Quantitative Biology

2019 marked the 75th anniversary of the publication of Erwin Schrödinger's "What is Life?", a short book described by Roger Penrose in his preface to a reprint of this classic as "among the most influential scientific writings of the 20th century." In this article, I review the long argument made by Schrödinger as he mused on how the laws of physics could help us understand "the events in space and time which take place within the spatial boundary of a living organism." Though Schrödinger's book is often hailed for its influence on some of the titans who founded molecular biology, this article takes a different tack. Instead of exploring the way the book touched biologists such as James Watson and Francis Crick, as well as its critical reception by others such as Linus Pauling and Max Perutz, I argue that Schrödinger's classic is a timeless manifesto, rather than a dated historical curiosity. "What is Life?" is full of timely outlooks and approaches to understanding the mysterious living world that includes and surrounds us and can instead be viewed as a call to arms to tackle the great unanswered challenges in the study of living matter that remain for 21 st century science.

Introduction. Can the infection due to the human immunodeficiency virus type 1 induce a change in the differentiation status or process in T cells?. Methods. We will consider two stochastic Markov chain models, one which will describe the T-helper cell differentiation process, and another one describing that process of infection of the T-helper cell by the virus; in these Markov chains, we will consider a set of states { X t } comprised of those proteins involved in each of the processes and their interactions (either differentiation or infection of the cell), such that we will obtain two stochastic transition matrices ( A,B ), one for each process; afterwards, the computation of their eigenvalues shall be performed, in which, should the eigenvalue λ i =1 exist, the computation for the equilibrium distribution ? n will be obtained for each of the matrices, which will inform us on the trends of interactions amongst the proteins in the long-term. Results. The stochastic processes considered possess an equilibrium distribution, when reaching their equilibrium distribution, there exists an increase in their informational entropy, and their log-rank distributions can be modeled as discrete beta generalized distributions (DGBD). Discussion. The equilibrium distributions of both process can be regarded as states in which the cell is well-differentiated, ergo there exists an induction of a novel HIV-dependent differentiated state in the T-cell; these processes due to their DGBD distribution can be considered complex processes; due to the increasing entropy, the equilibrium states are stable ones. Conclusion. The HIV virus can promote a novel differentiated state in the T-cell, which can give account for clinical features seen in patients; this model, notwithstanding does not give account of YES/NO logical switches involved in the regulatory networks.

Human pluripotent stem cells (hPSCs) have promising clinical applications in regenerative medicine, drug-discovery and personalised medicine due to their potential to differentiate into all cell types, a property know as pluripotency. A deeper understanding of how pluripotency is regulated is required to assist in controlling pluripotency and differentiation trajectories experimentally. Mathematical modelling provides a non-invasive tool through which to explore, characterise and replicate the regulation of pluripotency and the consequences on cell fate. Here we use experimental data of the expression of the pluripotency transcription factor OCT4 in a growing hPSC colony to develop and evaluate mathematical models for temporal pluripotency regulation. We consider fractional Brownian motion and the stochastic logistic equation and explore the effects of both additive and multiplicative noise. We illustrate the use of time-dependent carrying capacities and the introduction of Allee effects to the stochastic logistic equation to describe cell differentiation. This mathematical framework for describing intra-cellular OCT4 regulation can be extended to other transcription factors and developed into sophisticated predictive models.

Graph neural networks (GNNs) have been proposed for a wide range of graph-related learning tasks. In particular, in recent years, an increasing number of GNN systems were applied to predict molecular properties. However, a direct impediment is to select appropriate hyperparameters to achieve satisfactory performance with lower computational cost. Meanwhile, many molecular datasets are far smaller than many other datasets in typical deep learning applications. Most hyperparameter optimization (HPO) methods have not been explored in terms of their efficiencies on such small datasets in the molecular domain. In this paper, we conducted a theoretical analysis of common and specific features for two state-of-the-art and popular algorithms for HPO: TPE and CMA-ES, and we compared them with random search (RS), which is used as a baseline. Experimental studies are carried out on several benchmarks in MoleculeNet, from different perspectives to investigate the impact of RS, TPE, and CMA-ES on HPO of GNNs for molecular property prediction. In our experiments, we concluded that RS, TPE, and CMA-ES have their individual advantages in tackling different specific molecular problems. Finally, we believe our work will motivate further research on GNN as applied to molecular machine learning problems in chemistry and materials sciences.

This paper looks into the modeling of hallucination in the human's brain. Hallucinations are known to be causally associated with some malfunctions within the interaction of different areas of the brain involved in perception. Focusing on visual hallucination and its underlying causes, we identify an adversarial mechanism between different parts of the brain which are responsible in the process of visual perception. We then show how the characterized adversarial interactions in the brain can be modeled by a generative adversarial network.

Our knowledge of how individual cells self-organize to form complex multicellular systems is being revolutionized by a data outburst, coming from high-throughput experimental breakthroughs such as single-cell RNA sequencing and spatially resolved single-molecule FISH. This information is starting to be leveraged by machine learning approaches that are helping us establish a census and timeline of cell types in developing organisms, shedding light on how biochemistry regulates cell-fate decisions. In parallel, imaging tools such as light-sheet microscopy are revealing how cells self-assemble in space and time as the organism forms, thereby elucidating the role of cell mechanics in development. Here we argue that mathematical modeling can bring together these two perspectives, by enabling us to test hypotheses about specific mechanisms, which can be further validated experimentally. We review the recent literature on this subject, focusing on representative examples that use modeling to better understand how single-cell behavior shapes multicellular organisms.

Medication adherence is a major problem for patients with chronic diseases that require long term pharmacotherapy. Many unanswered questions surround adherence, including how adherence rates translate into treatment efficacy and how missed doses of medication should be handled. To address these questions, we formulate and analyze a mathematical model of the drug level in a patient with imperfect adherence. We find exact formulas for drug level statistics, including the mean, the coefficient of variation, and the deviation from perfect adherence. We determine how adherence rates translate into drug levels, and how this depends on the drug half-life, the dosing interval, and how missed doses are handled. While clinical recommendations should depend on drug and patient specifics, as a general principle we find that nonadherence is best mitigated by taking double doses following missed doses if the drug has a long half-life. This conclusion contradicts some existing recommendations that cite long drug half-lives as the reason to avoid a double dose after a missed dose. Furthermore, we show that a patient who takes double doses after missed doses can have at most only slightly more drug in their body than a perfectly adherent patient if the drug half-life is long. We also investigate other ways of handling missed doses, including taking an extra fractional dose following a missed dose. We discuss our results in the context of hypothyroid patients taking levothyroxine.

We introduce a novel data-driven framework for the design of targeted gene panels for estimating exome-wide biomarkers in cancer immunotherapy. Our first goal is to develop a generative model for the profile of mutation across the exome, which allows for gene- and variant type-dependent mutation rates. Based on this model, we then propose a new procedure for estimating biomarkers such as Tumour Mutation Burden and Tumour Indel Burden. Our approach allows the practitioner to select a targeted gene panel of a prespecified size, and then construct an estimator that only depends on the selected genes. Alternatively, the practitioner may apply our method to make predictions based on an existing gene panel, or to augment a gene panel to a given size. We demonstrate the excellent performance of our proposal using an annotated mutation dataset from 1144 Non-Small Cell Lung Cancer patients.

Tumour spheroids have the potential to be used as preclinical chemosensitivity assays. However, the production of three dimensional (3D) tumour spheroids remains challenging as not all tumour cell lines form spheroids with regular morphologies and spheroid transfer often induces disaggregation. In the field of pancreatic cancer, the MiaPaCa-2 cell line is an interesting model for research but it is known for its difficulty to form stable spheroids; also, when formed, spheroids from this cell line are weak and arduous to manage and to harvest for further analyses such as multiple staining and imaging. In this work, we compared different methods (i.e. hanging drop, round bottom wells and Matrigel embedding, each of them with or without methylcellulose in the media) to evaluate which one allowed to better overpass these limitations. Morphometric analysis indicated that hanging drop in presence of methylcellulose leaded to well-organized spheroids; interestingly, quantitative PCR (qPCR) analysis reflected the morphometric characterization, indicating that same spheroids expressed the highest values of CD44, VIMENTIN, TGF beta1 and Ki67. In addition, we investigated the generation of MiaPaCa-2 spheroids when cultured on substrates of different hydrophobicity, in order to minimize the area in contact with the culture media and to further improve spheroid formation.

Collective migration of cells and animals often relies on a specialised set of "leaders", whose role is to steer a population of naive followers towards some target. We formulate a continuous model to understand the dynamics and structure of such groups, splitting a population into separate follower and leader types with distinct orientation responses. We incorporate "leader influence" via three principal mechanisms: a bias in the orientation of leaders according to the destination, distinct speeds of movement and distinct levels of conspicuousness. Using a combination of analysis and numerical computation on a sequence of models of increasing complexity, we assess the extent to which leaders successfully shepherd the swarm. While all three mechanisms can lead to a successfully steered swarm, parameter regime is crucial with non successful choices generating a variety of unsuccessful attempts, including movement away from the target, swarm splitting or swarm dispersal.