High fidelity epigenetic inheritance: Information theoretic model predicts k-threshold filling of histone modifications post replication

Beyond the genetic code, there is another layer of information encoded as chemical modifications on histone proteins positioned along the DNA. Maintaining these modifications is crucial for survival and identity of cells. How the information encoded in the histone marks gets inherited, given that only half the parental nucleosomes are transferred to each daughter chromatin, is a puzzle. Mapping DNA replication and reconstruction of modifications to equivalent problems in communication of information, we ask how well enzymes can recover the parental modifications, if they were ideal computing machines. Studying a parameter regime where realistic enzymes can function, our analysis predicts that, pragmatically, enzymes may implement a threshold-k filling algorithm which fills unmodified regions of length at most k. This algorithm, motivated from communication theory, is derived from the maximum a` posteriori probability (MAP) decoding which identifies the most probable modification sequence based on available observations. Simulations using our method pro- duce modification patterns similar to what has been observed in recent experiments. We also show that our results can be naturally extended to explain inheritance of spatially distinct antagonistic modifications.

Turbo Decoder Design based on an LUT-Normalized Log-MAP Algorithm

Turbo codes have been widely used in wireless communication systems due to their good error correction performance. Under time division long term evolution (TD-LTE) of the 3rd generation partnership project (3GPP) wireless communication standard, a Log maximum a posteriori (Log-MAP) decoding algorithm with high complexity is usually approximated as a lookup-table Log-MAP (LUT-Log-MAP) algorithm and Max-Log-MAP algorithm, but these two algorithms have high complexity and high bit error rate, respectively. In this paper, we propose a normalized Log-MAP (Nor-Log-MAP) decoding algorithm in which the function max* is approximated by using a fixed normalized factor multiplied by the max function. Combining a Nor-Log-MAP algorithm with a LUT-Log-MAP algorithm creates a new kind of LUT-Nor-Log-MAP algorithm. Compared with the LUT-Log-MAP algorithm, the decoding performance of the LUT-Nor-Log-MAP algorithm is close to that of the LUT-Log-MAP algorithm. Based on the decoding method of the Nor-Log-MAP algorithm, we also put forward a normalization functional unit (NFU) for a soft-input soft-output (SISO) decoder computing unit. The simulation results show that the LUT-Nor-Log-MAP algorithm can save about 2.1% of logic resources compared with the LUT-Log-MAP algorithm. Compared with the Max-Log-MAP algorithm, the LUT-Nor-Log-MAP algorithm shows a gain of 0.25~0.5 dB in decoding performance. Using the Cyclone IV platform, the designed Turbo decoder can achieve a throughput of 36 Mbit/s under a maximum clock frequency of 44 MHz.