Level 4 — ApplicationSystems Biology & Frontiers

Systems Biology & Frontiers

⏱ 60 minutes60 marksprintable — key stays hidden on paper

Level 4 — Application (novel/unseen problems, no hints) Time Limit: 60 minutes Total Marks: 60

Question 1 — Gene Regulatory Network Dynamics (12 marks)

A synthetic biologist builds a two-gene "toggle switch." Gene A represses gene B, and gene B represses gene A. Each protein's repression follows Hill kinetics. The steady-state production rate of protein A is modeled as:

$\frac{dA}{dt} = \frac{\beta}{1 + (B/K)^n} - \gamma A$

with symmetric equations for B.

(a) A student observes that with $n = 1$ the circuit settles to a single intermediate state, but with $n = 4$ it locks into one of two stable states. Explain, in terms of network behavior, why increasing $n$ (cooperativity) changes the qualitative outcome. (5)

(b) At steady state with parameters $\beta = 20$ , $\gamma = 2$ , $K = 4$ , $n = 1$ , and given that the symmetric solution has $A = B$ , solve for the steady-state concentration $A$ . (5)

(c) Identify which single subtopic concept ("emergent behavior") this bistability illustrates and justify in one sentence. (2)

Question 2 — Metabolic Network Flux (12 marks)

Consider a simplified metabolic branch point. Metabolite M is produced at flux $v_{in} = 10$ mmol/gDW/h and consumed by two competing enzymes producing products P and Q. At steady state, no M accumulates.

(a) Write the steady-state (mass-balance) constraint equation for metabolite M in terms of $v_{in}$ , $v_P$ and $v_Q$ . (3)

(b) Enzyme routing to P carries twice the flux of routing to Q. Compute $v_P$ and $v_Q$ . (4)

(c) A knockout removes enzyme Q entirely. Assuming $v_{in}$ is unchanged and M cannot accumulate, state the new $v_P$ and explain what flux-balance principle forces this result. (3)

(d) Explain why flux-balance analysis (FBA) does NOT require enzyme kinetic constants, unlike the model in Q1. (2)

Question 3 — Multi-Omics & Single-Cell Integration (12 marks)

A research team profiles a tumor using: (i) bulk RNA-seq, (ii) single-cell RNA-seq, (iii) spatial transcriptomics, and (iv) DNA methylation (epigenomics).

(a) The bulk RNA-seq shows an intermediate expression level of gene X, but single-cell data reveals two distinct populations. Explain the phenomenon that bulk data masked and why single-cell resolves it. (4)

(b) The spatial transcriptomics adds one dimension of information that single-cell dissociation loses. State what it is and give one biological question it uniquely answers. (4)

(c) Methylation data show gene X is hypermethylated in the low-expressing population. Propose a coherent integrated mechanistic hypothesis linking all three datasets. (4)

Question 4 — Microbiome Systemic Effects & Modeling (12 marks)

A gnotobiotic (germ-free) mouse study measures a serum metabolite that drops to near zero when the gut microbiome is absent and recovers when bacteria are reintroduced.

(a) Explain how this experiment demonstrates a systemic effect of the microbiome that extends beyond the gut. (4)

(b) The metabolite level $M(t)$ after colonization follows logistic-like growth as bacteria establish:

$\frac{dM}{dt} = rM\left(1 - \frac{M}{M_{max}}\right)$

Given $r = 0.5\,\text{h}^{-1}$ and $M_{max} = 100\,\mu\text{M}$ , and $M(0)=10\,\mu\text{M}$ , compute $dM/dt$ at $t=0$ . (4)

(c) At what value of $M$ is $dM/dt$ maximal, and what is that maximal rate? (4)

Question 5 — Synthetic Genomes, Ethics & Emergence (12 marks)

A team constructs a "minimal cell" by stripping a bacterial genome to the smallest gene set permitting self-replication (~473 genes), yet ~30% of retained genes have unknown function.

(a) Explain what the persistence of essential-but-unknown-function genes reveals about the limits of the reductionist approach and why systems biology is needed. (4)

(b) Explain how "emergent behavior" could arise in this minimal cell that is not predictable from any single gene. (4)

(c) Identify TWO distinct ethical/societal challenges raised by synthetic minimal cells and briefly justify each. (4)

Answer keyMark scheme & solutions

Question 1 (12)

(a) (5)

With $n=1$ (non-cooperative), the mutual repression response is graded/shallow; the system has a single intersection of nullclines → one stable steady state (monostable). (2)
With high $n$ (cooperative, ultrasensitive), the repression response becomes switch-like/sigmoidal → the nullclines intersect three times: two stable states flanking one unstable state (saddle). (2)
This bistability means the circuit "remembers" and locks into one state — a hallmark of positive-feedback/double-negative loops requiring nonlinearity. (1)

(b) (5) At steady state $dA/dt=0$ and $A=B$ : $\gamma A = \frac{\beta}{1+(A/K)}$ Plug in: $2A = \dfrac{20}{1 + A/4}$ . (2) Multiply: $2A(1 + A/4) = 20 \Rightarrow 2A + 0.5A^2 = 20$ . (1) $\Rightarrow 0.5A^2 + 2A - 20 = 0 \Rightarrow A^2 + 4A - 40 = 0$ . (1) $A = \dfrac{-4 + \sqrt{16+160}}{2} = \dfrac{-4+\sqrt{176}}{2} \approx \dfrac{-4+13.27}{2} \approx 4.63$ (taking positive root). (1)

(c) (2)

Concept: emergent behavior (6.5.6). (1)
Justification: bistability/memory is a property of the network as a whole (feedback), absent from any single gene in isolation. (1)

Question 2 (12)

(a) (3) Steady state: production = consumption: $v_{in} = v_P + v_Q \quad\Rightarrow\quad 10 = v_P + v_Q$

(b) (4) Given $v_P = 2 v_Q$ : $2v_Q + v_Q = 10 \Rightarrow 3v_Q = 10 \Rightarrow v_Q = 3.33$ mmol/gDW/h (2); $v_P = 6.67$ mmol/gDW/h (2).

(c) (3) With Q knocked out, $v_Q=0$ , so $v_P = v_{in} = 10$ mmol/gDW/h (2). Forced by the steady-state mass-balance (conservation) constraint: input flux must fully equal output flux since M cannot accumulate. (1)

(d) (2) FBA relies only on stoichiometry and steady-state mass balance (a system of linear constraints) and optimizes an objective — it never needs $K_m/V_{max}$ because it does not model concentration dynamics over time. (2)

Question 3 (12)

(a) (4) Bulk data averages over the whole population, so two subpopulations (high & low) average to an intermediate value — population heterogeneity is masked (2). Single-cell RNA-seq measures each cell individually, resolving the bimodal distribution into two distinct clusters. (2)

(b) (4) Spatial transcriptomics preserves spatial/positional (tissue-location) context lost in dissociation (2). Unique question e.g.: where in the tumor microenvironment (core vs. margin, near immune cells) each population resides / cell–cell neighborhood interactions. (2)

(c) (4) Integrated hypothesis: The low-expressing subpopulation identified by scRNA-seq (1) is silenced via promoter hypermethylation of gene X (epigenomic cause) (1); spatial data can show this population is confined to a specific tumor region (1), giving a mechanistic chain: methylation → transcriptional silencing → spatially distinct subclone. (1) (Award for coherent linkage of all three layers.)

Question 4 (12)

(a) (4) The metabolite is measured in serum (systemic circulation), not the gut lumen (1); its dependence on microbial presence shows gut bacteria produce/enable a compound that enters the bloodstream and can act on distant organs (2) — demonstrating the microbiome influences whole-body physiology beyond local digestion. (1)

(b) (4) $\frac{dM}{dt} = 0.5 \times 10 \times (1 - 10/100) = 0.5 \times 10 \times 0.9 = 4.5\ \mu\text{M/h}$ . (4)

(c) (4) Logistic growth rate is maximal at $M = M_{max}/2 = 50\ \mu\text{M}$ (2). Maximal rate $= r \cdot \frac{M_{max}}{2}(1-\tfrac12) = 0.5 \times 50 \times 0.5 = 12.5\ \mu\text{M/h}$ . (2)

Question 5 (12)

(a) (4) Genes essential yet of unknown function show that knowing individual parts does not explain the living whole — you cannot deduce function from the gene list alone (2). A holistic/systems approach (studying interactions, networks, context) is required to understand why the cell needs them. (2)

(b) (4) Emergent behavior: self-replication, metabolic homeostasis, or robust growth arises from the coordinated interaction of the whole gene set/network (2); no single gene "encodes" the property — it appears only when components act together (whole ≠ sum of parts). (2)

(c) (4) Any two, 2 marks each:

Biosafety/biocontainment — engineered minimal organisms could escape or be misused (dual-use).
"Playing God"/moral status — creating life de novo raises philosophical & religious concerns.
Biosecurity/IP — patenting synthetic life, equitable access, ownership of engineered organisms.

[
  {"claim":"Q1b steady state A^2+4A-40=0 positive root ~4.633","code":"A=symbols('A',positive=True); sol=solve(Eq(2*A,20/(1+A/4)),A); val=[s for s in sol if s>0][0]; result=abs(float(val)-4.6332495807)<1e-4"},
  {"claim":"Q2b vQ=10/3, vP=20/3","code":"vQ=Rational(10,3); vP=2*vQ; result=(vP+vQ==10) and (vP==Rational(20,3))"},
  {"claim":"Q4b dM/dt at M=10 equals 4.5","code":"r=Rational(1,2); Mmax=100; M=10; rate=r*M*(1-M/Mmax); result=rate==Rational(9,2)"},
  {"claim":"Q4c max rate at M=50 is 12.5","code":"r=Rational(1,2); Mmax=100; M=Mmax/2; rate=r*M*(1-M/Mmax); result=(M==50) and (rate==Rational(25,2))"}
]