Learning in Transcriptional Network Models: Computational Discovery of Pathway-Level Memory and Effective Interventions

If neither of the memories are found within the combination of [UCS, NS, R], we call the case as no memory [78]. We consider all Pn3 combinations for memory evaluation and calculate percentage of each individual memory (also no memory NM) described above.

For the detection of serial memories, we considered all 35 biological and 35 random models. Each random model has the same network size (number of nodes) as the corresponding (i-th) biological model. For testing, we used all existing UCS and AM memories of a network obtained through the memory evaluation process previously found and tested all possible combinations of paired memories for this evaluation, i.e., UM–UM, UM–AM, AM–UM, and AM–AM. For evaluation of the second memory after the first memory had been established, we considered the last state of all genes (numeric values) of the evaluation of first memory as the starting state of second memory evaluation. We then followed the previously described memory evaluation procedure for each type of memory evaluation for the biological and random models. We evaluated the portions having both memories retained, either memory over-written or catastrophic forgetting in each network (see Figure 6 and Figure 7).

For the detection of parallel memories, we considered all 35 biological and 35 random models. Each random model has the same network size (number of nodes) as the corresponding (i-th) biological model. We tested all existing combination of paired UM–UM, UM–AM and AM–AM in a network that had been previously found, as above. We then tested both memories in parallel, i.e., we started the evaluation with the initial state of all genes provided in the model definition (as in the memory evaluation procedure). To evaluate the UCS for the pair, we trained with both UCS1 (UCS of the first memory) and UCS2 (UCS of the second memory) and tested if the memory response, R, was present (R of both first and second memory). Similarly, to evaluate the AM in a pair of memories, we trained with UCS1-NS1 and UCS2-NS2 and checked if one or both NS had turned into CS. We evaluated the fraction having both memories retained, either memory over-written, or catastrophic forgetting in each network side by side for biological vs. random models (see Figure 5 and Figure 6).

Repeated use of a drug can make it less and less effective for pharmacological use. This phenomenon is known as pharmacoresistance [111,162,163,164]. Here, we use pharmacoresistance when repeated (back-to-back) onset of a stimulus, UCS, causes gradual decrement of R. For this experiment, we prepared a setup where we stimulated the UCS 6 times each followed by a relaxation period. Stimulation periods were incremental in nature and started with 5000 steps and proceeded to 10,000 steps incrementing 1000 in each stimulation period. Length of a relaxation period was also incremental and equal in length with following stimulation period. For the stimulation and relaxation, we exercised the same procedure described in memory evaluation. We expected that at each stimulation period, the mean expression level of R would go down by the ratio 11.5 as compared to the mean expression of R at the previous stimulation period. If the same trend continued over all 6 stimulations, we classified it as pharmacoresistance between a UCS–R combination. We examined each UCS with up- or down-stimulation and tested the effect on each R, as in memory.

For breaking the pharmacoresistance already established through repeated stimulation of UCS, we tested stimulation of every other node in the model (except UCS and R). For this, we applied this breaking stimulation for a maximum of 3 trials to determine if the resistance was broken. In the first trial, we considered a new stimuli ST1, we stimulated for 10,000 steps and relaxed for 10,000 steps. Next, we tested if the pharmacoresistance had gone. For this, we used 2 stimulations of UCS for 10,000 steps, each followed by a relaxation of 10,000 steps. If the average expression of R over the second stimulation went down compared to that over the first stimulation by the ratio 11.5 or below, we considered it as a breaking of pharmacoresistance. Otherwise, we proceeded for the second trial. If this breaking still did not occur, we repeated the third trial where we performed training using a new stimuli ST2. If testing failed this time to break pharmacoresistance, we classified the habituation as permanent.

Multiple exposures of a drug/external protein can cause the target response to grow stronger and stronger over time. This phenomenon is known as sensitization [115,119,165]. In our study, if repeated onset of a stimulus caused gradual increment of R, we classified it as sensitization. Like pharmacoresistance, we used 6 instances of UCS stimulation and relaxation, with incrementally increasing periods. If the average expression of R in (i+1)th stimulation period of UCS was 1.5 times or higher than the average value of R over ith stimulation period of UCS and this trend held for all 6 stimulation periods of UCS, we considered there was the creation of sensitization in R.

Similar to the 3 trials we used to break pharmacoresistance, here also we used 3 trials to break the sensitization of R. In trial 1, we used 2 stimulations with a new stimuli ST1 of 10,000 time steps (each followed by a relaxation period of 10,000 steps). Next, we conducted a testing phase by stimulating UCS twice for 10,000 time steps (with intermediate relaxations) and checked R to see if the average expression of it over a UCS stimulation did not exceed 1.5 times of its average over previous stimulation of UCS. If the condition satisfied, we considered that as a breaking of sensitization of R. If the first trial failed, we used 2 similar trials where training phase was conducted by stimulating new stimuli ST1 and ST2, respectively. If these two trials failed as well, we called the sensitization as permanent. It is to be noted that (1) ST1 and ST2 are among the nodes of the model excepting UCS and R, and (2) we examined all such nodes (for a specific UCS-R combination) in their up/down stimulation to see breaking effects of sensitization in R.

We would like to thank Mayalen Etcheverry for internal review and discussion. We thank Juanita Mathews, Franz Kuchling, and Devon Davidian for feedback on visualization.

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/ijms24010285/s1.

Conceptualization, M.L., S.B. and W.C.; Methodology, S.B. and W.C.; Software, S.B.; Validation, S.B. and W.C.; Formal Analysis, S.B.; Investigation, S.B. and W.C.; Data Curation, S.B.; Writing—Original Draft Preparation, S.B.; Writing—Review and Editing, S.B., W.C. and M.L.; Visualization, S.B. and W.C.; Supervision, M.L.; Project Administration, M.L.; Funding Acquisition, M.L. All authors have read and agreed to the published version of the manuscript.

Code can be found on: https://github.com/wesleypclawson/GRN_ODE. Data available on request.

We gratefully acknowledge support via TWCF grant TWCF0606, via a sponsored research agreement to Tufts University from Astonishing Labs, and via the Air Force Office of Scientific Research under award number FA9550-22-1-0465, Cognitive & Computational Neuroscience program.

Code can be found on: https://github.com/wesleypclawson/GRN_ODE. Data available on request.