The bulk of marine dissolved organic matter (DOM) forms a large, old, refractory carbon pool in the deep ocean, yet a small fraction in the surface ocean is actively involved in the global carbon cycle and may contribute significantly to the biological pump. We argue that present models of plankton and DOM in the surface ocean are incompatible with current knowledge of marine DOM dynamics. We present a plankton model with an adaptive formulation of bacteria-DOM interactions which is more consistent with observations. Our model reproduces net accumulation of DOM and is the first to reconcile the prevailing reports of net consumption of inorganic nitrogen by bacteria with commonly found DOC:DON ratios in the surface ocean. Our model predicts that factors governing DOM production by phytoplankton and zooplankton have little influence on DOM accumulation in the surface ocean. Long-term accumulation, eventual export of DOM, and hence its contribution to the biological pump appear to be primarily controlled by characteristics of bacterial DOM utilization. The model implies a negative relation between temperature and DOM accumulation, which can be obscured, however, by the impact of temperature on water-column stability. On longer time scales, this negative relation could indicate a positive feedback between temperature and CO2. DOM can accumulate independently of inorganic nutrient content of the surface ocean. Therefore, the predicted positive feedback is potentially very strong and could help explain the large variations in atmospheric CO2 between glacial and interglacial periods.