The marionette mechanism of domain-domain communication in the antagonist, agonist, and coactivator responses of the estrogen receptor.

The human estrogen receptor α (hERα) is involved in the regulation of growth, development, and tissue homeostasis. Agonists that bind to the receptor's ligand-binding domain (LBD) lead to recruitment of coactivators and the enhancement of gene expression. In contrast, antagonists bind to the LBD and block the binding of coactivators thus decreasing gene expressions. In this work, we carry out simulations using the AWSEM (Associative memory, Water mediated, Structure and Energy Model)-Suite force field along with the 3SPN.2C force field for DNA to predict the structure of hERα and study its dynamics when binding to DNA and coactivators. Using simulations of antagonist-bound hERα and agonist-bound hERα by themselves and also along with bound DNA and coactivators, principal component analyses and free energy landscape analyses capture the pathway of domain-domain communication for agonist-bound hERα. This communication is mediated through the hinge domains that are ordinarily intrinsically disordered. These disordered segments manipulate the hinge domains much like the strings of a marionette as they twist in different ways when antagonists or agonists are bound to the ligand-binding domain.

Frustration and the Kinetic Repartitioning Mechanism of Substrate Inhibition in Enzyme Catalysis.

Substrate inhibition, whereby enzymatic activity decreases with excess substrate after reaching a maximum turnover rate, is among the most elusive phenomena in enzymatic catalysis. Here, based on a dynamic energy landscape model, we investigate the underlying mechanism by performing molecular simulations and frustration analysis for a model enzyme adenylate kinase (AdK), which catalyzes the phosphoryl transfer reaction ATP + AMP ⇋ ADP + ADP. Intriguingly, these reveal a kinetic repartitioning mechanism of substrate inhibition, whereby excess substrate AMP suppresses the population of an energetically frustrated, but kinetically activated, catalytic pathway going through a substrate (ATP)-product (ADP) cobound complex with steric incompatibility. Such a frustrated pathway plays a crucial role in facilitating the bottleneck product ADP release, and its suppression by excess substrate AMP leads to a slow down of product release and overall turnover. The simulation results directly demonstrate that substrate inhibition arises from the rate-limiting product-release step, instead of the steps for populating the catalytically competent complex as often suggested in previous works. Furthermore, there is a tight interplay between the enzyme conformational equilibrium and the extent of substrate inhibition. Mutations biasing to more closed conformations tend to enhance substrate inhibition. We also characterized the key features of single-molecule enzyme kinetics with substrate inhibition effect. We propose that the above molecular mechanism of substrate inhibition may be relevant to other multisubstrate enzymes in which product release is the bottleneck step.

Computationally exploring the mechanism of bacteriophage T7 gp4 helicase translocating along ssDNA.

Bacteriophage T7 gp4 helicase has served as a model system for understanding mechanisms of hexameric replicative helicase translocation. The mechanistic basis of how nucleoside 5'-triphosphate hydrolysis and translocation of gp4 helicase are coupled is not fully resolved. Here, we used a thermodynamically benchmarked coarse-grained protein force field, Associative memory, Water mediated, Structure and Energy Model (AWSEM), with the single-stranded DNA (ssDNA) force field 3SPN.2C to investigate gp4 translocation. We found that the adenosine 5'-triphosphate (ATP) at the subunit interface stabilizes the subunit-subunit interaction and inhibits subunit translocation. Hydrolysis of ATP to adenosine 5'-diphosphate enables the translocation of one subunit, and new ATP binding at the new subunit interface finalizes the subunit translocation. The LoopD2 and the N-terminal primase domain provide transient protein-protein and protein-DNA interactions that facilitate the large-scale subunit movement. The simulations of gp4 helicase both validate our coarse-grained protein-ssDNA force field and elucidate the molecular basis of replicative helicase translocation.

Exploring the Interplay between Disordered and Ordered Oligomer Channels on the Aggregation Energy Landscapes of α-Synuclein.

The abnormal aggregation of α-synulcein is associated with multiple neurodegenerative diseases such as Parkinson's disease. The hydrophobic non-amyloid component (NAC) region of α-synuclein comprises the core of the fibril in vitro and in vivo. In this work, we study the aggregation landscape of the hydrophobic NAC region of α-synuclein using a transferrable coarse-grained force field, the associative memory water-mediated structure, and energy model (AWSEM). Using structural similarity, we can group metastable states on the free energy landscape of aggregation into three types of oligomers: disordered oligomers, prefibrillar oligomers with disordered tips, and ordered prefibrillar oligomers. The prefibrillar oligomers with disordered tips have more in-register parallel ß strands than do the fully disordered oligomers but have fewer in-register parallel ß strands than the ordered prefibrillar oligomers. Along with the ordered prefibrillar species, the disordered oligomeric states dominate at small oligomer sizes while the prefibrillar species with disordered tips thermodynamically dominate with the growth of oligomers. The topology of the aggregation landscape and observations in simulations suggest there is backtracking between ordered prefibrillar oligomers and other kinds of oligomers as the aggregation proceeds. The significant structural differences between the ordered prefibrillar oligomers and the disordered oligomers support the idea that the growth of these two kinds of oligomers involves kinetically independent parallel pathways. In contrast, the overall structural similarity between the fully ordered prefibrillar oligomers and the prefibrillar oligomers with disordered tips implies that two channels can interconvert on slower time scales. We also evaluate the effects of phosphorylation on the aggregation free energy landscape using statistical mechanical perturbation theory.

224-Gbit/s 4-PAM operation of a high-modulation-bandwidth high-output-power Hi-FIT AXEL transmitter.

We fabricated an optical transmitter with high frequency and integrated design based on the flip-chip interconnection technique (Hi-FIT) and assisted extended reach electroadsorption modulator integrated distributed feedback (EADFB) laser (AXEL) for 200-Gbit/s/λ application. The Hi-FIT makes it possible to increase modulation bandwidth thanks to wire-free interconnection and peaking control techniques while the AXEL can increase the optical modulation output power thanks to an integrated semiconductor optical amplifier (SOA). The fabricated Hi-FIT AXEL transmitter has a 3-dB bandwidth of more than 66 GHz. We obtained clear 224-Gbit/s 4-level pulse amplitude modulation (4-PAM) eye diagrams with a chip-output optical modulation amplitude (OMA) of more than +7.9 dBm at distributed feedback (DFB) laser and SOA currents of 70 and 30 mA, respectively.

Frustration Dynamics and Electron-Transfer Reorganization Energies in Wild-Type and Mutant Azurins.

Long-range electron tunneling through metalloproteins is facilitated by evolutionary tuning of donor-acceptor electronic couplings, formal electrochemical potentials, and active-site reorganization energies. Although the minimal frustration of the folding landscape enables this tuning, residual frustration in the vicinity of the metallocofactor can allow conformational fluctuations required for protein function. We show here that the constrained copper site in wild-type azurin is governed by an intricate pattern of minimally frustrated local and distant interactions that together enable rapid electron flow to and from the protein. In contrast, sluggish electron transfer reactions (unfavorable reorganization energies) of active-site azurin variants are attributable to increased frustration near to as well as distant from the copper site, along with an exaggerated oxidation-state dependence of both minimally and highly frustrated interaction patterns.

OpenAWSEM with Open3SPN2: A fast, flexible, and accessible framework for large-scale coarse-grained biomolecular simulations.

We present OpenAWSEM and Open3SPN2, new cross-compatible implementations of coarse-grained models for protein (AWSEM) and DNA (3SPN2) molecular dynamics simulations within the OpenMM framework. These new implementations retain the chemical accuracy and intrinsic efficiency of the original models while adding GPU acceleration and the ease of forcefield modification provided by OpenMM's Custom Forces software framework. By utilizing GPUs, we achieve around a 30-fold speedup in protein and protein-DNA simulations over the existing LAMMPS-based implementations running on a single CPU core. We showcase the benefits of OpenMM's Custom Forces framework by devising and implementing two new potentials that allow us to address important aspects of protein folding and structure prediction and by testing the ability of the combined OpenAWSEM and Open3SPN2 to model protein-DNA binding. The first potential is used to describe the changes in effective interactions that occur as a protein becomes partially buried in a membrane. We also introduced an interaction to describe proteins with multiple disulfide bonds. Using simple pairwise disulfide bonding terms results in unphysical clustering of cysteine residues, posing a problem when simulating the folding of proteins with many cysteines. We now can computationally reproduce Anfinsen's early Nobel prize winning experiments by using OpenMM's Custom Forces framework to introduce a multi-body disulfide bonding term that prevents unphysical clustering. Our protein-DNA simulations show that the binding landscape is funneled towards structures that are quite similar to those found using experiments. In summary, this paper provides a simulation tool for the molecular biophysics community that is both easy to use and sufficiently efficient to simulate large proteins and large protein-DNA systems that are central to many cellular processes. These codes should facilitate the interplay between molecular simulations and cellular studies, which have been hampered by the large mismatch between the time and length scales accessible to molecular simulations and those relevant to cell biology.

Molecular-replacement phasing using predicted protein structures from AWSEM-Suite.

The phase problem in X-ray crystallography arises from the fact that only the intensities, and not the phases, of the diffracting electromagnetic waves are measured directly. Molecular replacement can often estimate the relative phases of reflections starting with those derived from a template structure, which is usually a previously solved structure of a similar protein. The key factor in the success of molecular replacement is finding a good template structure. When no good solved template exists, predicted structures based partially on templates can sometimes be used to generate models for molecular replacement, thereby extending the lower bound of structural and sequence similarity required for successful structure determination. Here, the effectiveness is examined of structures predicted by a state-of-the-art prediction algorithm, the Associative memory, Water-mediated, Structure and Energy Model Suite (AWSEM-Suite), which has been shown to perform well in predicting protein structures in CASP13 when there is no significant sequence similarity to a solved protein or only very low sequence similarity to known templates. The performance of AWSEM-Suite structures in molecular replacement is discussed and the results show that AWSEM-Suite performs well in providing useful phase information, often performing better than I-TASSER-MR and the previous algorithm AWSEM-Template.

Surveying biomolecular frustration at atomic resolution.

To function, biomolecules require sufficient specificity of interaction as well as stability to live in the cell while still being able to move. Thermodynamic stability of only a limited number of specific structures is important so as to prevent promiscuous interactions. The individual interactions in proteins, therefore, have evolved collectively to give funneled minimally frustrated landscapes but some strategic parts of biomolecular sequences located at specific sites in the structure have been selected to be frustrated in order to allow both motion and interaction with partners. We describe a framework efficiently to quantify and localize biomolecular frustration at atomic resolution by examining the statistics of the energy changes that occur when the local environment of a site is changed. The location of patches of highly frustrated interactions correlates with key biological locations needed for physiological function. At atomic resolution, it becomes possible to extend frustration analysis to protein-ligand complexes. At this resolution one sees that drug specificity is correlated with there being a minimally frustrated binding pocket leading to a funneled binding landscape. Atomistic frustration analysis provides a route for screening for more specific compounds for drug discovery.

Protein Structure Refinement Guided by Atomic Packing Frustration Analysis.

Recent advances in machine learning, bioinformatics, and the understanding of the folding problem have enabled efficient predictions of protein structures with moderate accuracy, even for targets where there is little information from templates. All-atom molecular dynamics simulations provide a route to refine such predicted structures, but unguided atomistic simulations, even when lengthy in time, often fail to eliminate incorrect structural features that would prevent the structure from becoming more energetically favorable owing to the necessity of making large scale motions and to overcoming energy barriers for side chain repacking. In this study, we show that localizing packing frustration at atomic resolution by examining the statistics of the energetic changes that occur when the local environment of a site is changed allows one to identify the most likely locations of incorrect contacts. The global statistics of atomic resolution frustration in structures that have been predicted using various algorithms provide strong indicators of structural quality when tested over a database of 20 targets from previous CASP experiments. Residues that are more correctly located turn out to be more minimally frustrated than more poorly positioned sites. These observations provide a diagnosis of both global and local quality of predicted structures and thus can be used as guidance in all-atom refinement simulations of the 20 targets. Refinement simulations guided by atomic packing frustration turn out to be quite efficient and significantly improve the quality of the structures.

Exploring the F-actin/CPEB3 interaction and its possible role in the molecular mechanism of long-term memory.

Dendritic spines are tiny membranous protrusions on the dendrites of neurons. Dendritic spines change shape in response to input signals, thereby strengthening the connections between neurons. The growth and stabilization of dendritic spines is thought to be essential for maintaining long-term memory. Actin cytoskeleton remodeling in spines is a key element of their formation and growth. More speculatively, the aggregation of CPEB3, a functional prion that binds RNA, has been reported to be involved in the maintenance of long-term memory. Here we study the interaction between actin and CPEB3 and propose a molecular model for the complex structure of CPEB3 and an actin filament (F-actin). The results of our computational modeling, including both energetic and structural analyses, are compared with novel data from peptide array experiments. Our model of the CPEB3/F-actin interaction suggests that F-actin potentially triggers the aggregation-prone structural transition of a short CPEB3 sequence by zipping it into a beta-hairpin form. We also propose that the CPEB3/F-actin interaction might be regulated by the SUMOylation of CPEB3, based on bioinformatic searches for potential SUMOylation sites as well as SUMO interacting motifs in CPEB3. On the basis of these results and the existing literature, we put forward a possible molecular mechanism underlying long-term memory that involves CPEB3's binding to actin, its aggregation, and its regulation by SUMOylation.

Protein Structure Prediction in CASP13 Using AWSEM-Suite.

Recently several techniques have emerged that significantly enhance the quality of predictions of protein tertiary structures. In this study, we describe the performance of AWSEM-Suite, an algorithm that incorporates template-based modeling and coevolutionary restraints with a realistic coarse-grained force field, AWSEM. With its roots in neural networks, AWSEM contains both physical and bioinformatical energies that have been optimized using energy landscape theory. AWSEM-Suite participated in CASP13 as a server predictor and generated reliable predictions for most targets. AWSEM-Suite ranked eighth in both the free-modeling category and the hard-to-model category and in one case provided the best submitted prediction. Here we critically discuss the prediction performance of AWSEM-Suite using several examples from different categories in CASP13. Structure prediction tests on these selected targets, two of them being hard-to-model targets, show that AWSEM-Suite can achieve high-resolution structure prediction after incorporating both template guidances and coevolutionary restraints even when homology is weak. For targets with reliable templates (template-easy category), introducing coevolutionary restraints sometimes damages the overall quality of the predictions. Free energy profile analyses demonstrate, however, that the incorporations of both of these evolutionarily informed terms effectively increase the funneling of the landscape toward native-like structures while still allowing sufficient flexibility to correct for discrepancies between the correct target structure and the provided guidance. In contrast to other predictors that are exclusively oriented toward structure prediction, the connection of AWSEM-Suite to a statistical mechanical basis and affiliated molecular dynamics and importance sampling simulations makes it suitable for functional explorations.

AWSEM-Suite: a protein structure prediction server based on template-guided, coevolutionary-enhanced optimized folding landscapes.

The accurate and reliable prediction of the 3D structures of proteins and their assemblies remains difficult even though the number of solved structures soars and prediction techniques improve. In this study, a free and open access web server, AWSEM-Suite, whose goal is to predict monomeric protein tertiary structures from sequence is described. The model underlying the server's predictions is a coarse-grained protein force field which has its roots in neural network ideas that has been optimized using energy landscape theory. Employing physically motivated potentials and knowledge-based local structure biasing terms, the addition of homologous template and co-evolutionary restraints to AWSEM-Suite greatly improves the predictive power of pure AWSEM structure prediction. From the independent evaluation metrics released in the CASP13 experiment, AWSEM-Suite proves to be a reasonably accurate algorithm for free modeling, standing at the eighth position in the free modeling category of CASP13. The AWSEM-Suite server also features a front end with a user-friendly interface. The AWSEM-Suite server is a powerful tool for predicting monomeric protein tertiary structures that is most useful when a suitable structure template is not available. The AWSEM-Suite server is freely available at: https://awsem.rice.edu.

Targeting FROUNT with disulfiram suppresses macrophage accumulation and its tumor-promoting properties.

Tumor-associated macrophages affect tumor progression and resistance to immune checkpoint therapy. Here, we identify the chemokine signal regulator FROUNT as a target to control tumor-associated macrophages. The low level FROUNT expression in patients with cancer correlates with better clinical outcomes. Frount-deficiency markedly reduces tumor progression and decreases macrophage tumor-promoting activity. FROUNT is highly expressed in macrophages, and its myeloid-specific deletion impairs tumor growth. Further, the anti-alcoholism drug disulfiram (DSF) acts as a potent inhibitor of FROUNT. DSF interferes with FROUNT-chemokine receptor interactions via direct binding to a specific site of the chemokine receptor-binding domain of FROUNT, leading to inhibition of macrophage responses. DSF monotherapy reduces tumor progression and decreases macrophage tumor-promoting activity, as seen in the case of Frount-deficiency. Moreover, co-treatment with DSF and an immune checkpoint antibody synergistically inhibits tumor growth. Thus, inhibition of FROUNT by DSF represents a promising strategy for macrophage-targeted cancer therapy.

Exploring the interplay between fibrillization and amorphous aggregation channels on the energy landscapes of tau repeat isoforms.

Filaments made up of different isoforms of tau protein are associated with a variety of neurodegenerative diseases. Filaments made up of the 4R-tau isoform, which has four repeat regions (R1 to R4), are found in patients suffering from Alzheimer's disease, while filaments made of the 3R-tau isoform, which contains only three repeat units (R1, R3, and R4), are found in patients with Pick's disease (frontotemporal dementia). In this work, a predictive coarse-grained protein force field, the associative memory water-mediated structure and energy model (AWSEM), is used to study the energy landscapes of nucleation of the two different fibrils derived from patients with Pick's and Alzheimer's diseases. The landscapes for nucleating both fibril types contain amorphous oligomers leading to branched structures as well as prefibrillar oligomers. These two classes of oligomers differ in their structural details: The prefibrillar oligomers have more parallel in-register ß-strands, which ultimately lead to amyloid fibrils, while the amorphous oligomers are characterized by a near random ß-strand stacking, leading to a distinct amorphous phase. The landscape topography suggests that there must be significant structural reordering, or "backtracking," to transit from the amorphous aggregation channel to the fibrillization channel. Statistical mechanical perturbation theory allows us to evaluate the effects of changing concentration on the aggregation free-energy landscapes and to predict the effects of phosphorylation, which is known to facilitate the aggregation of tau repeats.

Multiple Binding Configurations of Fis Protein Pairs on DNA: Facilitated Dissociation versus Cooperative Dissociation.

As a master transcription regulator, the Fis protein influences over two hundred genes of E. coli. The Fis protein's nonspecific binding to DNA is widely acknowledged, and its kinetics of dissociation from DNA is strongly influenced by its surroundings: the dissociation rate increases as the concentration of the Fis protein in the solution phase increases. In this study, we use computational methods to explore the global binding energy landscape of the Fis1:Fis2:DNA ternary complex. The complex contains a binary-Fis molecular dyad whose formation relies on complex structural rearrangements. The simulations allow us to distinguish several different pathways for the dissociation of the protein from DNA with different functional outcomes and involving different protein stoichiometries: (1) simple exchange of proteins and (2) cooperative unbinding of two Fis proteins to yield bare DNA. In the case of exchange, the protein on the DNA is replaced by the solution-phase protein through competition for DNA binding sites. This process seen in fluorescence imaging experiments has been called facilitated dissociation. In the latter case of cooperative unbinding of pairs, two neighboring Fis proteins on DNA form a unique binary-Fis configuration via protein-protein interactions, which in turn leads to the codissociation of both molecules simultaneously, a process akin to the "molecular stripping" seen in the NFκB/IκB genetic broadcasting system. This simulation shows that the existence of multiple binding configurations of transcription factors can have a significant impact on the kinetics and outcome of transcription factor dissociation from DNA, with important implications for the systems biology of gene regulation by Fis.

Assemblies of calcium/calmodulin-dependent kinase II with actin and their dynamic regulation by calmodulin in dendritic spines.

Calcium/calmodulin-dependent kinase II (CaMKII) plays a key role in the plasticity of dendritic spines. Calcium signals cause calcium-calmodulin to activate CaMKII, which leads to remodeling of the actin filament (F-actin) network in the spine. We elucidate the mechanism of the remodeling by combining computer simulations with protein array experiments and electron microscopic imaging, to arrive at a structural model for the dodecameric complex of CaMKII with F-actin. The binding interface involves multiple domains of CaMKII. This structure explains the architecture of the micrometer-scale CaMKII/F-actin bundles arising from the multivalence of CaMKII. We also show that the regulatory domain of CaMKII may bind either calmodulin or F-actin, but not both. This frustration, along with the multipartite nature of the binding interface, allows calmodulin transiently to strip CaMKII from actin assemblies so that they can reorganize. This observation therefore provides a simple mechanism by which the structural dynamics of CaMKII establishes the link between calcium signaling and the morphological plasticity of dendritic spines.

Forging tools for refining predicted protein structures.

Refining predicted protein structures with all-atom molecular dynamics simulations is one route to producing, entirely by computational means, structural models of proteins that rival in quality those that are determined by X-ray diffraction experiments. Slow rearrangements within the compact folded state, however, make routine refinement of predicted structures by unrestrained simulations infeasible. In this work, we draw inspiration from the fields of metallurgy and blacksmithing, where practitioners have worked out practical means of controlling equilibration by mechanically deforming their samples. We describe a two-step refinement procedure that involves identifying collective variables for mechanical deformations using a coarse-grained model and then sampling along these deformation modes in all-atom simulations. Identifying those low-frequency collective modes that change the contact map the most proves to be an effective strategy for choosing which deformations to use for sampling. The method is tested on 20 refinement targets from the CASP12 competition and is found to induce large structural rearrangements that drive the structures closer to the experimentally determined structures during relatively short all-atom simulations of 50 ns. By examining the accuracy of side-chain rotamer states in subensembles of structures that have varying degrees of similarity to the experimental structure, we identified the reorientation of aromatic side chains as a step that remains slow even when encouraging global mechanical deformations in the all-atom simulations. Reducing the side-chain rotamer isomerization barriers in the all-atom force field is found to further speed up refinement.

Template-Guided Protein Structure Prediction and Refinement Using Optimized Folding Landscape Force Fields.

When good structural templates can be identified, template-based modeling is the most reliable way to predict the tertiary structure of proteins. In this study, we combine template-based modeling with a realistic coarse-grained force field, AWSEM, that has been optimized using the principles of energy landscape theory. The Associative memory, Water mediated, Structure and Energy Model (AWSEM) is a coarse-grained force field having both transferable tertiary interactions and knowledge-based local-in-sequence interaction terms. We incorporate template information into AWSEM by introducing soft collective biases to the template structures, resulting in a model that we call AWSEM-Template. Structure prediction tests on eight targets, four of which are in the low sequence identity "twilight zone" of homology modeling, show that AWSEM-Template can achieve high-resolution structure prediction. Our results also confirm that using a combination of AWSEM and a template-guided potential leads to more accurate prediction of protein structures than simply using a template-guided potential alone. Free energy profile analyses demonstrate that the soft collective biases to the template effectively increase funneling toward native-like structures while still allowing significant flexibility so as to allow for correction of discrepancies between the target structure and the template. A further stage of refinement using all-atom molecular dynamics augmented with soft collective biases to the structures predicted by AWSEM-Template leads to a further improvement of both backbone and side-chain accuracy by maintaining sufficient flexibility but at the same time discouraging unproductive unfolding events often seen in unrestrained all-atom refinement simulations. The all-atom refinement simulations also reduce patches of frustration of the initial predictions. Some of the backbones found among the structures produced during the initial coarse-grained prediction step already have CE-RMSD values of less than 3 Å with 90% or more of the residues aligned to the experimentally solved structure for all targets. All-atom structures generated during the following all-atom refinement simulations, which started from coarse-grained structures that were chosen without reference to any knowledge about the native structure, have CE-RMSD values of less than 2.5 Å with 90% or more of the residues aligned for 6 out of 8 targets. Clustering low energy structures generated during the initial coarse-grained annealing picks out reliably structures that are within 1 Å of the best sampled structures in 5 out of 8 cases. After the all-atom refinement, structures that are within 1 Å of the best sampled structures can be selected using a simple algorithm based on energetic features alone in 7 out of 8 cases.

Surveying the Energy Landscapes of Aß Fibril Polymorphism.

Many unrelated proteins and peptides have been found spontaneously to form amyloid fibers above a critical concentration. Even for a single sequence, however, the amyloid fold is not a single well-defined structure. Although the cross-ß hydrogen bonding pattern is common to all amyloids, all other aspects of amyloid fiber structures are sensitive to both the sequence of the aggregating peptides and the solvent conditions under which the aggregation occurs. Amyloid fibers are easy to identify and grossly characterize using microscopy, but their insolubility and aperiodicity along the dimensions transverse to the fiber axis have complicated detailed experimental structural characterization. In this paper, we explore the landscape of possibilities for amyloid protofilament structures that are made up of a single stack of peptides associated in a parallel in-register manner. We view this landscape as a two-dimensional version of the usual three-dimensional protein folding problem: the survey of the two-dimensional folds of protein ribbons. Adopting this view leads to a practical method of predicting stable protofilament structures of arbitrary sequences. We apply this scheme to variants of Aß, the amyloid forming peptide that is characteristically associated with Alzheimer's disease. Consistent with what is known from experiment, we find that Aß protofibrils are polymorphic. To our surprise, however, the ribbon-folding landscape of Aß turned out to be strikingly simple. We confirm that, at the level of the monomeric protofilament, the landscape for the Aß sequence is reasonably well funneled toward structures that are similar to those that have been determined by experiment. The landscape has more distinct minima than does a typical globular protein landscape but fewer and deeper minima than the landscape of a randomly shuffled sequence having the same overall composition. It is tempting to consider the possibility that the significant degree of funneling of Aß's ribbon-folding landscape has arisen as a result of natural selection. More likely, however, the intermediate complexity of Aß's ribbon-folding landscape has come from the post facto selection of the Aß sequence as an object of study by researchers because only by having a landscape with some degree of funneling can ordered aggregation of such a peptide occur at in vivo concentrations. In addition to predicting polymorph structures, we show that predicted solubilities of polymorphs correlate with experiment and with their elongation free energies computed by coarse-grained molecular dynamics.