Towards Learned Simulators for Cell Migration Koen Minartz Eindhoven University of Technology

2025-05-06 0 0 830.38KB 10 页 10玖币

侵权投诉

Towards Learned Simulators for Cell Migration

Koen Minartz

Eindhoven University of Technology

k.minartz@tue.nl

Yoeri Poels

Eindhoven University of Technology

y.r.j.poels@tue.nl

Vlado Menkovski

Eindhoven University of Technology

v.menkovski@tue.nl

Abstract

Simulators driven by deep learning are gaining popularity as a tool for efﬁciently

emulating accurate but expensive numerical simulators. Successful applications

of such neural simulators can be found in the domains of physics, chemistry,

and structural biology, amongst others. Likewise, a neural simulator for cellular

dynamics can augment lab experiments and traditional computational methods to

enhance our understanding of a cell’s interaction with its physical environment. In

this work, we propose an autoregressive probabilistic model that can reproduce

spatiotemporal dynamics of single cell migration, traditionally simulated with the

Cellular Potts model. We observe that standard single-step training methods do

not only lead to inconsistent rollout stability, but also fail to accurately capture the

stochastic aspects of the dynamics, and we propose training strategies to mitigate

these issues. Our evaluation on two proof-of-concept experimental scenarios

shows that neural methods have the potential to faithfully simulate stochastic

cellular dynamics at least an order of magnitude faster than a state-of-the-art

implementation of the Cellular Potts model.

1 Introduction

Studying the variety of mechanisms through which cells migrate and interact with their physical

environment is of crucial importance for our understanding of cell biology. For example, cell

migration plays a key role in the interaction between the immune system and implant surfaces [

the development of embryos [

], and the progression of cancer [

]. As experimental capacity

in the lab is inherently limited, computational methods have emerged as a tool to investigate the

stochastic and dynamic movement and shape of cells. However, these methods can be computationally

demanding. This is especially restrictive in scenarios requiring many simulations, for example due to

substantial stochasticity or in the case of inverse design, where parameters are optimized iteratively

based on the simulator’s output. Moreover, parameterizing such models to realistically simulate cells

can be a difﬁcult task, requiring careful design and expert knowledge.

On the other hand, deep learning has been gaining traction as a tool for learning fast approximate

simulators. For example, for continuous-time and continuous-space systems deﬁned with partial

differential equations (PDEs), neural solvers learn to emulate a system’s dynamics from a dataset of

simulations generated by a more computationally demanding solver [

]. In this setting,

a large computational cost is paid up front to generate the training set, but once trained, approximate

solutions can be generated at a fraction of the original cost. Moreover, learned simulators hold the

promise of emulating systems for which the laws governing the dynamics are not known, by instead

training on experimental observations.

NeurIPS 2022 AI for Science Workshop.

arXiv:2210.01123v2 [q-bio.QM] 2 Nov 2022

Based on the above considerations, we propose to use neural simulators to simulate cellular dynamics.

More speciﬁcally, we consider the scenario where both the movement and shape of the cell show

stochastic aspects and are highly dynamic, which is typically modeled in the Cellular Potts modeling

framework, proposed in [

]. Given their various successful applications in modeling spatiotemporal

data, we hypothesize that neural simulators are capable of faithfully emulating the ground truth

dynamics, while accelerating the simulation process. Our contributions are summarized as follows:

•

We propose a neural simulation model to simulate stochastic single-cell dynamics similar to

those generated by the Cellular Potts model;

•

We develop and evaluate autoregressive training strategies, with the aim to improve the

model’s rollout performance and its ability to capture stochastic dynamics;

•

We observe that our method has the capacity to faithfully emulate the cellular dynamics of

the Cellular Potts model, while generating simulations an order of magnitude faster.

2 Background and Related Work

2.1 Cellular Potts Model

The Cellular Potts (CP) model is a computational modeling framework for simulating cellular

dynamics and the dynamic and ﬂuctuating morphology of cells on a lattice [

]. The CP model

has gained prominence due to its ﬂexibility in modeling cell shape and movement, the interaction

between multiple cells, stochastic aspects of cell behavior, and multiscale mechanisms [25, 20, 11].

In the CP framework, the system is modeled as a Euclidean lattice

and Hamiltonian

. The

function

x:L→S

maps each lattice site

li∈L

to its state

x(li)∈S

, where

is the set of all

cells and materials that can be present in the system. Note that in the CP literature

is commonly

referred to as

; we deviate from this to stick to machine learning convention. To evolve the system,

a Markov-Chain Monte Carlo sampling algorithm is used. At every iteration, a lattice site

is chosen

at random. Then, a proposal is made to modify

such that state

x(li)

is changed to

x(lj)

, where

a site adjacent to

. Finally, the difference in energy

∆H

is calculated between the proposed and

current system state. If

∆H≤0

, the proposed state is accepted as the new system state; if

∆H > 0

it is accepted with probability e−∆H

T, with Tbeing the temperature parameter of the model.

The Hamiltonian

itself differs per application, but typically consists of at least contact energy and

volume preservation terms, as originally proposed in [10]:

H=X

li,lj∈N (L)

J(x(li), x(lj)) 1−δx(li),x(lj)

| {z }

contact energy

c∈C

λV(V(c)−V∗(c))2

| {z }

volume preservation

+Hother,(1)

where

N(L)

is the set of all pairs of neighboring lattice sites in

J(x(li), x(lj))

is the contact

energy between cells and/or materials

x(li)

and

x(lj)

, and

δx,y

is the Kronecker delta. Furthermore,

is the set of all cells in the system,

V(c)

is the number of lattice sites occupied by cell

(from here on

referred to as the volume of cell

V∗(c)

is the target volume of cell

, and

λV

is a Lagrange multiplier.

Hother

can consist of many extensions and modiﬁcations of the original Hamiltonian, for example

taking into account cellular dynamics induced by forces, gradients in chemical concentrations, cell

surface area constraints, and many more biological concepts. The speciﬁc Hamiltonians used for

simulating our data can be found in Appendix A.

2.2 Neural Simulators

Neural networks have been employed for simulation in many domains [

], often by either

combining ML models with existing numerical solvers [

] or by using ML models to simulate

dynamics in their entirety [

]. The latter, which we refer to as neural simulators, encompass

the type of model proposed in this work, as we seek to emulate the CP simulations as a whole. Of

particular interest are autoregressive methods operating on a spatial grid, as these ﬁt both the temporal

and spatial component of the CP simulations. This setup generally comes with challenges of ensuring

prediction quality and stability over longer rollout trajectories. Common approaches to address this

include injecting noise and incorporating model rollouts in the training procedure [28, 4].

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

TowardsLearnedSimulatorsforCellMigrationKoenMinartzEindhovenUniversityofTechnologyk.minartz@tue.nlYoeriPoelsEindhovenUniversityofTechnologyy.r.j.poels@tue.nlVladoMenkovskiEindhovenUniversityofTechnologyv.menkovski@tue.nlAbstractSimulatorsdrivenbydeeplearningaregainingpopularityasatoolforefcientlyem...

展开>> 收起<<

Towards Learned Simulators for Cell Migration Koen Minartz Eindhoven University of Technology.pdf

共10页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Towards Learned Simulators for Cell Migration Koen Minartz Eindhoven University of Technology

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: