Accurate strain-level identification of microbes from limited data: characterizing, reducing, and quantifying ambiguity

The National Science Foundation Division of Mathematical Sciences awarded Indiana University (Trustees of Indiana University) $149,773 on January 1, 2027, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mathematical and statistical tools for strain-level identification of closely related bacterial strains from pooled sequencing data.

The project addresses ambiguity that arises when bacterial DNA from multiple colonies is pooled before sequencing, a cost-saving alternative to processing individual colonies separately. Different strain combinations may explain the same pooled data, making strain-level conclusions unreliable. The award funds research that clarifies when pooled sequencing can and cannot support strain identification by studying strain reconstruction as a constrained matrix factorization problem. The work will produce documented research code and reproducible examples to support biotechnology workflows and microbial surveillance applications, and will support graduate-student training at the interface of mathematics, statistics, computation, and microbial genomics.

Performance takes place in Bloomington, Indiana, with a period of performance from January 1, 2027, through December 31, 2029. The assistance type is a project grant.

Abstract

Identifying closely related bacterial strains is important for tracking outbreaks, understanding how microbes spread, and improving the use of sequencing in biotechnology and public health. In microbial surveillance, a sample from a patient, facility, or environment may contain several closely related bacterial strains. The most direct way to identify these strains is to grow the bacteria on a plate and sequence many individual colonies, but this can be expensive because each colony must be processed separately and many colonies may be needed to capture the full diversity in the sample. A cheaper alternative is pooled sequencing, in which DNA from several colonies is combined before sequencing. Pooling can save resources, but IT also creates ambiguity: different sets of strains may sometimes explain the same pooled data. This project develops mathematical and statistical tools for understanding when strain information can be recovered from pooled sequencing data and when the data are inherently ambiguous. By clarifying when pooled sequencing can and cannot support strain-level conclusions, the project will help make sequencing-based biotechnology workflows more reliable, interpretable, and cost-effective. The project will also support graduate-student training at the interface of mathematics, statistics, computation, and microbial genomics, and will produce documented research code and reproducible examples to support future work in biotechnology and microbial surveillance. Technically, the project studies strain reconstruction as a constrained matrix factorization problem in which the expected allele-frequency matrix has the form e[x]=WH. The matrix w encodes binary strain haplotypes, while the columns of h are mixing proportions for pooled samples. Unique recovery of w corresponds to uniqueness of a factorization whose vertices LIE in the boolean hypercube and whose observed pooled samples LIE in their convex hull. The project will develop a circuit-based geometric framework for characterizing low-complexity mechanisms of non-identifiability in this model and for deriving experimentally interpretable conditions under which pooling designs exclude competing factorizations. IT will also develop a prototype geometry-informed bayesian inference method that constructs candidate strain sets from the affine structure of the data and uses importance-sampling ideas to approximate posterior uncertainty over competing strain configurations. The computational work will emphasize research-grade implementation, diagnostics for distinguishing identifiable from ambiguous reconstructions, and representative simulations illustrating pooling-design tradeoffs. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the foundation's intellectual merit and broader impacts review criteria.- subawards are not planned for this award.