Searching for the Pareto frontier in multi-objective protein design.

The goal of protein engineering and design is to identify sequences that adopt three-dimensional structures of desired function. Often, this is treated as a single-objective optimization problem, identifying the sequence-structure solution with the lowest computed free energy of folding. However, many design problems are multi-state, multi-specificity, or otherwise require concurrent optimization of multiple objectives. There may be tradeoffs among objectives, where improving one feature requires compromising another. The challenge lies in determining solutions that are part of the Pareto optimal set-designs where no further improvement can be achieved in any of the objectives without degrading one of the others. Pareto optimality problems are found in all areas of study, from economics to engineering to biology, and computational methods have been developed specifically to identify the Pareto frontier. We review progress in multi-objective protein design, the development of Pareto optimization methods, and present a specific case study using multi-objective optimization methods to model the tradeoff between three parameters, stability, specificity, and complexity, of a set of interacting synthetic collagen peptides.

Genetic background and environmental conditions drive metabolic variation in wild type and transgenic soybean (Glycine max) seeds.

The metabolic profiles and composition of storage reserves of agricultural crop seeds are strongly regulated by heritable and environmental factors. Yet, very little is known about the genetic and environmental determinants of adaptive metabolic variation amongst wild type as well as transgenic seed populations derived from the same genetic background, grown under natural field conditions. The goal of the current study was to investigate the effects of natural environmental conditions on wild type and transgenic soybean seeds expressing a feedback-insensitive form of cystathionine γ-synthase, a methionine main regulatory enzyme. The seeds were grown in four geographically distinct habitats in China and then assayed for primary metabolic profiles using gas chromatography mass spectrometry, morphological traits and storage reserve accumulation. The analyses revealed changes in the levels of primary metabolites which evidently exhibited high correlation to methionine regardless of changes in environmental conditions. The environment, however, constituted a major determinant of metabolic profiles amongst seeds, as much more metabolites were observed to be affected by this variable, particularly along the north-to-south latitudinal gradient. The observations suggest that metabolic variation amongst seeds grown under natural field conditions depends upon the complex relationships existing amongst their genetic background and the environmental conditions characterizing their cultivation areas.

Efficient Isothermal Titration Calorimetry Technique Identifies Direct Interaction of Small Molecule Inhibitors with the Target Protein.

Protein-protein interactions (PPI) play a critical role in regulating many cellular processes. Finding novel PPI inhibitors that interfere with specific binding of two proteins is considered a great challenge, mainly due to the complexity involved in characterizing multi-molecular systems and limited understanding of the physical principles governing PPIs. Here we show that the combination of virtual screening techniques, which are capable of filtering a large library of potential small molecule inhibitors, and a unique secondary screening by isothermal titration calorimetry, a label-free method capable of observing direct interactions, is an efficient tool for finding such an inhibitor. In this study we applied this strategy in a search for a small molecule capable of interfering with the interaction of the tumor-suppressor p53 and the E3-ligase MDM2. We virtually screened a library of 15 million small molecules that were filtered to a final set of 80 virtual hits. Our in vitro experimental assay, designed to validate the activity of mixtures of compounds by isothermal titration calorimetry, was used to identify an active molecule against MDM2. At the end of the process the small molecule (4S,7R)-4-(4-chlorophenyl)-5-hydroxy-2,7-dimethyl-N-(6-methylpyridin-2-yl)-4,6,7,8 tetrahydrIoquinoline-3-carboxamide was found to bind MDM2 with a dissociation constant of ~2 µM. Following the identification of this single bioactive compound, spectroscopic measurements were used to further characterize the interaction of the small molecule with the target protein. 2D NMR spectroscopy was used to map the binding region of the small molecule, and fluorescence polarization measurement confirmed that it indeed competes with p53.

Exploring the complexity of quantum control optimization trajectories.

The control of quantum system dynamics is generally performed by seeking a suitable applied field. The physical objective as a functional of the field forms the quantum control landscape, whose topology, under certain conditions, has been shown to contain no critical point suboptimal traps, thereby enabling effective searches for fields that give the global maximum of the objective. This paper addresses the structure of the landscape as a complement to topological critical point features. Recent work showed that landscape structure is highly favorable for optimization of state-to-state transition probabilities, in that gradient-based control trajectories to the global maximum value are nearly straight paths. The landscape structure is codified in the metric R ≥ 1.0, defined as the ratio of the length of the control trajectory to the Euclidean distance between the initial and optimal controls. A value of R = 1 would indicate an exactly straight trajectory to the optimal observable value. This paper extends the state-to-state transition probability results to the quantum ensemble and unitary transformation control landscapes. Again, nearly straight trajectories predominate, and we demonstrate that R can take values approaching 1.0 with high precision. However, the interplay of optimization trajectories with critical saddle submanifolds is found to influence landscape structure. A fundamental relationship necessary for perfectly straight gradient-based control trajectories is derived, wherein the gradient on the quantum control landscape must be an eigenfunction of the Hessian. This relation is an indicator of landscape structure and may provide a means to identify physical conditions when control trajectories can achieve perfect linearity. The collective favorable landscape topology and structure provide a foundation to understand why optimal quantum control can be readily achieved.

Efficient retrieval of landscape Hessian: forced optimal covariance adaptive learning.

Knowledge of the Hessian matrix at the landscape optimum of a controlled physical observable offers valuable information about the system robustness to control noise. The Hessian can also assist in physical landscape characterization, which is of particular interest in quantum system control experiments. The recently developed landscape theoretical analysis motivated the compilation of an automated method to learn the Hessian matrix about the global optimum without derivative measurements from noisy data. The current study introduces the forced optimal covariance adaptive learning (FOCAL) technique for this purpose. FOCAL relies on the covariance matrix adaptation evolution strategy (CMA-ES) that exploits covariance information amongst the control variables by means of principal component analysis. The FOCAL technique is designed to operate with experimental optimization, generally involving continuous high-dimensional search landscapes (≳30) with large Hessian condition numbers (≳10^{4}). This paper introduces the theoretical foundations of the inverse relationship between the covariance learned by the evolution strategy and the actual Hessian matrix of the landscape. FOCAL is presented and demonstrated to retrieve the Hessian matrix with high fidelity on both model landscapes and quantum control experiments, which are observed to possess nonseparable, nonquadratic search landscapes. The recovered Hessian forms were corroborated by physical knowledge of the systems. The implications of FOCAL extend beyond the investigated studies to potentially cover other physically motivated multivariate landscapes.

Control of nitromethane photoionization efficiency with shaped femtosecond pulses.

The applicability of adaptive femtosecond pulse shaping is studied for achieving selectivity in the photoionization of low-density polyatomic targets. In particular, optimal dynamic discrimination (ODD) techniques exploit intermediate molecular electronic resonances that allow a significant increase in the photoionization efficiency of nitromethane with shaped near-infrared femtosecond pulses. The intensity bias typical of high-photon number, nonresonant ionization is accounted for by reference to a strictly intensity-dependent process. Closed-loop adaptive learning is then able to discover a pulse form that increases the ionization efficiency of nitromethane by ∼150%. The optimally induced molecular dynamics result from entry into a region of parameter space inaccessible with intensity-only control. Finally, the discovered pulse shape is demonstrated to interact with the molecular system in a coherent fashion as assessed from the asymmetry between the response to the optimal field and its time-reversed counterpart.

Adaptive niche radii and niche shapes approaches for niching with the CMA-ES.

While the motivation and usefulness of niching methods is beyond doubt, the relaxation of assumptions and limitations concerning the hypothetical search landscape is much needed if niching is to be valid in a broader range of applications. Upon the introduction of radii-based niching methods with derandomized evolution strategies (ES), the purpose of this study is to address the so-called niche radius problem. A new concept of an adaptive individual niche radius is applied to niching with the covariance matrix adaptation evolution strategy (CMA-ES). Two approaches are considered. The first approach couples the radius to the step size mechanism, while the second approach employs the Mahalanobis distance metric with the covariance matrix mechanism for the distance calculation, for obtaining niches with more complex geometrical shapes. The proposed approaches are described in detail, and then tested on high-dimensional artificial landscapes at several levels of difficulty. They are shown to be robust and to achieve satisfying results.