Chromatography is considered as a key operation in the downstream process (DSP) of biopharmaceuticals, including proteins. Therapeutic proteins such as monoclonal antibodies (mAbs) with high economic values in the global market require immediate innovation in the purification step to adapt to the increased throughput from upstream. Authorities have also initiated changes toward a more modernized pharmaceutical manufacturing platform which is agile and flexible without extensive oversight. Instead of the conventional batch operation and empirical models, the design and application of in silico modeling and simulation for integrated multi-column processes to improve their performance in capture chromatography steps have been explored in the dissertation. Due to the fact that mechanistic models can reveal adsorption and mass transfer behaviors better in the chromatography compared to statistical models, mechanistic frameworks were applied in the study. Ion-exchange and protein A chromatography, the main categories of therapeutic protein chromatography were examined. With an example of oligonucleotides, the mass transfer phenomenon of biomolecules in different types of ion-exchange resins was explored by mechanistic models. The results demonstrate the effectiveness of modeling approaches to understand the chromatography process of biopharmaceuticals. By focusing on the DSP of mAbs, multi-column continuous chromatography was examined with IgG samples. The study covered the repeating batch to 4-column settings in the continuous periodic counter-current (PCC) chromatography, with development in modeling and simulation tools for process quantification and evaluation. Process performances including productivity, capacity utilization, and buffer consumption were investigated by simulations with the aim to increase productivities and lower buffer consumptions, which are the main bottleneck in the current DSP. The critical operation parameter, breakthrough percent (BT%) for column switching in PCC processes, requires the information from binding capacity, mass transfer, and non-loading operations. To obtain the optimal BT% under synchronized conditions, numerical solvers developed from mechanistic models were employed. It was found that over 20% improvement in buffer consumption and resin utilization can be observed in PCC processes while the same productivity as batch operation is maintained. Furthermore, regressive relations were developed for predictions of process performances and BT% based on the findings from PCC simulations. With high coherence in R2 over 0.95, the linear regression function can act as an accelerated method in the PCC process design. Finally, a new strategy of linear flow-velocity gradient (LFG) in the loading step was explored as a supplement to increase process efficiency. The method controls the total column capacity and the loaded amount as functions of time. Based on the relationship between the dynamic binding capacity and residence time, the gradient time of LFG was obtained. The optimal flow velocities and time gradients were examined by scanning through the range of applicable residence times. A case study of the 4-column PCC process is presented. By integrating a linear decreasing flow gradient in the PCC loading operation, the productivity has 1.4 times enhancement along with a 13% reduction in the cost of resin per amount of processed mAbs compared to constant flows. Undoubtedly, the next generation of DSP platform technology is directed toward continuous and integrated systems. Regarding the advantages in process performances and regulation perspectives, continuous manufacturing can advance development and manufacturing while assuring the product quality. The evolution in modeling and simulation enables faster development of in silico process prediction and evaluation. With the support from models, process design and optimization in chromatography can rise to the challenge.