Search for: All records

How do cellular regulatory networks solve the challenges of life? This article presents computer software to study that question, focusing on how transcription factor networks transform internal and external inputs into cellular response outputs. The example challenge concerns maintaining a circadian rhythm of molecular concentrations. The system must buffer intrinsic stochastic fluctuations in molecular concentrations and entrain to an external circadian signal that appears and disappears randomly. The software optimizes a stochastic differential equation of transcription factor protein dynamics and the associated mRNAs that produce those transcription factors. The cellular network takes as inputs the concentrations of the transcription factors and produces as outputs the transcription rates of the mRNAs that make the transcription factors. An artificial neural network encodes the cellular input-output function, allowing efficient search for solutions to the complex stochastic challenge. Several good solutions are discovered, measured by the probability distribution for the tracking deviation between the stochastic cellular circadian trajectory and the deterministic external circadian pattern. The solutions differ significantly from each other, showing that overparameterized cellular networks may solve a given challenge in a variety of ways. The computation method provides a major advance in its ability to find transcription factor network dynamics that can solve environmental challenges. The article concludes by drawing an analogy between overparameterized cellular networks and the dense and deeply connected overparameterized artificial neural networks that have succeeded so well in deep learning. Understanding how overparameterized networks solve challenges may provide insight into the evolutionary design of cellular regulation.

 

Danger requires a strong rapid response. Speedy triggers are prone to false signals. False alarms can be costly, requiring strong negative regulators to oppose the initial triggers. Strongly opposed forces can easily be perturbed, leading to imbalance and disease. For example, immunity and fear response balance strong rapid triggers against widespread slow negative regulators. Diseases of immunity and behavior arise from imbalance. A different opposition of forces occurs in mammalian growth, which balances strong paternally expressed accelerators against maternally expressed suppressors. Diseases of overgrowth or undergrowth arise from imbalance. Other examples of opposing forces and disease include control of dopamine expression and male versus female favored traits.

 

Organisms perceive their environment and respond. The origin of perception–response traits presents a puzzle. Perception provides no value without response. Response requires perception. Recent advances in machine learning may provide a solution. A randomly connected network creates a reservoir of perceptive information about the recent history of environmental states. In each time step, a relatively small number of inputs drives the dynamics of the relatively large network. Over time, the internal network states retain a memory of past inputs. To achieve a functional response to past states or to predict future states, a system must learn only how to match states of the reservoir to the target response. In the same way, a random biochemical or neural network of an organism can provide an initial perceptive basis. With a solution for one side of the two-step perception–response challenge, evolving an adaptive response may not be so difficult. Two broader themes emerge. First, organisms may often achieve precise traits from sloppy components. Second, evolutionary puzzles often follow the same outlines as the challenges of machine learning. In each case, the basic problem is how to learn, either by artificial computational methods or by natural selection.

 

Multicellular organisms often start life as a single cell. Subsequent cell division builds the body. Each mutational event during those developmental cell divisions carries forward to all descendant cells. The overall number of mutant cells in the body follows the Luria–Delbrück process. This article first reviews the basic quantitative principles by which one can understand the likely number of mutant cells and the variation in mutational burden between individuals. A recent Fréchet distribution approximation simplifies calculation of likelihoods and intuitive understanding of process. The second part of the article highlights consequences of somatic mutational mosaicism for understanding diseases such as cancer, neurodegeneration, and atherosclerosis. 

Robustness protects organisms in two ways. Homeostatic buffering lowers the variation of traits caused by internal or external perturbations. Tolerance reduces the consequences of bad situations, such as extreme phenotypes or infections. This article shows that both types of robustness increase the heritability of protected traits. Additionally, robustness strongly increases the heritability of disease. The natural tendency for organisms to protect robustly against perturbations may partly explain the high heritability that occurs for some diseases.

 

A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters. Differentiation enhances the discovery of improved performance in large models, an achievement that was previously difficult or impossible. Recently, a second computational advance optimizes the temporal trajectories traced by differential equations. Optimization requires differentiating a measure of performance over a trajectory, such as the closeness of tracking the environment, with respect to the parameters of the differential equations. Because model trajectories are usually calculated numerically by multistep algorithms, such as Runge-Kutta, the automatic differentiation must be passed through the numerical algorithm. This article explains how such automatic differentiation of trajectories is achieved. It also discusses why such computational breakthroughs are likely to advance theoretical and statistical studies of biological problems, in which one can consider variables as dynamic paths over time and space. Many common problems arise between improving success in computational learning models over performance landscapes, improving evolutionary fitness over adaptive landscapes, and improving statistical fits to data over information landscapes. 

Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be difficult because each evaluation of the fit must calculate the distance between the model and target patterns at numerous points along a trajectory. The gradient of the fit with respect to the model parameters can be challenging to compute. Recent technical advances in automatic differentiation through numerical differential equation solvers potentially change the fitting process into a relatively easy problem, opening up new possibilities to study dynamics. However, application of the new tools to real data may fail to achieve a good fit. This article illustrates how to overcome a variety of common challenges, using the classic ecological data for oscillations in hare and lynx populations. Models include simple ordinary differential equations (ODEs) and neural ordinary differential equations (NODEs), which use artificial neural networks to estimate the derivatives of differential equation systems. Comparing the fits obtained with ODEs versus NODEs, representing small and large parameter spaces, and changing the number of variable dimensions provide insight into the geometry of the observed and model trajectories. To analyze the quality of the models for predicting future observations, a Bayesian‐inspired preconditioned stochastic gradient Langevin dynamics (pSGLD) calculation of the posterior distribution of predicted model trajectories clarifies the tendency for various models to underfit or overfit the data. Coupling fitted differential equation systems with pSGLD sampling provides a powerful way to study the properties of optimization surfaces, raising an analogy with mutation‐selection dynamics on fitness landscapes.

 

Background: A growing population of cells accumulates mutations. A single mutation early in the growth process carries forward to all descendant cells, causing the final population to have a lot of mutant cells. When the first mutation happens later in growth, the final population typically has fewer mutants. The number of mutant cells in the final population follows the Luria-Delbrück distribution. The mathematical form of the distribution is known only from its probability generating function. For larger populations of cells, one typically uses computer simulations to estimate the distribution. Methods: This article searches for a simple approximation of the Luria-Delbrück distribution, with an explicit mathematical form that can be used easily in calculations. Results: The Fréchet distribution provides a good approximation for the Luria-Delbrück distribution for neutral mutations, which do not cause a growth rate change relative to the original cells. Conclusions: The Fréchet distribution apparently provides a good match through its description of extreme value problems for multiplicative processes such as exponential growth.