Nathaniel Wagner

The Road to Non‐Enzymatic Molecular Networks

This Minireview gives an overview of recent progress in the design and analysis of chemical systems that utilize template-directed autocatalytic and cross-catalytic processes as a means of wiring dynamically interacting molecules. Synthetic networks comprising two to nine replicating species are discussed. It is shown that for larger systems, more catalytic pathways must be manipulated to control the entire network topology and specific functionality of the individual species or subnetworks. Cellular biochemistry is an example of a natural functional molecular network; synthetic self-organized networks can provide additional models of complex systems.

Self-Replicating Amphiphilic β-Sheet Peptides†

Several different non-enzymatic molecular replication systems have been prepared and analyzed, including nucleic acids, fatty acids, peptides, and organic molecules. This research was evidently motivated by the chemists enthusiasm to shine light on plausible scenarios that may have lead to the origin of life on earth and early molecular evolution, and it also provided new opportunities for understanding fundamental principles, such as molecular recognition and autocatalysis. The study of non-enzymatic replication has been expanded recently beyond autocatalysis, to small molecular networks, in which the replication is also a product of template-assisted cross-catalysis. The design of replicating peptides has centered mainly on helical coiled-coil structures, in which monomeric or dimeric peptides, twenty-five to forty amino acids in length, serve as templates for substrate binding and thus for enhanced condensation and replication. However, it has been postulated that shorter peptides with simpler sequences may also serve as templates for self replication, provided that they are able to arrange themselves into unique and welldefined structures. We show herein that rather simple peptides, close analogues of the synthetic amphiphilic Glu(Phe-Glu)n peptides, [27] can form soluble, one-dimensional b-sheet aggregates in water, which serve to significantly accelerate peptide ligation and self replication. It has been postulated and demonstrated that native amyloid fibrils can replicate, albeit with moderate efficiency. Specific design of synthetic peptides can be used to make soluble aggregates with defined structures and higher replication efficiencies. Towards this aim, it has been shown that peptides comprising of repetitive dyads of hydrophilic and hydrophobic amino acid residues tend to adopt b-pleated sheet arrangements. Recently, it was further revealed that the terminal proline residue, which is rigid, does not have a backbone N H group available for hydrogen bonding, and often acts as a b-sheet breaker, can be used to enhance the formation of ordered b-sheet assemblies. Based on this evidence, we have synthesized the sequence Aba-Glu-(PheGlu)5-Pro of peptide 2 in which the N-terminus proline of the b-sheet forming peptide PFE-5 [34] has been replaced by the capping aromatic 4-acetamidobenzoate (ABA; Table 1). The

Competition and Cooperation in Dynamic Replication Networks

The simultaneous replication of six coiled-coil peptide mutants by reversible thiol-thioester exchange reactions is described. Experimental analysis of the time dependent evolution of networks formed by the peptides under different conditions reveals a complex web of molecular interactions and consequent mutant replication, governed by competition for resources and by autocatalytic and/or cross-catalytic template-assisted reactions. A kinetic model, first of its kind, is then introduced, allowing simulation of varied network behaviour as a consequence of changing competition and cooperation scenarios. We suggest that by clarifying the kinetic description of these relatively complex dynamic networks, both at early stages of the reaction far from equilibrium and at later stages approaching equilibrium, one lays the foundation for studying dynamic networks out-of-equilibrium in the near future.

Emergence of native peptide sequences in prebiotic replication networks

Biopolymer syntheses in living cells are perfected by an elaborate error correction machinery, which was not applicable during polymerization on early Earth. Scientists are consequently striving to identify mechanisms by which functional polymers were selected and further amplified from complex prebiotic mixtures. Here we show the instrumental role of non-enzymatic replication in the enrichment of certain product(s). To this end, we analyzed a complex web of reactions in β-sheet peptide networks, focusing on the formation of specific intermediate compounds and template-assisted replication. Remarkably, we find that the formation of several products in a mixture is not critically harmful, since efficient and selective template-assisted reactions serve as a backbone correction mechanism, namely, for keeping the concentration of the peptide containing the native backbone equal to, or even higher than, the concentrations of the other products. We suggest that these findings may shed light on molecular evolution processes that led to current biology.The synthesis of biopolymers in living cells is perfected by complex machinery, however this was not the case on early Earth. Here the authors show the role of non-enzymatic replication in the enrichment of certain products within prebiotically relevant mixtures.

β‐Sheet‐Induced Chirogenesis in Polymerization of Oligopeptides

The origin of long homochiral biopolymers in living systems has recently been the focus of intense research. In one particular research line, scientists studied, experimentally and theoretically, chiral amplification obtained during peptide formation by polymerization of amino acid building blocks. It was suggested that processes leading to temporal or spatial separation, and thus, to the growth of homochiral polymers at the expense of their heterochiral counterparts, can explain the chirality observed in larger molecules. We introduce a simple model and stochastic simulation for the polymerization of amino acids and β-sheet formation, showing the crucial effects of the β sheets on the distributions of peptide lengths. When chiral affinities are included, racemic β sheets of alternating homochiral strands lead to the formation of chiral peptides, the isotacticity of which increases with length, consistent with previous experimental results in aqueous solutions. The tendency to form isotactic peptides is shown for both initially racemic and initially nonracemic systems, as well as for closed and open systems. We suggest that these or similar mechanisms may explain the origin of chiroselectivity in prebiotic environments.

A Bistable Switch in Dynamic Thiodepsipeptide Folding and Template‐Directed Ligation

Bistable reaction networks provide living cells with chemically controlled mechanisms for long-term memory storage. Such networks are also often switchable and can be flipped from one state to the other. We target here a major challenge in systems chemistry research, namely developing synthetic, non-enzymatic, networks that mimic such a complex function. Therefore, we describe a dynamic network that depending on initial thiodepsipeptide concentrations leads to one of two distinct steady states. This bistable system is readily switched by applying the appropriate stimuli. The relationship between the reaction network topology and its capacity to invoke bistability is then analyzed by control experiments and theory. We suggest that demonstrating bistable behavior using synthetic networks further highlights their possible role in early evolution, and may shine light on potential utility for novel applications, such as chemical memories.

Anomalous diffusion and continuum percolation

Anomalous diffusion for continuum percolation is simulated by considering systems of randomly distributed circles and spheres. Universal behavior is obtained for the case of equal local conductances and nonuniversal behavior for diverging distributions of the local conductances. Diffusion in the continuum has a behavior consistent with that of other transport properties in the continuum. In addition, the results suggest that different algorithms for diffusion, which differ only in the random walker sitting times, are equivalent.

Bistability and Bifurcation in Minimal Self-Replication and Nonenzymatic Catalytic Networks

Bistability and bifurcation, found in a wide range of biochemical networks, are central to the proper function of living systems. We investigate herein recent model systems that show bistable behavior based on nonenzymatic self-replication reactions. Such models were used before to investigate catalytic growth, chemical logic operations, and additional processes of self-organization leading to complexification. By solving for their steady-state solutions by using various analytical and numerical methods, we analyze how and when these systems yield bistability and bifurcation and discover specific cases and conditions producing bistability. We demonstrate that the onset of bistability requires at least second-order catalysis and results from a mismatch between the various forward and reverse processes. Our findings may have far-reaching implications in understanding early evolutionary processes of complexification, emergence, and potentially the origin of life.

The Nature of Stability in Replicating Systems

We review the concept of dynamic kinetic stability, a type of stability associated specifically with replicating entities, and show how it differs from the well-known and established (static) kinetic and thermodynamic stabilities associated with regular chemical systems. In the process we demonstrate how the concept can help bridge the conceptual chasm that continues to separate the physical and biological sciences by relating the nature of stability in the animate and inanimate worlds, and by providing additional insights into the physicochemical nature of abiogenesis.

Theoretical Models of Generalized Quasispecies

Theoretical modeling of quasispecies has progressed in several directions. In this chapter, we review the works of Emmanuel Tannenbaum, who, together with Eugene Shakhnovich at Harvard University and later with colleagues and students at Ben-Gurion University in Beersheva, implemented one of the more useful approaches, by progressively setting up various formulations for the quasispecies model and solving them analytically. Our review will focus on these papers that have explored new models, assumed the relevant mathematical approximations, and proceeded to analytically solve for the steady-state solutions and run stochastic simulations . When applicable, these models were related to real-life problems and situations, including changing environments, presence of chemical mutagens, evolution of cancer and tumor cells , mutations in Escherichia coli, stem cells , chromosomal instability (CIN), propagation of antibiotic drug resistance , dynamics of bacteria with plasmids , DNA proofreading mechanisms, and more.