1. Concept: is the start of a track a binding event? From your plot: Each track appears suddenly at some time, then decays / fluctuates and disappears. The accumulated trace shows clear upward steps at those times. In typical kymograph / spot-tracking data: A track is created when the tracking algorithm first detects a fluorescent spot above background. That is usually when a fluorophore binds (or comes into focus / into the ROI). The end of a track is when the spot disappears, often due to bleaching or unbinding. So, conceptually: Yes, in many experiments the first time point of a track is a natural candidate for the binding time of that molecule. But there are a few caveats you might want to mention to Vero: Some molecules may already be bound before the camera started recording – in that case the first frame is not the true binding time, just the first time you see it. Detection thresholds may delay the detected “start” by a few frames. If two tracks overlap in time, the accumulated signal will have multiple steps, and the HMM sees “binding” whenever the sum intensity increases. That also explains your observations: Per-track HMM: each trace is relatively short and noisy → few clear transitions, so the HMM doesn’t detect many events. HMM on the accumulated signal: all tracks summed → big, clean steps when a new molecule appears → HMM picks up almost all track starts as binding events. So it’s very reasonable to treat track starts as a kind of “ground truth” binding time, at least for benchmarking.
2. Improved text you can send to Vero Here’s a cleaned-up version of what you wrote, phrased as a question: From the plots of the individual tracks and the accumulated photon counts (see attached figure), I have a conceptual question about how to define the binding time. In the track-intensity file, each track appears at some time point and then decays. Would you consider the first time point of each track to be the “binding time” of that molecule? To me this looks like a very natural definition, because the track starts exactly when the signal first appears. Note: – When I run the HMM on individual tracks, only very few binding events are detected. – When I run the HMM on the accumulated signal, I can detect almost all of the track starts as binding events. This makes me think that the track starting times might be a good gold standard for binding time points. Does this interpretation match your understanding of the experiment? If you want I can also help you write a follow-up mail where you propose to use “track start = binding” and “track end = bleaching/unbinding” as ground truth for validating your HMM.

Here is a concise bilingual summary of your text explaining the idea and a cleaned-up proposal to send to Vero:

English Summary

1. Concept: Is the start of a track a binding event?

• Each fluorescent track appears suddenly, fluctuates, then disappears; cumulative traces show clear stepwise increments.
• A track starts when a fluorophore binds or enters detection (fluorescent) focus, and ends due to bleaching or unbinding.
• Thus, the start of a track commonly represents the molecule’s binding time.
• Caveats:
  • Some molecules may be bound before recording starts, so first observed frame is not true binding time.
  • Detection thresholds may delay start detection.
  • Overlapping tracks cause summed signal steps, and HMM detects any increase as binding.
• Per-track HMM sees few transitions due to noise and short traces; summed HMM on total signal detects most binding events.

2. Cleaned-up question to Vero: “From individual and cumulative photon count plots (see attached), does the first time point of each track represent the molecule’s binding time?

• HMM on single tracks detects very few events;
• HMM on accumulated trace detects nearly all track starts as bindings;
• This suggests track start time is a good benchmark for binding. Does this match your understanding? I can help draft a follow-up email proposing to use ‘track start = binding’ and ‘track end = bleaching/unbinding’ as ground truth for HMM validation.”

中文总结

1. 概念解释：轨迹开始是否代表结合事件？

• 每条轨迹突然出现，随后衰减或波动后消失，累积轨迹中出现明显的阶梯式上升。
• 轨迹的开始通常是荧光标记分子结合或进入焦点检测区域的时刻，结束则因漂白或解离。
• 因此轨迹开始时间通常被视为该分子结合的时间点。
• 注意事项：
  • 某些分子可能在录像开始前已结合，首帧不是准确结合时间；
  • 检测阈值可能导致结合时间存在几十帧延迟；
  • 轨迹重叠造成信号累积，HMM会将信号上升视为结合事件。
• 针对单条轨迹的HMM因噪声和轨迹短小，事件检测少；对累积信号的HMM检测到几乎所有结合。

2. 整理后可以发给Vero的文本： “根据个别轨迹和累积光子计数图（见附件），我有个问题：是否可以将每条轨迹的首个时间点视为该分子的结合时刻？

• 针对单轨迹的HMM只检测到少量结合事件；
• 针对累积轨迹的HMM则几乎检测到所有轨迹期初的结合；
• 这可能说明轨迹起始时间是一个可靠的结合时间‘黄金标准’。 这种理解符合你的看法吗？我也可以帮你起草一封邮件，提议用“轨迹开始=结合”，“轨迹结束=漂白/解离”作为验证HMM的真实标准。”

^12345678