arXiv subjects

Anne Condon

Publications and source records attributed to Anne Condon.

10 recordsLinked to original sources

arXiv2024

Struc2mapGAN: improving synthetic cryo-EM density maps with generative adversarial networks

Generating synthetic cryogenic electron microscopy 3D density maps from molecular structures has potential important applications in structural biology. Yet existing simulation-based methods cannot mimic all the complex features present in experimental maps, such as secondary structure elements. As an alternative, we propose struc2mapGAN, a novel data-driven method that employs a generative adversarial network to produce improved experimental-like density maps from molecular structures. More specifically, struc2mapGAN uses a nested U-Net architecture as the generator, with an additional L1 loss term and further processing of raw training experimental maps to enhance learning efficiency. While struc2mapGAN can promptly generate maps after training, we demonstrate that it outperforms existing simulation-based methods for a wide array of tested maps and across various evaluation metrics.

cs.LG↗

arXiv2023

Visualizing DNA reaction trajectories with deep graph embedding approaches

Synthetic biologists and molecular programmers design novel nucleic acid reactions, with many potential applications. Good visualization tools are needed to help domain experts make sense of the complex outputs of folding pathway simulations of such reactions. Here we present ViDa, a new approach for visualizing DNA reaction folding trajectories over the energy landscape of secondary structures. We integrate a deep graph embedding model with common dimensionality reduction approaches, to map high-dimensional data onto 2D Euclidean space. We assess ViDa on two well-studied and contrasting DNA hybridization reactions. Our preliminary results suggest that ViDa's visualization successfully separates trajectories with different folding mechanisms, thereby providing useful insight to users, and is a big improvement over the current state-of-the-art in DNA kinetics visualization.

q-bio.BM↗

arXiv2023

ViDa: Visualizing DNA hybridization trajectories with biophysics-informed deep graph embeddings

Visualization tools can help synthetic biologists and molecular programmers understand the complex reactive pathways of nucleic acid reactions, which can be designed for many potential applications and can be modelled using a continuous-time Markov chain (CTMC). Here we present ViDa, a new visualization approach for DNA reaction trajectories that uses a 2D embedding of the secondary structure state space underlying the CTMC model. To this end, we integrate a scattering transform of the secondary structure adjacency, a variational autoencoder, and a nonlinear dimensionality reduction method. We augment the training loss with domain-specific supervised terms that capture both thermodynamic and kinetic features. We assess ViDa on two well-studied DNA hybridization reactions. Our results demonstrate that the domain-specific features lead to significant quality improvements over the state-of-the-art in DNA state space visualization, successfully separating different folding pathways and thus providing useful insights into dominant reaction mechanisms.

q-bio.QM↗

arXiv2023

EMPOT: partial alignment of density maps and rigid body fitting using unbalanced Gromov-Wasserstein divergence

Aligning EM density maps and fitting atomic models are essential steps in single particle cryogenic electron microscopy (cryo-EM), with recent methods leveraging various algorithms and machine learning tools. As aligning maps remains challenging in the presence of a map that only partially fits the other (e.g. one subunit), we here propose a new procedure, EMPOT (EM Partial alignment with Optimal Transport), for partial alignment of 3D maps. EMPOT first finds a coupling between 3D point-cloud representations, which is associated with their so-called unbalanced Gromov Wasserstein divergence, and second, uses this coupling to find an optimal rigid body transformation. Upon running and benchmarking our method with experimental maps and structures, we show that EMPOT outperforms standard methods for aligning subunits of a protein complex and fitting atomic models to a density map, suggesting potential applications of Partial Optimal Transport for improving Cryo-EM pipelines.

q-bio.BM↗

arXiv2023

On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions

This paper studies the (discrete) \emph{chemical reaction network (CRN)} computational model that emerged in the last two decades as an abstraction for molecular programming. The correctness of CRN protocols is typically established under one of two possible schedulers that determine how the execution advances: (1) a \emph{stochastic scheduler} that obeys the (continuous time) Markov process dictated by the standard model of stochastic chemical kinetics; or (2) an \emph{adversarial scheduler} whose only commitment is to maintain a certain fairness condition. The latter scheduler is justified by the fact that the former one crucially assumes ``idealized conditions'' that more often than not, do not hold in real wet-lab experiments. However, when it comes to analyzing the \emph{runtime} of CRN protocols, the existing literature focuses strictly on the stochastic scheduler, thus raising the research question that drives this work: Is there a meaningful way to quantify the runtime of CRNs without the idealized conditions assumption? The main conceptual contribution of the current paper is to answer this question in the affirmative, formulating a new runtime measure for CRN protocols that does not rely on idealized conditions. This runtime measure is based on an adapted (weaker) fairness condition as well as a novel scheme that enables partitioning the execution into short \emph{rounds} and charging the runtime for each round individually (inspired by definitions for the runtime of asynchronous distributed algorithms). Following that, we turn to investigate various fundamental computational tasks and establish (often tight) bounds on the runtime of the corresponding CRN protocols operating under the adversarial scheduler. This includes an almost complete chart of the runtime complexity landscape of predicate decidability tasks.

cs.DC↗

arXiv2022

Output-Oblivious Stochastic Chemical Reaction Networks

We classify the functions $f:\mathbb{N}^2 \rightarrow \mathbb{N}$ which are stably computable by output-oblivious Stochastic Chemical Reaction Networks (CRNs), i.e., systems of reactions in which output species are never reactants. While it is known that precisely the semilinear functions are stably computable by CRNs, such CRNs sometimes rely on initially producing too many output species and then consuming the excess in order to reach a correct stable state. These CRNs may be difficult to integrate into larger systems: if the output of a CRN $\mathcal{C}$ becomes the input to a downstream CRN $\mathcal{C}'$, then $\mathcal{C}'$ could inadvertently consume too many outputs before $\mathcal{C}$ stabilizes. If, on the other hand, $\mathcal{C}$ is output-oblivious then $\mathcal{C}'$ may consume $\mathcal{C}$'s output as soon as it is available. In this work we prove that a semilinear function $f:\mathbb{N}^2 \rightarrow \mathbb{N}$ is stably computable by an output-oblivious CRN with a leader if and only if it is both increasing and either grid-affine (intuitively, its domains are congruence classes), or the minimum of a finite set of fissure functions (intuitively, functions behaving like the min function).

cs.CC↗

arXiv2021

Isometric Hamming embeddings of weighted graphs

A mapping $α: V(G) \to V(H)$ from the vertex set of one graph $G$ to another graph $H$ is an isometric embedding if the shortest path distance between any two vertices in $G$ equals the distance between their images in $H$. Here, we consider isometric embeddings of a weighted graph $G$ into unweighted Hamming graphs, called Hamming embeddings, when $G$ satisfies the property that every edge is a shortest path between its endpoints. Using a Cartesian product decomposition of $G$ called its pseudofactorization, we show that every Hamming embedding of $G$ may be partitioned into Hamming embeddings for each irreducible pseudofactor graph of $G$, which we call its canonical partition. This implies that $G$ permits a Hamming embedding if and only if each of its irreducible pseudofactors is Hamming embeddable. This result extends prior work on unweighted graphs that showed that an unweighted graph permits a Hamming embedding if and only if each irreducible pseudofactor is a complete graph. When a graph $G$ has nontrivial pseudofactors, determining whether $G$ has a Hamming embedding can be simplified to checking embeddability of two or more smaller graphs.

cs.DM↗

arXiv2021

Factorization and pseudofactorization of weighted graphs

For unweighted graphs, finding isometric embeddings is closely related to decompositions of $G$ into Cartesian products of smaller graphs. When $G$ is isomorphic to a Cartesian graph product, we call the factors of this product a factorization of $G$. When $G$ is isomorphic to an isometric subgraph of a Cartesian graph product, we call those factors a pseudofactorization of $G$. Prior work has shown that an unweighted graph's pseudofactorization can be used to generate a canonical isometric embedding into a product of the smallest possible pseudofactors. However, for arbitrary weighted graphs, which represent a richer variety of metric spaces, methods for finding isometric embeddings or determining their existence remain elusive, and indeed pseudofactorization and factorization have not previously been extended to this context. In this work, we address the problem of finding the factorization and pseudofactorization of a weighted graph $G$, where $G$ satisfies the property that every edge constitutes a shortest path between its endpoints. We term such graphs minimal graphs, noting that every graph can be made minimal by removing edges not affecting its path metric. We generalize pseudofactorization and factorization to minimal graphs and develop new proof techniques that extend the previously proposed algorithms due to Graham and Winkler [Graham and Winkler, '85] and Feder [Feder, '92] for pseudofactorization and factorization of unweighted graphs. We show that any $m$-edge, $n$-vertex graph with positive integer edge weights can be factored in $O(m^2)$ time, plus the time to find all pairs shortest paths (APSP) distances in a weighted graph, resulting in an overall running time of $O(m^2+n^2\log\log n)$ time. We also show that a pseudofactorization for such a graph can be computed in $O(mn)$ time, plus the time to solve APSP, resulting in an $O(mn+n^2\log\log n)$ running time.

cs.DS↗

arXiv2021

The pathway elaboration method for mean first passage time estimation in large continuous-time Markov chains with applications to nucleic acid kinetics

For predicting the kinetics of nucleic acid reactions, continuous-time Markov chains (CTMCs) are widely used. The rate of a reaction can be obtained through the mean first passage time (MFPT) of its CTMC. However, a typical issue in CTMCs is that the number of states could be large, making MFPT estimation challenging, particularly for events that happen on a long time scale (rare events). We propose the pathway elaboration method, a time-efficient probabilistic truncation-based approach for detailed-balance CTMCs. It can be used for estimating the MFPT for rare events in addition to rapidly evaluating perturbed parameters without expensive recomputations. We demonstrate that pathway elaboration is suitable for predicting nucleic acid kinetics by conducting computational experiments on 267 measurements that cover a wide range of rates for different types of reactions. We utilize pathway elaboration to gain insight on the kinetics of two contrasting reactions, one being a rare event. We then compare the performance of pathway elaboration with the stochastic simulation algorithm (SSA) for MFPT estimation on 237 of the reactions for which SSA is feasible. We further build truncated CTMCs with SSA and transition path sampling (TPS) to compare with pathway elaboration. Finally, we use pathway elaboration to rapidly evaluate perturbed model parameters during optimization with respect to experimentally measured rates for these 237 reactions. The testing error on the remaining 30 reactions, which involved rare events and were not feasible to simulate with SSA, improved comparably with the training error. Our framework and dataset are available at https://github.com/ DNA-and-Natural-Algorithms-Group/PathwayElaboration.

q-bio.QM↗

arXiv2012

The complexity of string partitioning

Given a string $w$ over a finite alphabet $Σ$ and an integer $K$, can $w$ be partitioned into strings of length at most $K$, such that there are no \emph{collisions}? We refer to this question as the \emph{string partition} problem and show it is \NP-complete for various definitions of collision and for a number of interesting restrictions including $|Σ|=2$. This establishes the hardness of an important problem in contemporary synthetic biology, namely, oligo design for gene synthesis.

cs.CC↗