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1. Elucidating the correlations between cancer initiation times and lifetime cancer risks

   https://doi.org/10.1038/s41598-019-55300-w  

   Teimouri, Hamid; Kochugaeva, Maria P.; Kolomeisky, Anatoly B. (December 2019, Scientific Reports)

   Abstract Cancer is a genetic disease that results from accumulation of unfavorable mutations. As soon as genetic and epigenetic modifications associated with these mutations become strong enough, the uncontrolled tumor cell growth is initiated, eventually spreading through healthy tissues. Clarifying the dynamics of cancer initiation is thus critically important for understanding the molecular mechanisms of tumorigenesis. Here we present a new theoretical method to evaluate the dynamic processes associated with the cancer initiation. It is based on a discrete-state stochastic description of the formation of tumors as a fixation of cancerous mutations in tissues. Using a first-passage analysis the probabilities for the cancer to appear and the times before it happens, which are viewed as fixation probabilities and fixation times, respectively, are explicitly calculated. It is predicted that the slowest cancer initiation dynamics is observed for neutral mutations, while it is fast for both advantageous and, surprisingly, disadvantageous mutations. The method is applied for estimating the cancer initiation times from experimentally available lifetime cancer risks for different types of cancer. It is found that the higher probability of the cancer to occur does not necessary lead to the faster times of starting the cancer. Our theoretical analysis helps to clarify microscopic aspects of cancer initiation processes. 

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2. Theoretical investigation of stochastic clearance of bacteria: first-passage analysis

   https://doi.org/http://dx.doi.org/10.1098/rsif.2018.0765  

   Teimouri, Hamid; Kolomeisky, Anatoly B (February 2019, Journal of the Royal Society interface)

   Understanding mechanisms of bacterial eradication is critically important for overcoming failures of antibiotic treatments. Current studies suggest that the clearance of large bacterial populations proceeds deterministically, while for smaller populations, the stochastic effects become more relevant. Here, we develop a theoretical approach to investigate the bacterial population dynamics under the effect of antibiotic drugs using a method of first-passage processes. It allows us to explicitly evaluate the most important characteristics of bacterial clearance dynamics such as extinction probabilities and extinction times. The new meaning of minimal inhibitory concentrations for stochastic clearance of bacterial populations is also discussed. In addition,we investigate the effect of fluctuations in population growth rates on the dynamics of bacterial eradication. It is found that extinction probabilities and extinction times generally do not correlate with each other when random fluctuations in the growth rates are taking place. Unexpectedly, for a significant range of parameters, the extinction times increase due to these fluctuations, indicating a slowing in the bacterial clearance dynamics. It is argued that this might be one of the initial steps in the pathway for the development of antibiotic resistance. Furthermore, it is suggested that extinction times is a convenient measure of bacterial tolerance. 

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3. The role of spatial structures of tissues in cancer initiation dynamics

   https://doi.org/10.1088/1478-3975/ac8515  

   Spaulding, Cade; Teimouri, Hamid; Kolomeisky, Anatoly B (August 2022, Physical Biology)

   Abstract It is widely believed that biological tissues evolved to lower the risks of cancer development. One of the specific ways to minimize the chances of tumor formation comes from proper spatial organization of tissues. However, the microscopic mechanisms of underlying processes remain not fully understood. We present a theoretical investigation on the role of spatial structures in cancer initiation dynamics. In our approach, the dynamics of single mutation fixations are analyzed using analytical calculations and computer simulations by mapping them to Moran processes on graphs with different connectivity that mimic various spatial structures. It is found that while the fixation probability is not affected by modifying the spatial structures of the tissues, the fixation times can change dramatically. The slowest dynamics is observed in ‘quasi-one-dimensional’ structures, while the fastest dynamics is observed in ‘quasi-three-dimensional’ structures. Theoretical calculations also suggest that there is a critical value of the degree of graph connectivity, which mimics the spatial dimension of the tissue structure, above which the spatial structure of the tissue has no effect on the mutation fixation dynamics. An effective discrete-state stochastic model of cancer initiation is utilized to explain our theoretical results and predictions. Our theoretical analysis clarifies some important aspects on the role of the tissue spatial structures in the cancer initiation processes. 

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4. Inferring Relational Potentials in Interacting Systems

   Comas, A.; Du, Y.; Fernandez Lopez, C.; Ghimire, S.; Sznaier, M.; Tenenbaum, J. B.; Camps, O. (January 2023, Proceedings of Machine Learning Research)

   Systems consisting of interacting agents are prevalent in the world, ranging from dynamical systems in physics to complex biological networks. To build systems which can interact robustly in the real world, it is thus important to be able to infer the precise interactions governing such systems. Existing approaches typically discover such interactions by explicitly modeling the feed-forward dynamics of the trajectories. In this work, we propose Neural Interaction Inference with Potentials (NIIP) as an alternative approach to discover such interactions that enables greater flexibility in trajectory modeling: it discovers a set of relational potentials, represented as energy functions, which when minimized reconstruct the original trajectory. NIIP assigns low energy to the subset of trajectories which respect the relational constraints observed. We illustrate that with these representations NIIP displays unique capabilities in test-time. First, it allows trajectory manipulation, such as interchanging interaction types across separately trained models, as well as trajectory forecasting. Additionally, it allows adding external hand-crafted potentials at test-time. Finally, NIIP enables the detection of out-of-distribution samples and anomalies without explicit training. 

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5. Inferring Relational Potentials in Interacting Systems

   Comas, A.; Du, Y.; Fernandez Lopez, C.; Ghimire, S.; Sznaier, M.; Tenenbaum, J.B.; Camps, O. (July 2023, Proceedings of Machine Learning Research)

   Systems consisting of interacting agents are prevalent in the world, ranging from dynamical systems in physics to complex biological networks. To build systems which can interact robustly in the real world, it is thus important to be able to infer the precise interactions governing such systems. Existing approaches typically dis- cover such interactions by explicitly modeling the feed-forward dynamics of the trajectories. In this work, we propose Neural Interaction Inference with Potentials (NIIP) as an alternative approach to discover such interactions that enables greater flexibility in trajectory modeling: it discovers a set of relational potentials, represented as energy functions, which when minimized reconstruct the original trajectory. NIIP assigns low energy to the subset of trajectories which respect the relational constraints observed. We illustrate that with these representations NIIP displays unique capabilities in test-time. First, it allows trajectory manipulation, such as interchanging interaction types across separately trained models, as well as trajectory forecasting. Additionally, it allows adding external hand-crafted potentials at test-time. Finally, NIIP enables the detection of out-of-distribution samples and anomalies without explicit training. 

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