Response to Reviewer e46j
We thank the reviewer for appreciating the novelty of our work and its extensive benchmark.
**Question 1 (Weakness):**
Experiments exclusively on the real protein dataset of AAV, hence the method may not readily translate to other proteins or protein datasets.
**Response:**
The choice of AAV dataset was mainly due to its wide mutational coverage (samples dispersed in the sequence space) which allows us to test the effectiveness of our approach. Most other experimental protein datasets do not have such wide coverage; this is because typically protein engineering seeks an optimum close to the starting point (wild type). However, there are protein engineering challenges in which the optimum is expected to lie far from the starting sequence, as explained in the paper, e.g., design of an enzyme for an unnatural target substrate.
We agree with the reviewer that the advantages of our method may not readily translate to the goals of other protein engineering tasks, e.g., when the designer can safely assume the existence of an optimum close to the starting sequence. We strongly believe that our method will open up the opportunity to address the more general but harder engineering problem where this assumption cannot be made. With our method in hand researchers will be more open to embarking on the harder problem, thus leading to more data sets of wide mutational coverage.
**Question 2**
How easily can PPGVAE be extended to prioritize or balance multiple properties simultaneously? Would this require a significant alteration to the existing framework?
**Response:**
Thanks for this important question/suggestion. There are two ways to approach this. The simpler approach will be to combine multiple properties into a single property with a proper transformation. A second possible approach may be through modified training of PPGVAE: assign a subset of dimensions in the latent space to each property and enforce the relationship loss for each subset of latent dimensions (property). This idea will require future implementation and testing.
**Question 3**
Could you provide insights into the sensitivity of the model's performance to changes in the temperature in the relationship loss?
**Response:**
To study the sensitivity of performance to temperature, we reran the GMM experiments in the lowest imbalance ratio and highest separation setting (the most challenging scenario), with varying temperature values. The results are included in Appendix E3. Based on this analysis, the performance is almost the same for $\log_{10}(\tau)\in [-1,1]$. Also, the sensitivity to temperature decreases as the number of MBO steps increases (see Figure A13).
In general, at very high temperature, even small differences in property values will be reflected in the ordering of samples in the latent space. On the other hand, at very low temperature all samples will have the same probability of generation and lie on the same sphere. As an added constraint to the reconstruction loss, both extremes damage a good reconstruction of samples and affect the quality and diversity of generated samples. Thus, it is important to set it to a reasonable value.
We should point out that we performed all the experiments in the paper with a fixed temperature, as mentioned in the paper. Further tuning of the temperature may improve the results, however we were able to show the usefulness of our approach without tailored tuning for each design scenario.