Zum Inhalt springen
Technische Universität München

Gradient estimators for parameter inference in discrete stochastic kinetic models

Stochastic kinetic models are ubiquitous in physics, yet inferring their parameters from experimental data remains challenging. For deterministic models, parameter inference often relies on gradients, which can be obtained efficiently through automatic differentiation (AD). However, AD cannot be applied directly to the Gillespie stochastic simulation algorithm (SSA), since sampling from a discrete set of reactions introduces non-differentiable operations. In this work, we adopt three gradient estimators from machine learning for the Gillespie SSA: the Gumbel-Softmax Straight-Through (GS-ST) estimator, the Score Function estimator, and the Alternative Path estimator. We use the estimators to evaluate gradients of steady-state and time-dependent observables, and compare their performance in representative biophysical systems with relaxation dynamics (bimolecular association) and oscillatory dynamics (repressilator). We find that the GS-ST estimator generally yields well-behaved gradient estimates, but exhibits diverging variance in challenging parameter regimes, which can cause parameter inference to fail. In these cases, other estimators provide more robust, lower variance gradients. Our results demonstrate that gradient-based parameter inference can be effectively combined with the Gillespie SSA, with different estimators offering complementary advantages.

Sequence motif dynamics in RNA pools

In RNA world scenarios, pools of RNA oligomers form strongly interacting, dynamic systems, which enable molecular evolution. In such pools, RNA oligomers hybridize and dehybridize, ligate, and break, ultimately generating longer RNA molecules, which may fold into catalytically active ribozymes. A key process for the elongation of RNA oligomers is templated ligation, which can occur when two RNA strands are adjacently hybridized onto a template strand. Detailed simulations of the dynamics in RNA pools involve a large variety of possible sequences and reactions. Here we develop a reduced description of these complex dynamics within the space of sequence motifs. We then explore to what extent our reduced description can capture the behavior of detailed simulations that account for the full dynamics in the space of RNA strands. Towards this end, we project the dynamics into a motif space, which accounts only for the abundance of all possible four-nucleotide motifs. A system of ordinary differential equations describes the dynamics of those motifs. Its control parameters are effective rate constants for reactions in motif space, which we obtain from the rate constants for the processes underlying the full dynamics in the space of RNA strands. We find that these reduced motif space dynamics indeed capture important aspects of the informational dynamics of RNA pools in sequence space. This approach could also provide a framework to rationalize and interpret features of the sequence dynamics observed in experimental systems.

A quantitative model of enzyme-free copying of RNA with dimers

Copying genetic information without enzymes may have been a crucial step toward the origin of life, but known RNA copying reactions, such as template-directed primer extension, are slow and inefficient. We combined experiments and kinetic modeling to investigate the most effective enzyme-free RNA copying system reported so far, which uses strongly pairing RNA dimers as building blocks. Our analysis shows that the main bottleneck is the formation of new phosphodiester bonds on the template. The model reproduces the experimentally observed copying of up to 12 template bases through primer extension, dimer coupling, and fragment ligation, while revealing how material flows through competing reaction pathways. Our results provide a detailed mechanistic picture of protein-free RNA copying and identify the key limitations that must be overcome to develop more efficient self-replicating systems.

Toward stable replication of genomic information in pools of RNA molecules

The transition from prebiotic chemistry to life required a way to copy genetic information without enzymes. We study a model for such replication, known as the Virtual Circular Genome (VCG). In this model, replication occurs in a pool of short RNA oligomers. Each oligomer contains part of a circular genome, and together the oligomers encode the complete sequence. Long oligomers contain genetic information, while monomers and short oligomers mainly serve as building blocks for further replication. A key challenge is the competition between two types of ligation reactions: the mostly accurate addition of a short building block to a long oligomer, and the more error-prone joining of two long oligomers. We show that replication accuracy improves when the long oligomers are longer and less concentrated. Errors can also be further reduced when every ligation reaction includes at least one monomer and direct joining between long oligomers is suppressed. Under these conditions, short oligomers are surprisingly extended faster than long ones, an effect that has also been observed experimentally. Our work explains this behavior and predicts how it depends on parameters of the system. Overall, the VCG provides a promising model for how genetic information may have been replicated before enzymes existed. It could help overcome major limitations of non-enzymatic template copying, including short product lengths and high error rates.

More about origins of life:

To top