Internal feedback in the cortical perception-action loop enables fast and accurate behavior.

Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control, drawing on control theory, have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single, unidirectional perception-action loop. However, the sensorimotor loop contains internal delays in sensory and motor pathways, which can lead to unstable control. We show here that these delays can be compensated by internal feedback signals that flow backward, from motor toward sensory areas. This internal feedback is ubiquitous in neural sensorimotor systems, and we show how internal feedback compensates internal delays. This is accomplished by filtering out self-generated and other predictable changes so that unpredicted, actionable information can be rapidly transmitted toward action by the fastest components, effectively compressing the sensory input to more efficiently use feedforward pathways: Tracts of fast, giant neurons necessarily convey less accurate signals than tracts with many smaller neurons, but they are crucial for fast and accurate behavior. We use a mathematically tractable control model to show that internal feedback has an indispensable role in achieving state estimation, localization of function (how different parts of the cortex control different parts of the body), and attention, all of which are crucial for effective sensorimotor control. This control model can explain anatomical, physiological, and behavioral observations, including motor signals in the visual cortex, heterogeneous kinetics of sensory receptors, and the presence of giant cells in the cortex of humans as well as internal feedback patterns and unexplained heterogeneity in neural systems.

Diversity-enabled sweet spots in layered architectures and speed-accuracy trade-offs in sensorimotor control.

Nervous systems sense, communicate, compute, and actuate movement using distributed components with severe trade-offs in speed, accuracy, sparsity, noise, and saturation. Nevertheless, brains achieve remarkably fast, accurate, and robust control performance due to a highly effective layered control architecture. Here, we introduce a driving task to study how a mountain biker mitigates the immediate disturbance of trail bumps and responds to changes in trail direction. We manipulated the time delays and accuracy of the control input from the wheel as a surrogate for manipulating the characteristics of neurons in the control loop. The observed speed-accuracy trade-offs motivated a theoretical framework consisting of two layers of control loops-a fast, but inaccurate, reflexive layer that corrects for bumps and a slow, but accurate, planning layer that computes the trajectory to follow-each with components having diverse speeds and accuracies within each physical level, such as nerve bundles containing axons with a wide range of sizes. Our model explains why the errors from two control loops are additive and shows how the errors in each control loop can be decomposed into the errors caused by the limited speeds and accuracies of the components. These results demonstrate that an appropriate diversity in the properties of neurons across layers helps to create "diversity-enabled sweet spots," so that both fast and accurate control is achieved using slow or inaccurate components.

Interpretation of the Precision Matrix and Its Application in Estimating Sparse Brain Connectivity during Sleep Spindles from Human Electrocorticography Recordings.

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an [Formula: see text] electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present.

Robust efficiency and actuator saturation explain healthy heart rate control and variability.

The correlation of healthy states with heart rate variability (HRV) using time series analyses is well documented. Whereas these studies note the accepted proximal role of autonomic nervous system balance in HRV patterns, the responsible deeper physiological, clinically relevant mechanisms have not been fully explained. Using mathematical tools from control theory, we combine mechanistic models of basic physiology with experimental exercise data from healthy human subjects to explain causal relationships among states of stress vs. health, HR control, and HRV, and more importantly, the physiologic requirements and constraints underlying these relationships. Nonlinear dynamics play an important explanatory role--most fundamentally in the actuator saturations arising from unavoidable tradeoffs in robust homeostasis and metabolic efficiency. These results are grounded in domain-specific mechanisms, tradeoffs, and constraints, but they also illustrate important, universal properties of complex systems. We show that the study of complex biological phenomena like HRV requires a framework which facilitates inclusion of diverse domain specifics (e.g., due to physiology, evolution, and measurement technology) in addition to general theories of efficiency, robustness, feedback, dynamics, and supporting mathematical tools.

Architecture, constraints, and behavior.

This paper aims to bridge progress in neuroscience involving sophisticated quantitative analysis of behavior, including the use of robust control, with other relevant conceptual and theoretical frameworks from systems engineering, systems biology, and mathematics. Familiar and accessible case studies are used to illustrate concepts of robustness, organization, and architecture (modularity and protocols) that are central to understanding complex networks. These essential organizational features are hidden during normal function of a system but are fundamental for understanding the nature, design, and function of complex biologic and technologic systems.

A proposal for a coordinated effort for the determination of brainwide neuroanatomical connectivity in model organisms at a mesoscopic scale.

In this era of complete genomes, our knowledge of neuroanatomical circuitry remains surprisingly sparse. Such knowledge is critical, however, for both basic and clinical research into brain function. Here we advocate for a concerted effort to fill this gap, through systematic, experimental mapping of neural circuits at a mesoscopic scale of resolution suitable for comprehensive, brainwide coverage, using injections of tracers or viral vectors. We detail the scientific and medical rationale and briefly review existing knowledge and experimental techniques. We define a set of desiderata, including brainwide coverage; validated and extensible experimental techniques suitable for standardization and automation; centralized, open-access data repository; compatibility with existing resources; and tractability with current informatics technology. We discuss a hypothetical but tractable plan for mouse, additional efforts for the macaque, and technique development for human. We estimate that the mouse connectivity project could be completed within five years with a comparatively modest budget.

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control.

Feedback control theory has been extensively implemented to theoretically model human sensorimotor control. However, experimental platforms capable of manipulating important components of multiple feedback loops lack development. This paper describes WheelCon, an open-source platform aimed at resolving such insufficiencies. Using only a computer, a standard display, and inexpensive gaming steering wheel equipped with a force feedback motor, WheelCon safely simulates the canonical sensorimotor task of riding a mountain bike down a steep, twisting, bumpy trail. The platform provides flexibility, as will be demonstrated in the demos provided, so that researchers may manipulate the disturbances, delay, and quantization (data rate) in the layered feedback loops, including a high-level advanced plan layer and a low-level delayed reflex layer. In this paper, we illustrate WheelCon's graphical user interface (GUI), the input and output of existing demos, and how to design new games. In addition, we present the basic feedback model and the experimental results from the demo games, which align well with the model's prediction. The WheelCon platform can be downloaded at https://github.com/Doyle-Lab/WheelCon. In short, the platform is featured to be cheap, simple to use, and flexible to program for effective sensorimotor neuroscience research and control engineering education.

Metabolic multistability and hysteresis in a model aerobe-anaerobe microbiome community.

Major changes in the microbiome are associated with health and disease. Some microbiome states persist despite seemingly unfavorable conditions, such as the proliferation of aerobe-anaerobe communities in oxygen-exposed environments in wound infections or small intestinal bacterial overgrowth. Mechanisms underlying transitions into and persistence of these states remain unclear. Using two microbial taxa relevant to the human microbiome, we combine genome-scale mathematical modeling, bioreactor experiments, transcriptomics, and dynamical systems theory to show that multistability and hysteresis (MSH) is a mechanism describing the shift from an aerobe-dominated state to a resilient, paradoxically persistent aerobe-anaerobe state. We examine the impact of changing oxygen and nutrient regimes and identify changes in metabolism and gene expression that lead to MSH and associated multi-stable states. In such systems, conceptual causation-correlation connections break and MSH must be used for analysis. Using MSH to analyze microbiome dynamics will improve our conceptual understanding of stability of microbiome states and transitions between states.

Architectural Principles for Characterizing the Performance of Antithetic Integral Feedback Networks.

As we begin to design increasingly complex synthetic biomolecular systems, it is essential to develop rational design methodologies that yield predictable circuit performance. Here we apply mathematical tools from the theory of control and dynamical systems to yield practical insights into the architecture and function of a particular class of biological feedback circuit. Specifically, we show that it is possible to analytically characterize both the operating regime and performance tradeoffs of an antithetic integral feedback circuit architecture. Furthermore, we demonstrate how these principles can be applied to inform the design process of a particular synthetic feedback circuit.

Hard Limits and Performance Tradeoffs in a Class of Antithetic Integral Feedback Networks.

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism called antithetic integral feedback, which can be implemented using the binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of antithetic integral feedback and contribute to a more general theory of biological control systems.

Module-based analysis of robustness tradeoffs in the heat shock response system.

Biological systems have evolved complex regulatory mechanisms, even in situations where much simpler designs seem to be sufficient for generating nominal functionality. Using module-based analysis coupled with rigorous mathematical comparisons, we propose that in analogy to control engineering architectures, the complexity of cellular systems and the presence of hierarchical modular structures can be attributed to the necessity of achieving robustness. We employ the Escherichia coli heat shock response system, a strongly conserved cellular mechanism, as an example to explore the design principles of such modular architectures. In the heat shock response system, the sigma-factor sigma32 is a central regulator that integrates multiple feedforward and feedback modules. Each of these modules provides a different type of robustness with its inherent tradeoffs in terms of transient response and efficiency. We demonstrate how the overall architecture of the system balances such tradeoffs. An extensive mathematical exploration nevertheless points to the existence of an array of alternative strategies for the existing heat shock response that could exhibit similar behavior. We therefore deduce that the evolutionary constraints facing the system might have steered its architecture toward one of many robustly functional solutions.

Novel computational method for predicting polytherapy switching strategies to overcome tumor heterogeneity and evolution.

The success of targeted cancer therapy is limited by drug resistance that can result from tumor genetic heterogeneity. The current approach to address resistance typically involves initiating a new treatment after clinical/radiographic disease progression, ultimately resulting in futility in most patients. Towards a potential alternative solution, we developed a novel computational framework that uses human cancer profiling data to systematically identify dynamic, pre-emptive, and sometimes non-intuitive treatment strategies that can better control tumors in real-time. By studying lung adenocarcinoma clinical specimens and preclinical models, our computational analyses revealed that the best anti-cancer strategies addressed existing resistant subpopulations as they emerged dynamically during treatment. In some cases, the best computed treatment strategy used unconventional therapy switching while the bulk tumor was responding, a prediction we confirmed in vitro. The new framework presented here could guide the principled implementation of dynamic molecular monitoring and treatment strategies to improve cancer control.

Even Noisy Responses Can Be Perfect If Integrated Properly.

Integral feedback for perfect adaptation is a ubiquitous strategy in engineering and biology. Long studied in deterministic settings, it can now be understood in the context of the fully stochastic systems that are prevalent in biology.

Glycolytic oscillations and limits on robust efficiency.

Both engineering and evolution are constrained by trade-offs between efficiency and robustness, but theory that formalizes this fact is limited. For a simple two-state model of glycolysis, we explicitly derive analytic equations for hard trade-offs between robustness and efficiency with oscillations as an inevitable side effect. The model describes how the trade-offs arise from individual parameters, including the interplay of feedback control with autocatalysis of network products necessary to power and catalyze intermediate reactions. We then use control theory to prove that the essential features of these hard trade-off "laws" are universal and fundamental, in that they depend minimally on the details of this system and generalize to the robust efficiency of any autocatalytic network. The theory also suggests worst-case conditions that are consistent with initial experiments.

Fire in the Earth system.

Fire is a worldwide phenomenon that appears in the geological record soon after the appearance of terrestrial plants. Fire influences global ecosystem patterns and processes, including vegetation distribution and structure, the carbon cycle, and climate. Although humans and fire have always coexisted, our capacity to manage fire remains imperfect and may become more difficult in the future as climate change alters fire regimes. This risk is difficult to assess, however, because fires are still poorly represented in global models. Here, we discuss some of the most important issues involved in developing a better understanding of the role of fire in the Earth system.

The "robust yet fragile" nature of the Internet.

The search for unifying properties of complex networks is popular, challenging, and important. For modeling approaches that focus on robustness and fragility as unifying concepts, the Internet is an especially attractive case study, mainly because its applications are ubiquitous and pervasive, and widely available exposition exists at every level of detail. Nevertheless, alternative approaches to modeling the Internet often make extremely different assumptions and derive opposite conclusions about fundamental properties of one and the same system. Fortunately, a detailed understanding of Internet technology combined with a unique ability to measure the network means that these differences can be understood thoroughly and resolved unambiguously. This article aims to make recent results of this process accessible beyond Internet specialists to the broader scientific community and to clarify several sources of basic methodological differences that are relevant beyond either the Internet or the two specific approaches focused on here (i.e., scale-free networks and highly optimized tolerance networks).

Reverse engineering of biological complexity.

Advanced technologies and biology have extremely different physical implementations, but they are far more alike in systems-level organization than is widely appreciated. Convergent evolution in both domains produces modular architectures that are composed of elaborate hierarchies of protocols and layers of feedback regulation, are driven by demand for robustness to uncertain environments, and use often imprecise components. This complexity may be largely hidden in idealized laboratory settings and in normal operation, becoming conspicuous only when contributing to rare cascading failures. These puzzling and paradoxical features are neither accidental nor artificial, but derive from a deep and necessary interplay between complexity and robustness, modularity, feedback, and fragility. This review describes insights from engineering theory and practice that can shed some light on biological complexity.