A major goal of natural computing is to design biomolecules, such as nucleic acid sequences, that can be used to perform computations. We design sequences of nucleic acids that are "guaranteed" to have long folding pathways relative to their length. This particular sequences with high probability follow low-barrier folding pathways that visit a large number of distinct structures. Long folding pathways are interesting, because they demonstrate that natural computing can potentially support long and complex computations. Formally, we provide the first scalable designs of molecules whose low-barrier folding pathways, with respect to a simple, stacked pair energy model, grow superlinearly with the molecule length, but for which all significantly shorter alternative folding pathways have an energy barrier that is [Formula: see text] times that of the low-barrier pathway for any [Formula: see text] and a sufficiently long sequence.

Many problems of practical interest rely on Continuous-time Markov chains (CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible with existing methods. For problems with countably infinite states, where classical methods such as matrix exponentiation are not applicable, the main alternative has been particle Markov chain Monte Carlo methods imputing both the holding times and sequences of visited states. We propose a particle-based Monte Carlo approach where the holding times are marginalized analytically. We demonstrate that in a range of realistic inferential setups, our scheme dramatically reduces the variance of the Monte Carlo approximation and yields more accurate parameter posterior approximations given a fixed computational budget. These experiments are performed on both synthetic and real datasets, drawing from two important examples of CTMCs having combinatorial state spaces: string-valued mutation models in phylogenetics and nucleic acid folding pathways.

Chemical reaction networks (CRNs) and DNA strand displacement systems (DSDs) are widely-studied and useful models of molecular programming. However, in order for some DSDs in the literature to behave in an expected manner, the initial number of copies of some reagents is required to be fixed. In this paper we show that, when multiple copies of all initial molecules are present, general types of CRNs and DSDs fail to work correctly if the length of the shortest sequence of reactions needed to produce any given molecule exceeds a threshold that grows polynomially with attributes of the system.

The perfect phylogeny problem is of central importance to both evolutionary biology and population genetics. Missing values are a common occurrence in both sequence and genotype data, but they make the problem of finding a perfect phylogeny NPhard even for binary characters. We introduce new and efficient perfect phylogeny algorithms for broad classes of binary and multistate data with missing values. Specifically, we address binary missing data consistent with the rich data hypothesis (RDH) introduced by Halperin and Karp and give an efficient algorithm for enumerating phylogenies. This algorithm is useful for computing the probability of data with missing values under the coalescent model. In addition, we use the partition intersection (PI) graph and chordal graph theory to generalize the RDH to multi-state characters with missing values. For a bounded number of states, we provide a fixed parameter tractable algorithm for the perfect phylogeny problem with missing data. Utilizing the PI graph, we are able to show that under multiple biologically motivated models for character data, our generalized RDH holds with high probability, and we evaluate our results with extensive empirical analysis.

Pedigrees, or family trees, are directed graphs used to identify sites of the genome that are correlated with the presence or absence of a disease. With the advent of genotyping and sequencing technologies, there has been an explosion in the amount of data available, both in the number of individuals and in the number of sites. Some pedigrees number in the thousands of individuals. Meanwhile, analysis methods have remained limited to pedigrees of <100 individuals which limits analyses to many small independent pedigrees. Disease models, such those used for the linkage analysis log-odds (LOD) estimator, have similarly been limited. This is because linkage anlysis was originally designed with a different task in mind, that of ordering the sites in the genome, before there were technologies that could reveal the order. LODs are difficult to interpret and nontrivial to extend to consider interactions among sites. These developments and difficulties call for the creation of modern methods of pedigree analysis. Drawing from recent advances in graphical model inference and transducer theory, we introduce a simple yet powerful formalism for expressing genetic disease models. We show that these disease models can be turned into accurate and efficient estimators. The technique we use for constructing the variational approximation has potential applications to inference in other large-scale graphical models. This method allows inference on larger pedigrees than previously analyzed in the literature, which improves disease site prediction.

MOTIVATION: The search for genetic variants that are linked to complex diseases such as cancer, Parkinson's;, or Alzheimer's; disease, may lead to better treatments. Since haplotypes can serve as proxies for hidden variants, one method of finding the linked variants is to look for case-control associations between the haplotypes and disease. Finding these associations requires a high-quality estimation of the haplotype frequencies in the population. To this end, we present, HaploPool, a method of estimating haplotype frequencies from blocks of consecutive SNPs. RESULTS: HaploPool leverages the efficiency of DNA pools and estimates the population haplotype frequencies from pools of disjoint sets, each containing two or three unrelated individuals. We study the trade-off between pooling efficiency and accuracy of haplotype frequency estimates. For a fixed genotyping budget, HaploPool performs favorably on pools of two individuals as compared with a state-of-the-art non-pooled phasing method, PHASE. Of independent interest, HaploPool can be used to phase non-pooled genotype data with an accuracy approaching that of PHASE. We compared our algorithm to three programs that estimate haplotype frequencies from pooled data. HaploPool is an order of magnitude more efficient (at least six times faster), and considerably more accurate than previous methods. In contrast to previous methods, HaploPool performs well with missing data, genotyping errors and long haplotype blocks (of between 5 and 25 SNPs).

We propose a novel, motion planning based approach to approximately map the energy landscape of an RNA molecule. Our method is based on the successful probabilistic roadmap motion planners that we have previously successfully applied to protein folding. The key advantage of our method is that it provides a sparse map that captures the main features of the landscape and which can be analyzed to compute folding kinetics. In this paper, we provide evidence that this approach is also well suited to RNA. We compute population kinetics and transition rates on our roadmaps using the master equation for a few moderately sized RNA and show that our results compare favorably with results of other existing methods.