Order-Stability in Complex Biosystems from the Viewpoint of the Theory of Open Quantum Systems

This paper is our attempt on the basis of physical theory to bring more clarification on the question ``What is life?'' formulated in the well-known book of Schr\"odinger in 1944. According to Schr\"odinger, the main distinguishing feature of biosystem's functioning is the ability to preserve its order structure or, in the mathematical terms, to prevent increasing of entropy. Since any biosystem is fundamentally open, it is natural to use open system's theory. However, Schr\"odinger's analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schr\"odinger should also appeal to the ambiguous notion of negative entropy. We suggest to apply the quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of the classical entropy. We consider a complex biosystem $S$ composed of many subsystems, say proteins, or cells, or neural networks in the brain, i.e., $S=(S_i).$ We study the following problem: if the composed system $S$ can preserve the ``global order'' in the situation of increase of local disorder and if $S$ can preserve its entropy while some of $S_i$ increase their entropies We show that within quantum information theory the answer is positive. The significant role plays entanglement of the subsystems states. In the absence of entanglement, increasing of local disorder generates disorder increasing in the compound system $S$ (as in the classical regime).

Order-Stability in Complex Biosystems from the Viewpoint of the Theory of Open Quantum Systems

This paper is our attempt on the basis of physical theory to bring more clarification on the question ``What is life?'' formulated in the well-known book of Schr\"odinger in 1944. According to Schr\"odinger, the main distinguishing feature of biosystem's functioning is the ability to preserve its order structure or, in the mathematical terms, to prevent increasing of entropy. Since any biosystem is fundamentally open, it is natural to use open system's theory. However, Schr\"odinger's analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schr\"odinger should also appeal to the ambiguous notion of negative entropy. We suggest to apply the quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of the classical entropy. We consider a complex biosystem $S$ composed of many subsystems, say proteins, or cells, or neural networks in the brain, i.e., $S=(S_i).$ We study the following problem: if the composed system $S$ can preserve the ``global order'' in the situation of increase of local disorder and if $S$ can preserve its entropy while some of $S_i$ increase their entropies We show that within quantum information theory the answer is positive. The significant role plays entanglement of the subsystems states. In the absence of entanglement, increasing of local disorder generates disorder increasing in the compound system $S$ (as in the classical regime).

Simulation of Human Limb Movement

Simulation of any processes is based on some laws that take place inside the simulated object and outside it (changing the environment in which the object is located). In the study of complex biosystems, the identification of patterns is complicated by the fact that such systems have a chaotic structure. In such systems, it is impossible to arbitrarily repeat the initial state xi, any intermediate xn and final xk. Simulation of complex biosystems should be based on random patterns. The created simulation model works based on the random number generation. There are no static values in the model. The inclusion of regulatory mechanisms of the model is based on the search of F-solutions. Chaotic dynamics of changes in the trajectory of a person's limb is established based on experimental data. In accordance with this, in the simulation model, the level of limb retention in space changes its direction by random images in real time. In the framework of the above patterns, a mathematical model of the interaction of muscle bundles was developed to solve the problem of holding the limb in space. When analyzing the performance of the simulation model, the basis of the evaluation measure was taken. The results were obtained on the basis of mathematical statistics and the calculation of the quasiattractor parameters in the framework of the theory of chaos and self-organization. As a result, the correspondence of experimental and model data was established. In the framework of mathematical statistics, when constructing matrices of paired comparisons for experimental data, the number of pairs of matches (the word "matches" refers to the possibility of assigning the compared pairs of samples to one general set) is k = 11 %. The same number of coincidence pairs in percentage terms was established when comparing model data and model with experimental data. In the framework of the theory of chaos and self-organization, the quasiattractor parameters coincide in their area and visual assessment of phase planes. As a result of the research, high accuracy of the model is established, which is ensured by some chaotic dynamics of the model with chaotic selfregulation mechanisms. There are no constants in the mathematical form of the simulation model, which ensures the reproduction of N.A. Bernstein "repetition without repetition" hypothesis, which has been proven for experimental data. For theoretical biophysics, the constructed simulation model is able to provide understanding of the neuromuscular system functioning, as well as, with some complication and expansion of the algorithm, the central nervous system.

Medical and Biological Cybernetics: Perspectives of Development

За последние 40-50 лет биологические науки сделали существенный прорыв в области молекулярно-клеточных исследований. При этом системный уровень за этот период претерпел существенное отставание. Со времен Н. Винера кибернетика перешла к решению частных задач, уйдя из области главных наук в изучении сложных систем. На наш взгляд, такая ситуация обусловлена общим кризисом детерминистского и стохастического подходов в изучении живых систем. Возрождение медицинской и биологической кибернетики как науки об управлении в биологических системах возможно только в связи с новым пониманием принципов регуляции и функционирования любых сложных биосистем (complexity). Это новое понимание должно базироваться на новых принципах регуляции биосистем, в которых хаос и многократные повторения одних и тех же процессов должны превалировать над детерминистской определенностью или стохастической неопределенностью. В этом возрождении интереса ко всей кибернетике особую роль должна сыграть новая теория хаосасамоорганизации, которая сейчас разрабатывается несколькими научными школами Москвы, Тулы, Самары и Сургута. В основе этого нового научного направления лежит эффект Еськова–Зинченко (отсутствие статистической устойчивости любых параметров организма человека) и новые модели поведения вектора состояния биосистемы x=x(t)=(x12, x21,…, xm) T в фазовом пространстве состояний. For the last 40–50 years all biological sciences made a significant breakthrough in molecular and cellular research. At the same time the system level has considerably fallen behind for this period. Since N. Wiener, cybernetics turned to solving particular problems instead of studying complex systems in the field of principle sciences. In our opinion, such a situation is connected with global crisis of deterministic and stochastic approaches of studying living systems. The restoration of biological and medical cybernetics as management science in biological systems is connected with new understanding of principles of regulation and operation of any complex biosystems. The new understanding must be based on the principles of regulation of biosystems where chaos and multiple repetitions of the same processes must prevail over deterministic certainty and stochastic uncertainty. A new theory of chaos and self-organization, which is under development in some scientific schools in Moscow, Tula, Samara and Surgut (in Russia), is expected to play a special role in restoring interest to all cybernetics. It is a new research direction based on Eskov–Zinchenko effect (the absence of statistical stability of any parameter of human body) and based on new models of biosystem state vector behavior x = x(t) = (x1, x2, . . . , xm) T in phase space of states.

Polarizable embedding QM/MM: the future gold standard for complex (bio)systems?

We provide a perspective of the induced dipole formulation of polarizable QM/MM, showing how efficient implementations will enable their application to the modeling of dynamics, spectroscopy, and reactivity in complex biosystems.

Nano-Enabled Approaches to Chemical Imaging in Biosystems

Understanding and predicting how biosystems function require knowledge about the dynamic physicochemical environments with which they interact and alter by their presence. Yet, identifying specific components, tracking the dynamics of the system, and monitoring local environmental conditions without disrupting biosystem function present significant challenges for analytical measurements. Nanomaterials, by their very size and nature, can act as probes and interfaces to biosystems and offer solutions to some of these challenges. At the nanoscale, material properties emerge that can be exploited for localizing biomolecules and making chemical measurements at cellular and subcellular scales. Here, we review advances in chemical imaging enabled by nanoscale structures, in the use of nanoparticles as chemical and environmental probes, and in the development of micro- and nanoscale fluidic devices to define and manipulate local environments and facilitate chemical measurements of complex biosystems. Integration of these nano-enabled methods will lead to an unprecedented understanding of biosystem function.

Living Systems (Complexity) From the Point of Chaos and Self-Organization Theory

Attempts to describe complex biological systems (complexity) in terms of modern mathematics and physics continue. However, it is now evident that complexity cannot be the object of modern science because of their continuous change in the parameters and the absence of arbitrary repetition of initial parameters x (to) of any complexity. This article presents the the arguments of lack of capacity modeling of complex biophysical systems under deterministic and stochastic approaches due to the constant chaotic change of the state vector parameters x = x(t) = (x1,x2....,xm)Tof any complex biosystem (complexity). At any point of time h, the chaotic dynamics of homeostasis in signals, such as tapping tremors, electromyograms, neurograms, cardiograms, electroencephalograms, and other biochemical recordings, can be observed. During constant and chaotic changes of x(t) (i.e., dx/dteQ), the amplitude-frequency characteristics (AFC) and the autocorrelation functions A(t) constantly change. Therefore, the mixing property fails and the Lyapunov exponents can chaotically and randomly change signs. Chaos of complex biosystems differs from chaos of physical systems primarily due to the irreproducible initial value x(to). There are two methods for studying such systems: a stochastic method for processing random samples based on a matrix of pairwise comparisons and a computing method that utilizes quasi-attractor parameters, Vg for x(t), in the phase space of states. Here, such calculations are presented for biomechanics and electrophysiology.

Features Samples Cardiointervals: Chaos and Stochastics in the Description of Complex Biosystems

Complex Biosystems (complexity) cannot be attributed to traditional chaotic systems, because for them it is impossible to calculate the autocorrelation function, Lyapunov exponent, no run properties of mixing, continuously the state vector x(t) demonstrates chaotic motion in the form άχίάίΦθ. Since the initial state x(to) is arbitrarily unrepeatable for such systems, type-one uncertainty and type-two uncertainty arise. Type-one uncertainty is characterized by absence of statistically significant differences between samples. The authors propose neurocomputing methods and theory of chaos and self-organization to differentiate these samples. The authors present examples of such a situation for the parameters of the cardio-respiratory system of humans in conditions of the latitudinal displacement of large groups of people. It is shown that the neuroemulator not only solves the problem of binary classification, but also identifies the order parameters in diagnostic signs. It is very important to increase the number of iterations in the repetition of binary classification. The number of iteration (when we repeat the neuroemulator procedure) has the fundamental role for identification of order parameters. Errors are possible within the order parameters with the high number of iterations.

Complex System Stationary Mode According to the Theory of Chaos-Self-Organization

Traditional biological science (biophysics, systems analyses of biosystems) stationary mode of biosystems describes according to equation dx/dt=0 for the systems state vector x=x(t)=(x1, x2,…xm)T. But real biosystems demonstrated uninterrupted chaotic dynamics when dx/dt≠0 is always uninterrupted. The authors present two types of approaches to stationary mode investigation for biosystems. The first approach is based on the compartmental-cluster theory and the second approach is based on the theory of chaos-self-organization. The last is more convenient for real biosystems description because there are pragmatic results of its use. The compartmental-cluster approach may be used for real complex biosystems and the authors present some typical examples of such theory. The stationary mode of hierarchical neural networks were illustrated according to specific audi - analyzator. It was demonstrated that short intervals of tremogram demonstrate the real difference of distribution function parameters. As a result of such experiments – the classical statistics methods don’t usefulness for investigation of postural tremor. The tremogram, cardiogram, encephalogram are the systems of third type. The main idea consists of uninterrupted chaotic movements (glimmering property) of system’s vector in phase space of state and evolution of such system’s state vector in phase space of state. The glimmering property and evolution don’t have properties which can be modeled by traditional deterministic and stochastic approaches.