Derivative-free optimization of rate parameters of capsid assembly models from bulk in vitro data

The assembly of virus capsids from free coat proteins proceeds by a complicated cascade of association and dissociation steps, the great majority of which cannot be directly experimentally observed. This has made capsid assembly a rich field for computational models to attempt to fill the gaps in what is experimentally observable. Nonetheless, accurate simulation predictions depend on accurate models and there are substantial obstacles to model inference for such systems. Here, we describe progress in learning parameters for capsid assembly systems, particularly kinetic rate constants of coat-coat interactions, by computationally fitting simulations to experimental data. We previously developed an approach to learn rate parameters of coat-coat interactions by minimizing the deviation between real and simulated light scattering data monitoring bulk capsid assembly in vitro. This is a difficult data-fitting problem, however, because of the high computational cost of simulating assembly trajectories, the stochastic noise inherent to the models, and the limited and noisy data available for fitting. Here we show that a newer classes of methods, based on derivative-free optimization (DFO), can more quickly and precisely learn physical parameters from static light scattering data. We further explore how the advantages of the approaches might be affected by alternative data sources through simulation of a model of time-resolved mass spectrometry data, an alternative technology for monitoring bulk capsid assembly that can be expected to provide much richer data. The results show that advances in both the data and the algorithms can improve model inference, with rich data leading to high-quality fits for all methods, but DFO methods showing substantial advantages over less informative data sources better representative of the current experimental practice.

Avoid Internal Loops in Steady State Flux Space Sampling

As a widely used method in metabolic network studies, Monte-Carlo sampling in the steady state flux space is known for its flexibility and convenience of carrying out different purposes, simply by alternating constraints or objective functions, or appending post processes. Recently the concept of a non-linear constraint based on the second thermodynamic law, known as Loop Law, is challenging current sampling algorithms which will inevitably give rise to the internal loops. A generalized method is proposed here to eradicate the probability of the appearance of internal loops during sampling process. Based on Artificial Centered Hit and Run (ACHR) method, each step of the new sampling process will avoid entering loop-forming subspaces. This method has been applied on the metabolic network of Helicobacter pylori with three different objective functions: uniform sampling, optimizing biomass synthesis, optimizing biomass synthesis efficiency over resources ingested. Comparison between results from the new method and conventional ACHR method shows effective elimination of loop fluxes without affecting non-loop fluxes.

Imposition of Different Optimizing Object with Non-Linear Constraints on Flux Sampling and Elimination of Free Futile Pathways

Constraint-based modeling has been widely used on metabolic networks analysis, such as biosynthetic prediction and flux optimization. The linear constraints, like mass conservation constraint, reversibility constraint, biological capacity constraint, can be imposed on linear algorithms. However, recently a non-linear constraint based on the second thermodynamic law, known as loop law, has emerged and challenged the existing algorithms. Proven to be unfeasible with linear solutions, this non-linear constraint has been successfully imposed on the sampling process. In this place, Monte - Carlo sampling with Metropolis criterion and Simulated Annealing has been introduced to optimize the Biomass synthesis of genome scale metabolic network of Helicobacter pylori (iIT341 GSM / GPR) under mass conservation constraint, biological capacity constraint, and thermodynamic constraints including reversibility and loop law. The sampling method has also been employed to optimize a non-linear objective function, the Biomass synthetic rate, which is unified by the total income number of reducible electrons. To verify whether a sample contains internal loops, an automatic solution has been developed based on solving a set of inequalities. In addition, a new type of pathway has been proposed here, the Futile Pathway, which has three properties: 1) its mass flow could be self-balanced; 2) it has exchange reactions; 3) it is independent to the biomass synthesis. To eliminate the fluxes of the Futile Pathways in the sampling results, a linear programming based method has been suggested and the results have showed improved correlations among the reaction fluxes in the pathways related to Biomass synthesis.