Physical Force Field Research Articles

Numerical Modeling Using Immersed Boundary-Lattice Boltzmann Method and Experiments for Particle Manipulation under Standing Surface Acoustic Waves.

In this work, we employed the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) to simulate the motion of a microparticle in a microchannel under the influence of a standing surface acoustic wave (SSAW). To capture the response of the target microparticle in a straight channel under the effect of the SSAW, in-house code was built in C language. The SSAW creates pressure nodes and anti-nodes inside the microchannel. Here, the target particle was forced to traverse toward the pressure node. A mapping mechanism was developed to accurately apply the physical acoustic force field in the numerical simulation. First, benchmarking studies were conducted to compare the numerical results in the IB-LBM with the available analytical, numerical, and experimental results. Next, several parametric studies were carried out in which the particle types, sizes, compressibility coefficients, and densities were varied. When the SSAW is applied, the microparticles (with a positive acoustic contrast factor) move toward the pressure node locations during their motion in the microchannel. Hence, their steady-state locations are controlled by adjusting the pressure nodes to the desired locations, such as the centerline or near the microchannel sidewalls. Moreover, the geometric parameters, such as radius, density, and compressibility of the particles affect their transient response, and the particles ultimately settle at the pressure nodes. To validate the numerical work, a microfluidic device was fabricated in-house in the cleanroom using lithographic techniques. Experiments were performed, and the target particle was moved either to the centerline or sidewalls of the channel, depending on the location of the pressure node. The steady-state placements obtained in the computational model and experiments exhibit excellent agreement and are reported.

Stimulus-responsive nonclose-packed photonic crystals: fabrications and applications.

Stimulus-responsive photonic crystals (PCs) possessing unconventional nonclosely packed structures have received growing attention due to their unique capability of mimicking the active structural colors of natural organisms (for example, chameleons' mechanochromic properties). However, there is rarely any systematic review regarding the progress of nonclose-packed photonic crystals (NPCs), involving their fabrication, working mechanisms, and applications. Herein, a comprehensive review of the fundamental principles and practical fabrication strategies of one/two/three-dimensional NPCs is summarized from the perspective of designing nonclose-packed structures. Subsequently, responsive NPCs with exciting functions and working mechanisms are sorted and delineated according to their diverse responses to physical (force, temperature, magnetic, and electric fields), chemical (ions, pH, vapors, and solvents), and biological (glucose, organophosphate, creatinine, and bacteria) stimuli. We then systematically introduced and discussed the applications of NPCs in sensors, printing, anticounterfeiting, display, optical devices, etc. Finally, the current challenges and development prospects for NPCs are presented. This review not only concludes the design principle for NPCs but also provides a significant basis for the exploration of next-generation NPCs.

Alternating direction method of multipliers-based distributed control for distributed manipulation by shaping physical force fields

This paper proposes an algorithm for decomposing and possibly distributing an optimization problem that naturally emerges in distributed manipulation by shaping physical force fields through actuators distributed in space (arrays of actuators). One or several manipulated objects located in this field can “feel the force” and move simultaneously and independently. The control system has to produce commands for all actuators so that desired forces are developed at several prescribed places. This can be formulated as an optimization problem that has to be solved in every sampling period. Exploiting the structure of the optimization problem is crucial for platforms with many actuators and many manipulated objects, hence the goal of decomposing the huge optimization problem into several subproblems. Furthermore, if the platform is composed of interconnected actuator modules with computational capabilities, the decomposition can give guidance for the distribution of the computation to the modules. We propose an algorithm for decomposing/distributing the optimization problem using Alternating Direction Method of Multipliers (ADMM). The proposed algorithm is shown to converge to modest accuracy for various distributed platforms in a few iterations. We demonstrate our algorithm through numerical experiments corresponding to three physical experimental platforms for distributed manipulation using electric, magnetic, and pressure fields. Furthermore, we deploy and test it on real experimental platforms for distributed manipulation using an array of solenoids and ultrasonic transducers.

Microfluidic Separation, Detection, and Engineering of Extracellular Vesicles for Cancer Diagnostics and Drug Delivery

ConspectusExtracellular vesicles (EVs) are cell-derived submicron bioparticles composed of lipid bilayer membrane and molecular cargos, acting as important mediators of physiopathological cellular processes. The analysis and engineering of EVs hold significant therapeutic potential in noninvasive cancer diagnostics and innovative drug delivery systems. Despite significant improvements in technologies for EV investigation, the clinical use of EVs has been hampered by several challenges including the requirement of expensive equipment such as ultracentrifuge for EV isolation from clinical samples, laborious and time-consuming procedures for EV analysis, and large batch-to-batch variation for EV engineering. In this respect, microfluidic technologies have attracted increasing attention as promising avenues to accelerate the study of EVs by offering advantages of small-volume capacity, cost effectiveness, precise manipulation of bioparticles, streamlined workflows, high levels of sensitivity and specificity, and good reproducibility and stability.In this Account, we review the state-of-the-art advances in the development of microfluidic platforms for EV separation, detection, and engineering with key applications in cancer diagnostics and drug delivery. We first elaborate a variety of passive and active microfluidic approaches for label-free, high-resolution separation of EVs from biological matrix based on their physical properties. As an example of passive method, viscoelastic microfluidics exploits the size-dependent elastic lift force imposed on EVs in a viscoelastic medium, allowing for the high-resolution isolation of EVs from biofluids. The active methods leverage the use of externally applied physical fields (e.g., electric and acoustic fields) to achieve rapid separation of submicron-sized EVs. We then summarize different signal amplification and detection strategies implemented with microfluidic platforms for sensitive and specific characterization of EVs in clinical samples. The combination of microfluidics with thermophoresis-assisted fluorescence detection, surface plasmon resonance (SPR), surface-enhanced Raman scattering (SERS), and magnetic detection have been employed to profile EV surface proteins, miRNAs, mRNAs, etc. These EV-associated biomarkers reveal great potential for the diagnosis, monitoring, and prognosis of cancer. We also survey the progress in microfluidic engineering of EVs that utilizes the intensive physical (acoustic and electric fields) or mechanical force fields to load active cargo into EVs in a reproducible, continuous manner. The engineered EVs have been developed as advanced delivery systems with improved immune evasion, targeting capability, and therapeutic effectiveness. Finally, we conclude this Account by outlining the challenges, opportunities, and future directions in the microfluidic investigation of EVs in the clinic and in vivo.

Selection of representative structures from large biomolecular ensembles.

Despite the incredible progress of experimental techniques, protein structure determination still remains a challenging task. Due to the rapid improvements of computer technology, simulations are often used to complement or interpret experimental data, particularly for sparse or low-resolution data. Many such in silico methods allow us to obtain highly accurate models of a protein structure either de novo or via refinement of a physical model with experimental restraints. One crucial question is how to select a representative member or ensemble out of the vast number of computationally generated structures. Here, we introduce such a method. As a representative task, we add co-evolutionary contact pairs as distance restraints to a physical force field and want to select a good characterization of the resulting native-like ensemble. To generate large ensembles, we run replica-exchange molecular dynamics (REMD) on five mid-sized test proteins and over a wide temperature range. High temperatures allow overcoming energetic barriers while low temperatures perform local searches of native-like conformations. The integrated bias is based on co-evolutionary contact pairs derived from a deep residual neural network to guide the simulation toward native-like conformations. We shortly compare and discuss the achieved model precision of contact-guided REMD for mid-sized proteins. Finally, we discuss four robust ensemble-selection algorithms in great detail, which are capable to extract the representative structure models with a high certainty. To assess the performance of the selection algorithms, we exemplarily mimic a "blind scenario," i.e., where the target structure is unknown, and select a representative structural ensemble of native-like folds.

EDock: blind protein\u2013ligand docking by replica-exchange monte carlo simulation

Protein–ligand docking is an important approach for virtual screening and protein function annotation. Although many docking methods have been developed, most require a high-resolution crystal structure of the receptor and a user-specified binding site to start. This information is, however, not available for the majority of unknown proteins, including many pharmaceutically important targets. Developing blind docking methods without predefined binding sites and working with low-resolution receptor models from protein structure prediction is thus essential. In this manuscript, we propose a novel Monte Carlo based method, EDock, for blind protein–ligand docking. For a given protein, binding sites are first predicted by sequence-profile and substructure-based comparison searches with initial ligand poses generated by graph matching. Next, replica-exchange Monte Carlo (REMC) simulations are performed for ligand conformation refinement under the guidance of a physical force field coupled with binding-site distance constraints. The method was tested on two large-scale datasets containing 535 protein–ligand pairs. Without specifying binding pockets on the experimental receptor structures, EDock achieves on average a ligand RMSD of 2.03 Å, which compares favorably with state-of-the-art docking methods including DOCK6 (2.68 Å) and AutoDock Vina (3.92 Å). When starting with predicted models from I-TASSER, EDock still generates reasonable docking models, with a success rate 159% and 67% higher than DOCK6 and AutoDock Vina, respectively. Detailed data analyses show that the major advantage of EDock lies in reliable ligand binding site predictions and extensive REMC sampling, which allows for the implementation of multiple van der Waals weightings to accommodate different levels of steric clashes and cavity distortions and therefore enhances the robustness of low-resolution docking with predicted protein structures.

SodaPop: a forward simulation suite for the evolutionary dynamics of asexual populations on protein fitness landscapes.

Protein evolution is determined by forces at multiple levels of biological organization. Random mutations have an immediate effect on the biophysical properties, structure and function of proteins. These same mutations also affect the fitness of the organism. However, the evolutionary fate of mutations, whether they succeed to fixation or are purged, also depends on population size and dynamics. There is an emerging interest, both theoretically and experimentally, to integrate these two factors in protein evolution. Although there are several tools available for simulating protein evolution, most of them focus on either the biophysical or the population-level determinants, but not both. Hence, there is a need for a publicly available computational tool to explore both the effects of protein biophysics and population dynamics on protein evolution. To address this need, we developed SodaPop, a computational suite to simulate protein evolution in the context of the population dynamics of asexual populations. SodaPop accepts as input several fitness landscapes based on protein biochemistry or other user-defined fitness functions. The user can also provide as input experimental fitness landscapes derived from deep mutational scanning approaches or theoretical landscapes derived from physical force field estimates. Here, we demonstrate the broad utility of SodaPop with different applications describing the interplay of selection for protein properties and population dynamics. SodaPop is designed such that population geneticists can explore the influence of protein biochemistry on patterns of genetic variation, and that biochemists and biophysicists can explore the role of population size and demography on protein evolution. Source code and binaries are freely available at https://github.com/louisgt/SodaPop under the GNU GPLv3 license. The software is implemented in C++ and supported on Linux, Mac OS/X and Windows. Supplementary data are available at Bioinformatics online.

On the universality of Maxwell’s equations

Einstein’s theory of relativity is based on the Principle of Equivalence, Hilbert’s on invariant theory and the calculus of variations. The two paradigms are not equivalent. Using the universality of Maxwell’s equations, Hilbert’s variational method is used to determine the energy–momentum tensor uniquely, and to show that general relativity can be formulated on the basis of Maxwellian, rather than specific physical force fields. A unified field theory is proved in which the Maxwellian force fields are all on an equal footing, distinct from the geometric field.

BindProfX: Assessing Mutation-Induced Binding Affinity Change by Protein Interface Profiles with Pseudo-Counts

Understanding how gene-level mutations affect the binding affinity of protein–protein interactions is a key issue of protein engineering. Due to the complexity of the problem, using physical force field to predict the mutation-induced binding free-energy change remains challenging. In this work, we present a renewed approach to calculate the impact of gene mutations on the binding affinity through the structure-based profiling of protein–protein interfaces, where the binding free-energy change (ΔΔG) is counted as the logarithm of relative probability of mutant amino acids over wild-type ones in the interface alignment matrix; three pseudo-counts are introduced to alleviate the limit of the current interface library. Compared with a previous profile score that was based on the log-odds likelihood calculation, the correlation between predicted and experimental ΔΔG of single-site mutations is increased in this approach from 0.33 to 0.68. The structure-based profile score is found complementary to the physical potentials, where a linear combination of the profile score with the FoldX potential could increase the ΔΔG correlation from 0.46 to 0.74. It is also shown that the profile score is robust for counting the coupling effect of multiple individual mutations. For the mutations involving more than two mutation sites where the correlation between FoldX and experimental data vanishes, the profile-based calculation retains a strong correlation with the experimental measurements.

Improving hybrid statistical and physical forcefields through local structure enumeration.

Forcefields used in biomolecular simulations are comprised of energetic terms that are physical in nature, based on parameter fitting to quantum mechanical simulation or experimental data, or statistical, drawing off high-resolution structural data to describe distributions of molecular features. Combining the two in a single forcefield is challenging, since physical terms describe some, but not all, of the observed statistics, leading to double counting. In this manuscript, we develop a general scheme for correcting statistical potentials used in combination with physical terms. We apply these corrections to the sidechain torsional potential used in the Rosetta all-atom forcefield. We show the approach identifies instances of double-counted interactions, including electrostatic interactions between sidechain and nearby backbone, and steric interactions between neighboring Cβ atoms within secondary structural elements. Moreover, this scheme allows for the inclusion of intraresidue physical terms, previously turned off to avoid overlap with the statistical potential. Combined, these corrections lead to a forcefield with improved performance on several structure prediction tasks, including rotamer prediction and native structure discrimination.

Theoretical Insights into the Biophysics of Protein Bi-stability and Evolutionary Switches.

Deciphering the effects of nonsynonymous mutations on protein structure is central to many areas of biomedical research and is of fundamental importance to the study of molecular evolution. Much of the investigation of protein evolution has focused on mutations that leave a protein’s folded structure essentially unchanged. However, to evolve novel folds of proteins, mutations that lead to large conformational modifications have to be involved. Unraveling the basic biophysics of such mutations is a challenge to theory, especially when only one or two amino acid substitutions cause a large-scale conformational switch. Among the few such mutational switches identified experimentally, the one between the GA all-α and GB α+β folds is extensively characterized; but all-atom simulations using fully transferrable potentials have not been able to account for this striking switching behavior. Here we introduce an explicit-chain model that combines structure-based native biases for multiple alternative structures with a general physical atomic force field, and apply this construct to twelve mutants spanning the sequence variation between GA and GB. In agreement with experiment, we observe conformational switching from GA to GB upon a single L45Y substitution in the GA98 mutant. In line with the latent evolutionary potential concept, our model shows a gradual sequence-dependent change in fold preference in the mutants before this switch. Our analysis also indicates that a sharp GA/GB switch may arise from the orientation dependence of aromatic π-interactions. These findings provide physical insights toward rationalizing, predicting and designing evolutionary conformational switches.

Protein NMR Structure Refinement based on Bayesian Inference

Nuclear Magnetic Resonance (NMR) spectroscopy is a tool to investigate threedimensional (3D) structures and dynamics of biomacromolecules at atomic resolution in solution or more natural environments such as living cells. Since NMR data are principally only spectra with peak signals, it is required to properly deduce structural information from the sparse experimental data with their imperfections and uncertainty, and to visualize 3D conformations by NMR structure calculation. In order to efficiently analyse the data, Rieping et al. proposed a new structure calculation method based on Bayes’ theorem. We implemented a similar approach into the program CYANA with some modifications. It allows us to handle automatic NOE cross peak assignments in unambiguous and ambiguous usages, and to create a prior distribution based on a physical force field with the generalized Born implicit water model. The sampling scheme for obtaining the posterior is performed by a hybrid Monte Carlo algorithm combined with Markov chain Monte Carlo (MCMC) by the Gibbs sampler, and molecular dynamics simulation (MD) for obtaining a canonical ensemble of conformations. Since it is not trivial to search the entire function space particularly for exploring the conformational prior due to the extraordinarily large conformation space of proteins, the replica exchange method is performed, in which several MCMC calculations with different temperatures run in parallel as replicas. It is shown with simulated data or randomly deleted experimental peaks that the new structure calculation method can provide accurate structures even with less peaks, especially compared with the conventional method. In particular, it dramatically improves in-cell structures of the proteins GB1 and TTHA1718 using exclusively information obtained in living Escherichia coli (E. coli) cells.

Screened Electrostatic Interactions in Molecular Mechanics.

In a typical application of molecular mechanics (MM), the electrostatic interactions are calculated from parametrized partial atomic charges treated as point charges interacting by radial Coulomb potentials. This does not usually yield accurate electrostatic interactions at van der Waals distances, but this is compensated by additional parametrized terms, for example Lennard-Jones potentials. In the present work, we present a scheme involving radial screened Coulomb potentials that reproduces the accurate electrostatics much more accurately. The screening accounts for charge penetration of one subsystem's charge cloud into that of another subsystem, and it is incorporated into the interaction potential in a way similar to what we proposed in a previous article (J. Chem. Theory Comput. 2010, 6, 3330) for combined quantum mechanical and molecular mechanical (QM/MM) simulations, but the screening parameters are reoptimized for MM. The optimization is carried out with electrostatic-potential-fitted partial atomic charges, but the optimized parameters should be useful with any realistic charge model. In the model we employ, the charge density of an atom is approximated as the sum of a point charge representing the nucleus and inner electrons and a smeared charge representing the outermost electrons; in particular, for all atoms except hydrogens, the smeared charge represents the two outermost electrons in the present model. We find that the charge penetration effect can cause very significant deviations from the popular point-charge model, and by comparison to electrostatic interactions calculated by symmetry-adapted perturbation theory, we find that the present results are considerably more accurate than point-charge electrostatic interactions. The mean unsigned error in electrostatics for a large and diverse data set (192 interaction energies) decreases from 9.2 to 3.3 kcal/mol, and the error in the electrostatics for 10 water dimers decreases from 1.7 to 0.5 kcal/mol. We could have decreased the average errors further, but at the cost of sometimes significantly overestimating the screening; instead we chose a more conservative (safer) parametrization that systematically underestimates the screening (which by definition means it improves over point charges) and only occasionally overestimates it. Despite this conservative choice, we find that the screened MM method is even more accurate for the electrostatics than unscreened QM/MM calculations. This new method is easy to implement in any MM program, and it can be used to develop more physical force fields for molecular simulations.

Probabilistic Determination of Native State Ensembles of Proteins

The motions of biological macromolecules are tightly coupled to their functions. However, while the study of fast motions has become increasingly feasible in recent years, the study of slower, biologically important motions remains difficult. Here, we present a method to construct native state ensembles of proteins by the combination of physical force fields and experimental data through modern statistical methodology. As an example, we use NMR residual dipolar couplings to determine a native state ensemble of the extensively studied third immunoglobulin binding domain of protein G (GB3). The ensemble accurately describes both local and nonlocal backbone fluctuations as judged by its reproduction of complementary experimental data. While it is difficult to assess precise time-scales of the observed motions, our results suggest that it is possible to construct realistic conformational ensembles of biomolecules very efficiently. The approach may allow for a dramatic reduction in the computational as well as experimental resources needed to obtain accurate conformational ensembles of biological macromolecules in a statistically sound manner.

Formulation of probabilistic models of protein structure in atomic detail using the reference ratio method

We propose a method to formulate probabilistic models of protein structure in atomic detail, for a given amino acid sequence, based on Bayesian principles, while retaining a close link to physics. We start from two previously developed probabilistic models of protein structure on a local length scale, which concern the dihedral angles in main chain and side chains, respectively. Conceptually, this constitutes a probabilistic and continuous alternative to the use of discrete fragment and rotamer libraries. The local model is combined with a nonlocal model that involves a small number of energy terms according to a physical force field, and some information on the overall secondary structure content. In this initial study we focus on the formulation of the joint model and the evaluation of the use of an energy vector as a descriptor of a protein's nonlocal structure; hence, we derive the parameters of the nonlocal model from the native structure without loss of generality. The local and nonlocal models are combined using the reference ratio method, which is a well-justified probabilistic construction. For evaluation, we use the resulting joint models to predict the structure of four proteins. The results indicate that the proposed method and the probabilistic models show considerable promise for probabilistic protein structure prediction and related applications.

Sampling of Protein Folding Transitions: Multicanonical Versus Replica Exchange Molecular Dynamics.

We compare the efficiency of multicanonical and replica exchange molecular dynamics for the sampling of folding/unfolding events in simulations of proteins with end-to-end β-sheet. In Go-model simulations of the 75-residue MNK6, we observe improvement factors of 30 in the number of folding/unfolding events of multicanonical molecular dynamics over replica exchange molecular dynamics. As an application, we use this enhanced sampling to study the folding landscape of the 36-residue DS119 with an all-atom physical force field and implicit solvent. Here, we find that the rate-limiting step is the formation of the central helix that then provides a scaffold for the parallel β-sheet formed by the two chain ends.

Utilization of efficient gradient and Hessian computations in the force field optimization process of molecular simulations

Computer simulations of chemical systems, especially systems of condensed matter, are highly important for both scientific and industrial applications. Thereby, molecular interactions are modeled on a microscopic level in order to study their impact on macroscopic phenomena. To be capable of predicting physical properties quantitatively, accurate molecular models are indispensable. Molecular interactions are described mathematically by force fields, which have to be parameterized. Recently, an automated gradient-based optimization procedure was published by the authors based on the minimization of a loss function between simulated and experimental physical properties. The applicability of gradient-based procedures is not trivial at all because of two reasons: firstly, simulation data are affected by statistical noise, and secondly, the molecular simulations required for the loss function evaluations are extremely time-consuming. Within the optimization process, gradients and Hessians were approximated by finite differences so that additional simulations for the respective modified parameter sets were required. Hence, a more efficient approach to computing gradients and Hessians is presented in this work. The method developed here is based on directional instead of partial derivatives. It is compared with the classical computations with respect to computation time. Firstly, molecular simulations are replaced by fit functions that define a functional dependence between specific physical observables and force field parameters. The goal of these simulated simulations is to assess the new methodology without much computational effort. Secondly, it is applied to real molecular simulations of the three chemical substances phosgene, methanol and ethylene oxide. It is shown that up to 75% of the simulations can be avoided using the new algorithm.

Modeling Structural Flexibility of Proteins with Go-Models

Structure-based models are an efficient tool for folding studies of proteins since by construction their energy landscape is only minimal frustrated. However, their intrinsic drawback is a lack of structural flexibility as usually only one target structure is employed to construct the potentials. Hence, a Go-model may not capture differences in mutation-induced protein dynamics, if - as in the case of the disease-related A629P mutant of the Menkes protein ATP7A - the structural differences between mutant and wild type are small. In this work, we introduced three implementations of Go-models that take into account the flexibility of proteins in the NMR ensemble. Comparing the wild type and the mutant A629P of the 75-residue large 6th domain Menkes protein, we find that these new Go-potentials lead to broader distributions than Go-models relying on a single member of the NMR-ensemble. This allows us to detect the transient unfolding of a loosely formed β1β4-sheet in the mutant protein. Our results are consistent with previous simulations using physical force field and an explicit solvent, and suggests a mechanism by which these mutations cause Menkes disease. In addition, the improved Go-models suggest differences in the folding pathway between wild type and mutant, an observation that was not accessible to simulations of this 75-residue protein with a physical all-atom force field and explicit solvent.

Beyond rotamers: a generative, probabilistic model of side chains in proteins

BackgroundAccurately covering the conformational space of amino acid side chains is essential for important applications such as protein design, docking and high resolution structure prediction. Today, the most common way to capture this conformational space is through rotamer libraries - discrete collections of side chain conformations derived from experimentally determined protein structures. The discretization can be exploited to efficiently search the conformational space. However, discretizing this naturally continuous space comes at the cost of losing detailed information that is crucial for certain applications. For example, rigorously combining rotamers with physical force fields is associated with numerous problems.ResultsIn this work we present BASILISK: a generative, probabilistic model of the conformational space of side chains that makes it possible to sample in continuous space. In addition, sampling can be conditional upon the protein's detailed backbone conformation, again in continuous space - without involving discretization.ConclusionsA careful analysis of the model and a comparison with various rotamer libraries indicates that the model forms an excellent, fully continuous model of side chain conformational space. We also illustrate how the model can be used for rigorous, unbiased sampling with a physical force field, and how it improves side chain prediction when used as a pseudo-energy term. In conclusion, BASILISK is an important step forward on the way to a rigorous probabilistic description of protein structure in continuous space and in atomic detail.

G Protein Mono-ubiquitination by the Rsp5 Ubiquitin Ligase

Emerging evidence suggests that ubiquitination serves as a protein trafficking signal in addition to its well characterized role in promoting protein degradation. The yeast G protein alpha subunit Gpa1 represents a rare example of a protein that undergoes both mono- and poly-ubiquitination. Whereas mono-ubiquitinated Gpa1 is targeted to the vacuole, poly-ubiquitinated Gpa1 is directed instead to the proteasome. Here we investigate the structural requirements for mono- and poly-ubiquitination of Gpa1. We find that variants of Gpa1 engineered to be unstable are more likely to be poly-ubiquitinated and less likely to be mono-ubiquitinated. In addition, mutants that cannot be myristoylated are no longer mono-ubiquitinated but are still polyubiquitinated. Finally, we show that the ubiquitin ligase Rsp5 is necessary for Gpa1 mono-ubiquitination in vivo and that the purified enzyme is sufficient to catalyze Gpa1 mono-ubiquitination in vitro. Taken together, these data indicate that mono- and poly-ubiquitination have distinct enzyme and substrate recognition requirements; whereas poly-ubiquitination targets misfolded protein for degradation, a distinct ubiquitination apparatus targets the fully mature, fully myristoylated G protein for mono-ubiquitination and delivery to the vacuole.