A Novel Algorithm Makes Accurate Single-Molecule Tracking a Desktop Reality

By Eric Sauter

Members of the Scripps Research Institute's Cell Biology Department have developed a remarkable new computational methodology for single-particle tracking that manages to achieve comprehensive tracking while keeping the computational cost low, at the level of a regular desktop workstation. This new computer program may help bring modern medicine one step closer to understanding how minute and rare changes from one cell to the next work in disease.

The study was published as the cover story of the August issue of the journal Nature Methods.

The new method is a tracking algorithm that uses a single mathematical framework known as the linear assignment problem (LAP) to provide an accurate solution to the various challenges that currently plague most single-particle tracking algorithms.

"Our algorithm allows us to track a molecule with high resolution detail, even under complex conditions," said Khuloud Jaqaman, a postdoctoral fellow at Scripps Research and the lead author of the study. "It allows us to follow the dynamics and interactions of many proteins at the same time, even if they're in a very dense population or if they bump into each other--and still tell one from the other. The larger goal is to see how proteins move in the membrane and how they act in response to external stimuli."

A Robust Tool

With the development of highly sensitive video cameras and bright fluorescent probes, live cell imaging has become a standard technique to study sub-cellular dynamics. But to gain insight into the molecular mechanisms that drive these dynamics, such experiments have to be combined with computer vision tools such as single-particle tracking that capture the full complexity of subcellular particle behavior.

Single-particle tracking algorithms allow scientists to analyze the trajectories of single molecules over time, revealing molecular motion as well as interactions with other molecules and the cellular environment.

The challenges to accurate single particle tracking in cell biology are substantial--high particle density, temporary particle disappearance, or two particles merging for a brief time and then splitting apart. While some of these problems have been overcome, previously existing solutions still had many drawbacks. As a result, the amount of data collected has been low, often hindering the observation of infrequent events such as particle merging and splitting.

And it's those infrequent interactions between the particles that the team is after.

"It is these bumping or merging molecules--events that were often lost before--that are critical", explained Gaudenz Danuser, an associate professor of cell biology at Scripps Research and one of the senior authors of the study. "Under single particle imaging conditions molecular collisions are exceedingly rare, often as low as four in every thousand cases, but their occurrence is often the signature of a normal or aberrant function of the cell."

In the new study, the scientists demonstrated the power of the new algorithm by showing how dynamin, a GTPase that pinches off endocytic pits from the cell membrane, affects the lifetime of endocytic structures in the membrane; the scientists also showed how the motion of the receptor protein CD36 in the membrane increases the aggregation chances of CD36 molecules. CD36 has been implicated in a number of diseases ranging from malaria to atherosclerosis.

While these findings are important in and of themselves, the study emphasizes the methodology and the opportunities it presents for future research.

"Microscopy has brought us to the level of the single molecule in understanding the workings of life," said Gaudenz, who earned a Ph.D. in electrical engineering and computer science before becoming a cell biologist. "There are many groups improving the microscopy side of imaging, but what has been underestimated is the IT aspect of it. What do you do with all these millions of dots crawling over your screen? We came up with a new solution to this old and ever-more-pressing problem "

Down to the Desktop

The new algorithm closely mimics the theoretically most accurate form of single particle tracking, known as multiple hypothesis tracking (MHT). In MHT, all particle paths within the bounds of expected behavior are constructed throughout the entire movie, simultaneously considering all particle positions at all points of time. Then, the most likely configuration of mutually exclusive paths is selected--which demands an extraordinary amount of computing power. There is no super-computer that can solve this problem within useful time for the typical particle number found in a live cell movie.

The new algorithm uses a single mathematical framework, the LAP, developed for the solution of problems in operations research, to closely approximate the MHT solution and meet the various challenges of single particle tracking in cell biology. The goal of any LAP algorithm is to minimize the overall cost of assigning a number of tasks to be completed by a number of agents. One analogy is designing a routing scenario for X number of taxis picking up Y number of passengers that reduces the amount of fuel and time needed to take the passengers where they want to go.

LAP is applied first to link detected particles between consecutive frames, with the caveat of losing time-information for the sake of computational speed. Then, in a second step, LAP is used to generate particle tracks by constructing all possible paths starting with those initial track segments to simultaneously close gaps resulting from temporary particle disappearance and to capture particle merging and splitting events. Overall, this approach provides a configuration of mutually exclusive paths that is close to the theoretically most likely yet unknown configuration. This near-optimal performance allows the robust tracking of particles under high-density conditions.

It also brings the solution down from the lofty realm of high-end computing, which is available only to a few, and puts it within reach of the average laboratory desktop.

"Similar algorithms have been implemented for radar technology," Danuser said. "That's where they originated--tracking airplanes in the sky. In principle, we have taken the same algorithms and rewritten them so they can deal with the complexity of dense molecular movements."

Toward the Clinic

In addition to its importance for research scientists, the methodology has potential use in the clinic.

"We can use these software tools to open a window into the small changes between normal and diseased single cell behaviors," Danuser said. "We can also use this to understand the heterogeneity of diseased cell behaviors. From there, personalized medicine becomes a real possibility."

For example, the technology could lead to such possibilities as observing cancer cells from two patients--and predicting that a particular type of chemotherapy would work for one, and not for the other. Or identifying that one cancer cell that is about to break loose and travel to another part of the body.

"A single cell that metastasizes can be enough to kill you," he said. "When you have a biopsy and you want to find out which chemotherapeutic treatment prevents that one cancer cell in a million to crawl away, our methodology is the one that can deliver the image to investigate this question."

Other authors of the study, Robust Single Particle Tracking In Live Cell Time-Lapse Sequences , include Dinah Loerke, Marcel Mettlen, and Sandra L. Schmid of The Scripps Research Institute; and Hirotaka Kuwata and Sergio Grinstein of The Hospital for Sick Children, Toronto, Canada. See http://www.nature.com/nmeth/index.html.

The study was supported by the National Institutes of Health, the Heart and Stroke Foundation of Canada and the Canadian Institutes for Health Research and The Helen Hay Whitney Foundation and The Agouron Institute.

Send comments to: mikaono[at]scripps.edu

A new Scripps Research method enabled the tracking of single-particle trajectories of the macrophage transmembrane receptor protein CD36.