Control theory in biology and medicine : Introduction to the special issue

How Does Escherichia coli Allocate Proteome?

Microorganisms are shown to actively partition their intracellular resources, such as proteins, for growth optimization. Recent experiments have begun to reveal molecular components unpinning the partition; however, quantitatively, it remains unclear how individual parts orchestrate to yield precise resource allocation that is both robust and dynamic. Here, we developed a coarse-grained mathematical framework that centers on guanosine pentaphosphate (ppGpp)-mediated regulation and used it to systematically uncover the design principles of proteome allocation in Escherichia coli. Our results showed that the cellular ability of resource partition lies in an ultrasensitive, negative feedback-controlling topology with the ultrasensitivity arising from zero-order amino acid kinetics and the negative feedback from ppGpp-controlled ribosome synthesis. In addition, together with the time-scale separation between slow ribosome kinetics and fast turnovers of ppGpp and amino acids, the network topology confers the organism an optimization mechanism that mimics sliding mode control, a nonlinear optimization strategy that is widely used in man-made systems. We further showed that such a controlling mechanism is robust against parameter variations and molecular fluctuations and is also efficient for biomass production over time. This work elucidates the fundamental controlling mechanism of E. coli proteome allocation, thereby providing insights into quantitative microbial physiology as well as the design of synthetic gene networks.

Genetic, individual, and familial risk correlates of brain network controllability in major depressive disorder

Many therapeutic interventions in psychiatry can be viewed as attempts to influence the brain's large-scale, dynamic network state transitions. Building on connectome-based graph analysis and control theory, Network Control Theory is emerging as a powerful tool to quantify network controllability-i.e., the influence of one brain region over others regarding dynamic network state transitions. If and how network controllability is related to mental health remains elusive. Here, from Diffusion Tensor Imaging data, we inferred structural connectivity and inferred calculated network controllability parameters to investigate their association with genetic and familial risk in patients diagnosed with major depressive disorder (MDD, n = 692) and healthy controls (n = 820). First, we establish that controllability measures differ between healthy controls and MDD patients while not varying with current symptom severity or remission status. Second, we show that controllability in MDD patients is associated with polygenic scores for MDD and psychiatric cross-disorder risk. Finally, we provide evidence that controllability varies with familial risk of MDD and bipolar disorder as well as with body mass index. In summary, we show that network controllability is related to genetic, individual, and familial risk in MDD patients. We discuss how these insights into individual variation of network controllability may inform mechanistic models of treatment response prediction and personalized intervention-design in mental health.

Control Theory and Cancer Chemotherapy: How They Interact

Control theory arises in most modern real-life applications, not least in biological and medical applications. In particular, in biological and medical contexts, the role of control theory began to take shape in the early 1980s when the first works appeared on the application of control theory in models of pharmacokinetics and pharmacodynamics for antitumor therapies. Forty years after those first works, the theory of control continues to be considered a mathematical analysis tool of extreme importance and usefulness, but the challenges it must overcome in order to manage the complexity of biological processes are in fact not yet overcome. In this article, we introduce the reader to the basic ideas of control theory, its aims and its mathematical formalization, and we review its use in cell phase-specific models for cancer chemotherapy. We discuss strengths and limitations of the control theory approach to the analysis pharmacokinetics and pharmacodynamics models, and we will see that most of them are strongly related to data availability and mathematical form of the model. We propose some future research directions that could prove useful in overcoming the these limitations and we indicate the crucial steps preliminary to a useful and informative application of control theory to cancer chemotherapy modeling.

Overcoming the Challenges to Enhancing Experimental Plant Biology With Computational Modeling

The study of complex biological systems necessitates computational modeling approaches that are currently underutilized in plant biology. Many plant biologists have trouble identifying or adopting modeling methods to their research, particularly mechanistic mathematical modeling. Here we address challenges that limit the use of computational modeling methods, particularly mechanistic mathematical modeling. We divide computational modeling techniques into either pattern models (e.g., bioinformatics, machine learning, or morphology) or mechanistic mathematical models (e.g., biochemical reactions, biophysics, or population models), which both contribute to plant biology research at different scales to answer different research questions. We present arguments and recommendations for the increased adoption of modeling by plant biologists interested in incorporating more modeling into their research programs. As some researchers find math and quantitative methods to be an obstacle to modeling, we provide suggestions for easy-to-use tools for non-specialists and for collaboration with specialists. This may especially be the case for mechanistic mathematical modeling, and we spend some extra time discussing this. Through a more thorough appreciation and awareness of the power of different kinds of modeling in plant biology, we hope to facilitate interdisciplinary, transformative research.

Using optimal control to understand complex metabolic pathways

BACKGROUND

Optimality principles have been used to explain the structure and behavior of living matter at different levels of organization, from basic phenomena at the molecular level, up to complex dynamics in whole populations. Most of these studies have assumed a single-criteria approach. Such optimality principles have been justified from an evolutionary perspective. In the context of the cell, previous studies have shown how dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point, and a single objective for the optimality criteria.

RESULTS

Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework which has been designed with scalability and efficiency in mind, including mechanisms to avoid the most common pitfalls. Third, we illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments.

CONCLUSIONS

We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we also show how to consider general cost/benefit trade-offs. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction or gene regulatory networks.

Seizure pathways change on circadian and slower timescales in individual patients with focal epilepsy

Personalized medicine requires that treatments adapt to not only the patient but also changing factors within each individual. Although epilepsy is a dynamic disorder characterized by pathological fluctuations in brain state, surprisingly little is known about whether and how seizures vary in the same patient. We quantitatively compared within-patient seizure network evolutions using intracranial electroencephalographic (iEEG) recordings of over 500 seizures from 31 patients with focal epilepsy (mean 16.5 seizures per patient). In all patients, we found variability in seizure paths through the space of possible network dynamics. Seizures with similar pathways tended to occur closer together in time, and a simple model suggested that seizure pathways change on circadian and/or slower timescales in the majority of patients. These temporal relationships occurred independent of whether the patient underwent antiepileptic medication reduction. Our results suggest that various modulatory processes, operating at different timescales, shape within-patient seizure evolutions, leading to variable seizure pathways that may require tailored treatment approaches.