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.

Amylin-Aß oligomers at atomic resolution using molecular dynamics simulations: a link between Type 2 diabetes and Alzheimer's disease.

Clinical studies have identified Type 2 diabetes (T2D) as a risk factor of Alzheimer's disease (AD). One of the potential mechanisms that link T2D and AD is the loss of cells associated with degenerative changes. Amylin1-37 aggregates (the pathological species in T2D) were found to be co-localized with those of Aß1-42 (the pathological species in AD) to form the Amylin1-37-Aß1-42 plaques, promoting aggregation and thus contributing to the etiology of AD. However, the mechanisms by which Amylin1-37 co-aggregates with Aß1-42 are still elusive. This work presents the interactions between Amylin1-37 oligomers and Aß1-42 oligomers at atomic resolution applying extensive molecular dynamics simulations for relatively large ensemble of cross-seeding Amylin1-37-Aß1-42 oligomers. The main conclusions of this study are first, Aß1-42 oligomers prefer to interact with Amylin1-37 oligomers to form single layer conformations (in-register interactions) rather than double layer conformations; and second, in some double layer conformations of the cross-seeding Amylin1-37-Aß1-42 oligomers, the Amylin1-37 oligomers destabilize the Aß1-42 oligomers and thus inhibit Aß1-42 aggregation, while in other double layer conformations, the Amylin1-37 oligomers stabilize Aß1-42 oligomers and thus promote Aß1-42 aggregation.

The Strong Influence of Structure Polymorphism on the Conductivity of Peptide Fibrils.

Peptide fibril nanostructures have been advocated as components of future biotechnology and nanotechnology devices. However, the ability to exploit the fibril functionality for applications, such as catalysis or electron transfer, depends on the formation of well-defined architectures. Fibrils made of peptides substituted with aromatic groups are described presenting efficient electron delocalization. Peptide self-assembly under various conditions produced polymorphic fibril products presenting distinctly different conductivities. This process is driven by a collective set of hydrogen bonding, electrostatic, and π-stacking interactions, and as a result it can be directed towards formation of a distinct polymorph by using the medium to enhance specific interactions rather than the others. This method facilitates the detailed characterization of different polymorphs, and allows specific conditions to be established that lead to the polymorph with the highest conductivity.

Orientations of residues along the ß-arch of self-assembled amylin fibril-like structures lead to polymorphism.

Amylin is an endocrine hormone peptide that consists of 37 residues and is the main component of extracellular amyloid deposits found in the pancreas of most type 2 diabetes patients. Amylin peptides are self-assembled to form oligomers and fibrils. So far, four different molecular structures of the self-assembled amylin fibrils have been observed experimentally: two ssNMR models and two crystal models. This study reveals, for the first time, that there are four self-assembled amylin forms that differ in the orientations of the side chains along the ß-arch and are all derived from the two ssNMR models. The two ssNMR models are composed of these four different self-assembled forms of amylin, and the two crystal models are composed of two different self-assembled forms of amylin. This study illustrates at the atomic level the differences among the four experimental models and proposes eight new models of self-assembled amylin that are also composed of the four different self-assembled forms of amylin. Our results show polymorphism of the self-assembled fibril-like amylin, with a slight preference of some of the newly constructed models over the experimental models. Finally, we propose that two different self-assembled fibril-like forms of amylin can interact to form a new fibril-like amylin. We investigated this argument and found that some fibril-like amylin prefers to interact to form stable fibril-like structures, whereas others disfavor it. Our work provides new insights that may suggest strategies for future pharmacological studies that aim to find ways to ameliorate the interactions between polymorphic oligomers and fibrils of amylin.

Mechanism of Side Chain-Controlled Proton Conductivity in Bioinspired Peptidic Nanostructures.

Bioinspired peptide assemblies are promising candidates for use as proton-conducting materials in electrochemical devices and other advanced technologies. Progress toward applications requires establishing foundational structure-function relationships for transport in these materials. This experimental-theoretical study sheds light on how the molecular structure and proton conduction are linked in three synthetic cyclic peptide nanotube assemblies that comprise the three canonical basic amino acids (lysine, arginine, and histidine). Experiments find an order of magnitude higher proton conductivity for lysine-containing peptide assemblies compared to histidine and arginine containing assemblies. The simulations indicate that, upon peptide assembly, the basic amino acid side chains are close enough to enable direct proton transfer. The proton transfer kinetics is determined in the simulations to be governed by the structure and flexibility of the side chains. Together, experiments and theory indicate that the proton mobility is the main determinant of proton conductivity, critical for the performance of peptide-based devices.

Unique Inversion Events of Residues around the Backbone in the Turn Domain of ß-Arches in Amylin Fibrils.

Orientational inversion events of residues along the turn domains of amylin fibrils have been detected. This exceptional phenomenon has been observed in isolated amylin fibrils and in the cross-seeding amylin-Aß and amylin-NAC fibrils. These new findings provide new avenues for detection of side chain flipping and side chain inversion events in turn domains and loops of various proteins.

Effect of late endosomal DOBMP lipid and traditional model lipids of electrophysiology on the anthrax toxin channel activity.

Anthrax toxin action requires triggering of natural endocytic transport mechanisms whereby the binding component of the toxin forms channels (PA63) within endosomal limiting and intraluminal vesicle membranes to deliver the toxin's enzymatic components into the cytosol. Membrane lipid composition varies at different stages of anthrax toxin internalization, with intraluminal vesicle membranes containing ~70% of anionic bis(monoacylglycero)phosphate lipid. Using model bilayer measurements, we show that membrane lipids can have a strong effect on the anthrax toxin channel properties, including the channel-forming activity, voltage-gating, conductance, selectivity, and enzymatic factor binding. Interestingly, the highest PA63 insertion rate was observed in bis(monoacylglycero)phosphate membranes. The molecular dynamics simulation data show that the conformational properties of the channel are different in bis(monoacylglycero)phosphate compared to PC, PE, and PS lipids. The anthrax toxin protein/lipid bilayer system can be advanced as a novel robust model to directly investigate lipid influence on membrane protein properties and protein/protein interactions.

Parameterization of Palmitoylated Cysteine, Farnesylated Cysteine, Geranylgeranylated Cysteine, and Myristoylated Glycine for the Martini Force Field.

Peripheral membrane proteins go through various post-translational modifications that covalently bind fatty acid tails to specific amino acids. These post-translational modifications significantly alter the lipophilicity of the modified proteins and allow them to anchor to biological membranes. Over 1000 different proteins have been identified to date that require such membrane-protein interactions to carry out their biological functions, including members of the Src and Ras superfamilies that play key roles in cell signaling and carcinogenesis. We have used all-atom simulations with the CHARMM36 force field to parameterize four of the most common post-translational modifications for the Martini 2.2 force field: palmitoylated cysteine, farnesylated cysteine, geranylgeranylated cysteine, and myristoylated glycine. The parameters reproduce the key features of clusters of configurations of the different anchors in lipid membranes as well as the water-octanol partitioning free energies of the anchors, which are crucial for the correct reproduction of the expected biophysical behavior of peripheral membrane proteins at the membrane-water interface. Implementation in existing Martini setup tools facilitates the use of the new parameters.

A minimal length rigid helical peptide motif allows rational design of modular surfactants.

Extensive work has been invested in the design of bio-inspired peptide emulsifiers. Yet, none of the formulated surfactants were based on the utilization of the robust conformation and self-assembly tendencies presented by the hydrophobins, which exhibited highest surface activity among all known proteins. Here we show that a minimalist design scheme could be employed to fabricate rigid helical peptides to mimic the rigid conformation and the helical amphipathic organization. These designer building blocks, containing natural non-coded α-aminoisobutyric acid (Aib), form superhelical assemblies as confirmed by crystallography and microscopy. The peptide sequence is amenable to structural modularity and provides the highest stable emulsions reported so far for peptide and protein emulsifiers. Moreover, we establish the ability of short peptides to perform the dual functions of emulsifiers and thickeners, a feature that typically requires synergistic effects of surfactants and polysaccharides. This work provides a different paradigm for the molecular engineering of bioemulsifiers.

Molecular Mechanisms of the Bindings between Non-Amyloid ß Component Oligomers and Amylin Oligomers.

It has been suggested that the connection between amyloidogenic diseases is related to the interactions between aggregates of amyloids, which are related to type 2 diabetes and Parkinson's disease. Herein, we illustrate the interactions between amylin oligomers and non-amyloid ß component (NAC) oligomers. Using molecular dynamics simulations and statistical calculations, we studied the mechanisms through which NAC oligomers interact with amylin oligomers to form NAC-amylin hetero-oligomers. Our simulations have shown that there are more than one possible pathways, which form the NAC-amylin hetero-oligomers. Our structural analyses demonstrate that the interactions in the NAC-amylin hetero-oligomers do not affect the structural features of the NAC oligomers, but they do stabilize the structures of the amylin oligomers. Taken together, our results strongly support the hypothesis that NAC oligomers may interact with amylin oligomers through several pathways, of which some pathways are more preferred because of the structural stability of the cross-seeding NAC-amylin oligomers.

Non-Amyloid-ß Component of Human α-Synuclein Oligomers Induces Formation of New Aß Oligomers: Insight into the Mechanisms That Link Parkinson's and Alzheimer's Diseases.

Parkinson's disease (PD) is characterized by the formation of Lewy bodies (LBs), of which their major component is the non-amyloid-ß component (NAC) of α-synuclein (AS). Clinical studies have identified a link between PD and Alzheimer's disease (AD), but the question of why PD patients are at risk to develop various types of dementia, such as AD, is still elusive. In vivo studies have shown that Aß can act as a seed for NAC/AS aggregation, promoting NAC/AS aggregation and thus contributing to the etiology of PD. However, the mechanisms by which NAC/AS oligomers interact with Aß oligomers are still elusive. This work presents the interactions between NAC oligomers and Aß oligomers at atomic resolution by applying extensive molecular dynamics simulations for an ensemble of cross-seeded NAC-Aß(1-42) oligomers. The main conclusions of this study are as follows: first, the cross-seeded NAC-Aß(1-42) oligomers represent polymorphic states, yet NAC oligomers prefer to interact with Aß(1-42) oligomers to form double-layer over single-layer conformations due to electrostatic/hydrophobic interactions; second, among the single-layer conformations, the NAC oligomers induce formation of new ß-strands in Aß(1-42) oligomers, thus leading to new Aß oligomer structures; and third, NAC oligomers stabilize the cross-ß structure of Aß oligomers, i.e., yielding compact Aß fibril-like structures.

A Proposed Atomic Structure of the Self-Assembly of the Non-Amyloid-ß Component of Human α-Synuclein As Derived by Computational Tools.

α-Synuclein (AS) fibrils are the major hallmarks of Parkinson's disease (PD). It is known that the central domain of the 140-residue AS protein, known as the non-amyloid-ß component (NAC), plays a crucial role in aggregation. The secondary structure of AS fibrils (including the NAC domain) has been proposed on the basis of solid-state nuclear magnetic resonance studies, but the atomic structure of the self-assembly of NAC (or AS itself) is still elusive. This is the first study that presents a detailed three-dimensional structure of NAC at atomic resolution. The proposed self-assembled structure of NAC consists of three ß-strands connected by two turn regions. Our study shows that calculated structural parameter values of the simulated fibril-like cross-ß structure of NAC are in excellent agreement with the experimental values. Moreover, the diameter dimensions of the proposed fibril-like structure are also in agreement with experimental measurements. The proposed fibril-like structure of NAC may assist in future work aimed at understanding the formation of aggregates in PD and developing compounds to modulate aggregation.

Spontaneous structural transition in phospholipid-inspired aromatic phosphopeptide nanostructures.

Phospholipid membranes could be considered a prime example of the ability of nature to produce complex yet ordered structures, by spontaneous and efficient self-assembly. Inspired by the unique properties and architecture of phospholipids, we designed simple amphiphilic decapeptides, intended to fold in the center of the peptide sequence, with a phosphorylated serine "head" located within a central turn segment, and two hydrophobic "tails". The molecular design also included the integration of the diphenylalanine motif, previously shown to facilitate self-assembly and increase nanostructure stability. Secondary structure analysis of the peptides indeed indicated the presence of stabilized conformations in solution, with a central turn connecting two hydrophobic "tails", and interactions between the hydrophobic strands. The mechanisms of assembly into supramolecular structures involved structural transitions between different morphologies, which occurred over several hours, leading to the formation of distinctive nanostructures, including half-elliptical nanosheets and curved tapes. The phosphopeptide building blocks appear to self-assemble via a particular combination of aromatic, hydrophobic and ionic interactions, as well as hydrogen bonding, as demonstrated by proposed constructed simulated models of the peptides and self-assembled nanostructures. Molecular dynamics simulations also gave insight into mechanisms of structural transitions of the nanostructures at a molecular level. Because of the biocompatibility of peptides, the phosphopeptide assemblies allow for expansion of the library of biomolecular nanostructures available for future design and application of biomedical devices.

Repression/depression of conjugative plasmids and their influence on the mutation-selection balance in static environments.

We study the effect that conjugation-mediated Horizontal Gene Transfer (HGT) has on the mutation-selection balance of a population in a static environment. We consider a model whereby a population of unicellular organisms, capable of conjugation, comes to mutation-selection balance in the presence of an antibiotic, which induces a first-order death rate constant [Formula: see text] for genomes that are not resistant. We explicitly take into consideration the repression/de-repression dynamics of the conjugative plasmid, and assume that a de-repressed plasmid remains temporarily de-repressed after copying itself into another cell. We assume that both repression and de-repression are characterized by first-order rate constants [Formula: see text]and [Formula: see text], respectively. We find that conjugation has a deleterious effect on the mean fitness of the population, suggesting that HGT does not provide a selective advantage in a static environment, but is rather only useful for adapting to new environments. This effect can be ameliorated by repression, suggesting that while HGT is not necessarily advantageous for a population in a static environment, its deleterious effect on the mean fitness can be negated via repression. Therefore, it is likely that HGT is much more advantageous in a dynamic landscape. Furthermore, in the limiting case of a vanishing spontaneous de-repression rate constant, we find that the fraction of conjugators in the population undergoes a phase transition as a function of population density. Below a critical population density, the fraction of conjugators is zero, while above this critical population density the fraction of conjugators rises continuously to one. Our model for conjugation-mediated HGT is related to models of infectious disease dynamics, where the conjugators play the role of the infected (I) class, and the non-conjugators play the role of the susceptible (S) class.