insight - Computational Biology - # Joint Trajectory and Network Inference

Leveraging Transient Dynamics and Perturbations for Joint Trajectory and Network Inference

Q: How can the proposed approach be extended to model non-autonomous systems where the network structure changes over time?

The proposed approach can be extended to model non-autonomous systems by allowing the interaction matrix ( A ) to be a function of time, thereby capturing the dynamic nature of the network structure. This can be achieved by introducing a time-dependent parameterization of ( A(t) ), where the interaction strengths between genes or molecular species vary as a function of time. To implement this, one could adopt a framework where ( A(t) ) is represented as a piecewise constant function or a smooth function that evolves according to a predefined model, such as a linear or nonlinear dynamical system. The optimization problem would then involve minimizing the action over a sequence of time points, incorporating the time-varying interaction matrix into the entropic optimal transport framework. Additionally, one could leverage techniques from control theory to model the influence of external factors or perturbations that may affect the network dynamics. By integrating these time-varying interactions into the reference fitting approach, the model can adapt to changes in the underlying biological processes, such as differentiation or response to environmental stimuli, thus providing a more accurate representation of the cellular dynamics.

Q: What are the theoretical guarantees on the identifiability and consistency of the inferred networks, especially in the presence of perturbations?

The theoretical guarantees on the identifiability and consistency of the inferred networks primarily hinge on the assumptions made regarding the underlying dynamical system and the nature of the perturbations applied. In the context of the proposed reference fitting approach, identifiability can be achieved under certain conditions, such as the availability of sufficient temporal data and perturbation information. Specifically, the use of perturbations, such as gene knockouts, helps to resolve ambiguities that arise from snapshot data alone, which often leads to non-identifiability of the interaction matrix ( A ). The regularization term ( R(A) ) plays a crucial role in ensuring that the optimization problem remains well-posed, thus facilitating the recovery of a unique solution for ( A ) under the assumption that the perturbations provide informative constraints on the system dynamics. Moreover, consistency of the inferred networks can be established through convergence results, which show that as the amount of data increases (both in terms of time points and perturbations), the estimated parameters converge to the true underlying parameters of the system. This is particularly relevant in the context of stochastic dynamics, where the presence of noise can affect the inference process. Theoretical results in the literature suggest that, under appropriate conditions, the reference fitting approach can yield consistent estimates of the interaction network, even in the presence of perturbations.

Q: How can the approach be combined with other sources of dynamical information, such as RNA velocity or metabolic labeling, to further improve the inference of cellular trajectories and gene regulatory networks?

The approach can be significantly enhanced by integrating additional sources of dynamical information, such as RNA velocity and metabolic labeling, into the reference fitting framework. RNA velocity provides insights into the directionality of gene expression changes over time, allowing for a more nuanced understanding of cellular trajectories. By incorporating RNA velocity data, the model can leverage the temporal dynamics of gene expression to refine the inferred trajectories and improve the accuracy of the interaction network. To achieve this, one could modify the optimization objective to include terms that account for RNA velocity, effectively treating it as an additional constraint or regularization term. This would involve estimating the velocity vector field and incorporating it into the entropic optimal transport framework, thereby guiding the inference process towards biologically plausible trajectories. Similarly, metabolic labeling can provide complementary information about cellular states and transitions. By integrating metabolic labeling data, the model can capture changes in metabolic activity that may correlate with specific gene regulatory interactions. This can be achieved by augmenting the reference fitting approach with additional data layers that represent metabolic states, allowing for a more comprehensive view of the cellular dynamics. Overall, the combination of these diverse data sources can lead to a more robust inference of cellular trajectories and gene regulatory networks, as it allows the model to capture the multifaceted nature of biological systems and their responses to various stimuli. By leveraging the strengths of each data type, the reference fitting approach can provide a more accurate and holistic understanding of the underlying biological processes.

Conceitos Básicos

A computational approach that leverages both transient dynamics and perturbation information to jointly infer cellular trajectories and gene regulatory networks.

Resumo

The author proposes a computational approach for joint trajectory and network inference, drawing inspiration from the theory of entropy regularized optimal transport and inference for linear dynamical systems. The key idea is to posit that the most likely system should be the one that minimizes the total action of the observed dynamics.

The approach is demonstrated on both simulated data from linear (Ornstein-Uhlenbeck) and non-linear (synthetic and biological) stochastic systems. The results show that leveraging perturbation information, even for a fraction of genes, greatly improves network inference compared to using only unperturbed dynamics.

The author also applies the method to a real biological time-series dataset with CRISPR perturbations of human induced pluripotent stem cells. The inferred networks agree with prior knowledge, and the author finds that providing perturbation data for a subset of genes is sufficient to significantly improve the network inference performance compared to using only wild-type data.

The author discusses potential future extensions, such as modeling non-autonomous systems and utilizing additional dynamical information like RNA velocity or metabolic labeling. Theoretical results on the identifiability and consistency of the approach are also identified as an important direction for future work.

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Estatísticas

The proposed approach can leverage both transient dynamics and perturbation information to jointly infer cellular trajectories and gene regulatory networks.
Providing perturbation data, even for a fraction of genes, greatly improves network inference performance compared to using only unperturbed dynamics.
Application to a real biological time-series dataset with CRISPR perturbations of human induced pluripotent stem cells shows that the inferred networks agree with prior knowledge.

Citações

"The observed trajectory taken by a dynamical system should minimise an energy relative to a reference process, which depends on the system structure."
"Perturbing a fraction of genes greatly improves network inference compared to only using unperturbed dynamics."
"Theoretical results on the identifiability and consistency of the approach are an important direction for future work."

Principais Insights Extraídos De

Joint trajectory and network inference via reference fitting

by Stephen Y Zh... às arxiv.org 09-12-2024

https://arxiv.org/pdf/2409.06879.pdf

Joint trajectory and network inference via reference fitting

Perguntas Mais Profundas

How can the proposed approach be extended to model non-autonomous systems where the network structure changes over time?

The proposed approach can be extended to model non-autonomous systems by allowing the interaction matrix ( A ) to be a function of time, thereby capturing the dynamic nature of the network structure. This can be achieved by introducing a time-dependent parameterization of ( A(t) ), where the interaction strengths between genes or molecular species vary as a function of time.
To implement this, one could adopt a framework where ( A(t) ) is represented as a piecewise constant function or a smooth function that evolves according to a predefined model, such as a linear or nonlinear dynamical system. The optimization problem would then involve minimizing the action over a sequence of time points, incorporating the time-varying interaction matrix into the entropic optimal transport framework.
Additionally, one could leverage techniques from control theory to model the influence of external factors or perturbations that may affect the network dynamics. By integrating these time-varying interactions into the reference fitting approach, the model can adapt to changes in the underlying biological processes, such as differentiation or response to environmental stimuli, thus providing a more accurate representation of the cellular dynamics.

What are the theoretical guarantees on the identifiability and consistency of the inferred networks, especially in the presence of perturbations?

The theoretical guarantees on the identifiability and consistency of the inferred networks primarily hinge on the assumptions made regarding the underlying dynamical system and the nature of the perturbations applied. In the context of the proposed reference fitting approach, identifiability can be achieved under certain conditions, such as the availability of sufficient temporal data and perturbation information.
Specifically, the use of perturbations, such as gene knockouts, helps to resolve ambiguities that arise from snapshot data alone, which often leads to non-identifiability of the interaction matrix ( A ). The regularization term ( R(A) ) plays a crucial role in ensuring that the optimization problem remains well-posed, thus facilitating the recovery of a unique solution for ( A ) under the assumption that the perturbations provide informative constraints on the system dynamics.
Moreover, consistency of the inferred networks can be established through convergence results, which show that as the amount of data increases (both in terms of time points and perturbations), the estimated parameters converge to the true underlying parameters of the system. This is particularly relevant in the context of stochastic dynamics, where the presence of noise can affect the inference process. Theoretical results in the literature suggest that, under appropriate conditions, the reference fitting approach can yield consistent estimates of the interaction network, even in the presence of perturbations.

How can the approach be combined with other sources of dynamical information, such as RNA velocity or metabolic labeling, to further improve the inference of cellular trajectories and gene regulatory networks?

The approach can be significantly enhanced by integrating additional sources of dynamical information, such as RNA velocity and metabolic labeling, into the reference fitting framework. RNA velocity provides insights into the directionality of gene expression changes over time, allowing for a more nuanced understanding of cellular trajectories. By incorporating RNA velocity data, the model can leverage the temporal dynamics of gene expression to refine the inferred trajectories and improve the accuracy of the interaction network.
To achieve this, one could modify the optimization objective to include terms that account for RNA velocity, effectively treating it as an additional constraint or regularization term. This would involve estimating the velocity vector field and incorporating it into the entropic optimal transport framework, thereby guiding the inference process towards biologically plausible trajectories.
Similarly, metabolic labeling can provide complementary information about cellular states and transitions. By integrating metabolic labeling data, the model can capture changes in metabolic activity that may correlate with specific gene regulatory interactions. This can be achieved by augmenting the reference fitting approach with additional data layers that represent metabolic states, allowing for a more comprehensive view of the cellular dynamics.
Overall, the combination of these diverse data sources can lead to a more robust inference of cellular trajectories and gene regulatory networks, as it allows the model to capture the multifaceted nature of biological systems and their responses to various stimuli. By leveraging the strengths of each data type, the reference fitting approach can provide a more accurate and holistic understanding of the underlying biological processes.