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Wavefunction Patterns the Embryo?

Irfan Lone

Published Aug 25, 2025• 0 citations
Publisher

Abstract

The problem of cell fate determination by morphogen gradients in the embryonic development of many multicellular organisms has been a long-standing and important one in developmental biophysics and dynamics. The first mathematical model was proposed by Francis Crick over 50 years ago by postulating a reaction-diffusion based mechanism underlying the whole process. The first real world morphogen, named Bicoid (Bcd), was identified by molecular biologists in late 1980s in the embryo of fruit fly Drosophila melanogaster . Subsequently, Crick’s classical random walk based model was used by biophysicists to explain the formation of Bicoid and other morphogen gradients. Very recently Fluorescence correlation spectroscopy (FCS) studies have revealed multiple modes of Bcd transport at different spatial and temporal locations across the embryo of Drosophila melanogaster. It has been be shown that these observations are best fitted by a model based on quantum mechanics. In such a model it is hypothesized that the transitory quantum coherences in collaboration with unitary noise are responsible for the observed dynamics and relaxation to a non-equilibrium steady-state of the Bcd morphogen gradient. In this paper, in addition to further clarifying the mathematical details underlying the quantum-classical model, we use the said model to explain the observed Bcd interpretation time by its primary target gene Hunchback ( hb ).

DOI
10.1101/2025.08.22.671254

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The problem of cell fate determination by morphogen gradients in the embryonic development of many multicellular organisms has been a long-standing and important one in developmental biophysics and dynamics. The first mathematical model was proposed by Francis Crick over 50 years ago by postulating a reaction-diffusion based mechanism underlying the whole process. The first real world morphogen, named Bicoid (Bcd), was identified by molecular biologists in late 1980s in the embryo of fruit fly Drosophila melanogaster . Subsequently, Crick’s classical random walk based model was used by biophysicists to explain the formation of Bicoid and other morphogen gradients. Very recently Fluorescence correlation spectroscopy (FCS) studies have revealed multiple modes of Bcd transport at different spatial and temporal locations across the embryo of Drosophila melanogaster. It has been be shown that these observations are best fitted by a model based on quantum mechanics. In such a model it is hypothesized that the transitory quantum coherences in collaboration with unitary noise are responsible for the observed dynamics and relaxation to a non-equilibrium steady-state of the Bcd morphogen gradient. In this paper, in addition to further clarifying the mathematical details underlying the quantum-classical model, we use the said model to explain the observed Bcd interpretation time by its primary target gene Hunchback ( hb ).
Extracellular diffusion coupled with degradation is considered a dominant mechanism behind the establishment of morphogen gradients. However, the fundamental nature of these biophysical processes, visa viz, the Bicoid (Bcd) morphogen gradient, remains unclear. Fluorescence correlation spectroscopy has recently revealed multiple modes of Bcd transport at different spatial and temporal locations across the embryo. Here, we show that these observations are best fitted by a model fundamentally based on quantum mechanics. It is thus hypothesized that the transient quantum coherences in collaboration with unitary noise are responsible for the observed dynamics and relaxation to a non-equilibrium steady-state of the Bcd morphogen gradient. Furthermore, simulating the associated probability distribution for the model shows that the observed non-zero concentration of the Bcd molecules in the posterior-most parts of the embryo is a result of non-Gaussian distribution characteristic to quantum evolution. We conclude that with the Bcd gradient being essentially a one-dimensional problem, a simple one-dimensional model suffices for its analysis.
The establishment and interpretation of the concentration gradient of the morphogen Bicoid ( Bcd ) is crucial for the successful embryonic development of fruit flies. However, the biophysical mechanisms behind the timely formation and subsequent interpretation of this prototypical morphogen gradient by its target genes are not yet completely understood. Recently a discrete time, one-dimensional quantum walk model of Bcd gradient formation has been successfully used to explain the observed multiple dynamic modes of the system. However, the question of its precise interpretation by its primary target gene hunchback ( hb ) remains still unanswered. In this paper it will be shown that the interpretation of the Bcd gradient by its primary target gene hb , with the observed precision of ∼ 10%, takes a time period of less than a second, as expected on the basis of recent experimental observations. Furthermore, the quantum walk model is also used to explain certain key observations of recent optogenetic experiments concerning the time windows for Bcd interpretation. Finally, it is concluded that the incorporation of quantum effects into the treatment of Bcd gradient represents a viable step in exploring its dynamics.
The establishment and interpretation of the concentration distribution of the morphogen Bicoid (BCD) is considered crucial for the successful embryonic development of fruit flies. However, the biophysical mechanisms behind the timely formation and subsequent interpretation of the BCD morphogen by its target genes are not yet completely understood. Here a discrete-time, one-dimensional quantum walk model of BCD gradient formation is used to explain both the observed values of diffusivity and its precise interpretation. It is shown that the decoding of positional information from the BCD morphogen by its primary target gene hb, with the observed precision of ∼ 10%, takes a time period of less than a second, as expected on the basis of recent experimental observations. From this the on-rate ( k on ) for the binding of BCD to its target loci is obtained. Furthermore, the model is also used to explain certain key observations of recent optogenetic experiments concerning the time windows for BCD interpretation. Finally, it is argued that the presented model represents a significant step in the utilization of quantum computation-based techniques in studying the dynamics of biological systems in general and in the field of developmental biophysics in particular.
A prototypical morphogen gradient that plays a key role in the early embryonic development of fruit flies, by providing positional information to cells, is that of the transcription factor Bicoid (Bcd). Recently a one-dimensional quantum walk model has been utilised to explain its multiple dynamic modes observed through fluorescence correlation spectroscopy (FCS) studies using a closed quantum system approach. In this work we use an open quantum system approach to the dynamics of the Bcd gradient formation and show that exactly the same dynamics are obtained through this more rigorous analysis. We then use the thus obtained expression for the fast dynamic modes to explain the Bcd transcription factor search times for binding to the promoter regions along the DNA. Specifically, we find that the large values of diffusivity allowed by quantum mechanics can avoid the paradox of faster-than-diffusion association rates without any need for the transcription factor to constantly alternate between 1D and 3D diffusion-based search processes. This might help explain the fast and precise transcriptional response elicited by such factors. We conclude that, since many transcription factors share a common search strategy for target gene regulatory regions, our mechanism may have a wide range of applicability.
In a recent proposal on the experimental tests of quantum gravity creation of non-Gaussianity in a Bose-Einstein condensate (BEC) has been suggested as a decisive confirmation of quantum gravity. In a related proposal, a gas of ultracold Rb or Cs atoms has previously been suggested as a possible platform for tests of quantum gravity. Since a practical demonstration of above proposals is a very challenging and costly affair, exploring cost-effective alternatives to these technologically demanding experimental protocols becomes very important. We here show that the phenomenon of Bicoid (Bcd) gradient formation in the early fruit fly embryo, considered basically here as a multipartite quantum system with an ensemble of initial states and a unitary evolution U that implements a quantum Newtonian Hamiltonian over this gravitationally interacting system, naturally combines the essential features of above proposals in a single system giving a viable signature of quantum gravity through the creation of non-Gaussianity. We conclude that although the phenomenon of Bcd gradient formation in the early Drosophila embryo is accompanied by quantum gravitational effects, it might need further experiments to verify such a noval claim.
In this paper, the classical Schrödinger equation (CSE), which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an additional single-valued condition for the Hamilton’s principal function, the CSE is obtained. This additional assumption implies inherent non-classical features on the description of the dynamics obtained from the CSE: the trajectories do not cross in the configuration space. Second, departing from Bohmian mechanics and invoking the quantum-to-classical transition, the CSE is obtained in a natural way for the center of mass of a quantum system with a large number of identical particles. This quantum development imposes the condition of dealing with a narrow wave packet, which implicitly avoids the non-classical features mentioned above. We illustrate all the above points with numerical simulations of the classical and quantum Schrödinger equations for different systems.