Quantum-like model of diauxie in Escherichia coli: Operational description of precultivation effect

Quantum modeling simulates nutrient effect of bioplastic polyhydroxyalkanoate (PHA) production in Pseudomonas putida

Polyhydroxyalkanoates (PHAs) could be used to make sustainable, biodegradable plastics. However, the precise and accurate mechanistic modeling of PHA biosynthesis, especially medium-chain-length PHA (mcl-PHA), for yield improvement remains a challenge to biology. PHA biosynthesis is typically triggered by nitrogen limitation and tends to peak at an optimal carbon-to-nitrogen (C/N) ratio. Specifically, simulation of the underlying dynamic regulation mechanisms for PHA bioprocess is a bottleneck owing to surfeit model complexity and current modeling philosophies for uncertainty. To address this issue, we proposed a quantum-like decision-making model to encode gene expression and regulation events as hidden layers by the general transformation of a density matrix, which uses the interference of probability amplitudes to provide an empirical-level description for PHA biosynthesis. We implemented our framework modeling the biosynthesis of mcl-PHA in Pseudomonas putida with respect to external C/N ratios, showing its optimization production at maximum PHA production of 13.81% cell dry mass (CDM) at the C/N ratio of 40:1. The results also suggest the degree of P. putida's preference in channeling carbon towards PHA production as part of the bacterium's adaptative behavior to nutrient stress using quantum formalism. Generic parameters (kD, kN and theta θ) obtained based on such quantum formulation, representing P. putida's PHA biosynthesis with respect to external C/N ratios, was discussed. This work offers a new perspective on the use of quantum theory for PHA production, demonstrating its application potential for other bioprocesses.

A quantum mechanical approach towards the calculation of transition probabilities between DNA codons

The role of quantum tunneling in altering the structure of nucleotides to each other and causing a mutational event in DNA has been a topic of debate for years. Here, we introduce a new quantum mechanical approach for analyzing a typical point-mutation in DNA strands. Assuming each codon as a base state, a superposition of codon states could provide a physical description for a set of codons encoding the same amino acid and there are transition amplitudes between them. We choose the amino acids Phe and Ile as our understudy bio-systems which are encoded by two and three codons, respectively. We treat them as large quantum systems and use double- and triple-well potential models to study the fundamental behaviors of them in interaction with a harmonic environment. We use the perturbation theory to calculate the transition probabilities between the codons which encoding the same amino acid and determine the transition rates of some point mutations. Moreover, we evaluate the quantum biological channel capacity for these transitions to show that the channel capacity depends on the system-environment interaction via the dissipation factor Γ. The obtained results demonstrate that the tunneling rate is under the control of capacity of the corresponding biological channel. In other words, the reduction in quantum channel capacity prevents the quantum tunneling rate to be increased.

State Entropy and Differentiation Phenomenon

In the formalism of quantum theory, a state of a system is represented by a density operator. Mathematically, a density operator can be decomposed into a weighted sum of (projection) operators representing an ensemble of pure states (a state distribution), but such decomposition is not unique. Various pure states distributions are mathematically described by the same density operator. These distributions are categorized into classical ones obtained from the Schatten decomposition and other, non-classical, ones. In this paper, we define the quantity called the state entropy. It can be considered as a generalization of the von Neumann entropy evaluating the diversity of states constituting a distribution. Further, we apply the state entropy to the analysis of non-classical states created at the intermediate stages in the process of quantum measurement. To do this, we employ the model of differentiation, where a system experiences step by step state transitions under the influence of environmental factors. This approach can be used for modeling various natural and mental phenomena: cell's differentiation, evolution of biological populations, and decision making.

A model of differentiation in quantum bioinformatics

Differentiation is a universal process found in various phenomena of nature. As seen in the example of cell differentiation, the creation diversity on individual's character is caused by environmental interactions. In this paper, we try to explain its mechanism, which has been discussed mainly in Biology, by using the formalism of quantum physics. Our approach known as quantum bioinformatics shows that the temporal change of statistical state called decoherence fits to describe non-local phenomena like differentiation.

Three-body system metaphor for the two-slit experiment and Escherichia coli lactose-glucose metabolism

We compare the contextual probabilistic structures of the seminal two-slit experiment (quantum interference experiment), the system of three interacting bodies andEscherichia colilactose-glucose metabolism. We show that they have the same non-Kolmogorov probabilistic structure resulting from multi-contextuality. There are plenty of statistical data with non-Kolmogorov features; in particular, the probabilistic behaviour of neither quantum nor biological systems can be described classically. Biological systems (even cells and proteins) are macroscopic systems and one may try to present a more detailed model of interactions in such systems that lead to quantum-like probabilistic behaviour. The system of interactions between three bodies is one of the simplest metaphoric examples for such interactions. By proceeding further in this way (by playing withn-body systems) we shall be able to find metaphoric mechanical models for complex bio-interactions, e.g. signalling between cells, leading to non-Kolmogorov probabilistic data.

Quantum-like model of unconscious-conscious dynamics

We present a quantum-like model of sensation–perception dynamics (originated in Helmholtz theory of unconscious inference) based on the theory of quantum apparatuses and instruments. We illustrate our approach with the model of bistable perception of a particular ambiguous figure, the Schröder stair. This is a concrete model for unconscious and conscious processing of information and their interaction. The starting point of our quantum-like journey was the observation that perception dynamics is essentially contextual which implies impossibility of (straightforward) embedding of experimental statistical data in the classical (Kolmogorov, 1933) framework of probability theory. This motivates application of nonclassical probabilistic schemes. And the quantum formalism provides a variety of the well-approved and mathematically elegant probabilistic schemes to handle results of measurements. The theory of quantum apparatuses and instruments is the most general quantum scheme describing measurements and it is natural to explore it to model the sensation–perception dynamics. In particular, this theory provides the scheme of indirect quantum measurements which we apply to model unconscious inference leading to transition from sensations to perceptions.

A model of epigenetic evolution based on theory of open quantum systems

We present a very general model of epigenetic evolution unifying (neo-)Darwinian and (neo-)Lamarckian viewpoints. The evolution is represented in the form of adaptive dynamics given by the quantum(-like) master equation. This equation describes development of the information state of epigenome under the pressure of an environment. We use the formalism of quantum mechanics in the purely operational framework. (Hence, our model has no direct relation to quantum physical processes inside a cell.) Thus our model is about probabilities for observations which can be done on epigenomes and it does not provide a detailed description of cellular processes. Usage of the operational approach provides a possibility to describe by one model all known types of cellular epigenetic inheritance.