by a stoichiometric matrix (S) of size m × n composed of its reactions and metabolites. The steady-state flow distribution is defined by the equation S*v = 0, where v is a flow vector. According to the objective function of interest, maximization or minimization is performed; optimization allows for the finding of the flux distribution that enables the optimal solution for this objective function while observing the restrictions given the principle of mass balance and the limits of reaction [21]. (B) The application of control theory starts from the use of matrix S. The vertices represent reactions, and the labeled edges represent the five coupling relationships (represented by different colors; see legend). The steady-state principle implies that some reactions operate in a concentrated manner, leading to reaction coupling relationships. Reaction i is directionally coupled with j if σj v = 0 implies σi v = 0. Partial coupling is a particular case of directional and full coupling: two reactions, i and j, are partially coupled if they have the same state. If one of the two reactions is inactive, then a steady-state flux is only possible if the other reaction has a non-zero flux, which would define two anti-coupled reactions. Finally, reaction i couples inhibition with reaction j if the maximum flux of reaction i implies that j is inactive. The above can be summarized as follows: (1) the directional and total (or active) flow of R1 leads to the activation of R2 and R3 and the inactivation of R4 and R5; (2) the inactive flow of R1 leads to the deactivation of R2 and the activation of R4 and R5; (3) the inactive flow of R1 leads to the activation of R2 and the deactivation of R4. Taken and modified from [29].

Figure 3

A simplified representation of the steps required in the construction of a GEM. This process involves the use of various databases, including but not limited to KEGG and UniProt, and it may involve a reference model.

Figure 4

Matrix S of size 5 × 7 illustrates the proportionality of the chemical species at a given time, multiplied by the flux vector. This flow vector is the set of paths participating in the objective solution. The result is the calculation of a vector of zeros, which allows us to assume an equilibrium state of the model where there is flow in the system. However, there are no changes in the concentration of the metabolites.

Figure 5

Applications of systems biology with control theory. (A) Timeline of studies using control theory to identify drug targets or metabolic perturbations mainly in cancer [29,32,34,101,174,176]. (B) Diagram showing the most common workflow evidenced in studies employing control theory for analyzing metabolic network models.