The (Un)Folding of Multidomain Proteins Through the Lens of Single-molecule Force-spectroscopy and Computer Simulation

Proteins are specialized molecules that catalyze most of the reactions that can sustain life, and they become functional by folding into a specific 3D structure. Despite their importance, the question, "how do proteins fold?" - first pondered in in the 1930's - is still listed as one of the top unanswered scientific questions as of 2005, according to the journal Science. Answering this question would provide a foundation for understanding protein function and would enable improved drug targeting, efficient biofuel production, and stronger biomaterials. Much of what we currently know about protein folding comes from studies on small, single-domain proteins, which may be quite different from the folding of large, multidomain proteins that predominate the proteomes of all organisms.

In this thesis I will discuss my work to fill this gap in understanding by studying the unfolding and refolding of large, multidomain proteins using the powerful combination of single-molecule force-spectroscopy experiments and molecular dynamic simulations.

The three model proteins studied - Luciferase, Protein S, and Streptavidin - lend insight into the inter-domain dependence for unfolding and the subdomain stabilization of binding ligands, and ultimately provide new insight into atomistic details of the intermediate states along the folding pathway.

Impact of simian immunodeficiency virus infection on chimpanzee population dynamics.

Like human immunodeficiency virus type 1 (HIV-1), simian immunodeficiency virus of chimpanzees (SIVcpz) can cause CD4+ T cell loss and premature death. Here, we used molecular surveillance tools and mathematical modeling to estimate the impact of SIVcpz infection on chimpanzee population dynamics. Habituated (Mitumba and Kasekela) and non-habituated (Kalande) chimpanzees were studied in Gombe National Park, Tanzania. Ape population sizes were determined from demographic records (Mitumba and Kasekela) or individual sightings and genotyping (Kalande), while SIVcpz prevalence rates were monitored using non-invasive methods. Between 2002-2009, the Mitumba and Kasekela communities experienced mean annual growth rates of 1.9% and 2.4%, respectively, while Kalande chimpanzees suffered a significant decline, with a mean growth rate of -6.5% to -7.4%, depending on population estimates. A rapid decline in Kalande was first noted in the 1990s and originally attributed to poaching and reduced food sources. However, between 2002-2009, we found a mean SIVcpz prevalence in Kalande of 46.1%, which was almost four times higher than the prevalence in Mitumba (12.7%) and Kasekela (12.1%). To explore whether SIVcpz contributed to the Kalande decline, we used empirically determined SIVcpz transmission probabilities as well as chimpanzee mortality, mating and migration data to model the effect of viral pathogenicity on chimpanzee population growth. Deterministic calculations indicated that a prevalence of greater than 3.4% would result in negative growth and eventual population extinction, even using conservative mortality estimates. However, stochastic models revealed that in representative populations, SIVcpz, and not its host species, frequently went extinct. High SIVcpz transmission probability and excess mortality reduced population persistence, while intercommunity migration often rescued infected communities, even when immigrating females had a chance of being SIVcpz infected. Together, these results suggest that the decline of the Kalande community was caused, at least in part, by high levels of SIVcpz infection. However, population extinction is not an inevitable consequence of SIVcpz infection, but depends on additional variables, such as migration, that promote survival. These findings are consistent with the uneven distribution of SIVcpz throughout central Africa and explain how chimpanzees in Gombe and elsewhere can be at equipoise with this pathogen.

Elucidating solvent contributions to solution reactions with ab initio QM/MM methods.

Computer simulations of reaction processes in solution in general rely on the definition of a reaction coordinate and the determination of the thermodynamic changes of the system along the reaction coordinate. The reaction coordinate often is constituted of characteristic geometrical properties of the reactive solute species, while the contributions of solvent molecules are implicitly included in the thermodynamics of the solute degrees of freedoms. However, solvent dynamics can provide the driving force for the reaction process, and in such cases explicit description of the solvent contribution in the free energy of the reaction process becomes necessary. We report here a method that can be used to analyze the solvent contributions to the reaction activation free energies from the combined QM/MM minimum free-energy path simulations. The method was applied to the self-exchange S(N)2 reaction of CH(3)Cl + Cl(-), showing that the importance of solvent-solute interactions to the reaction process. The results were further discussed in the context of coupling between solvent and solute molecules in reaction processes.

WriteSim TCExam--an open source text simulation environment for training novice researchers in scientific writing.

BACKGROUND: The ability to write clearly and effectively is of central importance to the scientific enterprise. Encouraged by the success of simulation environments in other biomedical sciences, we developed WriteSim TCExam, an open-source, Web-based, textual simulation environment for teaching effective writing techniques to novice researchers. We shortlisted and modified an existing open source application - TCExam to serve as a textual simulation environment. After testing usability internally in our team, we conducted formal field usability studies with novice researchers. These were followed by formal surveys with researchers fitting the role of administrators and users (novice researchers) RESULTS: The development process was guided by feedback from usability tests within our research team. Online surveys and formal studies, involving members of the Research on Research group and selected novice researchers, show that the application is user-friendly. Additionally it has been used to train 25 novice researchers in scientific writing to date and has generated encouraging results. CONCLUSION: WriteSim TCExam is the first Web-based, open-source textual simulation environment designed to complement traditional scientific writing instruction. While initial reviews by students and educators have been positive, a formal study is needed to measure its benefits in comparison to standard instructional methods.

Nonlinear oscillator metamaterial model: numerical and experimental verification.

We verify numerically and experimentally the accuracy of an analytical model used to derive the effective nonlinear susceptibilities of a varactor-loaded split ring resonator (VLSRR) magnetic medium. For the numerical validation, a nonlinear oscillator model for the effective magnetization of the metamaterial is applied in conjunction with Maxwell equations and the two sets of equations solved numerically in the time-domain. The computed second harmonic generation (SHG) from a slab of a nonlinear material is then compared with the analytical model. The computed SHG is in excellent agreement with that predicted by the analytical model, both in terms of magnitude and spectral characteristics. Moreover, experimental measurements of the power transmitted through a fabricated VLSRR metamaterial at several power levels are also in agreement with the model, illustrating that the effective medium techniques associated with metamaterials can accurately be transitioned to nonlinear systems.

A noisy linear map underlies oscillations in cell size and gene expression in bacteria.

During bacterial growth, a cell approximately doubles in size before division, after which it splits into two daughter cells. This process is subjected to the inherent perturbations of cellular noise and thus requires regulation for cell-size homeostasis. The mechanisms underlying the control and dynamics of cell size remain poorly understood owing to the difficulty in sizing individual bacteria over long periods of time in a high-throughput manner. Here we measure and analyse long-term, single-cell growth and division across different Escherichia coli strains and growth conditions. We show that a subset of cells in a population exhibit transient oscillations in cell size with periods that stretch across several (more than ten) generations. Our analysis reveals that a simple law governing cell-size control-a noisy linear map-explains the origins of these cell-size oscillations across all strains. This noisy linear map implements a negative feedback on cell-size control: a cell with a larger initial size tends to divide earlier, whereas one with a smaller initial size tends to divide later. Combining simulations of cell growth and division with experimental data, we demonstrate that this noisy linear map generates transient oscillations, not just in cell size, but also in constitutive gene expression. Our work provides new insights into the dynamics of bacterial cell-size regulation with implications for the physiological processes involved.

Influence of network topology and data collection on network inference.

We recently developed an approach for testing the accuracy of network inference algorithms by applying them to biologically realistic simulations with known network topology. Here, we seek to determine the degree to which the network topology and data sampling regime influence the ability of our Bayesian network inference algorithm, NETWORKINFERENCE, to recover gene regulatory networks. NETWORKINFERENCE performed well at recovering feedback loops and multiple targets of a regulator with small amounts of data, but required more data to recover multiple regulators of a gene. When collecting the same number of data samples at different intervals from the system, the best recovery was produced by sampling intervals long enough such that sampling covered propagation of regulation through the network but not so long such that intervals missed internal dynamics. These results further elucidate the possibilities and limitations of network inference based on biological data.

Radiotherapy Treatment Assessment using DCE-MRI

Abstract

The goal of modern radiotherapy is to precisely deliver a prescribed radiation dose to delineated target volumes that contain a significant amount of tumor cells while sparing the surrounding healthy tissues/organs. Precise delineation of treatment and avoidance volumes is the key for the precision radiation therapy. In recent years, considerable clinical and research efforts have been devoted to integrate MRI into radiotherapy workflow motivated by the superior soft tissue contrast and functional imaging possibility. Dynamic contrast-enhanced MRI (DCE-MRI) is a noninvasive technique that measures properties of tissue microvasculature. Its sensitivity to radiation-induced vascular pharmacokinetic (PK) changes has been preliminary demonstrated. In spite of its great potential, two major challenges have limited DCE-MRI’s clinical application in radiotherapy assessment: the technical limitations of accurate DCE-MRI imaging implementation and the need of novel DCE-MRI data analysis methods for richer functional heterogeneity information.

This study aims at improving current DCE-MRI techniques and developing new DCE-MRI analysis methods for particular radiotherapy assessment. Thus, the study is naturally divided into two parts. The first part focuses on DCE-MRI temporal resolution as one of the key DCE-MRI technical factors, and some improvements regarding DCE-MRI temporal resolution are proposed; the second part explores the potential value of image heterogeneity analysis and multiple PK model combination for therapeutic response assessment, and several novel DCE-MRI data analysis methods are developed.

I. Improvement of DCE-MRI temporal resolution. First, the feasibility of improving DCE-MRI temporal resolution via image undersampling was studied. Specifically, a novel MR image iterative reconstruction algorithm was studied for DCE-MRI reconstruction. This algorithm was built on the recently developed compress sensing (CS) theory. By utilizing a limited k-space acquisition with shorter imaging time, images can be reconstructed in an iterative fashion under the regularization of a newly proposed total generalized variation (TGV) penalty term. In the retrospective study of brain radiosurgery patient DCE-MRI scans under IRB-approval, the clinically obtained image data was selected as reference data, and the simulated accelerated k-space acquisition was generated via undersampling the reference image full k-space with designed sampling grids. Two undersampling strategies were proposed: 1) a radial multi-ray grid with a special angular distribution was adopted to sample each slice of the full k-space; 2) a Cartesian random sampling grid series with spatiotemporal constraints from adjacent frames was adopted to sample the dynamic k-space series at a slice location. Two sets of PK parameters’ maps were generated from the undersampled data and from the fully-sampled data, respectively. Multiple quantitative measurements and statistical studies were performed to evaluate the accuracy of PK maps generated from the undersampled data in reference to the PK maps generated from the fully-sampled data. Results showed that at a simulated acceleration factor of four, PK maps could be faithfully calculated from the DCE images that were reconstructed using undersampled data, and no statistically significant differences were found between the regional PK mean values from undersampled and fully-sampled data sets. DCE-MRI acceleration using the investigated image reconstruction method has been suggested as feasible and promising.

Second, for high temporal resolution DCE-MRI, a new PK model fitting method was developed to solve PK parameters for better calculation accuracy and efficiency. This method is based on a derivative-based deformation of the commonly used Tofts PK model, which is presented as an integrative expression. This method also includes an advanced Kolmogorov-Zurbenko (KZ) filter to remove the potential noise effect in data and solve the PK parameter as a linear problem in matrix format. In the computer simulation study, PK parameters representing typical intracranial values were selected as references to simulated DCE-MRI data for different temporal resolution and different data noise level. Results showed that at both high temporal resolutions (<1s) and clinically feasible temporal resolution (~5s), this new method was able to calculate PK parameters more accurate than the current calculation methods at clinically relevant noise levels; at high temporal resolutions, the calculation efficiency of this new method was superior to current methods in an order of 102. In a retrospective of clinical brain DCE-MRI scans, the PK maps derived from the proposed method were comparable with the results from current methods. Based on these results, it can be concluded that this new method can be used for accurate and efficient PK model fitting for high temporal resolution DCE-MRI.

II. Development of DCE-MRI analysis methods for therapeutic response assessment. This part aims at methodology developments in two approaches. The first one is to develop model-free analysis method for DCE-MRI functional heterogeneity evaluation. This approach is inspired by the rationale that radiotherapy-induced functional change could be heterogeneous across the treatment area. The first effort was spent on a translational investigation of classic fractal dimension theory for DCE-MRI therapeutic response assessment. In a small-animal anti-angiogenesis drug therapy experiment, the randomly assigned treatment/control groups received multiple fraction treatments with one pre-treatment and multiple post-treatment high spatiotemporal DCE-MRI scans. In the post-treatment scan two weeks after the start, the investigated Rényi dimensions of the classic PK rate constant map demonstrated significant differences between the treatment and the control groups; when Rényi dimensions were adopted for treatment/control group classification, the achieved accuracy was higher than the accuracy from using conventional PK parameter statistics. Following this pilot work, two novel texture analysis methods were proposed. First, a new technique called Gray Level Local Power Matrix (GLLPM) was developed. It intends to solve the lack of temporal information and poor calculation efficiency of the commonly used Gray Level Co-Occurrence Matrix (GLCOM) techniques. In the same small animal experiment, the dynamic curves of Haralick texture features derived from the GLLPM had an overall better performance than the corresponding curves derived from current GLCOM techniques in treatment/control separation and classification. The second developed method is dynamic Fractal Signature Dissimilarity (FSD) analysis. Inspired by the classic fractal dimension theory, this method measures the dynamics of tumor heterogeneity during the contrast agent uptake in a quantitative fashion on DCE images. In the small animal experiment mentioned before, the selected parameters from dynamic FSD analysis showed significant differences between treatment/control groups as early as after 1 treatment fraction; in contrast, metrics from conventional PK analysis showed significant differences only after 3 treatment fractions. When using dynamic FSD parameters, the treatment/control group classification after 1st treatment fraction was improved than using conventional PK statistics. These results suggest the promising application of this novel method for capturing early therapeutic response.

The second approach of developing novel DCE-MRI methods is to combine PK information from multiple PK models. Currently, the classic Tofts model or its alternative version has been widely adopted for DCE-MRI analysis as a gold-standard approach for therapeutic response assessment. Previously, a shutter-speed (SS) model was proposed to incorporate transcytolemmal water exchange effect into contrast agent concentration quantification. In spite of richer biological assumption, its application in therapeutic response assessment is limited. It might be intriguing to combine the information from the SS model and from the classic Tofts model to explore potential new biological information for treatment assessment. The feasibility of this idea was investigated in the same small animal experiment. The SS model was compared against the Tofts model for therapeutic response assessment using PK parameter regional mean value comparison. Based on the modeled transcytolemmal water exchange rate, a biological subvolume was proposed and was automatically identified using histogram analysis. Within the biological subvolume, the PK rate constant derived from the SS model were proved to be superior to the one from Tofts model in treatment/control separation and classification. Furthermore, novel biomarkers were designed to integrate PK rate constants from these two models. When being evaluated in the biological subvolume, this biomarker was able to reflect significant treatment/control difference in both post-treatment evaluation. These results confirm the potential value of SS model as well as its combination with Tofts model for therapeutic response assessment.

In summary, this study addressed two problems of DCE-MRI application in radiotherapy assessment. In the first part, a method of accelerating DCE-MRI acquisition for better temporal resolution was investigated, and a novel PK model fitting algorithm was proposed for high temporal resolution DCE-MRI. In the second part, two model-free texture analysis methods and a multiple-model analysis method were developed for DCE-MRI therapeutic response assessment. The presented works could benefit the future DCE-MRI routine clinical application in radiotherapy assessment.

Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function.

Based on Pulay's direct inversion iterative subspace (DIIS) approach, we present a method to accelerate self-consistent field (SCF) convergence. In this method, the quadratic augmented Roothaan-Hall (ARH) energy function, proposed recently by Høst and co-workers [J. Chem. Phys. 129, 124106 (2008)], is used as the object of minimization for obtaining the linear coefficients of Fock matrices within DIIS. This differs from the traditional DIIS of Pulay, which uses an object function derived from the commutator of the density and Fock matrices. Our results show that the present algorithm, abbreviated ADIIS, is more robust and efficient than the energy-DIIS (EDIIS) approach. In particular, several examples demonstrate that the combination of ADIIS and DIIS ("ADIIS+DIIS") is highly reliable and efficient in accelerating SCF convergence.

Performance metrics of an optical spectral imaging system for intra-operative assessment of breast tumor margins.

As many as 20-70% of patients undergoing breast conserving surgery require repeat surgeries due to a close or positive surgical margin diagnosed post-operatively [1]. Currently there are no widely accepted tools for intra-operative margin assessment which is a significant unmet clinical need. Our group has developed a first-generation optical visible spectral imaging platform to image the molecular composition of breast tumor margins and has tested it clinically in 48 patients in a previously published study [2]. The goal of this paper is to report on the performance metrics of the system and compare it to clinical criteria for intra-operative tumor margin assessment. The system was found to have an average signal to noise ratio (SNR) >100 and <15% error in the extraction of optical properties indicating that there is sufficient SNR to leverage the differences in optical properties between negative and close/positive margins. The probe had a sensing depth of 0.5-2.2 mm over the wavelength range of 450-600 nm which is consistent with the pathologic criterion for clear margins of 0-2 mm. There was <1% cross-talk between adjacent channels of the multi-channel probe which shows that multiple sites can be measured simultaneously with negligible cross-talk between adjacent sites. Lastly, the system and measurement procedure were found to be reproducible when evaluated with repeated measures, with a low coefficient of variation (<0.11). The only aspect of the system not optimized for intra-operative use was the imaging time. The manuscript includes a discussion of how the speed of the system can be improved to work within the time constraints of an intra-operative setting.

A low-cost, portable, and quantitative spectral imaging system for application to biological tissues.

The ability of diffuse reflectance spectroscopy to extract quantitative biological composition of tissues has been used to discern tissue types in both pre-clinical and clinical cancer studies. Typically, diffuse reflectance spectroscopy systems are designed for single-point measurements. Clinically, an imaging system would provide valuable spatial information on tissue composition. While it is feasible to build a multiplexed fiber-optic probe based spectral imaging system, these systems suffer from drawbacks with respect to cost and size. To address these we developed a compact and low cost system using a broadband light source with an 8-slot filter wheel for illumination and silicon photodiodes for detection. The spectral imaging system was tested on a set of tissue mimicking liquid phantoms which yielded an optical property extraction accuracy of 6.40 +/- 7.78% for the absorption coefficient (micro(a)) and 11.37 +/- 19.62% for the wavelength-averaged reduced scattering coefficient (micro(s)').

Generalized sampling using a compound-eye imaging system for multi-dimensional object acquisition.

In this paper, we propose generalized sampling approaches for measuring a multi-dimensional object using a compact compound-eye imaging system called thin observation module by bound optics (TOMBO). This paper shows the proposed system model, physical examples, and simulations to verify TOMBO imaging using generalized sampling. In the system, an object is modulated and multiplied by a weight distribution with physical coding, and the coded optical signal is integrated on to a detector array. A numerical estimation algorithm employing a sparsity constraint is used for object reconstruction.

Rapid ratiometric determination of hemoglobin concentration using UV-VIS diffuse reflectance at isosbestic wavelengths.

We developed a ratiometric method capable of estimating total hemoglobin concentration from optically measured diffuse reflectance spectra. The three isosbestic wavelength ratio pairs that best correlated to total hemoglobin concentration independent of saturation and scattering were 545/390, 452/390, and 529/390 nm. These wavelength pairs were selected using forward Monte Carlo simulations which were used to extract hemoglobin concentration from experimental phantom measurements. Linear regression coefficients from the simulated data were directly applied to the phantom data, by calibrating for instrument throughput using a single phantom. Phantoms with variable scattering and hemoglobin saturation were tested with two different instruments, and the average percent errors between the expected and ratiometrically-extracted hemoglobin concentration were as low as 6.3%. A correlation of r = 0.88 between hemoglobin concentration extracted using the 529/390 nm isosbestic ratio and a scalable inverse Monte Carlo model was achieved for in vivo dysplastic cervical measurements (hemoglobin concentrations have been shown to be diagnostic for the detection of cervical pre-cancer by our group). These results indicate that use of such a simple ratiometric method has the potential to be used in clinical applications where tissue hemoglobin concentrations need to be rapidly quantified in vivo.

Robust test method for time-course microarray experiments.

BACKGROUND: In a time-course microarray experiment, the expression level for each gene is observed across a number of time-points in order to characterize the temporal trajectories of the gene-expression profiles. For many of these experiments, the scientific aim is the identification of genes for which the trajectories depend on an experimental or phenotypic factor. There is an extensive recent body of literature on statistical methodology for addressing this analytical problem. Most of the existing methods are based on estimating the time-course trajectories using parametric or non-parametric mean regression methods. The sensitivity of these regression methods to outliers, an issue that is well documented in the statistical literature, should be of concern when analyzing microarray data. RESULTS: In this paper, we propose a robust testing method for identifying genes whose expression time profiles depend on a factor. Furthermore, we propose a multiple testing procedure to adjust for multiplicity. CONCLUSIONS: Through an extensive simulation study, we will illustrate the performance of our method. Finally, we will report the results from applying our method to a case study and discussing potential extensions.

Modeling the evolution of regulatory elements by simultaneous detection and alignment with phylogenetic pair HMMs.

The computational detection of regulatory elements in DNA is a difficult but important problem impacting our progress in understanding the complex nature of eukaryotic gene regulation. Attempts to utilize cross-species conservation for this task have been hampered both by evolutionary changes of functional sites and poor performance of general-purpose alignment programs when applied to non-coding sequence. We describe a new and flexible framework for modeling binding site evolution in multiple related genomes, based on phylogenetic pair hidden Markov models which explicitly model the gain and loss of binding sites along a phylogeny. We demonstrate the value of this framework for both the alignment of regulatory regions and the inference of precise binding-site locations within those regions. As the underlying formalism is a stochastic, generative model, it can also be used to simulate the evolution of regulatory elements. Our implementation is scalable in terms of numbers of species and sequence lengths and can produce alignments and binding-site predictions with accuracy rivaling or exceeding current systems that specialize in only alignment or only binding-site prediction. We demonstrate the validity and power of various model components on extensive simulations of realistic sequence data and apply a specific model to study Drosophila enhancers in as many as ten related genomes and in the presence of gain and loss of binding sites. Different models and modeling assumptions can be easily specified, thus providing an invaluable tool for the exploration of biological hypotheses that can drive improvements in our understanding of the mechanisms and evolution of gene regulation.