Translation is the universal process that synthesizes proteins in all living cells. Central to translation is the ribosome, which itself constitutes approximately one fourth of a bacterial cell's dry mass. Biogenesis of the ribosome, together with all cellular activities involved in translation consume a significant budget of the cell's total energy. The ribosome consists of two subunits, each constructed of bare ribosomal RNA and a large number of ribosomal protein. These protein bind to the nascent ribosomal subunits in an hierarchy where the binding of a protein is dependent on the prior binding of an other. Here we describe a model of the biogenesis of the 30S ribosomal small unit based on kinetic data from bulk experiments as well as single molecule experiments and molecular dynamics simulation. By using the thermodynamic dependencies of r-protein we construct a chemical reaction network enumerating all 1600 possible intermediates and all 7000 binding reactions. The full network is then reduced iteratively by removing the least utilized intermediate until an error tolerance of 1% RMS is reached. The reduced network is able to confirm the known 5' to 3' binding order as well as predict all important intermediates. The reduced network shows a single pathway constructing the 5' domain, followed by two independent pathways constructing the central and 3' domain, completed by a single pathway binding the remaining protein. This reduced network will be used to construct whole-cell models of ribosome biogenesis allowing detailed predictions of spatial distributions of ribosomes
Towards a whole-cell model of ribosome biogenesis: Kinetic modeling of SSU assembly Earnest TM, Lai J, Chen K, Hallock MJ, Williamson JR, Luthey-Schulten ZA, Biophysical Journal. 2015, Volume 109, Number 6, pages 1117-11135. doi: 10.1016/j.bpj.2015.07.030
Due to the stochastic nature of gene expression, genetically identical cells inhabiting the same environment can vary significantly in their numbers of key enzymes, which in turn results in strikingly different cellular behaviors. This cell-to-cell variability can manifest itself through differences in growth rates, usage of specific biochemical pathways, and the types of metabolic byproducts produced by each cell. Incorporating data from studies of gene regulation and protein distributions in single cells, we developed a population flux balance methodology that identified several behavioral subtypes within a population grown on minimal medium. Our computer model predicts the emission of acetate for slow growing subpopulations and pathway selection to balance energy (glycolysis pathway) and protein costs (ED pathway) as a function of growth. The research also suggests that tracking the behavior of a few genes "may be sufficient to capture most of the metabolic variability of the entire population. Our investigations provide the first calculations linking variation in specific pathway usages to the growth rate distribution of a microbial population. By looking beyond the average growth rate of a colony, our work provides insight into the different strategies used by bacteria for survival and is an important step in the development of physical systems biology.
Heterogeneity in protein expression induces metabolic variability in a modeled Escherichia coli population. Labhsetwar P, Cole JA, Roberts E, Price ND, Luthey-Schulten ZA, Proc Natl Acad Sci U S A. 2013, Volume 110, pages 14006-11. doi: 10.1073/pnas.1222569110
Spatially resolved stochastic simulation is a valuable technique for studying reactions on time and size scales relevant for biological systems. Here, CPLC faculty ZLS and postdoc ER introduce the Lattice Microbes GPU-based software package for simulating complex biochemical reaction networks on the level of the whole cell. Our approach integrates data from cyroelectron tomography, proteomics, and single molecule spectroscopy to capture the molecular crowding within cells. The software performs either well-stirred or spatially resolved stochastic simulations with approximated cytoplasmic crowding in a fast and efficient manner. Our new algorithm efficiently samples the reaction-diffusion master equation using NVIDIA graphics processing units and is shown to be two orders of magnitude faster than exact sampling for large systems while maintaining an accuracy of ∼0.1%. Display of cell models and animation of reaction trajectories involving millions of molecules is facilitated using a plug-in to the popular VMD visualization platform.
Lattice microbes: High-performance stochastic simulation method for the reaction-diffusion master equation. Elijah Roberts, John E. Stone and Zaida Luthey-Schulten, Journal of Computational Chemistry, Volume 34, 2013, Pages: 245–255. doi: 10.1002/jcc.23130
In a new collaborative direction between Luthey-Schulten and Goldenfeld, the work is primarily analytical, and will help us understand the emergence of heterogenous cell populations in initially clonal bacterial populations. Biological systems are of great interest to statistical physicists, because they contain a large number of strongly fluctuating degrees of freedom, but not enough that they are in the thermodynamic limit. Accordingly the noise characteristics and the dynamical behavior of such systems pose a unique challenge to theory that is rarely encountered in other areas of physics, leading to important biological phenomena. A population of clonal cells can become phenotypically differentiated as a result of environmental (i.e. extrinsic) noise and intrinsic noise, such as number fluctuations. These phenomena are now well-understood in the case where intrinsic gene expression stochasticity is the key noise source. But what is the role of extrinsic noise, arising from cell-to-cell variations in (e.g.) ribosome or RNA polymerase number, thus equally affecting each gene within the cell? How do mean switching times between allowed states depend on the extrinsic noise?
To address this, Goldenfeld and Luthey-Schulten have solved the problem of phenotype switching due to a single self-regulating gene with positive feedback. The technical advance that they and their CPLC associated postdocs introduced in this context was to use WKB and Hamilton-Jacobi methods to go beyond simple mass-action results. The key result was that the different phenotypes' lifetime is significantly altered, with increased parameter range for bistability. The mean switching time is lowered by many orders of magnitude even for a very moderate amount of extrinsic noise, which is important for bacterial communities that exploit heterogeneity in order to inhabit new ecological niches, for example. The semi-analytical results were validated through state of the art stochastic simulations available through the Luthey-Schulten’s Lattice Microbes to go beyond simple mass-action results.
Extrinsic Noise Driven Phenotype Switching in a Self-Regulating Gene. Michael Assaf, Elijah Roberts, Zaida Luthey-Schulten, and Nigel Goldenfeld. Physical Review Letters. Vol. 111, 2013, Pages: 058102- doi: 10.1103/PhysRevLett.111.05810
To our knowledge, this collaboration between CPLC faculty Ha and Luthey-Schulten with Woodson at Johns Hopkins presents the first use of single molecule spectroscopy and all-atom simulations to obtain the frequency and direction of helix motions (not only populations) in a large RNA-protein complex. The first proteins to bind the RNA change the rRNA structure in a way that makes it easier for later proteins to join. How ribosomal proteins recognize the RNA and change its structure so that other proteins can bind is not known. To address this gap, we used two and three-color single molecule FRET and molecular dynamics simulations to observe encounters between E. coli protein S4 and the 5’ domain of 16S rRNA in real time with precision and clarity unprecedented for any RNA-protein complexes. S4 is one of the first proteins to bind the 16S rRNA, and is needed to nucleate 30S ribosome assembly and for the fidelity of translation. At first, the S4-rRNA complex is dynamic and samples many structures, but after a few seconds, it converts to stable complexes that flip between two structures, a native structure and a non-native intermediate. Unexpectedly, nearly all successful S4 binding trajectories pass through the non-native intermediate, contradicting the usual assumption that proteins prefer to bind the natively folded RNA.
Protein-guided RNA dynamics during early ribosome assembly. Hajin Kim, Sanjaya C. Abeysirigunawardena, Ke Chen, Megan Mayerle, Kaushik Ragunathan,Zaida Luthey-Schulten, Taekjip Ha and Sarah A. Woodson. In press.
We develop a model of the lac genetic switch that describes the switching and coexistence of phenotypes as a function of extracellular lactose concentration. We present a first stochastic treatment of a gene–mRNA–protein model of the lac operon in E. coli interacting with extracellular inducer that includes transitions to looped DNA states. This highly interdisciplinary project, involving 2 post-docs and one graduate student, uses tools from physics and new mathematical tools to explain statistical aspects of stochastic gene expression.
DNA looping increases the range of bistability in a stochastic model of the lac genetic switch. Tyler M Earnest, Elijah Roberts, Michael Assaf, Karin Dahmen and Zaida Luthey-Schulten. Physical Biology. Vol. 10, No. 2, 2013, Pages: 026002- doi: 10.1088/1478-3975/10/2/026002