The Next Equation: How Zach Hendrix Is Redefining His Vision of Theoretical Physics

At Arizona State University, a young physicist is quietly building a reputation that could reshape how scientists interpret the microscopic world. Zach Hendrix, a Ph.D. student specializing in theory and statistical physics, has already drawn attention for achievements that most researchers spend entire careers chasing.

Recently awarded the Department of Physics' DEAN'S MEDAL, one of the university's highest academic honors, Hendrix is regarded by faculty and peers alike as one of ASU's most promising minds. His trajectory suggests not only potential but also the possibility of solving long-standing problems in biomedical imaging and statistical modeling.

Hendrix's path has been anything but ordinary. He began his academic journey in ASU's online undergraduate program, where his aptitude for abstract mathematics and theoretical modeling became immediately clear. Within a year, he was contributing to Professor Steve Pressé's lab work that would evolve into groundbreaking new tools for physics and biology.

Among those contributions: a NOVEL ALTERNATIVE TO THE RICHARDSON-LUCY DECONVOLUTION ALGORITHM, a mathematical approach used to sharpen blurry images, and a new method for PARTICLE TRACKING, a cornerstone of modern physics and biophysics research. Both hold promise for dramatically improving the accuracy and speed of biomedical imaging, where scientists often wrestle with faint signals and complex molecular movement.

But Hendrix's work is not confined to the blackboards of theory. As principal investigator on a pending $2 MILLION NATIONAL INSTITUTES OF HEALTH (NIH) GRANT, he is leading research into HIGH-SPEED IMAGING FOR BIOMEDICAL SCIENCE, an interdisciplinary project with the potential to accelerate medical diagnostics and cellular research. For a physicist whose passion began with abstract equations, the opportunity to make a direct impact on human health underscores the breadth of his vision.

"Zach is probably the strongest undergraduate I have had in my lab since arriving at ASU," says Professor Pressé. "In less than one year, he is making progress and will be the first author on two important manuscripts that I expect to exceed the typical entry-level publications in journals such as Physical Review E or the Journal of Chemical Physics."

Already, Hendrix is FIRST AUTHOR on two forthcoming manuscripts: one refining deconvolution techniques, the other probing the complex mathematics of ANOMALOUS DIFFUSION, which governs how particles move in irregular environments. Both fields sit at the cutting edge of physics, with applications ranging from understanding protein dynamics to advancing nanotechnology.

At his Tempe home, just a mile from the ASU campus, Hendrix welcomed us alongside his wife and their infant son, Heath. The setting reflects both the rigor of academia and the quiet rhythms of new family life.

Could you elaborate on why you believe motion models derived from processed tracking data are less reliable than those obtained directly from the original video or image data?

In widefield single-particle tracking (SPT), nearly all of the statistical information needed to decouple optical, fluorescence, and detection phenomena from the underlying molecular dynamics is found in raw images, not in post-processed trajectories. Such trajectories are extracted with prior assumptions and carry forward no information from photon statistics or detector physics. Thus, post-processed trajectories offer a lossy, biased summary of molecular motion. We demonstrated this empirically, showing that even accurately extracted trajectories of pure diffusion were misclassified as anomalous diffusion far more often than not. To wit, learning motion models and parameter values jointly from raw imaging data is the only way to circumvent compounding inferential biases from particle tracking, motion model classification, and the inference of dynamical parameters.

How do you distinguish between the "emission model" and the "motion model" in your study, and which do you find exerts a greater influence on the results?

Our emission model explains "how molecules are seen" by mapping latent positions during each exposure to pixel intensities, whereas our motion model informs us "how molecules should move" by specifying a transition law between recorded images. We discovered that physically realistic emission models are always more informative than motion models in single-molecule widefield fluorescence experiments. That is, optical, fluorescence, and measurement phenomena dominate the recovery of dynamical information in the signal-to-noise ratio (SNR) regime characteristic of single-molecule data. This conclusion is rather intuitive: how we imagine a single molecule matters at least as much as how it moves. At the conceptual limit, how could we measure unobservable motion?

In your view, how can measurement errors in particle position give rise to the false appearance of unusual particle motion when no such motion is occurring?

Localization errors perturb measured positions, which distorts displacement statistics. Motion model inference, which explicitly depends on displacement statistics, is therefore biased by such measurement errors. Even in ideal scenarios, where the signal greatly exceeds the noise, a molecule's exact position is still obscured by pixelation, finite photons, the breadth of the point spread function (PSF), finite exposure, etc. In turn, these errors bend MSD curves at short lags, mimicking anomalous subdiffusion or ATTM-like changes in diffusivity where none exist. On the other hand, if the measured intensity of signal and noise is similar in even one frame, it's easy to mistake a particle jumping to somewhere it's not; this could easily be misread as either a superdiffusive Lévy walk or a continuous time random walk (CTRW) featuring waiting-time statistics.

What were your key findings regarding tracking accuracy when an incorrect motion model was applied during analysis?

Even when tracking with the wrong motion model, you can properly recover every single position given an accurate emission model. In fact, we recovered 99.9% of true positions across all motion models within our 98% credible interval. That's because there's more information in how a particle is localized in each frame through the emission model than in how particle localizations are linked between frames via the motion model.

How did motion model detection tools, such as CONDOR and AnomDiffDB, perform in your tests when used with idealized datasets compared to data processed through tracking software?

Even against ground truth trajectories, classifications for pure diffusion were generally inaccurate and inconsistent across methods. Then, when supplied with corresponding inferred trajectories, apparent anomalous diffusion was recovered in 72% of pure diffusion trials. Worse yet, no method proved capable of learning motion models when given accurately inferred trajectories of anomalous diffusion; those results were internally inconsistent regardless of the underlying motion model. These results underscore how sensitive molecular trajectories are to static and dynamic localization errors.

Why do you think increasing the number of interpolated position estimates tends to amplify the influence of the motion model, and why do you believe this approach is generally avoided?

In general, interpolation can be as risky as extrapolation. And in particular here, interpolating positions between frames is essentially creating new information from prior assumptions; this extra information inflates the motion model's probability logarithm without necessarily reflecting the data-derived information. Hence, when assuming the wrong motion model, heavy interpolation can quickly become misguided guesswork. And to make matters worse, the computation time required for this extra work scales exponentially with the number of interpolated positions.

How do you interpret the finding that approximately 99% of the useful information in this type of tracking data comes from the emission model rather than the motion model?

The fact that nearly all of the statistical information is contributed by the emission model quantifies an identifiability asymmetry in diffraction-limited, finite-photon widefield SPT experiments: if positional measurements are primarily influenced by emission (i.e., optical, fluorescence, and detection) phenomena, then (1) assuming pure diffusion does not appreciably bias trajectory inference and (2) learning motion models from extracted trajectories is inherently information-starved.

In your opinion, how did the 2020 motion model competition overlook a critical step by failing to analyze the original raw video data?

Although the 2020 challenge aimed to lay the groundwork for analyzing anomalous diffusion, they overlooked modeling the very process by which molecular displacements are observed: all competitors started from information-starved trajectories rather than raw, highly informative imaging data. For modeling widefield SPT experiments, normally-distributed static localization noise doesn't cut it: this ad hoc imposition fails to account for pixel integration, motion blur, and detector-specific statistics that often dominate imaging in the single-molecule SNR regime.

What specific equipment settings and illumination levels did you choose for your experiments, and what factors guided those decisions?

In our experiments, we chose parameters based on extensive literature reviews from recent widefield single-molecule experiments. To demonstrate that our conclusions held for all real-world inputs, we performed extensive sensitivity and robustness tests by independently varying each statistical parameter. No matter how particles moved or how visible their movement was, the outcome was unchanged: the emission model was the principal driver in the recovery of molecular trajectories, irrespective of the underlying motion model.

What are the two most important recommendations you would offer for improving the reliability of motion model detection in future research?

The two most important factors in making motion model inference and classification reliable for the analysis of real-world data are (1) learning motion models from raw images rather than from inferred trajectories and (2) treating inferred dynamics cautiously in information-starved regimes that are characterized by short trajectories, low SNR, and detectors with poor spatiotemporal resolutions only detectors with exceptional temporal resolutions offer a chance to reliably recovering dynamical information. For Hendrix, the appeal lies in finding clarity within chaos. "Statistical physics gives us tools to take messy, complex data and extract hidden order and motion models," he explains. "That kind of problem-solving is what excites me most."

His ascent reflects more than personal talent; it signals a broader shift in science, where cross-disciplinary work is increasingly essential. Hendrix's ability to bridge mathematical rigor with real-world biomedical applications has already set him apart, and his recognition with ASU's Dean's Medal cements his status as a rising star.

As his research continues, Hendrix is poised to become one of the defining voices of his generation in theoretical physics. Whether his breakthroughs remain in the realm of equations or find their way into the clinic, one thing is clear: Zach Hendrix is a name the scientific community will be hearing for years to come.