Model for Quorum-Sensing Mediated Stochastic Biofilm Nucleation.

Surface-attached bacterial biofilms cause disease and industrial biofouling, as well as being widespread in the natural environment. Density-dependent quorum sensing is one of the mechanisms implicated in biofilm initiation. Here we present and analyze a model for quorum-sensing triggered biofilm initiation. In our model, individual, planktonic bacteria adhere to a surface, proliferate, and undergo a collective transition to a biofilm phenotype. This model predicts a stochastic transition between a loosely attached, finite layer of bacteria near the surface and a growing biofilm. The transition is governed by two key parameters: the collective transition density relative to the carrying capacity and the immigration rate relative to the detachment rate. Biofilm initiation is complex, but our model suggests that stochastic nucleation phenomena may be relevant.

Phenotypic delay in the evolution of bacterial antibiotic resistance: Mechanistic models and their implications.

Phenotypic delay-the time delay between genetic mutation and expression of the corresponding phenotype-is generally neglected in evolutionary models, yet recent work suggests that it may be more common than previously assumed. Here, we use computer simulations and theory to investigate the significance of phenotypic delay for the evolution of bacterial resistance to antibiotics. We consider three mechanisms which could potentially cause phenotypic delay: effective polyploidy, dilution of antibiotic-sensitive molecules and accumulation of resistance-enhancing molecules. We find that the accumulation of resistant molecules is relevant only within a narrow parameter range, but both the dilution of sensitive molecules and effective polyploidy can cause phenotypic delay over a wide range of parameters. We further investigate whether these mechanisms could affect population survival under drug treatment and thereby explain observed discrepancies in mutation rates estimated by Luria-Delbrück fluctuation tests. While the effective polyploidy mechanism does not affect population survival, the dilution of sensitive molecules leads both to decreased probability of survival under drug treatment and underestimation of mutation rates in fluctuation tests. The dilution mechanism also changes the shape of the Luria-Delbrück distribution of mutant numbers, and we show that this modified distribution provides an improved fit to previously published experimental data.

Growth-dependent drug susceptibility can prevent or enhance spatial expansion of a bacterial population.

As a population wave expands, organisms at the tip typically experience plentiful nutrients while those behind the front become nutrient-depleted. If the environment also contains a gradient of some inhibitor (e.g. a toxic drug), a tradeoff exists: the nutrient-rich tip is more exposed to the inhibitor, while the nutrient-starved region behind the front is less exposed. Here we show that this can lead to complex dynamics when the organism's response to the inhibitory substance is coupled to nutrient availability. We model a bacterial population which expands in a spatial gradient of antibiotic, under conditions where either fast-growing bacteria at the wave's tip, or slow-growing, resource-limited bacteria behind the front are more susceptible to the antibiotic. We find that growth-rate dependent susceptibility can have strong effects on the dynamics of the expanding population. If slow-growing bacteria are more susceptible, the population wave advances far into the inhibitory zone, leaving a trail of dead bacteria in its wake. In contrast, if fast-growing bacteria are more susceptible, the wave is blocked at a much lower concentration of antibiotic, but a large population of live bacteria remains behind the front. Our results may contribute to understanding the efficacy of different antimicrobials for spatially structured microbial populations such as biofilms, as well as the dynamics of ecological population expansions more generally.

Automated Markov state models for molecular dynamics simulations of aggregation and self-assembly.

Markov state models have become popular in the computational biochemistry and biophysics communities as a technique for identifying stationary and kinetic information of protein dynamics from molecular dynamics simulation data. In this paper, we extend the applicability of automated Markov state modeling to simulation data of molecular self-assembly and aggregation by constructing collective coordinates from molecular descriptors that are invariant to permutations of molecular indexing. Understanding molecular self-assembly is of critical importance if we want to deepen our understanding of neurodegenerative diseases where the aggregation of misfolded or disordered proteins is thought to be the main culprit. As a proof of principle, we demonstrate our Markov state model technique on simulations of the KFFE peptide, a subsequence of Alzheimer's amyloid-ß peptide and one of the smallest peptides known to aggregate into amyloid fibrils in vitro. We investigate the different stages of aggregation up to tetramerization and show that the Markov state models clearly map out the different aggregation pathways. Of note is that disordered and ß-sheet oligomers do not interconvert, leading to separate pathways for their formation. This suggests that amyloid aggregation of KFFE occurs via ordered aggregates from the very beginning. The code developed here is freely available as a Jupyter notebook called TICAgg, which can be used for the automated analysis of any self-assembling molecular system, protein, or otherwise.

Molecular Dynamics Simulations of Protein Aggregation: Protocols for Simulation Setup and Analysis with Markov State Models and Transition Networks.

Protein disorder and aggregation play significant roles in the pathogenesis of numerous neurodegenerative diseases, such as Alzheimer's and Parkinson's diseases. The end products of the aggregation process in these diseases are highly structured amyloid fibrils. Though in most cases, small, soluble oligomers formed during amyloid aggregation are the toxic species. A full understanding of the physicochemical forces that drive protein aggregation is thus required if one aims for the rational design of drugs targeting the formation of amyloid oligomers. Among a multitude of biophysical and biochemical techniques that are employed for studying protein aggregation, molecular dynamics (MD) simulations at the atomic level provide the highest temporal and spatial resolution of this process, capturing key steps during the formation of amyloid oligomers. Here we provide a step-by-step guide for setting up, running, and analyzing MD simulations of aggregating peptides using GROMACS. For the analysis, we provide the scripts that were developed in our lab, which allow to determine the oligomer size and inter-peptide contacts that drive the aggregation process. Moreover, we explain and provide the tools to derive Markov state models and transition networks from MD data of peptide aggregation.

A computational model for microbial colonization of an antifouling surface.

Biofouling of marine surfaces such as ship hulls is a major industrial problem. Antifouling (AF) paints delay the onset of biofouling by releasing biocidal chemicals. We present a computational model for microbial colonization of a biocide-releasing AF surface. Our model accounts for random arrival from the ocean of microorganisms with different biocide resistance levels, biocide-dependent proliferation or killing, and a transition to a biofilm state. Our computer simulations support a picture in which biocide-resistant microorganisms initially form a loosely attached layer that eventually transitions to a growing biofilm. Once the growing biofilm is established, immigrating microorganisms are shielded from the biocide, allowing more biocide-susceptible strains to proliferate. In our model, colonization of the AF surface is highly stochastic. The waiting time before the biofilm establishes is exponentially distributed, suggesting a Poisson process. The waiting time depends exponentially on both the concentration of biocide at the surface and the rate of arrival of resistant microorganisms from the ocean. Taken together our results suggest that biofouling of AF surfaces may be intrinsically stochastic and hence unpredictable, but immigration of more biocide-resistant species, as well as the biological transition to biofilm physiology, may be important factors controlling the time to biofilm establishment.

Receptor crosstalk improves concentration sensing of multiple ligands.

Cells need to reliably sense external ligand concentrations to achieve various biological functions such as chemotaxis or signaling. The molecular recognition of ligands by surface receptors is degenerate in many systems, leading to crosstalk between ligand-receptor pairs. Crosstalk is often thought of as a deviation from optimal specific recognition, as the binding of noncognate ligands can interfere with the detection of the receptor's cognate ligand, possibly leading to a false triggering of a downstream signaling pathway. Here we quantify the optimal precision of sensing the concentrations of multiple ligands by a collection of promiscuous receptors. We demonstrate that crosstalk can improve precision in concentration sensing and discrimination tasks. To achieve superior precision, the additional information about ligand concentrations contained in short binding events of the noncognate ligand should be exploited. We present a proofreading scheme to realize an approximate estimation of multiple ligand concentrations that reaches a precision close to the derived optimal bounds. Our results help rationalize the observed ubiquity of receptor crosstalk in molecular sensing.

On the Applicability of Force Fields To Study the Aggregation of Amyloidogenic Peptides Using Molecular Dynamics Simulations.

Molecular dynamics simulations play an essential role in understanding biomolecular processes such as protein aggregation at temporal and spatial resolutions which are not attainable by experimental methods. For a correct modeling of protein aggregation, force fields must accurately represent molecular interactions. Here, we study the effect of five different force fields on the oligomer formation of Alzheimer's Aß16-22 peptide and two of its mutants: Aß16-22(F19V,F20V), which does not form fibrils, and Aß16-22(F19L) which forms fibrils faster than the wild type. We observe that while oligomer formation kinetics depends strongly on the force field, structural properties, such as the most relevant protein-protein contacts, are similar between them. The oligomer formation kinetics obtained with different force fields differ more from each other than the kinetics between aggregating and nonaggregating peptides simulated with a single force field. We discuss the difficulties in comparing atomistic simulations of amyloid oligomer formation with experimental observables.

Comparison of force fields for Alzheimer's A ß42: A case study for intrinsically disordered proteins.

Intrinsically disordered proteins are essential for biological processes such as cell signalling, but are also associated to devastating diseases including Alzheimer's disease, Parkinson's disease or type II diabetes. Because of their lack of a stable three-dimensional structure, molecular dynamics simulations are often used to obtain atomistic details that cannot be observed experimentally. The applicability of molecular dynamics simulations depends on the accuracy of the force field chosen to represent the underlying free energy surface of the system. Here, we use replica exchange molecular dynamics simulations to test five modern force fields, OPLS, AMBER99SB, AMBER99SB*ILDN, AMBER99SBILDN-NMR and CHARMM22*, in their ability to model Aß42 , an intrinsically disordered peptide associated with Alzheimer's disease, and compare our results to nuclear magnetic resonance (NMR) experimental data. We observe that all force fields except AMBER99SBILDN-NMR successfully reproduce local NMR observables, with CHARMM22* being slightly better than the other force fields.

Epigallocatechin-3-gallate preferentially induces aggregation of amyloidogenic immunoglobulin light chains.

Antibody light chain amyloidosis is a rare disease caused by fibril formation of secreted immunoglobulin light chains (LCs). The huge variety of antibody sequences puts a serious challenge to drug discovery. The green tea polyphenol epigallocatechin-3-gallate (EGCG) is known to interfere with fibril formation in general. Here we present solution- and solid-state NMR studies as well as MD simulations to characterise the interaction of EGCG with LC variable domains. We identified two distinct EGCG binding sites, both of which include a proline as an important recognition element. The binding sites were confirmed by site-directed mutagenesis and solid-state NMR analysis. The EGCG-induced protein complexes are unstructured. We propose a general mechanistic model for EGCG binding to a conserved site in LCs. We find that EGCG reacts selectively with amyloidogenic mutants. This makes this compound a promising lead structure, that can handle the immense sequence variability of antibody LCs.

Advances in the Simulation of Protein Aggregation at the Atomistic Scale.

Protein aggregation into highly structured amyloid fibrils is associated with various diseases including Alzheimer's disease, Parkinson's disease, and type II diabetes. Amyloids can also have normal biological functions and, in the future, could be used as the basis for novel nanoscale materials. However, a full understanding of the physicochemical forces that drive protein aggregation is still lacking. Such understanding is crucial for the development of drugs that can effectively inhibit aberrant amyloid aggregation and for the directed design of functional amyloids. Atomistic simulations can help understand protein aggregation. In particular, atomistic simulations can be used to study the initial formation of toxic oligomers which are hard to characterize experimentally and to understand the difference in aggregation behavior between different amyloidogenic peptides. Here, we review the latest atomistic simulations of protein aggregation, concentrating on amyloidogenic protein fragments, and provide an outlook for the future in this field.

Oligomer Formation of Toxic and Functional Amyloid Peptides Studied with Atomistic Simulations.

Amyloids are associated with diseases, including Alzheimer's, as well as functional roles such as storage of peptide hormones. It is still unclear what differences exist between aberrant and functional amyloids. However, it is known that soluble oligomers formed during amyloid aggregation are more toxic than the final fibrils. Here, we perform molecular dynamics simulations to study the aggregation of the amyloid-ß peptide Aß25-35, associated with Alzheimer's disease, and two functional amyloid-forming tachykinin peptides: kassinin and neuromedin K. Although the three peptides have similar primary sequences, tachykinin peptides, in contrast to Aß25-35, form nontoxic amyloids. Our simulations reveal that the charge of the C-terminus is essential to controlling the aggregation process. In particular, when the kassinin C-terminus is not amidated, the aggregation kinetics decreases considerably. In addition, we observe that the monomeric peptides in extended conformations aggregate faster than those in collapsed hairpin-like conformations.

Extension of the FACTS Implicit Solvation Model to Membranes.

The generalized Born (GB) formalism can be used to model water as a dielectric continuum. Among the different implicit solvent models using the GB formalism, FACTS is one of the fastest. Here, we extend FACTS so that it can represent a membrane environment. This extension is accomplished by considering a position dependent dielectric constant and empirical surface tension parameter. For the calculation of the effective Born radii in different dielectric environments we present a parameter-free approximation to Kirkwood's equation, which uses the Born radii obtained with FACTS for the water environment as input. This approximation is tested for the calculation of self-free energies, pairwise interaction energies in solution and solvation free energies of complete protein conformations. The results compare well to those from the finite difference Poisson method. The new implicit membrane model is applied to estimate free energy insertion profiles of amino acid analogues and in molecular dynamics simulations of melittin, WALP23 and KALP23, glycophorin A, bacteriorhodopsin, and a Clc channel dimer. In all cases, the results agree qualitatively with experiments and explicit solvent simulations. Moreover, the implicit membrane model is only six times slower than a vacuum simulation.