Abstract
Motivated by growing evidence for pathway heterogeneity and alternative functions of molecular machines, we demonstrate a computational approach for investigating two questions: (1) Are there multiple mechanisms (state-space pathways) by which a machine can perform a given function, such as cotransport across a membrane? (2) How can additional functionality, such as proofreading/error-correction, be built into machine function using standard biochemical processes? Answers to these questions will aid both the understanding of molecular-scale cell biology and the design of synthetic machines. Focusing on transport in this initial study, we sample a variety of mechanisms by employing Metropolis Markov chain Monte Carlo. Trial moves adjust transition rates among an automatically generated set of conformational and binding states while maintaining fidelity to thermodynamic principles and a user-supplied fitness/functionality goal. Each accepted move generates a new model. The simulations yield both single and mixed reaction pathways for cotransport in a simple environment with a single substrate along with a driving ion. In a “competitive” environment including an additional decoy substrate, several qualitatively distinct reaction pathways are found which are capable of extremely high discrimination coupled to a leak of the driving ion, akin to proofreading. The array of functional models would be difficult to find by intuition alone in the complex state-spaces of interest.
Highlights
The proteins and protein complexes known as molecular machines perform essential functions in the cell, including transport, locomotion, energy production, and gene expression [1]
Sodiumglucose transporters (SGLT) are of biomedical interest due to the vital role that SGLT1 and SGLT2 play in the uptake of glucose in the small intestines and reabsorption in the kidneys, respectively [2], which in turn has prompted biophysical scrutiny of their mechanisms [3,4,5,6]
To highlight the power of the sampling strategy to discover non-trivial mechanisms, we examine the kinetic pathways of a model (Fig 4A) with enhanced selectivity. (Below this is referred to as “Model B”—Monte Carlo (MC) index 29000.1, see S2 Text)
Summary
The proteins and protein complexes known as molecular machines perform essential functions in the cell, including transport, locomotion, energy production, and gene expression [1]. The biological mechanisms of transporters as well as other molecular machines can be modeled using chemical reaction networks, typically along with mass action kinetics [13]. In a chemical reaction network, the system process is decomposed into discrete states connected by transition rates between states [13] forming a network of interconnected reactions in the state-space (Fig 1). These networks can be modeled using the chemical master equation: a set of differential equations describing the state probabilities and connected transition rates for each state [14]. Biochemical networks are generally Markovian [15], have a number of different control patterns [16], and typically adhere to specific design principles [17]
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