Session VIII — Mathematical Biology

Tuesday, October 27 · 4:30–6:00 p.m.
Chair: Tomas Rube

Season length controls coexistence of pathogen strains in a flow-kick model

Xuan (Kelsy) Fei · UC Davis

Many host-pathogen systems transmit only seasonally. Andreasen and Dwyer (2023) modeled competing strains, assuming each season is long enough to reach equilibrium. Season length plays no role, and only the removed class initiates the next outbreak. They found that a trade-off between infectiousness and interepidemic survival allows coexistence. We drop this idealization, treat season length as a parameter, and rigorously analyze persistence, invasion, and coexistence. When the season length is finite, still-infected hosts also seed the next outbreak. For a single strain, when they contribute less to carryover than the removed class, we prove a critical season length separating extinction from a unique globally stable endemic equilibrium. For two competing strains, we characterize coexistence and extinction via invasion analysis and show numerically that carryover from still-infected hosts broadens mutual invasibility, allowing coexistence only at intermediate season lengths.

Optimizing Metachronal Paddling with Reinforcement Learning at Low Reynolds Number

Alana Bailey · UC Davis

Metachronal paddling is a swimming strategy in which an organism oscillates sets of adjacent limbs with a constant phase lag, propagating a metachronal wave through its limbs and propelling it forward. This limb coordination strategy is utilized by swimmers across a wide range of Reynolds numbers, which suggests that this metachronal rhythm was selected for its optimality of swimming performance. In this study, we apply reinforcement learning to a swimmer at zero Reynolds number and investigate whether the learning algorithm selects this metachronal rhythm, or if other coordination patterns emerge. We design the swimmer agent with an elongated body and sets of paddles placed along the body for various fixed paddle spacings. We begin with rigid paddles to isolate the time coordination of the limbs, then add a hinge to allow the paddles to change their shape throughout the stroke. Based on paddle spacing and type, the swimmer agent learns qualitatively different coordination patterns.

Direct RNA sequence design under codon constraints using expressive tensor-based secondary structure models

Mark Fornace · Lawrence Berkeley National Laboratory

Nucleic acid sequence design via codon optimization is a fundamental task with applications across synthetic biology and metabolic engineering. Given a target protein, it is a major open challenge to navigate the combinatorially large design space of codon sequences mapping to its amino acid sequence. Computational approaches generally seek to optimize simple objectives based on the codon sequence, possibly together with more complicated contributions based on secondary structure analysis. In this talk, I describe a direct and efficient algorithm to sample sequences from a suitable Boltzmann distribution defined in terms of the codon sequence and a fully detailed secondary structure free energy model. This algorithm draws upon a recently developed tensor-based formulation of secondary structure thermodynamics and can leverage any available CPU and GPU resources for massive computational speedups.

SPRINT-MS: A high-throughput platform for identifying protein-protein interactions using pooled IP-MS and sparse signal recovery

Moitrish Majumdar · UC Merced

This talk will present SPRINT-MS (SParse Reconstruction of INTeractions by Mass Spectrometry), an integrated experimental and computational platform to accelerate the discovery of protein-protein interactions (PPIs). PPIs form extensive networks that vary across time, conditions, and cell types, creating a complex, high-dimensionality problem. Thus, there is a pressing need for universally applicable tools capable of mapping and quantifying PPI networks and their context-dependent dynamics with high efficiency. SPRINT-MS builds on compressed sensing and uses an algorithmically optimized pooling scheme, immunopurification-mass spectrometry (IP-MS), and a novel sparse signal reconstruction algorithm to enable pooled PPI capture experiments. This talk will discuss the mathematical methods underlying SPRINT-MS and demonstrate that it is comparable to standard individual IP-MS experiments for identifying PPIs, while increasing throughput and reducing sample input requirements.

Identifiability: Using Math and Trees to Solve Problems from Biology

Cash Bortner · California State University, Stanislaus

Linear compartmental models are widely used to describe transport and exchange processes in pharmacokinetics, ecology, and systems biology. These models are represented by directed graphs whose vertices correspond to compartments and whose edges are labeled by parameters (flow rates between compartments). Compartments may also receive external inputs, be measured as outputs, or allow material to leave the system through leaks. A central question is structural identifiability: whether the model parameters can be uniquely recovered from ideal input-output data. For small models, identifiability can often be determined using tools from algebraic geometry, but these computations become difficult as models grow. In this talk, we explore how the underlying graph, together with the placement of inputs, outputs, and leaks, can be used to establish identifiability without computationally intensive algebraic methods.