Computational analysis of protein synthesis, diffusion, and binding in compartmental biochips.

Protein complex assembly facilitates the combination of individual protein subunits into functional entities, and thus plays a crucial role in biology and biotechnology. Recently, we developed quasi-twodimensional, silicon-based compartmental biochips that are designed to study and administer the synthesis and assembly of protein complexes. At these biochips, individual protein subunits are synthesized from locally confined high-density DNA brushes and are captured on the chip surface by molecular traps. Here, we investigate single-gene versions of our quasi-twodimensional synthesis systems and introduce the trap-binding efficiency to characterize their performance. We show by mathematical and computational modeling how a finite trap density determines the dynamics of protein-trap binding and identify three distinct regimes of the trap-binding efficiency. We systematically study how protein-trap binding is governed by the system's three key parameters, which are the synthesis rate, the diffusion constant and the trap-binding affinity of the expressed protein. In addition, we describe how spatially differential patterns of traps modulate the protein-trap binding dynamics. In this way, we extend the theoretical knowledge base for synthesis, diffusion, and binding in compartmental systems, which helps to achieve better control of directed molecular self-assembly required for the fabrication of nanomachines for synthetic biology applications or nanotechnological purposes.

Dominance analysis of competing protein assembly pathways.

Most proteins form complexes consisting of two or more subunits, where complex assembly can proceed via two competing pathways: co-translational assembly of a mature and a nascent subunit, and post-translational assembly by two mature protein subunits. Assembly pathway dominance, i.e., which of the two pathways is predominant under which conditions, is poorly understood. Here, we introduce a reaction-diffusion system that describes protein complex formation via post- and co-translational assembly and use it to analyze the dominance of both pathways. Special features of this new system are (i) spatially inhomogeneous sources of reacting species, (ii) a combination of diffusing and immobile species, and (iii) an asymmetric binding competition between the species. We study assembly pathway dominance for the spatially homogeneous system and find that the ratio of production rates of the two protein subunits determines the long-term pathway dominance. This result is independent of the binding rate constants for post- and co-translational assembly and implies that a system with an initial post-translational assembly dominance can eventually exhibit co-translational assembly dominance and vice versa. For exactly balanced production of both subunits, the assembly pathway dominance is determined by the steady state concentration of the subunit that can bind both nascent and mature partners. The introduced system of equations can be applied to describe general dynamics of assembly processes involving both diffusing and immobile components.

Programming multi-protein assembly by gene-brush patterns and two-dimensional compartment geometry.

The assembly of protein machines in cells is precise, rapid, and coupled to protein synthesis with regulation in space and time. The assembly of natural and synthetic nanomachines could be similarly controlled by genetic programming outside the cell. Here, we present quasi-two-dimensional (2D) silicon compartments that enable programming of protein assembly lines by local synthesis from surface-immobilized DNA brushes. Using this platform, we studied the autonomous synthesis and assembly of a structural complex from a bacteriophage and a bacterial RNA-synthesizing machine. Local synthesis and surface capture of complexes provided high assembly yield and sensitive detection of spatially resolved assembly intermediates, with the 3D geometry of the compartment and the 2D pattern of brushes dictating the yield and mode of assembly steps. Localized synthesis of proteins in a single gene brush enhances their interactions, and displacement of their genes in separated brushes leads to step-by-step surface assembly. This methodology enables spatial regulation of protein synthesis, and deciphering, reconstruction and design of biological machine assembly lines.