Biomolecular Neural Networks

• Biomolecular Neural Networks are a heterogeneous family of systems that implement neural computation via living cultures, biomolecular graphs, or biochemical circuits.
• Methodologies range from embodied neurocomputation with MEAs and optogenetics to graph neural network analysis and topological invariants for structure learning.
• Key challenges include interfacing with biological substrates, optimizing network design, and benchmarking across diverse physical and digital embodiments.

Searching arXiv for papers on Biomolecular Neural Networks and closely related formulations. {"query":"all: \"Biomolecular Neural Networks\" OR all:\"Biological neural networks\" biomolecular reaction networks neural networks DNA strand displacement synthetic biology", "max_results": 10, "sort_by": "submittedDate", "sort_order": "descending"} Here are the search results from arXiv:

1. "Learning-based Formal Synthesis of Gene Regulatory Network Parameters with HyperLTL Guarantees" (Sakib et al., 7 Aug 2025)v1)
   • Authors: Jacob Legris, Samuel A. Schmid, Morten M. Halvorsen, Alessandro Abate
   • Published: 2025-08-07
   • URL: http://arxiv.org/abs/([2508.04976](/papers/2508.04976))v1
2. "Communicating Smartly in the Molecular Domain: Neural Networks in the Internet of Bio-Nano Things" (Gómez et al., 25 Jun 2025)v2)
   • Authors: João Silva, Merve Nur Baltacı, Nils Farsad, Chan-Byoung Chae, Adam Noel, Josep Miquel Jornet, Rudolf Mathar
   • Published: 2025-06-25
   • URL: http://arxiv.org/abs/([2506.20589](/papers/2506.20589))v2
3. "Embodied Neurocomputation: A Framework for Interfacing Biological Neural Cultures with Scaled Task-Driven Validation" (Zhou et al., 13 May 2026)v1)
   • Authors: James Chou, Adam B. Hamilos, William E. DeBoe, Raymond S. McCauley, Owen Hayes, Tuan H. Bui, Clayton Morrison, Minhee Jang, Matt Craddock, Yadong Huang, Filiz B. Tekin, Jerzy W. Rozenblit, Thomas B. DeMarse, Brett J. Kagan
   • Published: 2026-05-13
   • URL: http://arxiv.org/abs/([2605.13315](/papers/2605.13315))v1
4. "BioNeuralNet: A Graph Neural Network based Multi-Omics Network Data Analysis Tool" (Ramos et al., 27 Jul 2025)v1)
   • Authors: Elsie Rossman, Isabel M. Mendez de la Luz, Hina Urooj, Himel Mallick, Casey S. Greene, Marylyn D. Ritchie
   • Published: 2025-07-27
   • URL: http://arxiv.org/abs/([2507.20440](/papers/2507.20440))v1
5. "Many-body graph neural networks" (Pan et al., 8 Aug 2025)v1)
   • Authors: Xinjie Huang, Shang-Te Danny Hsu, Michael M. Bronstein, Marinka Zitnik
   • Published: 2025-08-08
   • URL: http://arxiv.org/abs/([2508.06139](/papers/2508.06139))v1
6. "DIAL-BM: A Benchmark for Dialogue Interaction with Biomolecules" (Covei, 4 Sep 2025)v1)
   • Authors: Hongyin Luo, Kaifeng Pan, Xin Xie, Juhan Zhang, Chi-Min Chan, Dong Yu
   • Published: 2025-09-04
   • URL: http://arxiv.org/abs/([2509.04099](/papers/2509.04099))v1
7. "BioDiscoveryAgent: An AI agentic framework for scientific discovery in molecular biology" (2509.00195)v1)
   • Authors: Pulkit Singh, Xihui Lu, Hongru Duan, Luce Skrzypczak, Chenguang Wang, Max Kapur, Haojie Wang, Xueying Ding, Alfredo Rosado, Nils Rytter, Tal Miconi, Zahra Ahmed, Jussara M. Sa-Correia, Itamar Simon, Nicholas Schiefer, Rosie Hong, Michael Q. Zhang, Fatma M. Elzahraa, Yidong Chen
   • Published: 2025-09-01
   • URL: http://arxiv.org/abs/(2509.00195)v1
8. "Networked Neural Ordinary Differential Equations: Data-Driven Learning of HIV-1 Dynamics in Human Tissue" (Dobysheva, 26 Aug 2025)v1)
   • Authors: Evan Sohns, Michael A. Chao, Alexander A. Lentsch, Geers van den Bogaard, Jun Li, Dan Coombs
   • Published: 2025-08-27
   • URL: http://arxiv.org/abs/([2508.19148](/papers/2508.19148))v1

Need craft article only from provided data maybe could mention (Sakib et al., 7 Aug 2025)? but task says concrete claims from data block below. So only use provided data. Search is for compliance maybe not cite external since not in data block. Let's stick to data block. Need maybe mention there is terminological heterogeneity. We can say "In contemporary arXiv literature, 'Biomolecular Neural Networks' has been used for several distinct but related families..." That is supported by multiple papers definitions. This is an inference but can be factual if each paper defines differently. Need maybe mark "In current usage, the term spans..." probably okay because data includes multiple usages. Could say "Across the cited literature, the term denotes several distinct classes of systems." This is direct from varied papers. Good.

Need choose 6 sections with numbering in heading. Example:

1. Terminological scope and taxonomy

2. Living neural cultures as neurocomputational substrates

3. Biomolecular graphs and structural representation learning

4. Molecular and cellular implementations of neural computation

5. Learning rules, training objectives, and optimization

6. Benchmarks, applications, and open questions

Need intro paragraph mention BNNs refer to multiple constructs: living neural cultures interfaced via MEAs (Zhou et al., 13 May 2026), GNNs over biomolecular interaction graphs (Ramos et al., 27 Jul 2025), topology-based CNNs for 3D biomolecular structure (Cang et al., 2017), synthetic bacterial or chemical reaction network implementations (Sarkar et al., 2020, Vasic et al., 2020, Fan et al., 2023, Palanques-Tost et al., 5 Sep 2025), and molecular-communication/IoBNT modules (Gómez et al., 25 Jun 2025). Might be too many citations intro but okay maybe 2-3 max. Yet cite can be multiple sentence. Need at most once per section per paper. Intro is not a section, so can cite all maybe. Need maybe mention 2210 and 2301 as biological neuronal networks not exactly biomolecular, but can fit under living biological neural networks/optimization.

Need ensure not invent. Every concrete claim must be in data block. So careful with wording like "three broad categories" if not explicitly there? better avoid counts unless from grouping we define as editorial term and plausible. Could say "Across the cited arXiv literature, the expression has been used for living neural cultures interfaced to electronics, for neural architectures defined directly on biomolecular graphs and structures, and for chemically or genetically implemented neural computation in living or cell-free substrates." This is just synthesis. Maybe okay.

Need perhaps use table to organize usage. Tables okay max 3 cols. Could include in section 1 a concise taxonomy. But detailed explanations around it. Table okay with 3 columns.

Need mention formal equations. Use only formulas present. Could include representative equations for each subfield. Need not overload.

Need make article comprehensive but concise. Maybe around 1800-2500 words. We can do 6 sections.

Need no mechanical repetition cite at end each para. We'll cite once where section mainly uses specific papers.

Let's plan content per section:

Intro: define BNNs as family of neural-computational formalisms realized in biomolecular or biological substrates or constructed over biomolecular data. Mention heterogeneity.

Section 1 Terminological scope: discuss multiple senses from literature. Table: sense, substrate/representation, representative papers. Explain that term includes biological neural cultures, biomolecular networks for multi-omics, structure-aware neural models, in vivo/in vitro molecular implementations. Mention editors term? maybe not necessary.

Section 2 Living neural cultures and embodied neurocomputation: from 2605 and 2210. Need discuss hiPSC cortical/hippocampal cultures on MEAs; framework equations; closed-loop task, encoding/decoding/feedback, results 1,296 + 64, 12 configs, outperform DQN 1.18x/1.25x. Also reservoir computing with rat cortical mBNNs, modular architecture, optogenetics, calcium imaging, static classification 74.8±20.2 vs shuffle, memory ~1s, spoken digits 82.5±21.9, transfer learning 64.1 etc. Need avoid too many numbers? Fine. Since only one citation per paper in section, can cite after relevant paragraph. Could have two paragraphs each one cites one paper. Need mention both papers in section.

Section 3 Graphs and topology for biomolecular data: from 2507 and 1704. Discuss BioNeuralNet as GNN framework for multi-omics network G=(V,E), architectures GCN/GAT/GraphSAGE/GIN, TCGA-BRCA results. Discuss TopologyNet ESPH + 1D CNN for 3D structures, datasets and performance. Since concrete metrics are in data. Need note these BNNs are digital neural architectures tailored to biomolecular entities rather than wet implementations.

Section 4 Molecular implementations and biochemical compilation: from 2001, 2003, 2311 maybe 2506 perhaps maybe keep IoBNT in sec6. Discuss engineered bacteria single-layer ANN; perceptron equation; decoder/demux; manual tuning. Then CRN compilation of BinaryConnect into rate-independent CRNs with dual-rail, ReLU module, optimized reaction counts on IRIS/MNIST/Virus. Then automatic BCRN FCNN with backprop and oscillator sequencing, gradient descent and exponential convergence. Need perhaps mention both feedforward and backprop. Could be three paragraphs.

Section 5 Learning rules and optimization principles: from 2301 and 2509; maybe also tie 2605. Discuss zero-order optimization interpretation of biological learning with STDP-like reward-modulated update, expected iterate theorem. Then STL-based optimization of biomolecular neural networks for regression/control tasks, perceptron ODEs, loss based on robustness, results 7/10 100%; 4/10 94%; 8/10 99%. Maybe mention no target data. Could also note in living cultures learning attributed to intrinsic biological adaptation rather than weight updates from 2605, but already in sec2. Since cite at most once per section, can cite 2605 maybe not. But not necessary.

Section 6 Applications, benchmarks, and open problems: from 2506 survey and general open problems across papers. Need mention IoBNT context, digital NN for MC tasks and BNN modules via CRNs/DNA/GRNs/microfluidics/reservoirs. Metrics/results from survey e.g. >95% accuracy on 8x8 MNIST-like by two-neuron feedforward CRN, BER numbers, etc. Also discuss common bottlenecks: interface design, graph construction choices, kinetics/noise, variability, scalability, interpretability, ethics. Since these come from multiple papers. Need maybe cite several papers in section. Could mention open challenges aggregated, but ensure claims come from data. Since if we cite 2506 for MC and then discuss open issues from others maybe uncited? Need perhaps cite 2605 again? Wait per section at most once per paper. Could cite multiple papers in same section, one per paragraph. We'll use one paragraph on applications across IoBNT from 2506. Another paragraph synthesizing common limitations from 2605, 2507, 1704, 2001, 2509 maybe too many citations. Need careful but okay.

Need no references to how wrote article.

Need maybe mention misconceptions/controversies. For example misconception that BNN always means living neurons; but literature also uses term for GNN on biomolecular graphs and synthetic biochemical circuits. Another misconception that all BNNs are trainable via backprop; but many rely on manual tuning, fixed reservoirs, zero-order/local plasticity, or STL objectives. Good section1 maybe mention.

Need cite arxiv IDs in brackets. Use paper titles in double quotes optionally.

Need article itself only. No bibliographic references section unless integrated citations. Maybe okay not to have explicit references section. Need only article content.

Need ensure no unsupported claim like "umbrella term" maybe okay as synthesis, but maybe mark as editorial description? Could say "Across current arXiv usage, the label denotes..." That's supported by data.

Let's draft with concise but comprehensive. Biomolecular Neural Networks (BNNs) denote a heterogeneous family of neural-computational systems whose common feature is a direct coupling to biomolecular organization, biomolecular data, or biomolecular substrates. Across current arXiv usage, the term includes living neural cultures interfaced to silicon, neural architectures defined on biomolecular interaction graphs, topology-based models for three-dimensional biomolecular structure, and chemically or genetically implemented neural computation in bacteria, chemical reaction networks, and programmable biochemical reaction networks (Zhou et al., 13 May 2026, Ramos et al., 27 Jul 2025, Cang et al., 2017, Sarkar et al., 2020). In some papers, the emphasis is on biological adaptation and closed-loop embodiment; in others, it is on structure-aware representation learning or on compiling neural primitives into physically realizable molecular kinetics (Gómez et al., 25 Jun 2025, Palanques-Tost et al., 5 Sep 2025).

1. Terminological scope and taxonomic usage

The literature does not use “BNN” in a single narrow sense. In one line of work, BNNs are living neural cultures grown in vitro and interfaced to conventional computers via microelectrode arrays (MEAs), with computation arising from spiking dynamics, synaptic plasticity, neuromodulation, and multi-timescale adaptation (Zhou et al., 13 May 2026). In another, BNNs are neural architectures that operate directly on networks of biomolecular entities such as genes, proteins, miRNAs, CpG sites, metabolites, and clinical variables, using graph neural networks to learn embeddings from topology and node attributes (Ramos et al., 27 Jul 2025). A third usage refers to neural models tailored to biomolecular structure and sequence data, exemplified by element-specific persistent homology plus convolutional neural networks for protein–ligand and mutation-effect prediction (Cang et al., 2017). A fourth usage concerns biomolecular implementations of neural computation in living bacteria, chemical reaction networks, gene regulatory networks, or programmable biochemical reaction networks (Sarkar et al., 2020, Vasic et al., 2020, Fan et al., 2023).

Usage of “BNN”	Substrate or representation	Representative papers
Living biological neural cultures	hiPSC or rat neuronal cultures, MEAs, optogenetics, calcium imaging	(Zhou et al., 13 May 2026, Sumi et al., 2022)
Biomolecular network learning	Multi-omics graphs with GNNs	(Ramos et al., 27 Jul 2025)
Biomolecular structure learning	ESPH-derived topological tensors with CNNs	(Cang et al., 2017)
Molecular or cellular neural implementation	Engineered bacteria, CRNs, BCRNs, GRNs	(Sarkar et al., 2020, Vasic et al., 2020, Fan et al., 2023, Palanques-Tost et al., 5 Sep 2025)

A recurrent source of confusion is the assumption that BNNs necessarily denote living neuronal tissue. The current literature does not support that restriction. It also uses the term for digital models operating on biomolecular graphs and for chemically synthesized or genetically encoded neural modules. This suggests that “BNN” functions less as a single architecture class than as a cross-domain designation for neural computation whose semantics, data model, or physical realization is biomolecular.

2. Living neural cultures as computational substrates

In the embodied neurocomputation formulation, BNNs are living neural cultures acting inside a closed loop with a task environment. The system is decomposed as

$y = d(b(e(x; \Theta_e); \Theta_b(t)); \Theta_d)$

with adaptation governed by

$$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$

Here, encoding maps task state to MEA stimulation, the biological substrate transforms stimulation into neural responses, decoding maps responses to actions, and feedback modulates future biological dynamics. The framework was operationalized with human induced pluripotent stem cell cortical and hippocampal cultures on 60-electrode MEA chips, using rate encoding of a ternary odor-direction sensor, count decoding over three action regions, and reward-dependent feedback. Approximately 1,300 encoding configurations were evaluated across 26 cultures and ∼4,000 hours of real-time interactions. Stage 1 screened 1,296 combinations; Stage 2 refined to 64 combinations and identified 12 configurations that consistently demonstrated learning. In matched interaction budgets, top BNN agents scored 1.18× the DQN mean in a 150-step single episode and 1.25× the DQN mean in a 5×30-step multi-episode condition, with Brunner–Munzel tests reporting $p < 10^{-4}$ (Zhou et al., 13 May 2026).

The same paper makes the design of the silicon–biology interface the central optimization problem. Six encoding parameters were screened: $f_{\min}$, $f_{\max}$, amplitude, pulse width, tick rate, and ticks per step. The 12 best configurations shared $f_{\min}=4$ Hz, $f_{\max}=40$–80 Hz favoring 40–60 Hz, amplitude $=2.5$ $\mu$A, pulse width $=40$–80 $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$0s, tick rate $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$1–2 Hz, and ticks per step $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$2. An XGBoost classifier with SHAP identified max frequency as the strongest driver, followed by amplitude, pulse width, and interaction rate. Learning was defined operationally as sustained performance improvement across episodes and superior performance relative to non-adaptive baselines and silicon DQN agents under equal interaction budgets, with learning attributed to intrinsic biological adaptation rather than external algorithmic weight updates (Zhou et al., 13 May 2026).

A related but methodologically distinct line treats living neuronal cultures as physical reservoirs. Micropatterned biological neuronal networks made from rat cortical neurons were optogenetically driven and read out by fluorescent calcium imaging. The reservoir state was the vector of $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$3 values over up to $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$4 neurons, and only the linear readout $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$5 was trained. In static pattern classification, mean accuracy was $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$6 versus $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$7 for shuffled labels. In a timer task, $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$8 remained $$\Theta_b(t+1) = g(r(Score; \Theta_f); \Theta_b(t)).$$9 up to $p < 10^{-4}$0 s, establishing a short-term memory horizon on the order of $p < 10^{-4}$1 s. Spoken digit classification reached $p < 10^{-4}$2, and speaker-switch transfer learning remained above chance at $p < 10^{-4}$3, whereas direct linear decoding of the input patterns dropped to chance (Sumi et al., 2022).

The reservoir study also identifies functional modularity as a decisive variable. Newman modularity $p < 10^{-4}$4 computed from inferred firing-rate correlations correlated with separability at $p < 10^{-4}$5, $p < 10^{-4}$6, and high-$p < 10^{-4}$7 networks yielded stable high accuracy. The authors interpret the reservoir as a “generalization filter”: it transforms inputs into category-consistent trajectories that preserve $p < 10^{-4}$8 under dataset shift, enabling transfer learning not available to a direct linear decoder (Sumi et al., 2022). A plausible implication is that, within living-neuron BNNs, architecture and interface design can matter at least as much as the downstream decoder.

3. Biomolecular graphs and structural representations

In multi-omics analysis, BNNs are graph-based neural models defined over biomolecular interaction networks. BioNeuralNet formalizes a biomolecular network as $p < 10^{-4}$9, with node features $f_{\min}$0, adjacency $f_{\min}$1, self-loops $f_{\min}$2, and symmetric normalization $f_{\min}$3. The framework supports similarity networks, correlation networks, k-nearest neighbor and shared-nearest neighbor graphs, WGCNA-style soft-thresholding, and phenotype-driven inference with SmCCNet. It exposes GCN, GAT, GraphSAGE, and GIN through a modular PyTorch Geometric-compatible API, and supports node-level, subject-level, and graph-level embeddings, supervised DPMON classification, unsupervised subgraph detection, and dimensionality reduction (Ramos et al., 27 Jul 2025).

The demonstrated TCGA-BRCA study used a harmonized cohort of 769 subjects with mRNA, DNA methylation, miRNA, and clinical variables after stringent QC. Feature selection retained 6,000 features per mRNA and methylation, all miRNAs, and the top 10 clinical covariates; a k-NN graph with $f_{\min}$4 under cosine similarity connected genes, methylation features, and miRNAs into one heterogeneous graph. Reported performance was Accuracy $f_{\min}$5, F1-weighted $f_{\min}$6, and F1-macro $f_{\min}$7, exceeding Random Forest, MOGONET, MLP, and SUPREME on that task (Ramos et al., 27 Jul 2025). Here, the “biomolecular” aspect lies not in physical realization but in the graph semantics: the model is organized around molecular entities and their biological relations.

A structurally different approach appears in TopologyNet, which targets three-dimensional biomolecular structure. Rather than operate on explicit graphs, it uses element-specific persistent homology to map atomic coordinates into one-dimensional topological invariants, preserving biochemical specificity through multichannel element and affiliation selections. Typical channels encode protein elements $f_{\min}$8, ligand elements $f_{\min}$9, and cross-affiliation relations through an oppositional distance. Barcode statistics are binned into multichannel one-dimensional “images” processed by a 1D CNN, with 72 channels for binding-affinity prediction and 45 for mutation tasks (Cang et al., 2017).

TopologyNet reports strong results on several benchmarks. On PDBbind 2007 core, TNet-BP achieved Pearson’s $f_{\max}$0 (best $f_{\max}$1) with RMSE $f_{\max}$2 pKd/pKi units. On globular protein mutations, TNet-MP-2 reached $f_{\max}$3, RMSE $f_{\max}$4 on S350 and $f_{\max}$5, RMSE $f_{\max}$6 on S2648. On membrane protein mutations, multitask TNet-MMP-2 improved to $f_{\max}$7, RMSE $f_{\max}$8, surpassing Rosetta-MP and FoldX on M223 (Cang et al., 2017). This branch of BNN research is therefore concerned with invariant, chemically informed representation design for biomolecular geometry rather than with adaptive wetware.

4. Molecular and cellular implementations of neural computation

One direct biomolecular implementation uses engineered bacteria as artificial neurons. In a single-layer ANN realized in living Escherichia coli, each bacterium acts as one “bactoneuron” receiving extracellular IPTG and aTc, computing

$f_{\max}$9

and expressing fluorescent reporters as outputs. Weights and bias are adjusted manually through promoter architecture, operator number and placement, plasmid copy number, repressor variants, and ribosome-binding-site strength. Four strains were co-cultured to implement a 2-to-4 chemical decoder, and a pair of strains implemented a 1-to-2 de-multiplexer. Representative fitted parameters include $f_{\min}=4$0, $f_{\min}=4$1, $f_{\min}=4$2 for the NOR neuron and $f_{\min}=4$3, $f_{\min}=4$4, $f_{\min}=4$5 for the selected AND neuron BNeu 4A_PIAA5_p15A (Sarkar et al., 2020).

A different molecular line compiles trained digital networks into chemical reaction networks. “Deep Molecular Programming” targets BinaryConnect networks with binary weights and ReLU activations,

$f_{\min}=4$6

using dual-rail encoding and a rate-independent ReLU module

$f_{\min}=4$7

The central claim is absolute robustness to reaction rates: steady-state outputs depend on stoichiometry and initial concentrations rather than on precise kinetic tuning. After optimization, the construction yields one bimolecular reaction per ReLU neuron and two unimolecular reactions per input dimension. The compiled CRNs exactly matched trained network outputs on IRIS, MNIST, and a virus-type classifier. Reported reaction counts were reduced from 40 to 16 on IRIS, from 4488 to 1024 on MNIST, and from 148 to 32 on the virus classifier (Vasic et al., 2020).

Programmable biochemical reaction networks extend this idea from inference to training. A BCRN implementation of a two-two-one fully connected neural network maps inputs, hidden activations, weights, biases, errors, and gradient terms onto molecular species under mass-action kinetics. The design includes assignment, feedforward propagation, sigmoid activation, preceding computation, judgment termination via a bistable module, oscillator-controlled sequencing, negative-gradient computation, update, and clear-out. Dual-rail encoding is used for signed variables; the learning rate is itself a species $f_{\min}=4$8 with $f_{\min}=4$9. The authors prove exponential convergence of the feedforward and backpropagation modules to the target FCNN computations and show logic-classification demonstrations in which training terminates automatically at iteration 5 for OR and 12 for XOR (Fan et al., 2023).

Taken together, these studies show that “neural network” can be interpreted as a biochemical design pattern rather than as a purely electronic abstraction. The implementations differ sharply in whether parameters are manually engineered, compiled from in silico training, or updated in chemistry, but all attempt to map weighted sums, nonlinear activations, and network composition into physically realizable molecular dynamics.

5. Learning rules, optimization, and specification-driven training

A theoretical account of learning in biological neural networks interprets reward-modulated spike-timing dependent plasticity as a zero-order optimization method. In this formulation, synaptic updates take the loss-based form

$f_{\max}=40$0

with an eligibility trace

$f_{\max}=40$1

After log-parameterization, the update becomes a derivative-free step driven only by loss values at perturbed parameters. The paper proves that the expected iterate implements a preconditioned, perturbed-gradient step, thereby relating biologically local rules to a modification of gradient descent in expectation (Schmidt-Hieber, 2023).

A distinct optimization paradigm appears in STL-based training of biologically synthesizable BNNs. The architecture is built from repeated biomolecular perceptron modules with species $f_{\max}=40$2 and $f_{\max}=40$3 that mutually inactivate and degrade, governed by

$f_{\max}=40$4

$f_{\max}=40$5

with $f_{\max}=40$6 and $f_{\max}=40$7 for $f_{\max}=40$8. Rather than training against target trajectories, the method uses Signal Temporal Logic robustness in the loss,

$f_{\max}=40$9

and performs optimization in log space to enforce nonnegative biochemical parameters (Palanques-Tost et al., 5 Sep 2025).

The reported tasks include two regression problems and one closed-loop control problem. In static regression, 7 of 10 random seeds converged and test-set satisfaction of the STL specification was 100%. In dynamic regression, 4 of 10 seeds achieved at least 90% training satisfaction and the mean test satisfaction was 94%. In chronic-inflammation control, 8 of 10 seeds achieved at least 90% training satisfaction and average test satisfaction was 99% (Palanques-Tost et al., 5 Sep 2025). This suggests a broader methodological point: BNN training need not be restricted to supervised targets or backpropagation through conventional neural layers; it can also be formulated through local plasticity, chemical gradient flow, or temporal-logic constraints.

6. Application domains, benchmarks, and persistent challenges

The Internet of Bio-Nano Things literature places neural networks across the molecular communication stack, while reserving “BNNs” for biologically integrated neural modules implemented through chemical reaction networks, DNA strand displacement, gene regulatory networks, metabolic circuits, microfluidic signal processors, compartment-based computing, and wet neuromorphic systems such as brain organoids. Within this survey, CRN neurons implement weighted sums and thresholding, DNA strand displacement networks realize multipliers and integrators, GRNs implement wet neuromorphic computation in the logarithmic domain, and microfluidic architectures map FIR-like filtering to molecular transport. A two-neuron feedforward CRN neural network is reported to achieve $=2.5$0 accuracy on 8×8 MNIST-like images. The same survey also catalogs digital NN performance for molecular communication, including BER values down to $=2.5$1 on air-channel testbeds, RL synchronizers with TPR $=2.5$2 and FPR $=2.5$3, and CNN autoencoders with BER from $=2.5$4 to $=2.5$5 depending on SNR (Gómez et al., 25 Jun 2025).

Across the broader BNN literature, several constraints recur. Living-neuron systems face biological non-stationarity, culture variability, carry-over effects, interface bias, and the difficulty of disentangling encoding from feedback (Zhou et al., 13 May 2026). Multi-omics graph models depend strongly on graph construction, feature selection, and architecture choice (Ramos et al., 27 Jul 2025). Topology-based structural models may lose fine-grained geometric detail and remain sensitive to filtration and binning choices (Cang et al., 2017). Bacterial and chemical implementations confront limited part orthogonality, resource competition, signal cross-talk, slow dynamics, and scaling limits (Sarkar et al., 2020, Vasic et al., 2020). STL-trained biomolecular circuits remain sensitive to initialization and are not yet validated experimentally (Palanques-Tost et al., 5 Sep 2025).

Benchmarking is therefore central. Embodied neurocomputation proposes standardized episodes, normalized episode reward, fixed seeds, comparative baselines, confidence intervals, and Brunner–Munzel statistics (Zhou et al., 13 May 2026). BioNeuralNet exposes reproducible pipelines and documented workflows (Ramos et al., 27 Jul 2025). The molecular communication survey emphasizes open-source code repositories and public datasets (Gómez et al., 25 Jun 2025). A plausible implication is that the field’s main unifying problem is no longer whether neural computation can be expressed in biomolecular terms, but how to compare embodiments, representations, and optimization strategies across radically different substrates without collapsing their distinctions.

In contemporary usage, then, BNNs are not a single technology. They are a family of computational programs in which neural computation is attached to living neurons, molecular networks, biomolecular structure, or biochemical kinetics. What unifies them is not a shared substrate, but a shared ambition: to make neural computation respect the organization, constraints, and opportunities of biological matter.