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 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.
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 ).
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.
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.
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.
• Published on bioRxiv, proposing the 'Quantum Hamiltonian-based gene-expression model (QHGM)' for Gene Regulatory Network (GRN) inference. • Treats genes as 'qubits', interpreting gene interactions over pseudotime by encoding them into quantum entanglement and Hamiltonian matrices. • Applied to glioblastoma (GBM) single-cell RNA sequencing data, successfully elucidating complex cancer cell developmental networks by overcoming the limitations of classical machine learning models. [Quantum Biology Society] Gene Regulatory Networks (GRNs), which determine the cell fate and phenotype of living organisms, are highly dynamic systems where numerous genes and proteins intricately entangle and interact. Despite the massive influx of data from recent advancements in single-cell RNA sequencing (scRNA-seq) technology, existing classical machine learning models have faced limitations in perfectly capturing the delicate context of biological regulation and non-classical probabilistic features. A recent study has been published that dramatically solves this challenge in systems biology through the 'Quantum Hamiltonian Learning (QHL)' framework, which infers the parameters of a many-body quantum system. The paper, titled "Quantum Hamiltonian Learning using Time-Resolved Measurement Data and its Application to Gene Regulatory Network Inference," published on the preprint repository bioRxiv, showcases an unconventional approach of modeling gene networks as macroscopic quantum systems. A joint research team, including Mohammad Aamir Sohail and Professor Arvind Rao from the University of Michigan, USA, led this innovative study. ■ Genes as Qubits, Regulatory Networks as Hamiltonians The 'Quantum Hamiltonian-based gene-expression model (QHGM)' proposed by the research team treats individual genes as qubits. The unexpressed state of a gene is defined as the basis state |0>, and the expressed state as |1>. Regulatory interactions, such as activation or repression between genes, are encoded as weights within a parameterized Hamiltonian matrix constructed using tensor products. Gene qubits, which initially start in independent separable states, evolve according to the Schrödinger equation along pseudotime, an indicator of cell development that acts as physical time. During this evolution process, complex correlations akin to quantum entanglement are formed between genes according to the interaction rules inputted into the Hamiltonian. ■ Combination of IC-POVM Measurements and VQ-Net AI To extract gene expression data from these entangled quantum states, the researchers introduced single-qubit IC-POVM, an informationally complete quantum measurement technique. These measurement results are linked to the discretized gene expression profiles observed in actual scRNA-seq data. Subsequently, the team developed VQ-Net, a variational quantum network inference algorithm based on a mini-batch empirical risk minimization framework. Based on the scRNA-seq data collected over pseudotime, this algorithm minimizes the negative log-likelihood loss and learns by inversely tracing the weight parameters of the Hamiltonian. ■ Elucidating the Glioblastoma (GBM) Network… Outperforming Classical Models This quantum-biology hybrid model did not stop at mere theory but was deployed in actual cancer research. By analyzing scRNA-seq data from patients with IDH-wild-type glioblastoma (GBM), a malignant brain tumor, the researchers inferred the gene regulatory program governing the differentiation of OPC-like cells. The analysis revealed that the QHGM model accurately pinpointed how core genes such as ASCL1, CDK4, and STMN1 interact with cell-cycle proliferation and extracellular matrix (ECM) components, identifying dense feedback loops and directionality consistent with biological literature. Notably, this method scales polynomially with system size, and recorded overwhelmingly higher accuracy and F1 scores in network edge recovery and weight sign identification than representative classical inference algorithms such as ARACNE, GENIE3, and GeneNet. This study is a groundbreaking achievement demonstrating how powerfully "quantum-like" modeling, which interprets complex biological systems using the mathematical tools of quantum information theory, can be utilized in analyzing actual clinical and multi-omics data. The researchers emphasized that this framework will provide crucial insights for understanding the heterogeneity and plasticity of cancer cells and discovering new therapeutic targets in the future.