Christopher E. Miles

Dramatic movements characterize rapid assembly of mitotic spindle in prometaphase: chromosomes congress to the spindle equator, while spindle poles segregate rapidly elongating the spindle. Direct biophysical measurements of forces driving these movements are lacking, but the forces could be learned from the rapid pole and chromosome movements. We analyzed 3D trajectories of chromosomes and spindle poles in the wild-type and PRC1-depleted cells during early prometaphase and reconstructed the spindle forces. This analysis posits that (i) chromosomes do not interact with each other, except for a short-range steric repulsion, (ii) effective pole-chromosome forces are repulsive at short and attractive at long distances, (iii) dominant forces of spindle poles segregation are interpolar in origin. The important implication of these results is that the pole-pole segregation is robust, largely insensitive to regional variations inside the cell and to complex process of chromosome congression. SIGNIFICANCE: Mechanics of prometaphase is crucial for mitotic spindle assembly, yet measurements of forces in prometaphase are lacking. We use movements of centrosomes and chromosomes in prometaphase to reconstruct the spindle forces. We find that the forces are hierarchical, with the interpolar force balance dominating smaller forces between the spindle poles and chromosomes. The important implication of these results is that the pole-pole segregation is robust, largely insensitive to regional variations inside the cell and to complex process of chromosome congression.

Mesenchymal cell migration starts with the protrusion of the cell’s leading edge, enabled by the branching growth of the actin network. Two crucial molecular players in protrusion are actin filaments and the Arp2/3 complex, the branching agent. Traditionally, protrusion models are intuited from several perturbative experiments. Recent multiplex microscopy imaging data promise to change this paradigm by providing measurements of naturally fluctuating densities of key proteins at the leading edge of unperturbed cells. We report an attempt to reconstruct the mechanistic protrusion model from such data. We analyze fluctuations of densities of actin filaments and Arp2/3 complex and cell edge velocity using phase space and regression analysis to reconstruct linearized dynamics of the coupled actin-Arp2/3-velocity system. We then build a nonlinear model of these dynamics based on previous knowledge of this system and parsimony. The resulting models recover the rates of reactions and mechanical and transport processes in the lamellipodium from a single nonperturbative experiment. The models posit that the dominant nonlinear term in the lamellipodial dynamics corresponds to the retrograde flow of the actin network in the cell frame. The models suggest that the protrusion is dominated by a damped oscillatory cycle resulting from a combination of positive feedback from the Arp2/3 complex to protrusion velocity and negative feedback from actin density to the velocity.

Simulation-based inference (SBI) offers a route to connect biological data with mechanistic models. At the frontier of biology, datasets continue to grow in scale and richness, and increasingly record heterogeneity between individual observations that a mechanistic model can take into account. Approximate Bayesian Computation (ABC) remains a popular approach to SBI due to its ease of use, but incorporating this heterogeneity often requires a separate simulation of each observation, which is prohibitively expensive at scale. A previously proposed technique, minibatch Sequential Monte Carlo ABC (SMC ABC), reduces this cost by simulating a fixed-size random subset of observations for each proposal, at the price of sampling noise that limits precision. Here, we present an adaptive minibatch approach that uses small batches during early exploration and increases the batch size as the posterior is refined. The adaptive batch size is set by the target precision and does not grow with the size of the dataset, so the savings over full-data SMC ABC increase for larger datasets. We demonstrate the method on synthetic biological models and on real single-cell gene-expression data that vary in scale and type of heterogeneity, including cell geometry and initial condition. In each case, the adaptive scheme obtains posteriors close to those of full-data SMC ABC at a fraction of the cost. Altogether, adaptive minibatching improves the tradeoff between speed and precision in SMC ABC and opens the door to mechanistic inference on large, heterogeneous biological datasets.

Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We develop a Bilevel Local Operator Learning framework for Bayesian inference in PDEs (B-BiLO). At the upper level, we sample parameters from the posterior via Hamiltonian Monte Carlo, while at the lower level we fine-tune a neural network via low-rank adaptation (LoRA) to approximate the solution operator locally. B-BiLO enables efficient gradient-based sampling without synthetic data or adjoint equations and avoids sampling in high-dimensional weight space, as in Bayesian neural networks, by optimizing weights deterministically. We analyze errors from approximate lower-level optimization and establish their impact on posterior accuracy. Numerical experiments across PDE models, including tumor growth, demonstrate that B-BiLO achieves accurate and efficient uncertainty quantification.

Markov state modeling has gained popularity in various scientific fields since it reduces complex time-series data sets into transitions between a few states. Yet common Markov state modeling frameworks assume a single Markov chain describes the data, so they suffer from an inability to discern heterogeneities. As an alternative, this paper models time-series data using a mixture of Markov chains, and it automatically determines the number of mixture components using the variational expectation-maximization algorithm. Variational EM simultaneously identifies the number of Markov chains and the dynamics of each chain without expensive model comparisons or posterior sampling. As a theoretical contribution, this paper identifies the natural limits of Markov chain mixture modeling by proving a lower bound on the classification error. This paper then presents numerical experiments where variational EM achieves performance consistent with the theoretically optimal error scaling. The experiments are based on synthetic and observational data sets including music listening, ultramarathon running, and gene expression. In each of the three data sets, variational EM leads to the identification of meaningful heterogeneities.

Mesenchymal cell migration starts with the protrusion of the cell’s leading edge, enabled by the branching growth of the actin network. Two crucial molecular players in protrusion are actin filaments and the Arp2/3 protein complex, the branching agent. Traditionally, protrusion models are intuited from several perturbative experiments. Recent multiplex microscopy imaging data promise to drastically change this paradigm by providing measurements of naturally fluctuating densities of key proteins at the leading edge of unperturbed cells. We report the first attempt to reconstruct the mechanistic protrusion model from such data. We analyze fluctuations of F-actin and Arp2/3 densities and cell edge velocity using phase space and regression analysis to reconstruct linearized stochastic actin-Arp2/3-velocity coupled dynamics. We then build a nonlinear partial differential equation model of these dynamics based on previous knowledge of this system and parsimony. The resulting model recovers the rates of reactions and mechanical and transport processes in the lamellipodium from a single non-perturbative experiment. The model posits that the only essential nonlinearities in the lamellipodial dynamics stem from the retrograde flow of F-actin. The model suggests that the protrusion is dominated by a damped oscillatory cycle resulting from a combination of positive feedback from Arp2/3 to protrusion velocity and negative feedback from F-actin to the velocity. Significance statement: Traditionally, models of intracellular mechanochemistry are intuited from perturbative experiments. Multiplex microscopy imaging changes this by providing measurements of naturally fluctuating densities of key proteins in unperturbed cells. We use such data to reconstruct a mechanistic model of cell leading edge. We build equations for actin system and edge velocity using data, previous knowledge and parsimony. The resulting model recovers the rates of reactions and mechanical and transport processes at the leading edge. The model suggests that the protrusion is dominated by a damped oscillatory cycle resulting from a combination of positive feedback from Arp2/3 to protrusion velocity and negative feedback from F-actin to the velocity.

For proper segregation of chromosomes and successful cytokinesis, chromosomes must first “congress”—gather in a tight plate near the spindle equator. Molecular mechanism(s) of congression are not fully understood. Here we combine live-cell microscopy, perturbations of microtubule motor activities, correlative light/electron microscopy, and computational modeling, to quantitatively characterize the early-prometaphase movements that bring the scattered chromosomes to the equator in human RPE1 cells. We find that the early-prometaphase movements are directed toward the center of the spindle axis and not the spindle poles. Centromere velocity of the centripetal movements is not constant, with centromeres moving faster at larger distances from the spindle center. We also detect that numerous short microtubules appear at kinetochores at the earliest stages of spindle assembly and prior to chromosome congression. Computational modeling reveals that a mechanism based on brief, stochastic, minus-end directed interactions between the short microtubules protruding from the kinetochores and long appropriately curved microtubules within the spindle accurately predicts the observed distance-velocity function. Further, the model predicts that insufficient numbers of microtubules protruding from the kinetochores decreases the velocity and randomizes directionality of congression movements. These predictions match changes in the chromosome behavior observed in cells with suppressed nucleation of microtubules at the kinetochore corona (RPE1 Rod ^Δ/Δ ). In contrast, predictions of computational models based on continuous pulling forces at kinetochores differ significantly from the experimental observations. Together, live-cell observations and modeling reveal a mechanism that enables the efficient and synchronized arrival of chromosomes to the spindle equator.

Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We develop a Bilevel Local Operator Learning framework for Bayesian inference in PDEs (B-BiLO). At the upper level, we sample parameters from the posterior via Hamiltonian Monte Carlo, while at the lower level we fine-tune a neural network via low-rank adaptation (LoRA) to approximate the solution operator locally. B-BiLO enables efficient gradient-based sampling without synthetic data or adjoint equations and avoids sampling in high-dimensional weight space, as in Bayesian neural networks, by optimizing weights deterministically. We analyze errors from approximate lower-level optimization and establish their impact on posterior accuracy. Numerical experiments across PDE models, including tumor growth, demonstrate that B-BiLO achieves accurate and efficient uncertainty quantification. MSC Classification: 65M32, 62F15, 68T07

We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to locally approximate the PDE solution operator in the neighborhood of a given set of PDE parameters, which enables an accurate approximation of the descent direction for the upper level optimization problem. The lower level loss function includes the least-square penalty of both the residual and its derivative with respect to the PDE parameters. We apply gradient descent simultaneously on both the upper and lower level optimization problems, leading to an effective and fast algorithm. The method, which we refer to as BiLO (Bilevel Local Operator learning), is also able to efficiently infer unknown functions in the PDEs through the introduction of an auxiliary variable. We provide a theoretical analysis that justifies our approach. Through extensive experiments over multiple PDE systems, we demonstrate that our method enforces strong PDE constraints, is robust to sparse and noisy data, and eliminates the need to balance the residual and the data loss, which is inherent to the soft PDE constraints in many existing methods.