Building a minimum frustration framework for brain functions over long time scales

Removing uncertainty in neural networks

Neuroscientists draw lines of separation among structures and functions that they judge different, arbitrarily excluding or including issues in our description, to achieve positive demarcations that permits a pragmatic treatment of the nervous activity based on regularity and uniformity. However, uncertainty due to disconnectedness, lack of information and absence of objects' sharp boundaries is a troubling issue that prevents these scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial neural networks. Starting from the detection of metamorphoses of shapes inside a Euclidean manifold, we propose a technique to detect the topological changes that occur during their reciprocal interactions and shape morphing. This method, that allows the detection of topological holes development and disappearance, makes it possible to solve the problem of uncertainty in the assessment of countless dynamical phenomena, such as cognitive processes, protein homeostasis deterioration, fire propagation, wireless sensor networks, migration flows, and cosmic bodies analysis.

Towards dewetting monoclonal antibodies for therapeutical purposes

Dewetting transition - a concept borrowed from fluid mechanics - is a physiological process that takes place inside the hydrophobic pores of ion channels. This transient phenomenon causes a metastable state that forbids water molecules to cross microscopic receptor cavities. This leads to a decreased conductance, a closure of the pore and, subsequently, severe impairment of cellular performance. We suggest that artificially-provoked dewetting transition in ion channel hydrophobic pores might stand for a molecular candidate to erase detrimental organisms, such as viruses, bacteria, and cancer cells. We describe a novel type of high-affinity monoclonal antibody, that: a) targets specific trans-membrane receptor structures of harmful or redundant cells; b) is equipped with lipophilic and/or hydrophobic fragments that prevent physiological water flow inside ion channels. Therefore, we achieve an artificial dewetting transition inside receptor cavities, that causes discontinuity within transmembrane ionic flows, channel blockage, and subsequent damage of morbid cells. As an example, we describe dewetting monoclonal antibodies that target the M2 channel of the Influenza A virus: they might prevent water from entering pores thus leading to virion impairment.

Entropy Balance in the Expanding Universe: A Novel Perspective

We describe cosmic expansion as correlated with the standpoints of local observers' co-moving horizons. In keeping with relational quantum mechanics, which claims that quantum systems are only meaningful in the context of measurements, we suggest that information gets ergodically "diluted" in our isotropic and homogeneous expanding Universe, so that an observer detects just a limited amount of the total cosmic bits. The reduced bit perception is due the decreased density of information inside the expanding cosmic volume in which the observer resides. Further, we show that the second law of thermodynamics can be correlated with cosmic expansion through a relational mechanism, because the decrease in information detected by a local observer in an expanding Universe is concomitant with an increase in perceived cosmic thermodynamic entropy, via the Bekenstein bound and the Laudauer principle. Reversing the classical scheme from thermodynamic entropy to information, we suggest that the cosmological constant of the quantum vacuum, which is believed to provoke the current cosmic expansion, could be one of the sources of the perceived increases in thermodynamic entropy. We conclude that entropies, including the entangled entropy of the recently developed framework of quantum computational spacetime, might not describe independent properties, but rather relations among systems and observers.

EEG dynamics on hyperbolic manifolds

Biological activities, including cellular metabolic pathways, protein folding and brain function, can be described in terms of curved trajectories in hyperbolic spaces which are constrained by energetic requirements. Here, starting from theorems recently-developed by a deceased Field Medal young mathematician, we show how it is feasible to find and quantify the shortest, energy-sparing functional trajectories taking place in nervous systems' concave phase spaces extracted from real EEG traces. This allows neuroscientists to focus their studies on the few, most prominent functional EEG's paths and loops able to explain, elucidate and experimentally assess the rather elusive mental activity.

The Energy Landscape of Neurophysiological Activity Implicit in Brain Network Structure

A critical mystery in neuroscience lies in determining how anatomical structure impacts the complex functional dynamics of the brain. How does large-scale brain circuitry constrain states of neuronal activity and transitions between those states? We address these questions using a maximum entropy model of brain dynamics informed by white matter tractography. We demonstrate that the most probable brain states - characterized by minimal energy - display common activation profiles across brain areas: local spatially-contiguous sets of brain regions reminiscent of cognitive systems are co-activated frequently. The predicted activation rate of these systems is highly correlated with the observed activation rate measured in a separate resting state fMRI data set, validating the utility of the maximum entropy model in describing neurophysiological dynamics. This approach also offers a formal notion of the energy of activity within a system, and the energy of activity shared between systems. We observe that within- and between-system energies cleanly separate cognitive systems into distinct categories, optimized for differential contributions to integrated versus segregated function. These results support the notion that energetic and structural constraints circumscribe brain dynamics, offering insights into the roles that cognitive systems play in driving whole-brain activation patterns.

Towards plasma-like collisionless trajectories in the brain

Plasma studies depict collisionless, collective movements of charged particles. In touch with these concepts, originally developed by the far-flung branch of high energy physics, here we evaluate the role of collective behaviors and long-range functional couplingsof charged particlesin brain dynamics. We build a novel, empirically testable, brain model which takes into account collisionless movements of charged particles in a system, the brain, equipped with oscillations. The model is cast in a mathematical fashion with the potential of being operationalized, because it can be assessed in terms of McKean-Vlasov equations, derived from the classical Vlasov equations for plasma. A plasma-like brain also elucidates cortical phase transitions in the context of a brain at the edge of chaos, describing the required order parameters. In sum, showing how the brain might exhibit plasma-like features,we go through the concept of holistic behavior of nervous functions.

A timeless biology

Contrary to claims that physics is timeless while biology is time-dependent, we take the opposite standpoint: physical systems' dynamics are constrained by the arrow of time, while living assemblies are time-independent. Indeed, the concepts of "constraints" and "displacements" shed new light on the role of continuous time flow in life evolution, allowing us to sketch a physical gauge theory for biological systems in long timescales. In the very short timescales of biological systems' individual lives, time looks like "frozen" and "fixed", so that the second law of thermodynamics is momentarily wrecked. The global symmetries (standing for biological constrained trajectories, i.e. the energetic gradient flows dictated by the second law of thermodynamics in long timescales) are broken by local "displacements" where time is held constant, i.e., modifications occurring in living systems. Such displacements stand for brief local forces, able to temporarily "break" the cosmic increase in entropy. The force able to restore the symmetries (called "gauge field") stands for the very long timescales of biological evolution. Therefore, at the very low speeds of life evolution, time is no longer one of the four phase space coordinates of a spacetime Universe: it becomes just a gauge field superimposed to three-dimensional biological systems. We discuss the implications in biology: when assessing living beings, the underrated role of isolated "spatial" modifications needs to be emphasized, living apart the evolutionary role of time.

Cellular Gauge Symmetry and the Li Organization Principle: A Mathematical Addendum. Quantifying energetic dynamics in physical and biological systems through a simple geometric tool and geodetic curves

The present Addendum complements the accompanying paper "Cellular Gauge Symmetry and the Li Organization Principle"; it illustrates a recently-developed geometrical physical model able to assess electronic movements and energetic paths in atomic shells. The model describes a multi-level system of circular, wavy and zigzag paths which can be projected onto a horizontal tape. This model ushers in a visual interpretation of the distribution of atomic electrons' energy levels and the corresponding quantum numbers through rather simple tools, such as compasses, rulers and straightforward calculations. Here we show how this geometrical model, with the due corrections, among them the use of geodetic curves, might be able to describe and quantify the structure and the temporal development of countless physical and biological systems, from Langevin equations for random paths, to symmetry breaks occurring ubiquitously in physical and biological phenomena, to the relationships among different frequencies of EEG electric spikes. Therefore, in our work we explore the possible association of binomial distribution and geodetic curves configuring a uniform approach for the research of natural phenomena, in biology, medicine or the neurosciences.

From abstract topology to real thermodynamic brain activity

Recent approaches to brain phase spaces reinforce the foremost role of symmetries and energy requirements in the assessment of nervous activity. Changes in thermodynamic parameters and dimensions occur in the brain during symmetry breakings and transitions from one functional state to another. Based on topological results and string-like trajectories into nervous energy landscapes, we provide a novel method for the evaluation of energetic features and constraints in different brain functional activities. We show how abstract approaches, namely the Borsuk-Ulam theorem and its variants, may display real, energetic physical counterparts. When topology meets the physics of the brain, we arrive at a general model of neuronal activity, in terms of multidimensional manifolds and computational geometry, that has the potential to be operationalized.

New Perspectives on Spontaneous Brain Activity: Dynamic Networks and Energy Matter

Spontaneous brain activity has received increasing attention as demonstrated by the exponential rise in the number of published article on this topic over the last 30 years. Such “intrinsic” brain activity, generated in the absence of an explicit task, is frequently associated with resting-state or default-mode networks (DMN)s. The focus on characterizing spontaneous brain activity promises to shed new light on questions concerning the structural and functional architecture of the brain and how they are related to “mind”. However, many critical questions have yet to be addressed. In this review, we focus on a scarcely explored area, specifically the energetic requirements and constraints of spontaneous activity, taking into account both thermodynamical and informational perspectives. We argue that the “classical” definitions of spontaneous activity do not take into account an important feature, that is, the critical thermodynamic energetic differences between spontaneous and evoked brain activity. Spontaneous brain activity is associated with slower oscillations compared with evoked, task-related activity, hence it exhibits lower levels of enthalpy and “free-energy” (i.e., the energy that can be converted to do work), thus supporting noteworthy thermodynamic energetic differences between spontaneous and evoked brain activity. Increased spike frequency during evoked activity has a significant metabolic cost, consequently, brain functions traditionally associated with spontaneous activity, such as mind wandering, require less energy that other nervous activities. We also review recent empirical observations in neuroscience, in order to capture how spontaneous brain dynamics and mental function can be embedded in a non-linear dynamical framework, which considers nervous activity in terms of phase spaces, particle trajectories, random walks, attractors and/or paths at the edge of the chaos. This takes us from the thermodynamic free-energy, to the realm of “variational free-energy”, a theoretical construct pertaining to probability and information theory which allows explanation of unexplored features of spontaneous brain activity.