Before revision:  Surprisingly, time-integration with multiple receptor types is qualitatively different from gradient sensing by a single receptor type - it is possible for cells to extract orders of magnitude more information out of a signal by using a maximum likelihood estimate than naive time integration  .
After revision:  Surprisingly, time-integration with multiple receptor types is qualitatively different from gradient sensing by a single receptor type - it is possible for cells to extract orders of magnitude more information out of a signal by using a maximum likelihood estimate than naive time integration . Our results show when cells should express multiple receptor types to chemotax, and how cells can efficiently interpret the data from these receptors .