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They provide coding benefits including firing-rate stabilization, improved detectability of weak sensory signals, and enhanced transmission of information by improving signal-to-noise ratio. Primary electrosensory afferent spike-trains in weakly electric fish fall into two categories based on the pattern of ISI correlations: non-bursting units have negative correlations which remain negative but decay to zero with increasing lags (Type\u00a0I ISI correlations), and bursting units have oscillatory (alternating sign) correlation which damp to zero with increasing lags (Type II ISI correlations). Here, we predict and match observed ISI correlations in these afferents using a stochastic dynamic threshold model. We determine the ISI correlation function as a function of an arbitrary discrete noise correlation function\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$${{\\,\\mathrm{\\mathbf {R}}\\,}}_k$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mrow>\n                              <mml:mspace\/>\n                              <mml:mi>R<\/mml:mi>\n                              <mml:mspace\/>\n                            <\/mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , where\n                    <jats:italic>k<\/jats:italic>\n                    is a multiple of the mean ISI. The function permits forward and inverse calculations of the correlation function. Both types of correlation functions can be generated by adding colored noise to the spike threshold with Type\u00a0I correlations generated with slow noise and Type\u00a0II correlations generated with fast noise. A first-order autoregressive (AR) process with a single parameter is sufficient to predict and accurately match both types of afferent ISI correlation functions, with the type being determined by the sign of the AR parameter. The predicted and experimentally observed correlations are in geometric progression. The theory predicts that the limiting sum of ISI correlations is\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$-0.5$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mo>-<\/mml:mo>\n                            <mml:mn>0.5<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    yielding a perfect DC-block in the power spectrum of the spike train. Observed ISI correlations from afferents have a limiting sum that is slightly larger at\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$-0.475 \\pm 0.04$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mo>-<\/mml:mo>\n                            <mml:mn>0.475<\/mml:mn>\n                            <mml:mo>\u00b1<\/mml:mo>\n                            <mml:mn>0.04<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    (\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\text {mean} \\pm \\text {s.d.}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mtext>mean<\/mml:mtext>\n                            <mml:mo>\u00b1<\/mml:mo>\n                            <mml:mtext>s.d.<\/mml:mtext>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    ). We conclude that the underlying process for generating ISIs may be a simple combination of low-order AR and moving average processes and discuss the results from the perspective of optimal coding.\n                  <\/jats:p>","DOI":"10.1007\/s00422-022-00946-5","type":"journal-article","created":{"date-parts":[[2022,10,16]],"date-time":"2022-10-16T07:02:31Z","timestamp":1665903751000},"page":"611-633","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A dynamic spike threshold with correlated noise predicts observed patterns of negative interval correlations in neuronal spike trains"],"prefix":"10.1007","volume":"116","author":[{"given":"Robin S.","family":"Sidhu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erik C.","family":"Johnson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Douglas L.","family":"Jones","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9931-7846","authenticated-orcid":false,"given":"Rama","family":"Ratnam","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,16]]},"reference":[{"key":"946_CR1","first-page":"235","volume-title":"Information processing in the nervous system","author":"VE Amassian","year":"1964","unstructured":"Amassian VE, Macy J, Waller HJ, Leader HS, Swift M (1964) Transformations of afferent activity at the cuneate nucleus. 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