RNA Graph Partitioning for the Discovery of RNA Modularity: A Novel Application of Graph Partition Algorithm to Biology

Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG) framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2) corresponding to the second eigenvalues (λ2) associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2′s components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2′s components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼220 nucleotides). While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs also suggest design strategies for novel RNA motifs.     

Fast Generation of Sparse Random Kernel Graphs

The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most 𝒪(n(logn)²). As a practical example we show how to generate samples of power-law degree distribution graphs with tunable assortativity.     

CellGeo: A computational platform for the analysis of shape changes in cells with complex geometries

Cell biologists increasingly rely on computer-aided image analysis, allowing them to collect precise, unbiased quantitative results. However, despite great progress in image processing and computer vision, current computational approaches fail to address many key aspects of cell behavior, including the cell protrusions that guide cell migration and drive morphogenesis. We developed the open source MATLAB application CellGeo, a user-friendly computational platform to allow simultaneous, automated tracking and analysis of dynamic changes in cell shape, including protrusions ranging from filopodia to lamellipodia. Our method maps an arbitrary cell shape onto a tree graph that, unlike traditional skeletonization algorithms, preserves complex boundary features. CellGeo allows rigorous but flexible definition and accurate automated detection and tracking of geometric features of interest. We demonstrate CellGeo’s utility by deriving new insights into (a) the roles of Diaphanous, Enabled, and Capping protein in regulating filopodia and lamellipodia dynamics in Drosophila melanogaster cells and (b) the dynamic properties of growth cones in catecholaminergic a–differentiated neuroblastoma cells.     

Using Random Walks to Generate Associations between Objects

Measuring similarities between objects based on their attributes has been an important problem in many disciplines. Object-attribute associations can be depicted as links on a bipartite graph. A similarity measure can be thought as a unipartite projection of this bipartite graph. The most widely used bipartite projection techniques make assumptions that are not often fulfilled in real life systems, or have the focus on the bipartite connections more than on the unipartite connections. Here, we define a new similarity measure that utilizes a practical procedure to extract unipartite graphs without making a priori assumptions about underlying distributions. Our similarity measure captures the relatedness between two objects via the likelihood of a random walker passing through these nodes sequentially on the bipartite graph. An important aspect of the method is that it is robust to heterogeneous bipartite structures and it controls for the transitivity similarity, avoiding the creation of unrealistic homogeneous degree distributions in the resulting unipartite graphs. We test this method using real world examples and compare the obtained results with alternative similarity measures, by validating the actual and orthogonal relations between the entities.     

Structure and Growth of the Leeward Kohala Field System: An Analysis with Directed Graphs

This study illustrates how the theory of directed graphs can be used to investigate the structure and growth of the leeward Kohala field system, a traditional Hawaiian archaeological site that presents an unparalleled opportunity to investigate relative chronology. The relative chronological relationships of agricultural walls and trails in two detailed study areas are represented as directed graphs and then investigated using graph theoretic concepts including cycle, level, and connectedness. The structural properties of the directed graphs reveal structure in the field system at several spatial scales. A process of deduction yields a history of construction in each detailed study area that is different than the history produced by an earlier investigation. These results indicate that it is now possible to study the structure and growth of the entire field system remnant using computer software implementations of graph theoretic concepts applied to observations of agricultural wall and trail intersections made on aerial imagery and/or during fieldwork. A relative chronology of field system development with a resolution of one generation is a possible result.     

Discovery of Influenza A Virus Sequence Pairs and Their Combinations for Simultaneous Heterosubtypic Targeting that Hedge against Antiviral Resistance

The multiple circulating human influenza A virus subtypes coupled with the perpetual genomic mutations and segment reassortment events challenge the development of effective therapeutics. The capacity to drug most RNAs motivates the investigation on viral RNA targets. 123,060 segment sequences from 35,938 strains of the most prevalent subtypes also infecting humans–H1N1, 2009 pandemic H1N1, H3N2, H5N1 and H7N9, were used to identify 1,183 conserved RNA target sequences (≥15-mer) in the internal segments. 100% theoretical coverage in simultaneous heterosubtypic targeting is achieved by pairing specific sequences from the same segment (“Duals”) or from two segments (“Doubles”); 1,662 Duals and 28,463 Doubles identified. By combining specific Duals and/or Doubles to form a target graph wherein an edge connecting two vertices (target sequences) represents a Dual or Double, it is possible to hedge against antiviral resistance besides maintaining 100% heterosubtypic coverage. To evaluate the hedging potential, we define the hedge-factor as the minimum number of resistant target sequences that will render the graph to become resistant i.e. eliminate all the edges therein; a target sequence or a graph is considered resistant when it cannot achieve 100% heterosubtypic coverage. In an n-vertices graph (n ≥ 3), the hedge-factor is maximal (= n– 1) when it is a complete graph i.e. every distinct pair in a graph is either a Dual or Double. Computational analyses uncover an extensive number of complete graphs of different sizes. Monte Carlo simulations show that the mutation counts and time elapsed for a target graph to become resistant increase with the hedge-factor. Incidentally, target sequences which were reported to reduce virus titre in experiments are included in our target graphs. The identity of target sequence pairs for heterosubtypic targeting and their combinations for hedging antiviral resistance are useful toolkits to construct target graphs for different therapeutic objectives.     

Automated Cell Tracking and Analysis in Phase-Contrast Videos (iTrack4U): Development of Java Software Based on Combined Mean-Shift Processes

Cell migration is a key biological process with a role in both physiological and pathological conditions. Locomotion of cells during embryonic development is essential for their correct positioning in the organism; immune cells have to migrate and circulate in response to injury. Failure of cells to migrate or an inappropriate acquisition of migratory capacities can result in severe defects such as altered pigmentation, skull and limb abnormalities during development, and defective wound repair, immunosuppression or tumor dissemination. The ability to accurately analyze and quantify cell migration is important for our understanding of development, homeostasis and disease. In vitro cell tracking experiments, using primary or established cell cultures, are often used to study migration as cells can quickly and easily be genetically or chemically manipulated. Images of the cells are acquired at regular time intervals over several hours using microscopes equipped with CCD camera. The locations (x,y,t) of each cell on the recorded sequence of frames then need to be tracked. Manual computer-assisted tracking is the traditional method for analyzing the migratory behavior of cells. However, this processing is extremely tedious and time-consuming. Most existing tracking algorithms require experience in programming languages that are unfamiliar to most biologists. We therefore developed an automated cell tracking program, written in Java, which uses a mean-shift algorithm and ImageJ as a library. iTrack4U is a user-friendly software. Compared to manual tracking, it saves considerable amount of time to generate and analyze the variables characterizing cell migration, since they are automatically computed with iTrack4U. Another major interest of iTrack4U is the standardization and the lack of inter-experimenter differences. Finally, iTrack4U is adapted for phase contrast and fluorescent cells.     

A heuristic graph comparison algorithm and its application to detect functionally related enzyme clusters

The availability of computerized knowledge on biochemical pathways in the KEGG database opens new opportunities for developing computational methods to characterize and understand higher level functions of complete genomes. Our approach is based on the concept of graphs; for example, the genome is a graph with genes as nodes and the pathway is another graph with gene products as nodes. We have developed a simple method for graph comparison to identify local similarities, termed correlated clusters, between two graphs, which allows gaps and mismatches of nodes and edges and is especially suitable for detecting biological features. The method was applied to a comparison of the complete genomes of 10 microorganisms and the KEGG metabolic pathways, which revealed, not surprisingly, a tendency for formation of correlated clusters called FRECs (functionally related enzyme clusters). However, this tendency varied considerably depending on the organism. The relative number of enzymes in FRECs was close to 50% for Bacillus subtilis and Escherichia coli, but was <10% for Synechocystis and Saccharomyces cerevisiae. The FRECs collection is reorganized into a collection of ortholog group tables in KEGG, which represents conserved pathway motifs with the information about gene clusters in all the completely sequenced genomes.     

Hamming-shifting graph of genomic short reads: Efficient construction and its application for compression

Graphs such as de Bruijn graphs and OLC (overlap-layout-consensus) graphs have been widely adopted for the de novo assembly of genomic short reads. This work studies another important problem in the field: how graphs can be used for high-performance compression of the large-scale sequencing data. We present a novel graph definition named Hamming-Shifting graph to address this problem. The definition originates from the technological characteristics of next-generation sequencing machines, aiming to link all pairs of distinct reads that have a small Hamming distance or a small shifting offset or both. We compute multiple lexicographically minimal k-mers to index the reads for an efficient search of the weight-lightest edges, and we prove a very high probability of successfully detecting these edges. The resulted graph creates a full mutual reference of the reads to cascade a code-minimized transfer of every child-read for an optimal compression. We conducted compression experiments on the minimum spanning forest of this extremely sparse graph, and achieved a 10 − 30% more file size reduction compared to the best compression results using existing algorithms. As future work, the separation and connectivity degrees of these giant graphs can be used as economical measurements or protocols for quick quality assessment of wet-lab machines, for sufficiency control of genomic library preparation, and for accurate de novo genome assembly.     

Lentiviral and targeted cellular barcoding reveals ongoing clonal dynamics of cell lines in vitro and in vivo

Background

Cell lines are often regarded as clonal, even though this simplifies what is known about mutagenesis, transformation and other processes that destabilize them over time. Monitoring these clonal dynamics is important for multiple areas of biomedical research, including stem cell and cancer biology. Tracking the contributions of individual cells to large populations, however, has been constrained by limitations in sensitivity and complexity.

Results

We utilize cellular barcoding methods to simultaneously track the clonal contributions of tens of thousands of cells. We demonstrate that even with optimal culturing conditions, common cell lines including HeLa, K562 and HEK-293 T exhibit ongoing clonal dynamics. Starting a population with a single clone diminishes but does not eradicate this phenomenon. Next, we compare lentiviral and zinc-finger nuclease barcode insertion approaches, finding that the zinc-finger nuclease protocol surprisingly results in reduced clonal diversity. We also document the expected reduction in clonal complexity when cells are challenged with genotoxic stress. Finally, we demonstrate that xenografts maintain clonal diversity to a greater extent than in vitro culturing of the human non-small-cell lung cancer cell line HCC827.

Conclusions

We demonstrate the feasibility of tracking and quantifying the clonal dynamics of entire cell populations within multiple cultured cell lines. Our results suggest that cell heterogeneity should be considered in the design and interpretation of in vitro culture experiments. Aside from clonal cell lines, we propose that cellular barcoding could prove valuable in modeling the clonal behavior of heterogeneous cell populations over time, including tumor populations treated with chemotherapeutic agents.     

Influence of FADS polymorphisms on tracking of serum glycerophospholipid fatty acid concentrations and percentage composition in children

Background

Tracking of fatty acid (FA) contribution to plasma or serum lipids over time was shown in children and adults. However, the potential role of FADS gene variants has not been investigated.

Methods and Principal Findings

Serum GP FA composition of 331 children aged 2 and 6 years, participating in an ongoing birth cohort study, was analyzed. Correlation coefficients were estimated to describe FA tracking over 4 years and to assess the influence of FADS variants on tracking. We found low to moderate tracking (r = 0.12–0.49) of FA compositions and concentration between 2 and 6 years. Concentration changes of total monounsaturated FA and total saturated FA over time correlated closely (r = 0.79) but percentage values were unrelated (r = −0.02). Tracking for n-6 long chain polyunsaturated fatty acid (LC-PUFA) concentrations was lower in subjects homozygous for the major allele of FADS variants and higher in carriers of at least one minor allele, whereas for total n-3 LC-PUFA concentrations and compositions this was vice versa. For individual n-3 PUFA inconsistent results were found.

Conclusions and Significance

Serum GP FA composition shows low to moderate tracking over 4 years with a higher tracking for LC-PUFA metabolites than for their precursor FA. Serum PUFA levels and their tracking seem to be more influenced by lipid and lipoprotein metabolism than by FA specific pathways.     

Efficient FPT Algorithms for (Strict) Compatibility of Unrooted Phylogenetic Trees

In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species X; these relationships are often depicted via a phylogenetic tree—a tree having its leaves labeled bijectively by elements of X and without degree-2 nodes—called the “species tree.” One common approach for reconstructing a species tree consists in first constructing several phylogenetic trees from primary data (e.g., DNA sequences originating from some species in X), and then constructing a single phylogenetic tree maximizing the “concordance” with the input trees. The obtained tree is our estimation of the species tree and, when the input trees are defined on overlapping—but not identical—sets of labels, is called “supertree.” In this paper, we focus on two problems that are central when combining phylogenetic trees into a supertree: the compatibility and the strict compatibility problems for unrooted phylogenetic trees. These problems are strongly related, respectively, to the notions of “containing as a minor” and “containing as a topological minor” in the graph community. Both problems are known to be fixed parameter tractable in the number of input trees k, by using their expressibility in monadic second-order logic and a reduction to graphs of bounded treewidth. Motivated by the fact that the dependency on k of these algorithms is prohibitively large, we give the first explicit dynamic programming algorithms for solving these problems, both running in time \(2^{O(k^2)} \cdot n\), where n is the total size of the input.     

Optimized Staining and Proliferation Modeling Methods for Cell Division Monitoring using Cell Tracking Dyes

Fluorescent cell tracking dyes, in combination with flow and image cytometry, are powerful tools with which to study the interactions and fates of different cell types in vitro and in vivo .^1-5 Although there are literally thousands of publications using such dyes, some of the most commonly encountered cell tracking applications include monitoring of:

1. stem and progenitor cell quiescence, proliferation and/or differentiation^6-8
2. antigen-driven membrane transfer⁹ and/or precursor cell proliferation^3,4,10-18 and
3. immune regulatory and effector cell function^1,18-21.

Commercially available cell tracking dyes vary widely in their chemistries and fluorescence properties but the great majority fall into one of two classes based on their mechanism of cell labeling. "Membrane dyes", typified by PKH26, are highly lipophilic dyes that partition stably but non-covalently into cell membranes^1,2,11. "Protein dyes", typified by CFSE, are amino-reactive dyes that form stable covalent bonds with cell proteins^4,16,18. Each class has its own advantages and limitations. The key to their successful use, particularly in multicolor studies where multiple dyes are used to track different cell types, is therefore to understand the critical issues enabling optimal use of each class^2-4,16,18,24.The protocols included here highlight three common causes of poor or variable results when using cell-tracking dyes. These are:

1. Failure to achieve bright, uniform, reproducible labeling . This is a necessary starting point for any cell tracking study but requires attention to different variables when using membrane dyes than when using protein dyes or equilibrium binding reagents such as antibodies.
2. Suboptimal fluorochrome combinations and/or failure to include critical compensation controls . Tracking dye fluorescence is typically 10² - 10³ times brighter than antibody fluorescence. It is therefore essential to verify that the presence of tracking dye does not compromise the ability to detect other probes being used.
3. Failure to obtain a good fit with peak modeling software . Such software allows quantitative comparison of proliferative responses across different populations or stimuli based on precursor frequency or other metrics. Obtaining a good fit, however, requires exclusion of dead/dying cells that can distort dye dilution profiles and matching of the assumptions underlying the model with characteristics of the observed dye dilution profile.

Examples given here illustrate how these variables can affect results when using membrane and/or protein dyes to monitor cell proliferation.     

Mathematical modeling of multiple pathways in colorectal carcinogenesis using dynamical systems with Kronecker structure

Like many other types of cancer, colorectal cancer (CRC) develops through multiple pathways of carcinogenesis. This is also true for colorectal carcinogenesis in Lynch syndrome (LS), the most common inherited CRC syndrome. However, a comprehensive understanding of the distribution of these pathways of carcinogenesis, which allows for tailored clinical treatment and even prevention, is still lacking. We suggest a linear dynamical system modeling the evolution of different pathways of colorectal carcinogenesis based on the involved driver mutations. The model consists of different components accounting for independent and dependent mutational processes. We define the driver gene mutation graphs and combine them using the Cartesian graph product. This leads to matrix components built by the Kronecker sum and product of the adjacency matrices of the gene mutation graphs enabling a thorough mathematical analysis and medical interpretation. Using the Kronecker structure, we developed a mathematical model which we applied exemplarily to the three pathways of colorectal carcinogenesis in LS. Beside a pathogenic germline variant in one of the DNA mismatch repair (MMR) genes, driver mutations in APC, CTNNB1, KRAS and TP53 are considered. We exemplarily incorporate mutational dependencies, such as increased point mutation rates after MMR deficiency, and based on recent experimental data, biallelic somatic CTNNB1 mutations as common drivers of LS-associated CRCs. With the model and parameter choice, we obtained simulation results that are in concordance with clinical observations. These include the evolution of MMR-deficient crypts as early precursors in LS carcinogenesis and the influence of variants in MMR genes thereon. The proportions of MMR-deficient and MMR-proficient APC-inactivated crypts as first measure for the distribution among the pathways in LS-associated colorectal carcinogenesis are compatible with clinical observations. The approach provides a modular framework for modeling multiple pathways of carcinogenesis yielding promising results in concordance with clinical observations in LS CRCs.     

Magnetic Resonance Detection of CD34+ Cells from Umbilical Cord Blood Using a 19F Label

Impaired homing and delayed recovery upon hematopoietic stem cell transplantation (HSCT) with hematopoietic stem cells (HSC) derived from umbilical cord blood (UCB) is a major problem. Tracking transplanted cells in vivo will be helpful to detect impaired homing at an early stage and allows early interventions to improve engraftment and outcome after transplantation. In this study, we show sufficient intracellular labeling of UCB-derived CD34⁺ cells, with ¹⁹F-containing PLGA nanoparticles which were detectable with both flow cytometry and magnetic resonance spectroscopy (MRS). In addition, labeled CD34⁺ cells maintain their capacity to proliferate and differentiate, which is pivotal for successful engraftment after transplantation in vivo. These results set the stage for in vivo tracking experiments, through which the homing efficiency of transplanted cells can be studied.     

Engineering cell alignment in vitro

Cell alignment plays a critical role in various cell behaviors including cytoskeleton reorganization, membrane protein relocation, nucleus gene expression, and ECM remodeling. Cell alignment is also known to exert significant effects on tissue regeneration (e.g., neuron) and modulate mechanical properties of tissues including skeleton, cardiac muscle and tendon. Therefore, it is essential to engineer cell alignment in vitro for biomechanics, cell biology, tissue engineering and regenerative medicine applications. With advances in nano- and micro-scale technologies, a variety of approaches have been developed to engineer cell alignment in vitro, including mechanical loading, topographical patterning, and surface chemical treatment. In this review, we first present alignments of various cell types and their functionality in different tissues in vivo including muscle and nerve tissues. Then, we provide an overview of recent approaches for engineering cell alignment in vitro. Finally, concluding remarks and perspectives are addressed for future improvement of engineering cell alignment.     

Algorithms for energy efficient mobile object tracking in wireless sensor networks

Wireless sensor networks have found more and more applications in a variety of pervasive computing environments, in their functions as data acquisition in pervasive applications. However, how to get better performance to support data acquisition of pervasive applications over WSNs remains to be a nontrivial and challenging task. The network lifetime and application requirement are two fundamental, yet conflicting, design objectives in wireless sensor networks for tracking mobile objects. The application requirement is often correlated to the delay time within which the application can send its sensing data back to the users in tracking networks. In this paper we study the network lifetime maximization problem and the delay time minimization problem together. To make both problems tractable, we have the assumption that each sensor node keeps working since it turns on. And we formulate the network lifetime maximization problem as maximizing the number of sensor nodes who don’t turn on, and the delay time minimization problem as minimizing the routing path length, after achieving the required tracking tasks. Since we prove the problems are NP-complete and APX-complete, we propose three heuristic algorithms to solve them. And we present several experiments to show the advantages and disadvantages referring to the network lifetime and the delay time among these three algorithms on three models, random graphs, grids and hypercubes. Furthermore, we implement the distributed version of these algorithms.     

Functional assessment of human dendritic cells labeled for in vivo 19F magnetic resonance imaging cell tracking

Background aimsDendritic cells (DC) are increasingly being used as cellular vaccines to treat cancer and infectious diseases. While there have been some promising results in early clinical trials using DC-based vaccines, the inability to visualize non-invasively the location, migration and fate of cells once adoptively transferred into patients is often cited as a limiting factor in the advancement of these therapies. A novel perflouropolyether (PFPE) tracer agent was used to label human DC ex vivo for the purpose of tracking the cells in vivo by ¹⁹F magnetic resonance imaging (MRI). We provide an assessment of this technology and examine its impact on the health and function of the DC.MethodsMonocyte-derived DC were labeled with PFPE and then assessed. Cell viability was determined by examining cell membrane integrity and mitochondrial lipid content. Immunostaining and flow cytometry were used to measure surface antigen expression of DC maturation markers. Functional tests included bioassays for interleukin (IL)-12p70 production, T-cell stimulatory function and chemotaxis. MRI efficacy was demonstrated by inoculation of PFPE-labeled human DC into NOD-SCID mice.ResultsDC were effectively labeled with PFPE without significant impact on cell viability, phenotype or function. The PFPE-labeled DC were clearly detected in vivo by ¹⁹F MRI, with mature DC being shown to migrate selectively towards draining lymph node regions within 18 h.ConclusionsThis study is the first application of PFPE cell labeling and MRI cell tracking using human immunotherapeutic cells. These techniques may have significant potential for tracking therapeutic cells in future clinical trials.     

Quantification of Three-Dimensional Cell-Mediated Collagen Remodeling Using Graph Theory

Background

Cell cooperation is a critical event during tissue development. We present the first precise metrics to quantify the interaction between mesenchymal stem cells (MSCs) and extra cellular matrix (ECM). In particular, we describe cooperative collagen alignment process with respect to the spatio-temporal organization and function of mesenchymal stem cells in three dimensions.

Methodology/Principal Findings

We defined two precise metrics: Collagen Alignment Index and Cell Dissatisfaction Level, for quantitatively tracking type I collagen and fibrillogenesis remodeling by mesenchymal stem cells over time. Computation of these metrics was based on graph theory and vector calculus. The cells and their three dimensional type I collagen microenvironment were modeled by three dimensional cell-graphs and collagen fiber organization was calculated from gradient vectors. With the enhancement of mesenchymal stem cell differentiation, acceleration through different phases was quantitatively demonstrated. The phases were clustered in a statistically significant manner based on collagen organization, with late phases of remodeling by untreated cells clustering strongly with early phases of remodeling by differentiating cells. The experiments were repeated three times to conclude that the metrics could successfully identify critical phases of collagen remodeling that were dependent upon cooperativity within the cell population.

Conclusions/Significance

Definition of early metrics that are able to predict long-term functionality by linking engineered tissue structure to function is an important step toward optimizing biomaterials for the purposes of regenerative medicine.     

Four-Dimensional Spatial Nanometry of Single Particles in Living Cells Using Polarized Quantum Rods

Single particle tracking is widely used to study protein movement with high spatiotemporal resolution both in vitro and in cells. Quantum dots, which are semiconductor nanoparticles, have recently been employed in single particle tracking because of their intense and stable fluorescence. Although single particles inside cells have been tracked in three spatial dimensions (X, Y, Z), measurement of the angular orientation of a molecule being tracked would significantly enhance our understanding of the molecule’s function. In this study, we synthesized highly polarized, rod-shaped quantum dots (Qrods) and developed a coating method that optimizes the Qrods for biological imaging. We describe a Qrod-based single particle tracking technique that blends optical nanometry with nanomaterial science to simultaneously measure the three-dimensional and angular movements of molecules. Using Qrods, we spatially tracked a membrane receptor in living cells in four dimensions with precision close to the single-digit range in nanometers and degrees.