Engineering the self-organizing behavior of molecular systems

• Martha Grover Gallivan, Chemical & Biomolecular Engineering, Georgia Institute of Technology
• Pete Ludovice, Chemical & Biomolecular Engineering, Georgia Institute of Technology
• Eric Klavins, Electrical Engineering, University of Washington
• David Baker, Biochemistry, University of Washington

Systems of molecules, atoms, or nanoparticles interact and organize to create larger structures and materials. For example, a sequence of amino acids forms a protein, which interacts with other molecules in the cell to form a signaling network. As another example, the evolution of surface roughness during thin film deposition depends on the interactions between individual atoms. To control these processes, models having the appropriate level of abstraction are required. In some cases it is possible to derive high-level models directly from the details of the particle interactions, while in many other cases, performing the many-body simulations of a large collection of particles seems to be the only way to make predictions of the overall behavior of the system.

An increasing number of control systems researchers are interested in these types of system. This is due to several factors: the tools developed to manipulate dynamical systems have recently become applicable to highly complex systems; molecular engineering and biochemistry have become increasingly quantitative disciplines, in need of models and analytical tools; and, most importantly, the laboratory techniques to build and characterize molecular devices are maturing at a rapid pace.

In this tutorial session, the participants will review efforts in modeling and designing self-organizing molecular systems. The goal of the session is to introduce a variety of engineered molecular systems and the models used to describe their behaviors. The control theorist attending the session should take away a broader understanding of the intricacies of molecular modeling, an appreciation of several application domains where modeling and control is required, and a set of challenges in modeling, model-reduction and control appropriate for future research in control systems.

The format will be four 30 minute talks plus a 20 minute panel discussion with all four speakers at the end of the session. The first two talks focus on applications in materials, while the second two talks are on biomolecular systems. The abstracts of the individual talks follow.

ABSTRACTS OF TALKS

Reduced order modeling and dynamic optimization in molecular simulations

Martha Grover Gallivan
Chemical & Biomolecular Engineering
Georgia Institute of Technology

This talk will summarize work by Professor Gallivan and other researchers in the controls community on the topic of model reduction for many-body molecular simulations. In many applications in materials and processing, the plant model consists of a large number of indistinguishable particles, so it should be possible to accomplish a state reduction by eliminating symmetries in the system. However, there are many options for defining the full state, and for identifying the reduced state. Since the processes are generally nonlinear, many alternatives exist for the functional form of the reduced order model. One option that has been explored is to generate reduced order models with the same mathematical structure as the originalunderlying master equation, by constructing discrete state Markov chain models with a state-affine mathematical structure. In general, a challenge is that the original state is of an extremely high dimension, such that mathematical manipulation of the full state is not practical. A key challenge is to develop methods that are practical for extremely large systems, and one approach has been to use the full stochastic simulations to generate input-output data for model building.

By exploiting the process dynamics via kinetic pathways, it is possible to drive a system into a metastable state. Thus, one may obtain altered material properties, although it is difficult to design and optimize a process using a molecular system, due to the high computational burden and the lack of a closed form equation for analysis. A reduced order model could bridge this gap and enable the design and control of systems described by molecular dynamics and kinetic Monte Carlo
simulations. An application of reduced order modeling and dynamic optimization in a thin film deposition process will be presented (Itoh, Progress in Surface Science, 66, 2001; Oguz and Gallivan, ACC, 2007). The approach enables the optimization of atomic scale surface structure, by computing a time-varying flux profile. Each conceptual step in the reduction and modeling building process will be described, and placed in the context of alternative approaches presented in the statistical mechanics and control communities. Joint work with Cihan Oguz.

Reduction approaches in molecular simulations

Pete Ludovice
Chemical & Biomolecular Engineering
Georgia Institute of Technology

Professor Ludovice will begin by giving an introduction to molecular modeling and the various algorithms used to sample phase space such as molecular dynamics (MD) and other stochastic algorithms. Feedback algorithms used to control state variables and potentially speed up the convergence of such simulations will also be discussed. While molecular modeling provides an atomically detailed description of matter, it is difficult to extract macroscopic bulk properties because of the large disparity between the time and length scales of MD simulations and those relevant to the equilibrium behavior of bulk chemicals and materials. This explains the limited application of MD simulations to bulk materials and chemicals in contrast to drug design applications which often rely on simulations of only a few molecules. Effective application of
molecular modeling to bulk materials and the processing thereof depends on the reduction of variable dimensions to increase the efficiency of such simulations.

Example applications will be examined to determine how to physically reduce the dimensionality of such atomicallydetailed model systems. Various mesoscale methods for the modeling of such reduced systems including Dissipative Particle Dynamics and other stochastic and analytical models will be discussed. It is the renormalization of the atomically detailed system to the reduced model that is the most challenging task regardless of the reduced model simulation algorithm used. Examples of making this data reduction on real polymer systems will be used to illustrate the challenges inherent in this necessary data reduction.

Characterization and optimization of biomolecular circuits

Eric Klavins
Electrical Engineering
University of Washington

In vitro transcriptional networks, consisting of double stranded DNA fragments (sometimes called genelets) acting as genes, single stranded DNA strands acting as activators and repressors, and the enzymes RNA polymerase and Ribonuclease H, can be demonstrated in the lab. RNA transcribed by one genelet can activate or repress other genelets. Furthermore, the dynamical behavior of the networks can be tuned by varying the relative concentrations of the component DNA strands. For example, Kim and Winfree, who introduced this technology (Molecular Systems Biology, 2, Dec 2006), demonstrate that a network consisting of two mutually repressing genelets acts as a bistable switch.

New behaviors can be engineered by building new networks of genelets. Ideally, the dynamical behavior of a given network can be determined from the behaviors of the components, but several problems arise. First, the genelets share the available enzymes in varying proportions as genes in the networks turn on and off. Second, RNA signals from can nonspecifically bind to non-target genelets, producing crosstalk. Thus, the forward problem (predicting behavior from network structure) suffers from a lack of good models. The inverse problem (finding a structure given the desired behavior) is therefore all the more difficult and requires a new approach to modeling these systems.

In his talk, Klavins will review the technology of in vitro transcription and describe our efforts to find simple models based on optimization and search to fit experimental data. He will also discuss efforts based on these models to automatically tune transcriptional networks in the lab to produce optimal behaviors. Joint work with Josh Bishop, University of Washington.

Computational de novo enzyme design

David Baker
Biochemistry
University of Washington

Naturally occurring enzymes are incredibly efficient catalysts. They bind their substrates in a well-defined active site with precisely aligned catalytic residues to form highly active and selective catalysts, which can perform difficult chemical reactions under mild conditions. Because of their high selectivity, no naturally occurring enzymes exist for many important synthetic reactions. Hence, the design of stable enzymes with novel catalytic activities is of great practical interest with potential applications in biotechnology, biomedicine, and industrial processes. Further, the rational design of novel enzymes provides a stringent benchmark of our understanding of how enzymes work. In the past several years, there has been exciting progress in designing new biocatalysts for reactions that are catalyzed by naturally occurring enzymes.

In this talk, David Baker will review computational approaches to enzyme design, focusing in particular on the Rosetta Match algorithm (Zanghellini et al., Protein Science, 15:2785-2794, 2006). He will describe the computational design of twelve novel enzymes which utilize one of two different mechanisms to catalyze the Kemp elimination reaction (Hellfelder et al., J. Amer. Chem. Soc., 122:1022, 2000) with experimentally measured rate enhancements. Mutational analysis confirms that catalysis depends on the computationally designed active sites, and the high resolution crystal structure of one of the designs illustrates that the models have close to atomic accuracy. Application of in vitro evolution methodologies to enhance the computational designs produced more than a 100 fold increase in enzymatic activity. Both the crystal structure and the in vitro evolution results provide insight into routes for improving the computational design procedure. Taken together, the results demonstrate the power of the combination of computational protein design and molecular evolution for creating novel
enzymes, enabling the creation of a wide range of useful new catalysts using this combination in the years to come. Joint work with Daniela Grabs-Rothlisberger, University of Washington.