text: user15700: I am seeking statistical support for the following bacterial growth time series.
  In the lab, we have cell cultures growing in bioreactors. Every day we measure the concentration in mmol-1 of a set of metabolites and amino acids in the media with a cell culture analyser.
  Some metabolites are consumed by the cells and some are produced during the time-course of the culture. Along with this, we also count the number of cells every day to calculate the cell growth dynamics.
  We wish to assess the relationship between the consumption or production of any of these compounds and cell growth. For example, if the consumption of a specific metabolite from the media has a significant effect on increasing the cell count and would assist media formulation.
  One measurement per day is taken over four consecutive days from multiple bioreactors.
  What kind of analysis is would be appropriate?
  
  user3848: This is a machine learning application. Its clear cut. Whether you want to perform unsupervised learning is your call.
  Input data is for the cell growth, metabolite concentration time series would be:
  
  T1 ... T4 (cell growth) + T1 ... T4 (metabolite 1) etc ...
  
  The training target is:
  
  media type
  
  I would start with a simple naive Bayes model and see how it goes. If you obtain a high accuracy score you're in business, its worked. You would simply plot the result. The classification may not be linear in which case an alternative model is used.
  You can manually test it, by inputing the data of cell growth etc ... and seeing if it correctly predicts the media type.
  You then ask the ML algorithm which the metabolite/cell growth the 'media type' is influencing and it will tell you. Setting it up is complex I agree, but thats the gist and was the question.
  Just to finish, if you want to limit what a given media is in particular influencing, i.e. not loads of measurements but just a few inputs/variables, e.g. a metabolite at a particular time point and/or cell growth at a given time point, then ML delivers that information. Thats a key part of its strength. Thus you can then trial loads of different media - even stuff not trained - and just measure a small number of select inputs/variables rather than the entire kitchen sink - which is what the OP is doing right now.
  
  The overall input of ML into biological problems is a bit worrying in truth and tends to be over-represented in a select number of fields, protein modelling, and zero in everything else.
  
original_text: 15700: <p>I am seeking statistical support for the following bacterial growth time series.</p>
  <p>In the lab, we have cell cultures growing in bioreactors. Every day we measure the concentration in <em>m</em>mol<sup>-1</sup> of a set of metabolites and amino acids in the media with a cell culture analyser.</p>
  <p>Some metabolites are consumed by the cells and some are produced during the time-course of the culture. Along with this, we also count the number of cells every day to calculate the cell growth dynamics.</p>
  <p>We wish to assess the relationship between the consumption or production of any of these compounds and cell growth. For example, if the consumption of a specific metabolite from the media has a significant effect on increasing the cell count and would assist media formulation.</p>
  <p>One measurement per day is taken over four consecutive days from multiple bioreactors.</p>
  <p>What kind of analysis is would be appropriate?</p>
   3848: <p>This is a machine learning application. Its clear cut. Whether you want to perform unsupervised learning is your call.</p>
  <p>Input data is for the cell growth, metabolite concentration time series would be:</p>
  <blockquote>
  <p>T1 ... T4 (cell growth) + T1 ... T4 (metabolite 1) etc ...</p>
  </blockquote>
  <p>The training target is:</p>
  <blockquote>
  <p>media type</p>
  </blockquote>
  <p>I would start with a simple naive Bayes model and see how it goes. If you obtain a high accuracy score you're in business, its worked. You would simply plot the result. The classification may not be linear in which case an alternative model is used.</p>
  <p>You can manually test it, by inputing the data of cell growth etc ... and seeing if it correctly predicts the media type.</p>
  <p>You then ask the ML algorithm which the metabolite/cell growth the 'media type' is influencing and it will tell you. Setting it up is complex I agree, but thats the gist and was the question.</p>
  <p>Just to finish, if you want to limit what a given media is in particular influencing, i.e. not loads of measurements but just a few inputs/variables, e.g. a metabolite at a particular time point and/or cell growth at a given time point, then ML delivers that information. Thats a key part of its strength. Thus you can then trial loads of different media - even stuff not trained - and just measure a small number of select inputs/variables rather than the entire kitchen sink - which is what the OP is doing right now.</p>
  <hr />
  <p>The overall input of ML into biological problems is a bit worrying in truth and tends to be over-represented in a select number of fields, protein modelling, and zero in everything else.</p>
  