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Recently, dynamic metasurface antennas (DMAs) have emerged as a promising technology for implementing large antenna arrays with reduced hardware cost and power consumption. In this work, we study the joint transmitter and receiver design for DMA-based uplink multi-user MIMO systems. We formulate the achievable sum-rate maximization problem for the considered system. Then we translate the original problem into quadratic form applying the matrix fractional programming and eliminate the structure constraints imposed by the DMA weight matrix for tractability. Accordingly, we propose to solve the equivalent problem in an alternating manner, in which each subproblem can be tackled via well-developed solvers. Numerical results demonstrate the convergence of our proposed technique and that the proposed technique outperforms the baseline.